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Nitrogen-15 nuclear magnetic resonance spectroscopy ( nitrogen-15 NMR spectroscopy , or just simply 15 N NMR ) is a version of nuclear magnetic resonance spectroscopy that examines samples containing the 15 N nucleus. [ 1 ] [ 2 ] 15 N NMR differs in several ways from the more common 13 C and 1 H NMR. To circumvent the difficulties associated with measurement of the quadrupolar, spin-1 14 N nuclide, 15 N NMR is employed in samples for detection since it has a ground-state spin of ½. Since 14 N is 99.64% abundant, incorporation of 15 N into samples often requires novel synthetic techniques. [ 3 ]
Nitrogen-15 is frequently used in nuclear magnetic resonance spectroscopy (NMR), because unlike the more abundant nitrogen-14, that has an integer nuclear spin and thus a quadrupole moment, 15 N has a fractional nuclear spin of one-half, which offers advantages for NMR like narrower line width. Proteins can be isotopically labeled by cultivating them in a medium containing nitrogen-15 as the only source of nitrogen. In addition, nitrogen-15 is used to label proteins in quantitative proteomics (e.g. SILAC ).
15 N NMR has complications not encountered in 1 H and 13 C NMR spectroscopy. The 0.36% natural abundance of 15 N results in a major sensitivity penalty. Sensitivity is made worse by its low gyromagnetic ratio (γ = −27.126 × 10 6 T −1 s −1 ), which is 10.14% that of 1 H. The signal-to-noise ratio for 1 H is about 300-fold greater than 15 N at the same magnetic field strength. [ 4 ]
The physical properties of 15 N are quite different from other nuclei. Its properties along with several common nuclei are summarized in the below table.
From these data, one can see that at full enrichment, 15 N is about one tenth (-27.126/267.522) as sensitive as 1 H.
The International Union of Pure and Applied Chemistry (IUPAC) recommends using CH 3 NO 2 as the experimental standard; however in practice many spectroscopists utilize pressurized NH 3 (l) instead. For 15 N, chemical shifts referenced with NH 3 (l) are 380.5 ppm upfield from CH 3 NO 2 (δ NH 3 = δ CH 3 NO 2 + 380.5 ppm). Chemical shifts for 15 N are somewhat erratic but typically they span a range of -400 ppm to 1100 ppm with respect to CH 3 NO 2 . Below is a summary of 15 N chemical shifts for common organic groups referenced with respect to NH 3 , whose chemical shift is assigned 0 ppm. [ 6 ] [ 2 ]
Unlike most nuclei, the gyromagnetic ratio for 15 N is negative. With the spin precession phenomenon, the sign of γ determines the sense (clockwise vs counterclockwise) of precession. Most common nuclei have positive gyromagnetic ratios such as 1 H and 13 C. [ 3 ] [ 4 ]
15 N NMR is used in a wide array of areas from biological to inorganic techniques. A famous application in organic synthesis is to utilize 15 N to monitor tautomerization equilibria in heteroaromatics because of the dramatic change in 15 N shifts between tautomers. [ 1 ]
15 N NMR is also extremely valuable in protein NMR investigations. Most notably, the introduction of three-dimensional experiments with 15 N lifts the ambiguity in 13 C– 13 C two-dimensional experiments. In solid-state nuclear magnetic resonance (ssNMR), for example, 15 N is most commonly utilized in NCACX, NCOCX, and CANcoCX pulse sequences.
15 N NMR is the most effective method for investigation of structure of heterocycles with a high content of nitrogen atoms (tetrazoles, triazines and their annelated analogs). [ 7 ] [ 8 ] 15 N labeling followed by analysis of 13 C– 15 N and 1 H– 15 N couplings may be used for establishing structures and chemical transformations of nitrogen heterocycles. [ 9 ]
Insensitive nuclei enhanced by polarization transfer (INEPT) is a signal resolution enhancement method. Because 15 N has a gyromagnetic ratio that is small in magnitude, the resolution is quite poor. A common pulse sequence which dramatically improves the resolution for 15 N is INEPT. The INEPT is an elegant solution in most cases because it increases the Boltzmann polarization and lowers T 1 values (thus scans are shorter). Additionally, INEPT can accommodate negative gyromagnetic ratios, whereas the common nuclear Overhauser effect (NOE) cannot. | https://en.wikipedia.org/wiki/Nitrogen-15_nuclear_magnetic_resonance_spectroscopy |
The nitrogen-vacancy center ( N-V center or NV center ) is one of numerous photoluminescent point defects in diamond . Its most explored and useful properties include its spin-dependent photoluminescence (which enables measurement of the electronic spin state using optically detected magnetic resonance ), and its relatively long spin coherence at room temperature, lasting up to milliseconds. [ 1 ] The NV center energy levels are modified by magnetic fields, [ 2 ] electric fields , [ 3 ] temperature , [ 4 ] and strain , [ 5 ] which allow it to serve as a sensor of a variety of physical phenomena. Its atomic size and spin properties can form the basis for useful quantum sensors . [ 6 ]
NV centers enable nanoscale measurements of magnetic and electric fields, temperature, and mechanical strain with improved precision. External perturbation sensitivity makes NV centers ideal for applications in biomedicine—such as single-molecule imaging and cellular process modeling. [ 7 ] NV centers can also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has also been explored for applications in quantum computing (e.g. for entanglement generation [ 8 ] ), quantum simulation, [ 9 ] and spintronics . [ 10 ]
The nitrogen-vacancy center is a point defect in the diamond lattice . It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy .
Two charge states of this defect, neutral NV 0 and negative NV − , are known from spectroscopic studies using optical absorption , [ 12 ] [ 13 ] photoluminescence (PL), [ 14 ] electron paramagnetic resonance (EPR) [ 15 ] [ 16 ] [ 17 ] and optically detected magnetic resonance (ODMR), [ 18 ] which can be viewed as a hybrid of PL and EPR; most details of the structure originate from EPR. The nitrogen atom on one hand has five valence electrons. Three of them are covalently bonded to the carbon atoms, while the other two remain non-bonded and are called a lone pair . The vacancy on the other hand has three unpaired electrons. Two of them form a quasi covalent bond and one remains unpaired. The overall symmetry, however, is axial (trigonal C 3V ); one can visualize this by imagining the three unpaired vacancy electrons continuously exchanging their roles.
The NV 0 thus has one unpaired electron and is paramagnetic. However, despite extensive efforts, electron paramagnetic resonance signals from NV 0 avoided detection for decades until 2008. Optical excitation is required to bring the NV 0 defect into the EPR-detectable excited state; the signals from the ground state are presumably too broad for EPR detection. [ 19 ]
The NV 0 centers can be converted into NV − by changing the Fermi level position. This can be achieved by applying external voltage to a p-n junction made from doped diamond, e.g., in a Schottky diode . [ 11 ]
In the negative charge state NV − , an extra electron is located at the vacancy site forming a spin S=1 pair with one of the vacancy electrons. This extra electron induces spin triplet ground states of the form | 3 A⟩ and excited states of the form | 3 E⟩. [ 20 ] There is an additional metastable state that exists between these spin triplets, that often manifests as a singlet. These states play a crucial role in enabling ground state depletion (GSD) microscopy . [ 21 ] As in NV 0 , the vacancy electrons are "exchanging roles" preserving the overall trigonal symmetry. This NV − state is what is commonly, and somewhat incorrectly, called "the nitrogen-vacancy center". The neutral state is not generally used for quantum technology.
The NV centers are randomly oriented within a diamond crystal. Ion implantation techniques can enable their artificial creation in predetermined positions. [ 22 ]
Nitrogen-vacancy centers are typically produced from single substitutional nitrogen centers (called C or P1 centers in diamond literature) by irradiation followed by annealing at temperatures above 700 °C. [ 12 ] A wide range of high-energy particles is suitable for such irradiation, including electrons, protons, neutrons, ions, and gamma photons. Irradiation produces lattice vacancies, which are a part of NV centers. Those vacancies are immobile at room temperature, and annealing is required to move them. Single substitutional nitrogen produces strain in the diamond lattice; [ 23 ] it therefore efficiently captures moving vacancies, [ 24 ] producing the NV centers.
During chemical vapor deposition of diamond, a small fraction of single substitutional nitrogen impurity (typically <0.5%) traps vacancies generated as a result of the plasma synthesis. Such nitrogen-vacancy centers are preferentially aligned to the growth direction. [ 26 ] [ 27 ] Delta doping of nitrogen during CVD growth can be used to create two-dimensional ensembles of NV centers near the diamond surface for enhanced sensing [ 28 ] or simulation. [ 29 ]
Diamond is notorious for having a relatively large lattice strain. Strain splits and shifts optical transitions from individual centers resulting in broad lines in the ensembles of centers. [ 12 ] [ 30 ] Special care is taken to produce extremely sharp NV lines (line width ~10 MHz) [ 31 ] required for most experiments: high-quality, natural (type IIa) diamonds are selected, although synthetic diamonds are preferential. Many of them already have sufficient concentrations of grown-in NV centers and are suitable for applications. If not, they are irradiated by high-energy particles and annealed. Selection of a certain irradiation dose allows tuning the concentration of produced NV centers such that individual NV centers are separated by micrometre-large distances. Then, individual NV centers can be studied with standard optical microscopes or, better, near-field scanning optical microscopes having sub-micrometre resolution. [ 18 ] [ 32 ]
The NV center has a ground-state triplet ( 3 A) , an excited-state triplet ( 3 E) and two intermediate-state singlets ( 1 A and 1 E) . [ note 1 ] [ 36 ] [ 37 ] Both 3 A and 3 E contain m s = ±1 spin states, in which the two electron spins are aligned (either up, such that m s = +1 or down, such that m s = -1), and an m s = 0 spin state where the electron spins are antiparallel. Due to the magnetic interaction, the energy of the m s = ±1 states is higher than that of the m s = 0 state. 1 A and 1 E only contain a spin state singlet each with m s = 0.
If an external magnetic field is applied along the defect axis (the axis which aligns with the nitrogen atom and the vacancy) of the NV center, it does not affect the m s = 0 states, but it splits the m s = ±1 levels ( Zeeman effect ). Similarly the following other properties of the environment influence the energy level diagram (further discussed under #Effects of external fields ) :
The above-described energy structure [ note 2 ] is by no means exceptional for a defect in diamond or other semiconductor. [ 41 ] It was not this structure alone, but a combination of several favorable factors (previous knowledge, easy production, biocompatibility, simple initialisation, use at room temperature etc.) which suggested the use of the NV center as a qubit and quantum sensor .
NV centers emit bright red light ( 3 E→ 3 A transitions), if excited off-resonantly by visible green light ( 3 A → 3 E transitions). This can be done with convenient light sources such as argon or krypton lasers , frequency doubled Nd:YAG lasers , dye lasers , or He-Ne lasers . Excitation can also be achieved at energies below that of zero phonon emission . [ 42 ]
As the relaxation time from the excited state is small (~10 ns ), [ 43 ] [ 44 ] the emission happens almost instantly after the excitation. At room temperature the NV center's optical spectrum exhibits no sharp peaks due to thermal broadening. However, cooling the NV centers with liquid nitrogen or liquid helium dramatically narrows the lines down to a width of a few MHz. At low temperature it also becomes possible to specifically address the zero-phonon line (ZPL).
An important property of the luminescence from individual NV centers is its high temporal stability. Whereas many single-molecular emitters bleach (i.e. change their charge state and become dark) after emission of 10 6 –10 8 photons, bleaching is unlikely for NV centers at room temperature. [ 45 ] [ 32 ] Strong laser illumination, however, may also convert some NV − into NV 0 centers. [ 14 ]
Because of these properties, the ideal technique to address the NV centers is confocal microscopy , both at room temperature and at low temperature.
Optical transitions must preserve the total spin and occur only between levels of the same total spin. Specifically, transitions between the ground and excited states (with equal spin) can be induced using a green laser with a wavelength of 546 nm. Transitions 3 E→ 1 A and 1 E→ 3 A are non-radiative, while 1 A → 1 E has both a non-radiative and infrared decay path.
The diagram on the right shows the multi-electronic states of the NV center labeled according to their symmetry (E or A) and their spin state (3 for a triplet (S=1) and 1 for a singlet (S=0)). There are two triplet states and two intermediate singlet states. [ 50 ]
An important property of the non-radiative transition between 3 E and 1 A is that it is stronger for m s = ±1 and weaker for m s = 0. This provides the basis a very useful manipulation strategy, which is called spin state initialisation (or optical spin-polarization). To understand the process, first consider an off-resonance excitation which has a higher frequency (typically 2.32 eV (532 nm)) than the frequencies of all transitions and thus lies in the vibronic bands for all transitions. By using a pulse of this wavelength, one can excite all spin states from 3 A to 3 E. An NV center in the ground state with m s = 0 will be excited to the corresponding excited state with m s = 0 due to the conservation of spin. Afterwards it decays back to its original state. For a ground state with m s = ±1, the situation is different. After the excitation, it has a relatively high probability to decay into the intermediate state 1 A by non-radiative transition [ note 3 ] [ 51 ] and further into the ground state with m s = 0. After many cycles, the state of the NV center (independently of whether it started in m s = 0 or m s = ±1) will end up in the m s = 0 ground state. This process can be used to initialize the quantum state of a qubit for quantum information processing or quantum sensing.
Sometimes the polarisability of the NV center is explained by the claim that the transition from 1 E to the ground state with m s = ±1 is small, compared to the transition to m s = 0. However, it has been shown that the comparatively low decay probability for m s = 0 states w.r.t. m s = ±1 states into 1 A is enough to explain the polarization. [ 52 ]
The energy difference between the m s = 0 and m s = ±1 states corresponds to the microwave regime. Population can be transferred between the states by applying a resonant magnetic field perpendicular to the defect axis. Numerous dynamic effects ( spin echo , Rabi oscillations , etc.) can be exploited by applying a carefully designed sequence of microwave pulses. [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] Such protocols are rather important for the practical realization of quantum computers . By manipulating the population, it is possible to shift the NV center into a more sensitive or stable state. [ 58 ] [ 59 ] Its own resulting fluctuating fields may also be used to influence the surrounding nuclei [ 60 ] or protect the NV center itself from noise. [ 61 ] This is typically done using a wire loop (microwave antenna) which creates an oscillating magnetic field. [ 62 ]
There are inherent difficulties in achieving miniaturization and effective error reduction in microwave and radio frequency driven spin manipulation techniques. This poses special challenge on application of spin based quantum sensors on sensing electric and magnetic field or any physical phenomena at nanoscale level. The recent developments in microwave-free and optically driven methods [ 63 ] [ 64 ] pave the way towards energy efficient and coherent quantum sensing. This technique is based on coherent mapping of the spin states of the Nitrogen nucleus to that of the NV center under the application of external magnetic field transverse to the NV symmetry axis. The optical pumping then prepares the system in a coherent superposition state which is the key element in a quantum network.
If a magnetic field is oriented along the defect axis it leads to Zeeman splitting separating the m s = +1 from the m s = -1 states. This technique is used to lift the degeneracy and use only two of the spin states (usually the ground states with m s = -1 and m s = 0) as a qubit. Population can then be transferred between them using a microwave field. In the specific instance that the magnetic field reaches 1027 G (or 508 G) then the m s = –1 and m s = 0 states in the ground (or excited) state become equal in energy (Ground/Excited State Level Anticrossing). The following strong interaction results in so-called spin polarization , which strongly affects the intensity of optical absorption and luminescence transitions involving those states. [ 35 ]
Importantly, this splitting can be modulated by applying an external electric field , [ 38 ] [ 39 ] in a similar fashion to the magnetic field mechanism outlined above, though the physics of the splitting is somewhat more complex. Nevertheless, an important practical outcome is that the intensity and position of the luminescence lines is modulated. Strain has a similar effect on the NV center as electric fields. [ 65 ]
There is an additional splitting of the m s = ±1 energy levels, which originates from the hyperfine interaction between surrounding nuclear spins and the NV center. These nuclear spins create magnetic and electric fields of their own leading to further distortions of the NV spectrum (see nuclear Zeeman and quadrupole interaction). Also the NV center's own spin–orbit interaction and orbital degeneracy leads to additional level splitting in the excited 3 E state.
Temperature and pressure directly influence the zero-field term of the NV center leading to a shift between the ground and excited state levels.
The Hamiltonian , a quantum mechanical equation describing the dynamics of a system, which shows the influence of different factors on the NV center can be found below.
Although it can be challenging, all of these effects are measurable, making the NV center a perfect candidate for a quantum sensor. [ 59 ]
It is also possible to switch the charge state of the NV center (i.e. between NV − , NV + and NV 0 ) by applying a gate voltage. [ 66 ] The gate voltage electrically shifts the Fermi level at the diamond surface and changes its surface band bending. Upon varying the gate voltage, individual centers are allowed to switch from an unknown non-fluorescent state to the neutral charge state NV 0 . The ensemble of centers can be transitioned from NV 0 to the qubit state NV − . The diamond surface termination additionally influences the charge state of near-surface NV centers. Oxygen termination is known to stabilize the NV − state by reducing surface conductivity and mitigating band bending [ 67 ] This improves charge state stability and coherence. In a similar capacity, nitrogen termination also affects surface properties and can optimize NV centers for specific sensing applications.
Optical excitation methods additionally play a role in charge state manipulation. Illumination with specific wavelengths can induce transitions between charge states. Near-infrared light at 1064 nm has been shown to convert NV 0 to NV − , enhancing photoluminescence. [ 68 ] Additionally, it has been demonstrated that NV + centers can be switched to NV 0 by photons with energies ≥ {\displaystyle \geq } 1.23 eV. [ 69 ]
The spectral shape and intensity of the optical signals from the NV − centers are sensitive to external perturbation, such as temperature, strain, electric and magnetic field. However, the use of spectral shape for sensing those perturbation is impractical, as the diamond would have to be cooled to cryogenic temperatures to sharpen the NV − signals. A more realistic approach is to use luminescence intensity (rather than lineshape), which exhibits a sharp resonance when a microwave frequency is applied to diamond that matches the splitting of the ground-state levels. The resulting optically detected magnetic resonance signals are sharp even at room temperature, and can be used in miniature sensors. Such sensors can detect magnetic fields of a few nanotesla [ 71 ] or electric fields of about 10 V/cm [ 72 ] at kilohertz frequencies after 100 seconds of averaging. This sensitivity allows detecting a magnetic or electric field produced by a single electron located tens of nanometers away from an NV − center.
Using the same mechanism, the NV − centers were employed in scanning thermal microscopy to measure high-resolution spatial maps of temperature and thermal conductivity (see image). [ 70 ]
Because the NV center is sensitive to magnetic fields, it is being actively used in scanning probe measurements to study myriad condensed matter phenomena both through measuring a spatially varying magnetic field or inferring local currents in a device. [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ]
Another possible use of the NV − centers is as a detector to measure the full mechanical stress tensor in the bulk of the crystal. For this application, the stress-induced splitting of the zero-phonon-line is exploited, and its polarization properties. [ 78 ] A robust frequency-modulated radio receiver using the electron-spin-dependent photoluminescence that operated up to 350 °C demonstrates the possibility for use in extreme conditions. [ 79 ]
In addition to the quantum optical applications, luminescence from the NV − centers can be applied for imaging biological processes, such as fluid flow in living cells. [ 80 ] [ 81 ] This application relies on good compatibility of diamond nano-particles with the living cells and on favorable properties of photoluminescence from the NV − centers (strong intensity, easy excitation and detection, temporal stability, etc.). Compared with large single-crystal diamonds, nanodiamonds are cheap (about US$1 per gram) and available from various suppliers. NV − centers are produced in diamond powders with sub-micrometre particle size using the standard process of irradiation and annealing described above. Due to the relatively small size of nanodiamond, NV centers can be produced by irradiating nanodiamond of 100 nm or less with medium energy H+ beam. This method reduces the required ion dose and reaction, making it possible to mass-produce fluorescent nanodiamonds in ordinary laboratory. [ 82 ] Fluorescent nanodiamond produced with such method is bright and photostable, making it excellent for long-term, three dimensional tracking of single particle in living cell. [ 83 ] Those nanodiamonds are introduced in a cell, and their luminescence is monitored using a standard fluorescence microscope . [ 84 ]
Stimulated emission from the NV − center has been demonstrated, though it could be achieved only from the phonon side-band (i.e. broadband light) and not from the ZPL. For this purpose, the center has to be excited at a wavelength longer than ~650 nm, as higher-energy excitation ionizes the center. [ 85 ]
The first continuous-wave room-temperature maser has been demonstrated. [ 86 ] [ 87 ] It used 532-nm pumped NV − centers held within a high Purcell factor microwave cavity and an external magnetic field of 4300 G. Continuous maser oscillation generated a coherent signal at ~9.2 GHz.
The NV center can have a very long spin coherence time approaching the second regime. [ 88 ] This is advantageous for applications in quantum sensing [ 89 ] and quantum communication . [ 90 ] Disadvantageous for these applications is the long radiative lifetime (~12 ns [ 91 ] [ 92 ] ) of the NV center and the strong phonon sideband in its emission spectrum. Both issues can be addressed by putting the NV center in an optical cavity . [ 93 ]
The microscopic model and most optical properties of ensembles of the NV − centers have been firmly established in the 1970s based on the optical measurements combined with uniaxial stress [ 12 ] and on the electron paramagnetic resonance. [ 15 ] [ 16 ] However, a minor error in EPR results (it was assumed that illumination is required to observe NV − EPR signals) resulted in the incorrect multiplicity assignments in the energy level structure. In 1991 it was shown that EPR can be observed without illumination, [ 17 ] which established the energy level scheme shown above. The magnetic splitting in the excited state has been measured only recently. [ 35 ]
The characterization of single NV − centers has become a very competitive field nowadays, with many dozens of papers published in the most prestigious scientific journals. One of the first results was reported back in 1997. [ 18 ] In that paper, it was demonstrated that the fluorescence of single NV − centers can be detected by room-temperature fluorescence microscopy and that the defect shows perfect photostability. Also one of the outstanding properties of the NV center was demonstrated, namely room-temperature optically detected magnetic resonance. | https://en.wikipedia.org/wiki/Nitrogen-vacancy_center |
Nitrogen assimilation is the formation of organic nitrogen compounds like amino acids from inorganic nitrogen compounds present in the environment. Organisms like plants , fungi and certain bacteria that can fix nitrogen gas (N 2 ) depend on the ability to assimilate nitrate or ammonia for their needs. Other organisms, like animals, depend entirely on organic nitrogen from their food.
Plants absorb nitrogen from the soil in the form of nitrate (NO 3 − ) and ammonium (NH 4 + ). In aerobic soils where nitrification can occur, nitrate is usually the predominant form of available nitrogen that is absorbed. [ 1 ] [ 2 ] However this is not always the case as ammonia can predominate in grasslands [ 3 ] and in flooded, anaerobic soils like rice paddies . [ 4 ] Plant roots themselves can affect the abundance of various forms of nitrogen by changing the pH and secreting organic compounds or oxygen. [ 5 ] This influences microbial activities like the inter-conversion of various nitrogen species, the release of ammonia from organic matter in the soil and the fixation of nitrogen by non-nodule-forming bacteria .
Ammonium ions are absorbed by the plant via ammonia transporters . Nitrate is taken up by several nitrate transporters that use a proton gradient to power the transport. [ 6 ] [ 7 ] Nitrogen is transported from the root to the shoot via the xylem in the form of nitrate, dissolved ammonia and amino acids. Usually [ 8 ] (but not always [ 9 ] ) most of the nitrate reduction is carried out in the shoots while the roots reduce only a small fraction of the absorbed nitrate to ammonia. Ammonia (both absorbed and synthesized) is incorporated into amino acids via the glutamine synthetase - glutamate synthase (GS-GOGAT) pathway. [ 10 ] While nearly all [ 11 ] the ammonia in the root is usually incorporated into amino acids at the root itself, plants may transport significant amounts of ammonium ions in the xylem to be fixed in the shoots. [ 12 ] This may help avoid the transport of organic compounds down to the roots just to carry the nitrogen back as amino acids.
Nitrate reduction is carried out in two steps. Nitrate is first reduced to nitrite (NO 2 − ) in the cytosol by nitrate reductase using NADH or NADPH. [ 7 ] Nitrite is then reduced to ammonia in the chloroplasts ( plastids in roots) by a ferredoxin dependent nitrite reductase . In photosynthesizing tissues, it uses an isoform of ferredoxin (Fd1) that is reduced by PSI while in the root it uses a form of ferredoxin (Fd3) that has a less negative midpoint potential and can be reduced easily by NADPH. [ 13 ] In non photosynthesizing tissues, NADPH is generated by glycolysis and the pentose phosphate pathway .
In the chloroplasts, [ 14 ] glutamine synthetase incorporates this ammonia as the amide group of glutamine using glutamate as a substrate. Glutamate synthase ( Fd-GOGAT and NADH-GOGAT ) transfer the amide group onto a 2-oxoglutarate molecule producing two glutamates. Further transaminations are carried out make other amino acids (most commonly asparagine ) from glutamine. While the enzyme glutamate dehydrogenase (GDH) does not play a direct role in the assimilation, it protects the mitochondrial functions during periods of high nitrogen metabolism and takes part in nitrogen remobilization. [ 15 ]
Every nitrate ion reduced to ammonia produces one OH − ion. To maintain a pH balance, the plant must either excrete it into the surrounding medium or neutralize it with organic acids. This results in the medium around the plants roots becoming alkaline when they take up nitrate.
To maintain ionic balance, every NO 3 − taken into the root must be accompanied by either the uptake of a cation or the excretion of an anion. Plants like tomatoes take up metal ions like K + , Na + , Ca 2+ and Mg 2+ to exactly match every nitrate taken up and store these as the salts of organic acids like malate and oxalate . [ 16 ] Other plants like the soybean balance most of their NO 3 − intake with the excretion of OH − or HCO 3 − . [ 17 ]
Plants that reduce nitrates in the shoots and excrete alkali from their roots need to transport the alkali in an inert form from the shoots to the roots. To achieve this they synthesize malic acid in the leaves from neutral precursors like carbohydrates. The potassium ions brought to the leaves along with the nitrate in the xylem are then sent along with the malate to the roots via the phloem. In the roots, the malate is consumed. When malate is converted back to malic acid prior to use, an OH − is released and excreted. (RCOO − + H 2 O -> RCOOH +OH − ) The potassium ions are then recirculated up the xylem with fresh nitrate. Thus the plants avoid having to absorb and store excess salts and also transport the OH − . [ 18 ]
Plants like castor reduce a lot of nitrate in the root itself, and excrete the resulting base. Some of the base produced in the shoots is transported to the roots as salts of organic acids while a small amount of the carboxylates are just stored in the shoot itself. [ 19 ]
Nitrogen use efficiency (NUE) is the proportion of nitrogen present that a plant absorbs and uses. Improving nitrogen use efficiency and thus fertilizer efficiency is important to make agriculture more sustainable, [ 20 ] by reducing pollution ( fertilizer runoff ) and production cost and increasing yield. Worldwide, crops generally have less than 50% NUE. [ 21 ] Better fertilizers, improved crop management, [ 21 ] selective breeding, [ 22 ] and genetic engineering [ 20 ] [ 23 ] can increase NUE.
Nitrogen use efficiency can be measured at various levels: the crop plant, the soil, by fertilizer input, by ecosystem productivity, etc. [ 24 ] At the level of photosynthesis in leaves, it is termed photosynthetic nitrogen use efficiency (PNUE). [ 25 ] [ 26 ] | https://en.wikipedia.org/wiki/Nitrogen_assimilation |
Nitrogen difluoride , also known as difluoroamino, is a reactive radical molecule with formula N F 2 . This small molecule is in equilibrium with its dimer tetrafluorohydrazine . [ 2 ]
As the temperature increases the proportion of NF 2 increases. [ 3 ]
The molecule is unusual in that it has an odd number of electrons, yet is stable enough to study experimentally. [ 4 ]
The energy needed to break the N–N bond in N 2 F 4 is 20.8 kcal/mol (87 kJ/mol), with an entropy change of 38.6 eu . [ 5 ] For comparison, the dissociation energy of the N–N bond is 14.6 kcal/mol (61 kJ/mol) in N 2 O 4 , 10.2 kcal/mol (43 kJ/mol) in N 2 O 2 , and 60 kcal/mol (250 kJ/mol) in N 2 H 4 . The enthalpy of formation of N 2 F 4 (Δ f H ) is 8.227 kcal/mol (34.421 kJ/mol). [ 6 ]
At room temperature N 2 F 4 is mostly associated with only 0.7% in the form of NF 2 at 5 mmHg (670 Pa) pressure. When the temperature rises to 225 °C, it mostly dissociates with 99% in the form of NF 2 . [ 5 ]
In NF 2 , the N–F bond length is 1.3494 Å and the angle subtended at F–N–F is 103.33°. [ 7 ]
In the infrared spectrum the N–F bond in NF 2 has a symmetrical stretching frequency of 1075 cm −1 . This compares to 1115 cm −1 in NF, 1021 cm −1 in NF 3 and 998 cm −1 in N 2 F 4 . [ 5 ]
The microwave spectrum shows numerous lines due to spin transitions, with or without nuclear spin transitions. The lines form set of two triplets for antisymmetric singlet, or two triplets of triplets for symmetric triplet. Lines appear around 14–15, 24, 25, 26, 27, 28–29, 33, 60, 61, 62, and 65 GHz. The rotational constants for the NF 2 molecule are A = 70 496 MHz , B = 11 872 .2 MHz , and C = 10 136 .5 MHz . The inertial defect Δ = 0.1204 m u ·Å 2 . The centrifugal distortion constants are τ aaaa = −7.75, τ bbbb = −0.081, τ aabb = 0.30, and τ abab = −0.13. [ 7 ]
The dipole moment is 0.13 D ( 4.5 × 10 −31 C·m ). [ 7 ]
The ground electronic state of the molecule is 2 B 1 . [ 7 ]
The gas is often contaminated with NO or N 2 O . [ 5 ]
Nitrogen difluoride is formed during the function of a xenon monofluoride excimer laser. Nitrogen trifluoride is the halide carrier gas, which releases fluoride ions when impacted by electrons: [ 1 ]
The free fluoride ion goes on to react with xenon cations. [ 1 ]
Nitrogen difluoride can be consumed further to yield nitrogen monofluoride . [ 1 ] | https://en.wikipedia.org/wiki/Nitrogen_difluoride |
Dinitrogen tetroxide Dinitrogen trioxide Nitric oxide Nitrous oxide
Nitrogen dioxide is a chemical compound with the formula NO 2 . One of several nitrogen oxides , nitrogen dioxide is a reddish-brown gas. It is a paramagnetic , bent molecule with C 2v point group symmetry . Industrially, NO 2 is an intermediate in the synthesis of nitric acid , millions of tons of which are produced each year, primarily for the production of fertilizers .
Nitrogen dioxide is poisonous and can be fatal if inhaled in large quantities. [ 8 ] Cooking with a gas stove produces nitrogen dioxide which causes poorer indoor air quality . Combustion of gas can lead to increased concentrations of nitrogen dioxide throughout the home environment which is linked to respiratory issues and diseases . [ 9 ] [ 10 ] The LC 50 ( median lethal dose ) for humans has been estimated to be 174 ppm for a 1-hour exposure. [ 11 ] It is also included in the NO x family of atmospheric pollutants .
Nitrogen dioxide is a reddish-brown gas with a pungent, acrid odor above 21.2 °C (70.2 °F; 294.3 K) and becomes a yellowish-brown liquid below 21.2 °C (70.2 °F; 294.3 K). It forms an equilibrium with its dimer , dinitrogen tetroxide ( N 2 O 4 ), and converts almost entirely to N 2 O 4 below −11.2 °C (11.8 °F; 261.9 K). [ 6 ]
The bond length between the nitrogen atom and the oxygen atom is 119.7 pm . This bond length is consistent with a bond order between one and two.
Unlike ozone ( O 3 ) the ground electronic state of nitrogen dioxide is a doublet state , since nitrogen has one unpaired electron, [ 12 ] which decreases the alpha effect compared with nitrite and creates a weak bonding interaction with the oxygen lone pairs. The lone electron in NO 2 also means that this compound is a free radical , so the formula for nitrogen dioxide is often written as • NO 2 .
The reddish-brown color is a consequence of preferential absorption of light in the blue region of the spectrum (400–500 nm), although the absorption extends throughout the visible (at shorter wavelengths) and into the infrared (at longer wavelengths). Absorption of light at wavelengths shorter than about 400 nm results in photolysis (to form NO + O , atomic oxygen); in the atmosphere the addition of the oxygen atom so formed to O 2 results in ozone.
Industrially, nitrogen dioxide is produced and transported as its cryogenic liquid dimer, dinitrogen tetroxide . It is produced industrially by the oxidation of ammonia, the Ostwald Process . This reaction is the first step in the production of nitric acid: [ 13 ]
It can also be produced by the oxidation of nitrosyl chloride :
Instead, most laboratory syntheses stabilize and then heat the nitric acid to accelerate the decomposition. For example, the thermal decomposition of some metal nitrates generates NO 2 : [ 14 ]
Alternatively, dehydration of nitric acid produces nitronium nitrate ...
...which subsequently undergoes thermal decomposition:
NO 2 is generated by the reduction of concentrated nitric acid with a metal (such as copper):
Nitric acid decomposes slowly to nitrogen dioxide by the overall reaction:
The nitrogen dioxide so formed confers the characteristic yellow color often exhibited by this acid. However, the reaction is too slow to be a practical source of NO 2 .
At low temperatures, NO 2 reversibly converts to the colourless gas dinitrogen tetroxide ( N 2 O 4 ):
The exothermic equilibrium has enthalpy change Δ H = −57.23 kJ/mol . [ 15 ]
At 150 °C (302 °F; 423 K), NO 2 decomposes with release of oxygen via an endothermic process ( Δ H = 14 kJ/mol ):
As suggested by the weakness of the N–O bond, NO 2 is a good oxidizer. Consequently, it will combust, sometimes explosively, in the presence of hydrocarbons . [ 16 ]
NO 2 reacts with water to give nitric acid and nitrous acid :
This reaction is one of the steps in the Ostwald process for the industrial production of nitric acid from ammonia. [ 13 ] This reaction is negligibly slow at low concentrations of NO 2 characteristic of the ambient atmosphere, although it does proceed upon NO 2 uptake to surfaces. Such surface reaction is thought to produce gaseous HNO 2 (often written as HONO ) in outdoor and indoor environments. [ 17 ]
NO 2 is used to generate anhydrous metal nitrates from the oxides: [ 15 ]
Alkyl and metal iodides give the corresponding nitrates: [ 12 ]
The reactivity of nitrogen dioxide toward organic compounds has long been known. [ 18 ] For example, it reacts with amides to give N-nitroso derivatives. [ 19 ] It is used for nitrations under anhydrous conditions. [ 20 ]
NO 2 is used as an intermediate in the manufacturing of nitric acid , as a nitrating agent in the manufacturing of chemical explosives , as a polymerization inhibitor for acrylates , as a flour bleaching agent , [ 21 ] : 223 and as a room temperature sterilization agent. [ 22 ] It is also used as an oxidizer in rocket fuel , for example in red fuming nitric acid ; it was used in the Titan rockets , to launch Project Gemini , in the maneuvering thrusters of the Space Shuttle , and in uncrewed space probes sent to various planets. [ 23 ]
Nitrogen dioxide typically arises via the oxidation of nitric oxide by oxygen in air (e.g. as result of corona discharge ): [ 15 ]
NO 2 is introduced into the environment by natural causes, including entry from the stratosphere , bacterial respiration, volcanos, and lightning. These sources make NO 2 a trace gas in the atmosphere of Earth , where it plays a role in absorbing sunlight and regulating the chemistry of the troposphere , especially in determining ozone concentrations. [ 24 ]
Nitrogen dioxide also forms in most combustion processes. At elevated temperatures nitrogen combines with oxygen to form nitrogen dioxide:
For the general public, the most prominent sources of NO 2 are internal combustion engines , as combustion temperatures are high enough to thermally combine some of the nitrogen and oxygen in the air to form NO 2 . [ 8 ] Nitrogen dioxide accounts for a small fraction (generally well under 0.1) of NOx auto emissions. [ 25 ]
Outdoors, NO 2 can be a result of traffic from motor vehicles. [ 26 ] Indoors, exposure arises from cigarette smoke, [ 27 ] and butane and kerosene heaters and stoves. [ 28 ] Indoor exposure levels of NO 2 are, on average, at least three times higher in homes with gas stoves compared to electric stove. [ 29 ] [ 30 ]
Workers in industries where NO 2 is used are also exposed and are at risk for occupational lung diseases , and NIOSH has set exposure limits and safety standards. [ 6 ] Workers in high voltage areas especially those with spark or plasma creation are at risk. [ citation needed ] Agricultural workers can be exposed to NO 2 arising from grain decomposing in silos; chronic exposure can lead to lung damage in a condition called " silo-filler's disease ". [ 31 ] [ 32 ]
NO 2 diffuses into the epithelial lining fluid (ELF) of the respiratory epithelium and dissolves. There, it chemically reacts with antioxidant and lipid molecules in the ELF. The health effects of NO 2 are caused by the reaction products or their metabolites, which are reactive nitrogen species and reactive oxygen species that can drive bronchoconstriction , inflammation, reduced immune response, and may have effects on the heart. [ 33 ]
Acute harm due to NO 2 exposure is rare. 100–200 ppm can cause mild irritation of the nose and throat, 250–500 ppm can cause edema , leading to bronchitis or pneumonia , and levels above 1000 ppm can cause death due to asphyxiation from fluid in the lungs. There are often no symptoms at the time of exposure other than transient cough, fatigue or nausea, but over hours inflammation in the lungs causes edema. [ 34 ] [ 35 ]
For skin or eye exposure, the affected area is flushed with saline. For inhalation, oxygen is administered, bronchodilators may be administered, and if there are signs of methemoglobinemia , a condition that arises when nitrogen-based compounds affect the hemoglobin in red blood cells, methylene blue may be administered. [ 36 ] [ 37 ]
It is classified as an extremely hazardous substance in the United States as defined in Section 302 of the U.S. Emergency Planning and Community Right-to-Know Act (42 U.S.C. 11002), and it is subject to strict reporting requirements by facilities which produce, store, or use it in significant quantities. [ 38 ]
Exposure to low levels of NO 2 over time can cause changes in lung function. [ 39 ] Cooking with a gas stove is associated with poorer indoor air quality . Combustion of gas can lead to increased concentrations of nitrogen dioxide throughout the home environment which is linked to respiratory issues and diseases . [ 9 ] [ 10 ] Children exposed to NO 2 are more likely to be admitted to hospital with asthma . [ 40 ]
In 2019, the Court of Justice of the EU , found that France did not comply with the limit values of the EU air quality standards applicable to the concentrations of nitrogen dioxide (NO 2 ) in 12 air quality zones. [ 41 ]
Interaction of NO 2 and other NO x with water, oxygen and other chemicals in the atmosphere can form acid rain which harms sensitive ecosystems such as lakes and forests. [ 42 ] Elevated levels of NO 2 can also harm vegetation, decreasing growth, and reduce crop yields. [ 43 ] | https://en.wikipedia.org/wiki/Nitrogen_dioxide |
Nitrogen dioxide poisoning is the illness resulting from the toxic effect of nitrogen dioxide ( NO 2 ). It usually occurs after the inhalation of the gas beyond the threshold limit value . [ 1 ] Nitrogen dioxide is reddish-brown with a very harsh smell at high concentrations, at lower concentrations it is colorless but may still have a harsh odour. Nitrogen dioxide poisoning depends on the duration, frequency, and intensity of exposure.
Nitrogen dioxide is an irritant of the mucous membrane linked with another air pollutant that causes pulmonary diseases such as obstructive lung disease , asthma , chronic obstructive pulmonary disease and sometimes acute exacerbation of COPD and in fatal cases, deaths. [ 2 ] Its poor solubility in water enhances its passage and its ability to pass through the moist oral mucosa of the respiratory tract.
Like most toxic gases, the dose inhaled determines the toxicity on the respiratory tract. Occupational exposures constitute the highest risk of toxicity and domestic exposure is uncommon. Prolonged exposure to low concentration of the gas may have lethal effects, as can short-term exposure to high concentrations like chlorine gas poisoning . It is one of the major air pollutants capable of causing severe health hazards such as coronary artery disease as well as stroke . [ 3 ] Nitrogen dioxide is often released into the environment as a byproduct of fuel combustion but rarely released by spontaneous combustion . Known sources of nitrogen dioxide gas poisoning include automobile exhaust and power stations .
The toxicity may also result from non-combustible sources such as the one released from anaerobic fermentation of food grains and anaerobic digestion of biodegradable waste . [ 4 ]
The World Health Organization (WHO) developed a global recommendation limiting exposures to less than 20 parts per billion for chronic exposure and value less 100 ppb for one hour for acute exposure, using nitrogen dioxide as a marker for other pollutants from fuel combustion. [ 5 ] There is a significant association between indoor NO 2 levels and increased respiratory symptoms such as wheeze, chest tightness and severity of infections among children with asthma. [ 6 ] Historically, some cities in the United States including Chicago and Los Angeles have higher levels of nitrogen dioxide than the EPA maximum exposure limits of 100 ppb for a one-hour exposure and less than 53 ppb for chronic exposure. [ 7 ] [ 8 ]
Nitrogen dioxide poisoning is harmful to all forms of life just like chlorine gas poisoning and carbon monoxide poisoning . It is easily absorbed through the lungs and its inhalation can result in heart failure and sometimes death in severe cases. [ 9 ] Individuals and races may differ in nitrogen dioxide tolerance level and individual tolerance level for the gas may be altered by several factors, such as metabolic rate, barometric pressure, and hematological disorders but significant exposure may result in fatal conditions that could lead to shorter lifespan due to heart failure. [ 10 ]
Exposure to high level of nitrogen dioxide may lead to inflammation of the mucous membrane and the lower and upper respiratory tracts. [ 11 ] The symptoms of acute nitrogen dioxide poisoning is non-specific and have a semblance with ammonia gas poisoning, chlorine gas poisoning , and carbon monoxide poisoning . The symptoms also resembles that of pneumonia or viral infection and other inhalational injuries but common symptoms includes rhinitis wheezing or coughing, conjunctivitis , headache, throat irritation and dyspnea which may progress to nasal fissures, ulcerations , or perforation. [ 12 ] The patient is usually ill-appearing and presents with hypoxemia coupled with shallow rapid breathing.
Therapy is supportive and includes removal from further nitrogen dioxide exposure.
Systemic symptoms include fever and anorexia . Electrocardiography and chest radiography can help in revealing diffuse, bilateral alveolar infiltrates.
Chest radiography may be used in diagnosis and the baseline could be established with pulmonary function testing . [ 13 ] [ 14 ] There is no specific laboratory diagnostic test for acute nitrogen dioxide poisoning but analysis of arterial blood gas level, methemoglobin level, complete blood count , glucose test , lactate threshold measurement and r peripheral blood smear may be helpful in the diagnosis of nitrogen dioxide poisoning. [ 15 ] The determination of nitrogen dioxide in urine or tissue does not establish the diagnosis, and there are technical and interpretive problems with these tests. [ 16 ]
Prolonged exposure to high levels of nitrogen dioxide can have an inflammatory effect that principally targets the respiratory tracts leading to chronic nitrogen dioxide poisoning which can occur within days or weeks after the threshold limit value is excessively exceeded. [ 17 ]
This condition causes fever, rapid breathing coupled with rapid heart rate, labored breathing and severe shortness of breath. Other effects include diaphoresis, chest pain, and persistent dry cough, all of which may result in weight loss, anorexia and may also lead to right-side heart enlargement and heart disease in advanced cases.
Prolonged exposure to relatively low levels of nitrogen (II) oxide may cause persistent headaches and nausea. [ 18 ] Like chlorine gas poisoning, symptoms usually resolve themselves upon removal from further nitrogen dioxide exposure, unless there had been an episode of severe acute poisoning. [ 19 ] Treatment and management vary with symptoms. Patients are often observed for hypoxemia for a minimum of 12 hours if there are no initial symptoms and if the patient is hypoxemic, oxygen may be administered but high-dose steroids are recommended for patients with pulmonary manifestations. Patients may also be hospitalized for 12 to 24 hours or longer for observation if the gaseous exchange is impaired.
In a case where gaseous exchange is impaired, mechanical ventilation and intubation may be necessary and if bronchiolitis obliterans develop within 2 to 6 weeks of nitrogen dioxide exposure, corticosteroid therapy or anticholinergic medications may be required for 6 to 12 months to lower the body overreaction to nitrogen dioxide gas. [ 20 ]
Occupational exposures constitute the highest risk of toxicity and it is often high for farmers especially those that deal with food grains. It is equally high for firefighters and military personnel, especially those officers that deal in explosives. The risk is also high for arc welders, traffic officers, aerospace staffs and miners as well as those people whose occupations are connected with the nitric acid . [ 21 ] Silo-filler's disease is a consequence of exposure to nitrogen dioxide poisoning by farmers dealing with silos . Food grains such as corn and millet , as well as grasses such as alfalfa and some other plant material, produces nitrogen dioxide within hours due to anaerobic fermentation . [ 22 ] The threshold concentrations of nitrogen dioxide are often attained within 1 to 2 days and begin to decline gradually after 10 to 14 days but if the silos is well sealed, the gas may remain in there for weeks. Heavily fertilized silage , particularly the ones produced from immature plants, generate a higher concentration of the gas within the silo. [ 23 ] Nitrogen dioxide is about 1.5 times heavier than air and during silage storage, nitrogen dioxide remains in the silage material.
Improper ventilation may result in exposure during the leveling of the silage. [ 24 ]
Nitrogen dioxide is sparingly soluble in water and on inhalation, it diffuses into the lung and slowly hydrolyzes to nitrous and nitric acid which causes pulmonary edema and pneumonitis leading to the inflammation of the bronchioles and pulmonary alveolus resulting from lipid peroxidation and oxidative stress . [ 25 ] Mucous membrane is primarily affected along with type I pneumocyte and the respiratory epithelium . The generation of free radicals from lipid peroxidation results in irritation of the bronchioles and alveoli that causes rapid destruction of the respiratory epithelial cells.
The overall reaction results in the release of fluid that causes pulmonary edema. [ 26 ]
Nitrogen dioxide poisoning may alter macrophage activity and immune function leading to susceptibility of the body to a wide range of infections, and overexposure to the gas may also lead to methemoglobinemia , a disorder characterized by a higher than normal level of methemoglobin (metHb, i.e., ferric [Fe 3+ ] rather than ferrous [Fe 2+ ] haemoglobin) in the blood .
Methemoglobinemia prevents the binding of oxygen to haemoglobin causing oxygen depletion that could lead to severe hypoxia. [ 27 ]
If nitrogen dioxide poisoning is untreated, fibrous granulation tissue is likely to develop within the alveolar ducts , tiny ducts that connect the respiratory bronchioles to alveolar sacs, each of which contains a collection of alveoli (small mucus-lined pouches made of flattened epithelial cells). The overall reaction may cause an obstructive lung disease . Meanwhile, proliferative bronchiolitis is a secondary effect of nitrogen dioxide poisoning. [ 28 ]
The EPA have some regulations and guidelines for monitoring nitrogen dioxide levels. Historically, some states in the US including Chicago , Northeast corridor and Los Angeles have had high levels of nitrogen dioxide.
In 2006, the WHO estimated that over 2 million deaths result annually from air pollution in which nitrogen dioxide constitute one of the pollutants. While over 50% of the disease that results from these pollutants are common in developing countries and the effects in developed countries is also significant. [ 29 ] An EPA survey in the US suggests that 16 percent of United States' housing units are sited close to an airport , highway or railroad increasing in the United States the exposure risk of approximately 48 million people.
A feasibility study of the ozone formed from the oxidation of nitrogen dioxide in ambient air reported by the WHO suggested that daily deaths of 1 to 2% is attributed to exposure to ozone concentration above 47.3 ppb and exposure above 75.7 ppb is attributed to 3 to 5% increase in daily mortality. A level of 114 ppb was attributed to 5 to 9% increase daily mortality.
Silo filler's disease is pervasive during the harvest seasons of food grains. [ 30 ]
In May 2015, the National Green Tribunal directed Delhi and other states in India to ban diesel vehicles over 10 years old as a measure to reduce nitrogen dioxide emission that may result in nitrogen dioxide poisoning. [ 31 ] In 2008, the report of United Kingdom Committee on the Medical Effects of Air Pollutants (COMEAP) suggested that air pollution is the cause of about 29,000 deaths in UK. [ 32 ] The WHO urban air quality database estimated Delhi's mean annual PM 10 levels in 2010 as 286 μg /m 3 and London as 23 μg /m 3 . In 2014, the database estimated Delhi's annual mean PM 2.5 particulate matter levels in 2013 as 156 μg /m 3 whereas, London have only 8 μg /m 3 in 2010 but the nitrogen dioxide in London breach the European Union 's standard. [ 33 ] In 2013, the annual mean nitrogen dioxide level in London was estimated as 58 μg /m 3 but the save and "threshold limit value" is 40 μg /m 3 . [ 34 ] In March 2015, Brussels took the United Kingdom into court for breaching emissions limits of nitrogen dioxide at its coal-fired Aberthaw power stations in Wales . [ 35 ] The plant operated under a permit allowing emissions of 1200 mg/Nm 3 , which is more than twice the 5 mg/Nm 3 limit specified in the EU's large combustion plant directive. [ 36 ]
Generally, long-term prognosis is helpful to survival of initial exposure to nitrogen dioxide. Some cases of nitrogen dioxide poisoning resolves with no observable symptoms and patient may be determined by pulmonary function testing. [ 37 ] If chronic exposure causes lung damage, it could take several days or months for the pulmonary function to improve. Meanwhile, permanent mild dysfunction may result from bronchiolitis obliterans and could manifest as abnormal flow at 50 to 70 percent of vital capacity. It may also manifest as mild hyperinflammation, airway obstruction and in that case, patient may be subject to steroid treatment to treat deconditioning . [ 38 ] Complications from prolong exposure includes bronchiolitis obliterans and other secondary infections such as pneumonia due to injuries on the mucous membrane from pulmonary edema and inhibition of immune system by nitrogen dioxide. [ 39 ] Nitrogen dioxide inhalation can result in short and long-term morbidity or death depending on the extent of exposure and inhaled concentration and the exposure time.
Illness resulting from acute exposure is usually not fatal although some exposure may cause bronchiolitis obliterans, pulmonary edema as well as rapid asphyxiation . [ 40 ] If the concentration of exposure is excessively high, the gas may displace oxygen resulting in fatal asphyxiation. [ 41 ]
Generally, patients and workers should be educated by medical personnel on how to identify the signs and symptoms of Nitrogen dioxide poisoning.
Farmers and other farm workers should be educated on the proper way of food grain storage to prevent silo filler's disease. [ 42 ]
Chronic exposure to high level of nitrogen dioxide results in the allosteric inhibition of glutathione peroxidase and glutathione S-transferase , both of which are important enzymes found in the mucous membrane antioxidant defense system, that catalyse nucleophilic attack by reduced glutathione (GSH) on non-polar compounds that contain an electrophilic carbon and nitrogen . These inhibition mechanisms generates free radicals that causes peroxidation from the lipids in the mucous membrane leading to increased peroxidized erythrocyte lipids, a reaction that proceeds by a free radical chain reaction mechanism that result in oxidative stress. [ 43 ] The oxidative stress on the mucous membrane causes the dissociation of the GSTp-JNK complex, oligomerization of GSTP and induction of the JNK pathway , resulting in apoptosis or inflammation of the bronchioles and pulmonary alveolus in mild cases. [ 44 ] On migrating to the bloodstream , nitrogen dioxide poisoning results in an irreversible inhibition of the erythrocyte membrane acetylcholinesterase which may lead to muscular paralysis , convulsions, bronchoconstriction , the narrowing of the airways in the lungs (bronchi and bronchioles) and death by asphyxiation . [ 45 ] [ 46 ] [ 47 ] It also causes a decrease in glucose-6-phosphate dehydrogenase which may results in glucose-6-phosphate dehydrogenase deficiency known as favism, a condition that predisposes to hemolysis (spontaneous destruction of red blood cells ). [ 48 ] Acute and chronic exposure also reduces glutathione reductase , an enzyme that catalyzes the reduction of glutathione disulfide (GSSG) to the sulfhydryl form glutathione (GSH), which is a critical molecule in resisting oxidative stress and maintaining the reducing environment of the cell. [ 49 ] [ 50 ] [ 51 ]
Exposure to nitrogen dioxide has a significant effect on the male reproductive system by inhibiting the production of Sertoli cells , the "nurse" cells of the testicles that are part of a seminiferous tubule and help in the process of spermatogenesis . [ 52 ] These effects consequently retard the production of sperm cells.
The effects of nitrogen dioxide poisoning on female reproduction may be linked with the effects of oxidative stress on female reproduction. [ 53 ] Nitrogen dioxide poisoning disrupts the balance of reactive oxygen species (ROS), which results in oxidative stress, leading to significant effects on the female reproductive lifespan. ROS play a significant role in body physiology, from oocyte production, development and maturation to fertilization , development of the embryo and gestation .
Exposure to nitrogen dioxide causes ovulation-induced oxidative damage to the DNA of ovarian epithelium. [ 54 ] There is a growing body of literature on the pathological effects of ROS on female reproduction as evidenced by free-radical-induced birth defects, abortions, hydatidiform moles and pre-eclampsia. ROS also play a significant role in the etiopathogenesis of endometriosis , a disease in which tissue that normally grows inside the uterus grows outside of it. [ 55 ] Oxidative stress causes defective placentation , which is likely to lead to placental hypoxia, shortage of oxygen in the placental as well as reperfusion injury resulting from ischemia, which may lead to endothelial cell dysfunction. [ 56 ] Increased oxidative stress caused by nitrogen dioxide poisoning may result in ovarian epithelium inflammation and potentially to cancer in the most severe cases. [ 57 ] | https://en.wikipedia.org/wiki/Nitrogen_dioxide_poisoning |
Nitrogen fixation is a chemical process by which molecular dinitrogen ( N 2 ) is converted into ammonia ( NH 3 ). [ 1 ] It occurs both biologically and abiologically in chemical industries . Biological nitrogen fixation or diazotrophy is catalyzed by enzymes called nitrogenases . [ 2 ] These enzyme complexes are encoded by the Nif genes (or Nif homologs ) and contain iron , often with a second metal (usually molybdenum , but sometimes vanadium ). [ 3 ]
Some nitrogen-fixing bacteria have symbiotic relationships with plants , especially legumes , mosses and aquatic ferns such as Azolla . [ 4 ] Looser non-symbiotic relationships between diazotrophs and plants are often referred to as associative, as seen in nitrogen fixation on rice roots. Nitrogen fixation occurs between some termites and fungi . [ 5 ] It occurs naturally in the air by means of NO x production by lightning . [ 6 ] [ 7 ]
Fixed nitrogen is essential to life on Earth . All nitrogen-containing organic compounds such as DNA and proteins contain nitrogen. Industrial nitrogen fixation underpins the manufacture of all nitrogenous industrial products , which include fertilizers , pharmaceuticals , textiles , dyes and explosives .
Biological nitrogen fixation was discovered by Jean-Baptiste Boussingault in 1838. [ 8 ] [ 9 ] Later, in 1880, the process by which it happens was discovered by German agronomist Hermann Hellriegel and Hermann Wilfarth [ de ] [ 10 ] and was fully described by Dutch microbiologist Martinus Beijerinck . [ 11 ]
"The protracted investigations of the relation of plants to the acquisition of nitrogen begun by de Saussure , Ville , Lawes , Gilbert and others, and culminated in the discovery of symbiotic fixation by Hellriegel and Wilfarth in 1887." [ 12 ]
"Experiments by Bossingault in 1855 and Pugh, Gilbert & Lawes in 1887 had shown that nitrogen did not enter the plant directly. The discovery of the role of nitrogen fixing bacteria by Herman Hellriegel and Herman Wilfarth in 1886–1888 would open a new era of soil science ." [ 13 ]
In 1901, Beijerinck showed that Azotobacter chroococcum was able to fix atmospheric nitrogen. This was the first species of the azotobacter genus, so-named by him. It is also the first known diazotroph , species that use diatomic nitrogen as a step in the complete nitrogen cycle . [ 14 ]
Biological nitrogen fixation (BNF) occurs when atmospheric nitrogen is converted to ammonia by a nitrogenase enzyme. [ 1 ] The overall reaction for BNF is:
N 2 + 16ATP + 16H 2 O + 8e − + 8H + → 2NH 3 +H 2 + 16ADP + 16P i
The process is coupled to the hydrolysis of 16 equivalents of ATP and is accompanied by the co-formation of one equivalent of H 2 . The conversion of N 2 into ammonia occurs at a metal cluster called FeMoco , an abbreviation for the iron- molybdenum cofactor. The mechanism proceeds via a series of protonation and reduction steps wherein the FeMoco active site hydrogenates the N 2 substrate. [ 1 ] In free-living diazotrophs , nitrogenase-generated ammonia is assimilated into glutamate through the glutamine synthetase /glutamate synthase pathway. The microbial nif genes required for nitrogen fixation are widely distributed in diverse environments. [ 15 ]
Nitrogenases are rapidly degraded by oxygen. For this reason, many bacteria cease production of the enzyme in the presence of oxygen. Many nitrogen-fixing organisms exist only in anaerobic conditions, respiring to draw down oxygen levels, or binding the oxygen with a protein such as leghemoglobin . [ 16 ] [ 17 ]
Atmospheric nitrogen cannot be metabolized by most organisms, [ 18 ] because its triple covalent bond is very strong. Most take up fixed nitrogen from various sources. For every 100 atoms of carbon, roughly 2 to 20 atoms of nitrogen are assimilated. The atomic ratio of carbon (C) : nitrogen (N) : phosphorus (P) observed on average in planktonic biomass was originally described by Alfred Redfield, [ 19 ] who determined the stoichiometric relationship between C:N:P atoms, The Redfield Ratio, to be 106:16:1. [ 19 ]
The protein complex nitrogenase is responsible for catalyzing the reduction of nitrogen gas (N 2 ) to ammonia (NH 3 ). [ 20 ] [ 21 ] In cyanobacteria , this enzyme system is housed in a specialized cell called the heterocyst . [ 22 ] The production of the nitrogenase complex is genetically regulated, and the activity of the protein complex is dependent on ambient oxygen concentrations, and intra- and extracellular concentrations of ammonia and oxidized nitrogen species (nitrate and nitrite). [ 23 ] [ 24 ] [ 25 ] Additionally, the combined concentrations of both ammonium and nitrate are thought to inhibit N Fix , specifically when intracellular concentrations of 2- oxoglutarate (2-OG) exceed a critical threshold. [ 26 ] The specialized heterocyst cell is necessary for the performance of nitrogenase as a result of its sensitivity to ambient oxygen. [ 27 ]
Nitrogenase consist of two proteins, a catalytic iron-dependent protein, commonly referred to as MoFe protein and a reducing iron-only protein (Fe protein). Three iron-dependent proteins are known: molybdenum -dependent, vanadium -dependent, and iron -only, with all three nitrogenase protein variations containing an iron protein component. Molybdenum-dependent nitrogenase is most common. [ 1 ] The different types of nitrogenase can be determined by the specific iron protein component. [ 28 ] Nitrogenase is highly conserved. Gene expression through DNA sequencing can distinguish which protein complex is present in the microorganism and potentially being expressed. Most frequently, the nif H gene is used to identify the presence of molybdenum-dependent nitrogenase, followed by closely related nitrogenase reductases (component II) vnf H and anf H representing vanadium-dependent and iron-only nitrogenase, respectively. [ 29 ] In studying the ecology and evolution of nitrogen-fixing bacteria , the nifH gene is the biomarker most widely used. [ 30 ] nif H has two similar genes anf H and vnfH that also encode for the nitrogenase reductase component of the nitrogenase complex. [ 31 ]
Nitrogenase is thought to have evolved sometime between 1.5-2.2 billion years ago (Ga), [ 32 ] [ 33 ] although some isotopic support showing nitrogenase evolution as early as around 3.2 Ga. [ 34 ] Nitrogenase appears to have evolved from maturase -like proteins, although the function of the preceding protein is currently unknown. [ 35 ]
Nitrogenase has three different forms ( Nif, Anf, and Vnf ) that correspond with the metal found in the active site of the protein (molybdenum, iron, and vanadium respectively). [ 36 ] Marine metal abundances over Earth's geologic timeline are thought to have driven the relative abundance of which form of nitrogenase was most common. [ 37 ] Currently, there is no conclusive agreement on which form of nitrogenase arose first.
Diazotrophs are widespread within domain Bacteria including cyanobacteria (e.g. the highly significant Trichodesmium and Cyanothece ), green sulfur bacteria , purple sulfur bacteria , Azotobacteraceae , rhizobia and Frankia . [ 38 ] [ 39 ] Several obligately anaerobic bacteria fix nitrogen including many (but not all) Clostridium spp. Some archaea such as Methanosarcina acetivorans also fix nitrogen, [ 40 ] and several other methanogenic taxa , are significant contributors to nitrogen fixation in oxygen-deficient soils. [ 41 ]
Cyanobacteria , commonly known as blue-green algae, inhabit nearly all illuminated environments on Earth and play key roles in the carbon and nitrogen cycle of the biosphere . In general, cyanobacteria can use various inorganic and organic sources of combined nitrogen, such as nitrate , nitrite , ammonium , urea , or some amino acids . Several cyanobacteria strains are also capable of diazotrophic growth, an ability that may have been present in their last common ancestor in the Archean eon. [ 42 ] Nitrogen fixation not only naturally occurs in soils but also aquatic systems, including both freshwater and marine. [ 43 ] [ 44 ] Indeed, the amount of nitrogen fixed in the ocean is at least as much as that on land. [ 45 ] The colonial marine cyanobacterium Trichodesmium is thought to fix nitrogen on such a scale that it accounts for almost half of the nitrogen fixation in marine systems globally. [ 46 ] Marine surface lichens and non-photosynthetic bacteria belonging in Proteobacteria and Planctomycetes fixate significant atmospheric nitrogen. [ 47 ] Species of nitrogen fixing cyanobacteria in fresh waters include: Aphanizomenon and Dolichospermum (previously Anabaena). [ 48 ] Such species have specialized cells called heterocytes , in which nitrogen fixation occurs via the nitrogenase enzyme. [ 49 ] [ 50 ]
One type of organelle , originating from cyanobacterial endosymbionts called UCYN-A 2, [ 51 ] [ 52 ] can turn nitrogen gas into a biologically available form. This nitroplast was discovered in algae , particularly in the marine algae Braarudosphaera bigelowii . [ 53 ]
Diatoms in the family Rhopalodiaceae also possess cyanobacterial endosymbionts called spheroid bodies or diazoplasts. [ 54 ] These endosymbionts have lost photosynthetic properties, but have kept the ability to perform nitrogen fixation, allowing these diatoms to fix atmospheric nitrogen. [ 55 ] [ 56 ] Other diatoms in symbiosis with nitrogen-fixing cyanobacteria are among the genera Hemiaulus , Rhizosolenia and Chaetoceros . [ 57 ]
Plants that contribute to nitrogen fixation include those of the legume family — Fabaceae — with taxa such as kudzu , clover , soybean , alfalfa , lupin , peanut and rooibos . [ 39 ] They contain symbiotic rhizobia bacteria within nodules in their root systems , producing nitrogen compounds that help the plant to grow and compete with other plants. [ 58 ] When the plant dies, the fixed nitrogen is released, making it available to other plants; this helps to fertilize the soil . [ 16 ] [ 59 ] The great majority of legumes have this association, but a few genera (e.g., Styphnolobium ) do not. In many traditional farming practices, fields are rotated through various types of crops, which usually include one consisting mainly or entirely of clover . [ citation needed ]
Fixation efficiency in soil is dependent on many factors, including the legume and air and soil conditions. For example, nitrogen fixation by red clover can range from 50 to 200 lb/acre (56 to 224 kg/ha). [ 60 ]
The ability to fix nitrogen in nodules is present in actinorhizal plants such as alder and bayberry , with the help of Frankia bacteria. They are found in 25 genera in the orders Cucurbitales , Fagales and Rosales , which together with the Fabales form a nitrogen-fixing clade of eurosids . The ability to fix nitrogen is not universally present in these families. For example, of 122 Rosaceae genera, only four fix nitrogen. Fabales were the first lineage to branch off this nitrogen-fixing clade; thus, the ability to fix nitrogen may be plesiomorphic and subsequently lost in most descendants of the original nitrogen-fixing plant; however, it may be that the basic genetic and physiological requirements were present in an incipient state in the most recent common ancestors of all these plants, but only evolved to full function in some of them. [ 61 ]
In addition, Trema ( Parasponia ), a tropical genus in the family Cannabaceae , is unusually able to interact with rhizobia and form nitrogen-fixing nodules. [ 62 ]
Some other plants live in association with a cyanobiont (cyanobacteria such as Nostoc ) which fix nitrogen for them:
Some symbiotic relationships involving agriculturally-important plants are: [ 65 ]
A method for nitrogen fixation was first described by Henry Cavendish in 1784 using electric arcs reacting nitrogen and oxygen in air. This method was implemented in the Birkeland–Eyde process of 1903. [ 67 ] The fixation of nitrogen by lightning is a very similar natural occurring process.
The possibility that atmospheric nitrogen reacts with certain chemicals was first observed by Desfosses in 1828. He observed that mixtures of alkali metal oxides and carbon react with nitrogen at high temperatures. With the use of barium carbonate as starting material, the first commercial process became available in the 1860s, developed by Margueritte and Sourdeval. The resulting barium cyanide reacts with steam, yielding ammonia. In 1898 Frank and Caro developed what is known as the Frank–Caro process to fix nitrogen in the form of calcium cyanamide . The process was eclipsed by the Haber process , which was discovered in 1909. [ 68 ] [ 69 ]
The dominant industrial method for producing ammonia is the Haber process also known as the Haber-Bosch process. [ 70 ] Fertilizer production is now the largest source of human-produced fixed nitrogen in the terrestrial ecosystem . Ammonia is a required precursor to fertilizers , explosives , and other products. The Haber process requires high pressures (around 200 atm) and high temperatures (at least 400 °C), which are routine conditions for industrial catalysis. This process uses natural gas as a hydrogen source and air as a nitrogen source. The ammonia product has resulted in an intensification of nitrogen fertilizer globally [ 71 ] and is credited with supporting the expansion of the human population from around 2 billion in the early 20th century to roughly 8 billion people now. [ 72 ]
Much research has been conducted on the discovery of catalysts for nitrogen fixation, often with the goal of lowering energy requirements. However, such research has thus far failed to approach the efficiency and ease of the Haber process. Many compounds react with atmospheric nitrogen to give dinitrogen complexes . The first dinitrogen complex to be reported was Ru(NH 3 ) 5 ( N 2 ) 2+ . [ 73 ] Some soluble complexes do catalyze nitrogen fixation. [ 74 ]
Nitrogen can be fixed by lightning converting nitrogen gas ( N 2 ) and oxygen gas ( O 2 ) in the atmosphere into NO x ( nitrogen oxides ). The N 2 molecule is highly stable and nonreactive due to the triple bond between the nitrogen atoms. [ 75 ] Lightning produces enough energy and heat to break this bond [ 75 ] allowing nitrogen atoms to react with oxygen, forming NO x . These compounds cannot be used by plants, but as this molecule cools, it reacts with oxygen to form NO 2 , [ 76 ] which in turn reacts with water to produce HNO 2 ( nitrous acid ) or HNO 3 ( nitric acid ). When these acids seep into the soil, they make NO 3 − (nitrate) , which is of use to plants. [ 77 ] [ 75 ] | https://en.wikipedia.org/wiki/Nitrogen_fixation |
A nitrogen fixation package is a piece of research equipment for studying nitrogen fixation in plants. One product of this kind, the Q-Box NF1LP made by Qubit Systems, operates by measuring the hydrogen (H 2 ) given off in the nitrogen-fixing chemical reaction enabled by nitrogenase enzymes.
Nitrogen is produced by bacteria, which have an endo-symbiotic relationship with the legume host. [ 1 ] In this relationship, the plant shares its carbohydrates with the bacteria so that the bacteria can thrive, and the plant benefits by having excess nitrogen made available. The bacteria's creation of nitrogen also creates hydrogen, which is what the unit measures to determine the nitrogen produced. [ 2 ] Measurement of H 2 evolution as a means of determining nitrogenase activity is an alternative technique to acetylene reduction assay, [ 3 ] and allows real-time monitoring of changes in nitrogenase activity.
Q-Box NF1LP is an experimental package using an open-flow gas exchange system for measurement of nitrogen fixation in H 2 -producing legume symbioses. A flow-through H 2 sensor (Q-S121) measures the production rate of H 2 from N 2 -fixing tissues, allowing in vivo measurement of nitrogenase activity in real time. Measurements of nitrogenase activity on up to three plants is possible, i.e. a four-channel system including a reference sample.
Nitrogen fixation packages must be used in a laboratory-type environment. This can be a temporary laboratory set up in the field, as long as it is under stable, uncontaminated conditions. The product must be supplied with many potted samples of the plants and of the neighbouring soil, taken from separate areas on the farm or field under study. [ 2 ] The tests rely on the availability of the Herbaspirillum bacteria in the soil. [ 4 ] This bacterium is found at the root of most legumes, which is where they produce nitrogen. [ 4 ] To test soil properly, it must be free of added nitrogen fertilizers, which have harmful effects on the Herbaspirillum bacteria needed for fixation. [ 2 ]
Different aspects of nitrogen fixation can be examined with these products, such as effects of temperature on the fixation process, the regulation of the process by oxygen , and the inhibition of nitrogen fixation by an over-abundance of fertilizers . [ 2 ] | https://en.wikipedia.org/wiki/Nitrogen_fixation_package |
Nitrogen generators and stations are stationary or mobile air-to- nitrogen production complexes.
The adsorption gas separation process in nitrogen generators is based on the phenomenon of fixing various gas mixture components by a solid substance called an adsorbent . This phenomenon is brought about by the gas and adsorbent molecules' interaction. [ 1 ]
The technology of air-to-nitrogen production with the use of adsorption processes in nitrogen generators is well studied and widely applied at industrial facilities for the recovery of high-purity nitrogen. [ 2 ] [ 3 ]
The operating principle of a nitrogen generator utilizing the adsorption technology is based upon the dependence of the adsorption rates featured by various gas mixture components upon pressure and temperature factors. Among nitrogen adsorption plants of various types, pressure swing adsorption (PSA) plants have found the broadest application world-wide.
The system's design is based on the regulation of gas adsorption and adsorbent regeneration by means of changing pressures in two adsorber–adsorbent-containing vessels. This process requires constant temperature, close to ambient. With this process, nitrogen is produced by the plant at the above-atmospheric pressure, while the adsorbent regeneration is accomplished at below-atmospheric pressure.
The swing adsorption process in each of the two adsorbers consists of two stages running for a few minutes. At the adsorption stage oxygen, H 2 O and CO 2 molecules diffuse into the pore structure of the adsorbent whilst the nitrogen molecules are allowed to travel through the adsorber–adsorbent-containing vessel. At the regeneration stage the adsorbed components are released from the adsorbent vented into the atmosphere. The process is then multiplely repeated. [ 4 ]
The operation of membrane systems is based on the principle of differential velocity with which various gas mixture components permeate membrane substance. The driving force in the gas separation process is the difference in partial pressures on different membrane sides. [ 7 ]
Structurally, a hollow-fiber membrane represents a cylindrical cartridge functioning as a spool with specifically reeled polymer fibers. Gas flow is supplied under pressure into a bundle of membrane fibers. Due to the difference in partial pressures on the external and internal membrane surface gas flow separation is accomplished. | https://en.wikipedia.org/wiki/Nitrogen_generator |
In chemistry , pyramidal inversion (also umbrella inversion ) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH 3 ) "turns inside out". [ 1 ] [ 2 ] It is a rapid oscillation of the atom and substituents, the molecule or ion passing through a planar transition state . [ 3 ] For a compound that would otherwise be chiral due to a stereocenter , pyramidal inversion allows its enantiomers to racemize . The general phenomenon of pyramidal inversion applies to many types of molecules, including carbanions , amines , phosphines , arsines , stibines , and sulfoxides . [ 4 ] [ 2 ]
The identity of the inverting atom has a dominating influence on the barrier. Inversion of ammonia is rapid at room temperature , inverting 30 billion times per second. Three factors contribute to the rapidity of the inversion: a low energy barrier (24.2 kJ/mol ; 5.8 kcal/mol), a narrow barrier width (distance between geometries), and the low mass of hydrogen atoms, which combine to give a further 80-fold rate enhancement due to quantum tunnelling . [ 5 ] In contrast, phosphine (PH 3 ) inverts very slowly at room temperature (energy barrier: 132 kJ/mol ). [ 6 ] Consequently, amines of the type RR′R"N usually are not optically stable (enantiomers racemize rapidly at room temperature), but P -chiral phosphines are. [ 7 ] Appropriately substituted sulfonium salts, sulfoxides , arsines , etc. are also optically stable near room temperature. Steric effects can also influence the barrier.
Pyramidal inversion in nitrogen and amines is known as nitrogen inversion . [ 8 ] It is a rapid oscillation of the nitrogen atom and substituents, the nitrogen "moving" through the plane formed by the substituents (although the substituents also move - in the other direction); [ 9 ] the molecule passing through a planar transition state . [ 10 ] For a compound that would otherwise be chiral due to a nitrogen stereocenter , nitrogen inversion provides a low energy pathway for racemization , usually making chiral resolution impossible. [ 11 ]
Ammonia exhibits a quantum tunnelling due to a narrow tunneling barrier, [ 12 ] and not due to thermal excitation. Superposition of two states leads to energy level splitting , which is used in ammonia masers .
The inversion of ammonia was first detected by microwave spectroscopy in 1934. [ 13 ]
In one study the inversion in an aziridine was slowed by a factor of 50 by placing the nitrogen atom in the vicinity of a phenolic alcohol group compared to the oxidized hydroquinone . [ 14 ]
The system interconverts by oxidation by oxygen and reduction by sodium dithionite .
Conformational strain and structural rigidity can effectively prevent the inversion of amine groups. Tröger's base analogs [ 15 ] (including the Hünlich's base [ 16 ] ) are examples of compounds whose nitrogen atoms are chirally stable stereocenters and therefore have significant optical activity . [ 17 ] | https://en.wikipedia.org/wiki/Nitrogen_inversion |
Fish sauce is a liquid condiment made from fish or krill that have been coated in salt and fermented for up to two years. [ 1 ] [ 2 ] : 234 It is used as a staple seasoning in East Asian cuisine and Southeast Asian cuisine , particularly Myanmar , Cambodia , Laos , Philippines , Thailand , and Vietnam . Some garum -related fish sauces have been used in the West since the Roman times .
Due to its ability to add a savory umami flavor to dishes, it has been embraced globally by chefs and home cooks. The umami flavor in fish sauce is due to its glutamate content. [ 3 ]
Fish sauce is used as a seasoning during or after cooking, and as a base in dipping sauces . Soy sauce is regarded by some in the West as a vegetarian alternative to fish sauce though they are very different in flavor. [ 1 ] : 234
Sauces that included fermented fish parts with other ingredients such as meat and soy bean were recorded in China , 2300 years ago. [ 4 ] During the Zhou dynasty of ancient China, fish fermented with soybeans and salt was used as a condiment. [ 5 ] [ 6 ] By the time of the Han dynasty , soy beans were fermented without the fish into soy paste and its by-product soy sauce , [ 7 ] : 346, 358–359 with fermented fish-based sauces developing separately into fish sauce. [ 8 ] A fish sauce, called kôechiap in Hokkien Chinese, might be the precursor of ketchup . [ 9 ] [ 1 ] : 233
By 50-100 BC, demand for fish sauces and fish pastes in China had fallen drastically, with fermented bean products becoming a major trade commodity. Fish sauce, however, developed massive popularity in Southeast Asia. Food scholars traditionally divide East Asia into two distinct condiment regions, separated by a bean-fish divide: Southeast Asia, mainly using fermented fish (Vietnam, Thailand, Cambodia), and Northeast Asia, using mainly fermented beans (China, Korea, Japan). Fish sauce re-entered China in the 17th and 18th centuries, brought from Vietnam and Cambodia by Chinese traders up the coast of the southern provinces Guangdong and Fujian. [ 10 ]
Fish sauces were widely used in ancient Mediterranean cuisine . The earliest recorded production was between 4th–3rd century BC by the Ancient Greeks, who fermented scraps of fish called garos into one. [ 1 ] : 235 [ 11 ] It is believed to have been made with a lower salt content than modern fish sauces. [ 12 ]
The Romans made a similar condiment called either garum or liquamen. [ 1 ] : 235 According to Pliny the Elder , "garum consists of the guts of fish and other parts that would otherwise be considered refuse so that garum is really the liquor from putrefaction." [ 13 ] Garum was made in the Roman outposts of Spain almost exclusively from mackerel by salting the scrap fish innards, and then sun fermenting the flesh until it fell apart, usually for several months. The brown liquid would then be strained, bottled, and sold as a condiment. Remains of Roman fish salting facilities can still be seen, including in Algeciras in Spain and near Setúbal in Portugal. The process lasted until the 16th century when garum makers switched to anchovy and removed the innards. [ 1 ] : 235
Garum was ubiquitous in Classical Roman cooking. Mixed with wine it was known as oenogarum , or with vinegar, oxygarum , or mixed with honey, meligarum . Garum was one of the trade specialties in Hispania Baetica . [ 14 ] [ page needed ] Garum was frequently maligned as smelling bad or rotten, being called, for example, "evil-smelling fish sauce" [ 15 ] and is said to be similar to modern colatura di alici , a fish sauce used in Neapolitan cuisine . [ who? ]
In English garum was formerly translated as fish pickle . The original Worcestershire sauce is a related product because it is fermented and contains anchovies.
While fish sauce and oyster sauce are both briny and may have related histories, they are different products. Fish sauce is watery, clear, and salty, whereas oyster sauce is made by reducing oyster extracts and therefore sweeter with a hint of salt and not as strong an aroma as fish sauce. [ 16 ]
Fish sauces historically have been prepared from different species of fish and shellfish, and from using the whole fish, or by using just fish blood or viscera . Most modern fish sauces contain only fish and salt , usually made from anchovy, shrimp, mackerel, or other strong-flavored, high oil fish. Some variants add herbs and spices . For modern fish sauces, fish or shellfish are mixed with salt at a concentration of 10% to 30%. It is then sealed in a closed container for up to two years. [ 1 ] : 234
Once the original draft has been made, some fish sauces will be produced through a re-extraction of the fish mass via boiling. To improve the visual appearance and add taste, second-pass fish sauces often have added caramel, molasses, or roasted rice. [ 1 ] : 234 They are thinner, and less costly. Some volume manufacturers of fish sauce will also water down a first-press to manufacture more products.
Fish sauce that has been only briefly fermented has a pronounced fishy taste. Extended fermentation reduces this and gives the product a nuttier , richer and more savory flavor. [ 17 ] An anonymous article, "Neuc-num", in Diderot and d'Alembert 's 18th-century Encyclopédie , states: "It is said that Europeans become accustomed enough to this type of sauce". [ 18 ]
Southeast Asian fish sauce is often made from anchovies , salt, and water, and is intensely flavoured. Anchovies and salt are arranged in wooden barrels to ferment and are slowly pressed, yielding the salty, fishy liquid. The salt extracts the liquid via osmosis .
Southeast Asians generally use fish sauce as a cooking sauce. However, there is a sweet and sour version of this sauce which is used more commonly as a dipping sauce.
Fish sauce in Myanmar is called ngan bya yay (ငါးငံပြာရည်). It's often a by-product of Hmyin ngapi (မျှင်ငပိ)(Burmese Fish Paste made from small fishes, anchovies,krills and shrimps) [ 19 ]
In Cambodia , fish sauce is called tik trei ( Khmer : ទឹកត្រី , tœ̆k trei ). Just like prahok , it is believed to date back to the pre-Angkorean era . Industrially fish sauce is produced by mixing trei aing keuy or anchovies with coarse salt and fermenting it in large wooden vats . Over the period of six to eight months, it is distilled five times, before being transferred into jars and sun-fermented for the final 2–3 months. The most famous fish sauce is produced in the Kampot Province . Food Production Company of Kampot produces a speciality fish sauce containing roe . [ 20 ] Fish sauce is mixed with sugar, lime juice , chili peppers and crushed roasted peanuts to create sweet fish sauce, which is the most popular dipping sauce in Cambodia. [ 21 ]
In Lao / Isan , it is called nam pa ( Lao : ນ້ໍາປາ ). A chunkier, more aromatic version known as padaek is also used. [ 22 ] [ 23 ]
The Philippine fish sauce is known as patis . It is one of the most important ingredients in Filipino cuisine. [ 24 ] Patis is a by-product of bagoong production, which include bagoong isda (fermented fish) and bagoong alamang (fermented krill ), as well as the rarer bagoong macabebe (fermented oysters ) and bagoong sisi (fermented clams ). The fish used are typically small like sardines , anchovies , ambassids , and the fry of larger fish. Unlike other fish sauce variants, the fermented solids are not discarded but are sold as separate products. The patis is skimmed from the upper layers of fermenting bagoong and is not pressed. As such, patis usually takes longer to produce than other types of fish sauce as it is reliant on the readiness of bagoong . [ 25 ] [ 26 ] [ 27 ]
Patis is nearly always cooked prior to consumption, even when used as an accent to salads or other raw dishes. Patis is also used as an ingredient in cooked dishes, including a rice porridge called arroz caldo , as a condiment for fried fish or an umami accent in a common dish, sinigang . Patis is also used in place of table salt in meals to enhance the flavor of the food, where it can either be dashed from a dispensing bottle onto the food, or poured into a saucer and mixed with calamansi and labuyo chilis and used as a dipping sauce. [ 28 ] [ 27 ] [ 29 ] [ 25 ]
Fish sauce in Thailand is called nam pla ( Thai : น้ำปลา ). In Isan , it is called nam pa . Similar to the Laotian padaek is pla ra ( Thai : ปลาร้า ), also used in Thai cuisine . In Thailand, fish sauce is used both in cooking and also served at the table as a condiment, for instance in noodle soups. Nearly every Thai meal is served with phrik nam pla as a condiment: a mixture of fish sauce, lime juice, and chopped bird's eye chilies . Sliced garlic is often added to this sauce.
Historically, there were two types of fish sauce made in Thailand: that made from freshwater fish, pla soi , and that made from saltwater fish, pla kratak . Either fish is fermented for at least eight months, three parts fish to two parts salt. The resulting mash is filtered. This yields the best fish sauce called the "base". The dregs are then mixed with water and salt and again fermented for three to four months. This yields a second-grade fish sauce, mostly used in cooking. [ 30 ]
In 2014, the US Food and Drug Administration (FDA) banned the import of Thai fish sauces due to a lack of information about tests for botulinum toxin . The toxin can cause death if more than 0.5 micrograms are consumed. The Thai Office of Food Safety and Quality then tested 48 brands of fish sauce to determine the content of botulinum toxin in the products. Of 48 brands tested, 28 were genuine fish sauces from 18 production sites in 12 provinces. Twenty samples from production sites in eight provinces were adulterated fish sauce. Tests showed that none were contaminated with botulinum toxin types A, B, E, and F and were free of Clostridium botulinum bacteria. [ 31 ] In 2018, rumours again surfaced concerning banned Thai fish sauce. [ 32 ]
The variety from Vietnam is called nước mắm . [ 33 ] There are two areas in Vietnam that are most famous for producing fish sauce: Phú Quốc and Phan Thiết .
Fish sauce has a 300-year history dating back to the Champa kingdom of the Cham people . [ 34 ] Phan Thiết can be identified with the birthplace of Vietnamese fish sauce. Before 1693, Phan Thiết was a territory of Champa . The Vietnamese occupied the area in 1693 and commercialized the fish sauce by keeping it in barrels and selling throughout the country. This business was popularized by Trần Gia Hòa who was born in 1872. There is a fish sauce museum in Phan Thiết. Popular brands in the US include Mega Chef, Red Boat, 3 Crabs, Golden Boy, and Hòn Phan Thiết. [ 35 ]
Vietnamese fish sauces are made with anchovies, mackerel, scabbard fish, and salt. High mercury concentration can be found in larger fish, especially in predator fish like scabbard fish. They do not have any additives like sugar, hydrolyzed protein , or preservatives. [ 36 ] Vietnamese prefer sauces without a strong smell, and transparent with a deep golden amber color. "First press" fish sauce, meaning the sauce is bottled from the first time the fermenting barrels are drained, also indicates quality. Lastly, when measuring the nitrogen level of fish sauces (°N, or grams of nitrogen per liter), most fish sauce on the market falls within the mid 20°N range. Anything over 30°N is considered high-grade, and 40°N is optimal. [ 37 ] [ 38 ]
Nước chấm is a Vietnamese prepared fish-based condiment (also referred to as a "sauce") that is savory, lightly sweet and salty tasting, and can be sour and spicy if lime and chili peppers are added. The main components are fish sauce, water, and sugar.
Mắm is made much like fish sauce, except that it is not fermented as long, and the fish is kept along with its liquid extract, not just the extract. Mắm can be used as a base condiment in dipping sauces with additional ingredients, used in soups, stir-fries and meat loaves, or eaten with rice as a main dish.
In January 2016, the Institute of Food Technologists published a study asserting that using Vietnamese fish sauce as a substitute for sodium chloride (salt) in chicken broth, tomato sauce, and coconut curry reduced the amount of sodium chloride by 10 to 25 percent while still maintaining the perceived deliciousness, saltiness, and overall flavor intensity. [ 39 ] This idea is similar to the use of umami flavor enhancers such as MSG to increase flavor intensity and reduce sodium requirement. [ 40 ]
According to the General Statistics Office , in 2020, the output of fish sauce reached nearly 380 million liters. [ 41 ] [ 42 ] [ 43 ] According to the Vietnam Fish Sauce Association, the output of fish sauce in 2023 is expected to reach about 420 million liters. [ 44 ] [ 45 ] The reason for this growth is due to the increasing domestic demand and the strong development of the fish sauce export industry. [ 46 ] [ 47 ] Vietnamese fish sauce is currently exported to more than 60 countries and territories around the world. [ 48 ] [ 49 ] [ 50 ] [ 51 ] According to statistics, Vietnam currently has 783 fish sauce production facilities with 1,500 participating farming households, [ 52 ] [ 53 ] producing about 250 million liters of fish sauce per year. Of which, 35 facilities produce fish sauce for export to 20 markets. [ 54 ] [ 55 ]
In China, fish sauce is called yúlù ( simplified Chinese : 鱼露 ; traditional Chinese : 魚露 ; pinyin : yúlù , literally "fish dew") and is native to the provinces of Guangdong and Fujian. In Chaoshan cuisine, fish sauce is made with Reeve's shad ( Tenualosa reevesii ), which is unsuitable for direct eating due to being fatty, bony, and odorous. [ 56 ]
In Japan, fish sauce is called gyoshō (魚醤); another name is uoshōyu (魚醤油). There are several variations used in regional cuisines. Ishiru in the Noto Peninsula is made from sardine and squid . Shottsuru , the best-known type of Japanese fish sauce and often used as a synonym for all gyoshō , is from Akita Prefecture and is mainly made from sailfin sandfish . Ikanago shoyu of Kagawa Prefecture is made from sand lance . They are used in nabemono , in salad dressings, and as a flavoring ingredient in ramen soups. Imported Thai / Vietnamese fish sauce in Japan is referred to as nanpurā (ナンプラー), from the Thai word for fish sauce nam pla .
In Korea, fish sauce is called eojang ( 어장 ).
Across the Korean Peninsula , aekjeot ( 액젓 , literally "liquid jeotgal "), a type of fish sauce usually made from fermented anchovies or kkanari ( pacific sand lances ), is used as a crucial ingredient in many types of kimchi , both for taste and fermentation. [ 57 ] [ 58 ]
In Jeju island , eoganjang ( 어간장 ), made of fermented godori (young chub mackerel ) or horse mackerel , is used in place of soy sauce .
Colatura di alici is an Italian fish sauce originating in the village of Cetara, Campania .
Worcestershire sauce contains fermented anchovies among other ingredients, which is common in the Anglosphere countries.
Common commercial brands of fish sauce generally contain about 50% to 60% of the FDA's daily recommended amount of sodium per tablespoon serving. Most commercial brands of reasonable quality contain one or two grams of protein per serving; however, higher-quality brands may have four grams of protein or more, while lower-quality brands may have less than one gram of protein per serving. Fish sauce has an insignificant amount of carbohydrates and fats. Vitamin B12 , vitamin B-6 , and magnesium are present in small amounts. | https://en.wikipedia.org/wiki/Nitrogen_level_(fish_sauce) |
Nitrogen monofluoride (fluoroimidogen) is a metastable species that has been observed in laser studies. It is isoelectronic with O 2 . Like boron monofluoride , it is an instance of the rare multiply-bonded fluorine atom. [ 1 ] [ 2 ] It is unstable with respect to its formal dimer, dinitrogen difluoride , as well as to its elements, nitrogen and fluorine .
Nitrogen monofluoride is produced when radical species (H, O, N, CH 3 ) abstracts a fluorine atom from nitrogen difluoride (NF 2 ). Stoichiometrically, the reaction is extremely efficient, regenerating a radical for long-lasting chain propagation . However, radical impurities in the end product also catalyze that product's decomposition. Azide decomposition offers a less-efficient but more pure technique: fluorine azide (which can be formed in situ via reaction of atomic fluorine with hydrazoic acid) decomposes upon shock into NF and N 2 . [ 3 ] [ 4 ]
Many NF-producing reactions give the product in an excited state with characteristic chemiluminescence at 870 and 875 nm (infrared), or at 525–530 nm (green). They have thus been investigated for development as a chemical laser . [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Nitrogen_monofluoride |
Nitrogen nutrition in the arbuscular mycorrhizal system refers to...
Nitrogen is a vital macronutrient for plants, necessary for the biosynthesis of many basic cellular components, such as DNA , RNA and proteins . Nitrogen is obtained by plants through roots from inorganic or organic sources, such as amino acids . [ 1 ] In agricultural settings, nitrogen may be a limiting factor for plant growth and yield, and in total, as a critical cellular component that a plant deficient in this nitrogen will shunt resources away from its shoot in order to expand its root system so that it can acquire more nitrogen. [ 2 ] Arbuscular mycorrhizal fungi are divided into two parts depending on where the mycelium is located. The intra-radical mycelia (IRM) are found within the root itself while the extra-radical mycelium (ERM) are tiny hyphal threads which reach far out into the soil. The IRM is the site of nutrient exchange between the symbionts , while the ERM effectively serves as an extension of the plant's root system by increasing the surface area available for nutrient acquisition, including nitrogen, which can be taken up in the form of ammonium , nitrate or from organic sources. [ 3 ] [ 4 ] Working with an in vitro system, studies have shown that as much as 29% [ 5 ] to 50% [ 6 ] of the root nitrogen was taken up via the fungus. This is also true in in planta studies, such as an experiment in which the researchers showed that 75% of the nitrogen in a young maize leaf originated from the ERM. [ 7 ]
The precise mechanism(s) by which nitrogen is taken up from the soil by the ERM, transported to the IRM, and then turned over to the plant are still under investigation. Toward elucidating the mechanisms through which nitrogen transfer is completed, the sum of numerous studies have provided the necessary tools to study this process. For example, the detection and measurement of gene expression has enabled researchers to determine which genes are up-regulated in the plant and fungus under various nitrogen conditions. Another important tool is the use of the nitrogen isotope [[ 15 N]], which can be distinguished from the more common 14 N isotope. Nitrogen-containing compounds thus labeled can be tracked and measured as they move through the fungus and into the plant, as well as how they are incorporated into nitrogen-containing molecules.
The current model, first put forth in 2005, proposes that the nitrogen taken up by the fungus is converted in the ERM to arginine , which is then transported to the IRM, where it is released as ammonium into the apoplast for the plant to use. [ 8 ] A growing body of data has supported and expanded upon this model. Support has been found primarily in two ways: labeling experiments and the study of gene expression, as demonstrated in a 2010 paper by Tian et al. When labeled nitrogen compounds were added to the ERM compartment of an in vitro bsystem, six fungal genes encoding enzymes involved in the incorporation of inorganic nitrogen into glutamine and its subsequent conversion to arginine were rapidly up-regulated. After a delay, gene expression in the IRM began to show increasing levels of mRNA for genes involved in the breakdown of arginine into urea and the subsequent cleaving of ammonium from the urea molecule. This change in gene expression takes place concurrently with the arrival of 15 N labeled arginine from the ERM compartment. [ 9 ]
Once inside the ERM, the nitrogen molecule may have to travel many centimeters to reach the root. While much progress has been made on either end of the transfer of nitrogen, the mechanism by which the arginine actually moves from the ERM to the IRM remains unresolved. AM fungi are non-septate and lack cell walls between cells, forming one long filament. However, passive flow through the continuous cytoplasm is too slow to explain the transport of nutrients. The mechanism by which the newly manufactured arginine is transported to the plant requires further investigation.
A single plant with its associated fungus is not an isolated entity. It has been shown that mycelia from the roots of one plant actually colonize the roots of nearby plants, creating an underground network of plants of the same or different species. This network is known as a common mycorrhizal network (CMN) . It has been demonstrated that nitrogen is transferred between plants via the hyphal network, sometimes in large amounts. For example, Cheng and Baumgartner found that about 25% of the labeled nitrogen supplied to a source plant, in this case a grass species, was transferred to the sink plant, grapevine. [ 10 ] It is widely believed that these hyphal networks are important to local ecosystems and may have agricultural implications.
Some plants, called legumes , can form simultaneous symbiotic relationships with both AM fungi and the nitrogen-fixing bacteria Rhizobia . In fact, both organisms trigger the same pathways in plants during early colonization, indicating that the two very different responses could share a common origin. While the bacteria can supply nitrogen, they cannot provide other benefits of AM fungi; AM actually enhances bacterial colonization, probably by supplying extra phosphorus for the formation of the bacterial habitat within the plant, and thus contributing indirectly to the plant's nitrogen status. [ 11 ] It is not known if there is signaling between the two, or only between the plant and each microbe. There is almost certainly competition between the bacterial and fungal partners, whether directly or indirectly, due to the fact that both are dependent on the plant as their sole source of energy. The plant must strive to strike a delicate balance between the maintenance of both partners based on its nutrient status.
A large body of research has shown that AM fungi can, and do, transfer nitrogen to plants and transfer nitrogen between plants, including crop plants. However, it has not been shown conclusively that there is a growth benefit from AM due to nitrogen. Some researchers doubt that AM contribute significantly to plant N status in nature. [ 12 ] In one field study, there was negligible transfer between soybeans and corn. [ 13 ] Furthermore, AM sometimes appears to be parasitic. This has primarily been seen under conditions of high nitrogen, which is not the usual state in a natural environment. However, it has been shown that in at least one case, colonization by AM fungi under nitrogen-limiting conditions lead to decreased shoot biomass, [ 14 ] implying that the relationship does the plant more harm than good. Likewise in a multi-plant system it would be very difficult to find the advantage to the source plants when their nutrients are being shunted to sink plants. These findings are at odds with the observed phenomenon that under conditions of low phosphorus, the degree of AM colonization is inversely proportional to nitrogen availability. [ 15 ] Since the plant must supply all of the energy needed to grow and sustain the fungus, it seems counter-intuitive that it would do so without some benefit to itself. Further studies are definitely needed to delineate the details of the relationship between the symbionts, including a gradient of interaction that runs from mutualism to parasitism. | https://en.wikipedia.org/wiki/Nitrogen_nutrition_in_the_arbuscular_mycorrhizal_system |
Nitrogen oxide may refer to a binary compound of oxygen and nitrogen , or a mixture of such compounds:
In atmospheric chemistry :
Due to relatively weak N–O bonding, all nitrogen oxides are unstable with respect to N 2 and O 2 , which is the principle behind the catalytic converter , and prevents the oxygen and nitrogen in the atmosphere from combusting . | https://en.wikipedia.org/wiki/Nitrogen_oxide |
Nitrogen pentafluoride is a theoretical compound of nitrogen and fluorine with the chemical formula N F 5 . It is hypothesized to exist based on the existence of the pentafluorides of the atoms below nitrogen in the periodic table, such as phosphorus pentafluoride . Theoretical models of the nitrogen pentafluoride molecule are either a trigonal bipyramidal covalently bound molecule with symmetry group D 3h , or [NF 4 ] + F − (tetrafluoroammonium fluoride), which would be an ionic solid.
A variety of other tetrafluoroammonium salts are known ( [NF 4 ] + X − ), as are fluoride salts of other ammonium cations ( [NR 4 ] + F − ).
In 1966, W. E. Tolberg first synthesized a five-valent nitrogen compound of nitrogen and fluorine when tetrafluoroammonium compounds, tetrafluoroammonium hexafluoroantimonate(V) [NF 4 ] + [SbF 6 ] − and tetrafluoroammonium hexafluoroarsenate(V) [NF 4 ] + [AsF 6 ] − were made. [ 2 ] In 1971 C. T. Goetschel announced the preparation of [NF 4 ] + [BF 4 ] − and also produced a white solid assumed to be tetrafluoroammonium fluoride ( [NF 4 ] + F − ). This was made by treating nitrogen trifluoride and fluorine with 3 MeV electron radiation at 77 K. It decomposed above 143 K back into those ingredients. [ 2 ] Theoretical studies also show the ionic compound is very likely to decompose to nitrogen trifluoride and fluorine gas. [ 3 ]
Karl O. Christe synthesised bis(tetrafluoroammonium) hexafluoronickelate(IV) ([NF 4 ] + ) 2 [NiF 6 ] 2− . [ 4 ] He also prepared compounds with manganese, a fluorouranate, tetrafluoroammonium perchlorate [NF 4 ] + ClO − 4 , tetrafluoroammonium fluorosulfate [NF 4 ] + SO 3 F − and [N 2 F 3 ] + (trifluorodiazenium) salts. [ 5 ] Christe attempted to make [NF 4 ] + F − by metathesis of [NF 4 ] + [SbF 6 ] − with CsF in HF solvent at 20 °C. However, a variant, tetrafluoroammonium bifluoride hydrofluorates ( [NF 4 ] + [HF 2 ] − · n HF ), was produced. At room temperature it was a milky liquid, but when cooled, turned pasty. At −45 °C it had the form of a white solid. When reheated it frothed, giving off F 2 , HF and NF 3 as gases . [ 5 ] This has CAS number 71485-49-9. [ 6 ]
I. J. Solomon believed that nitrogen pentafluoride was produced by the thermal decomposition of [NF 4 ] + [AsF 6 ] − , but experimental results were not reproduced. [ 7 ]
Dominik Kurzydłowski and Patryk Zaleski-Ejgierd predict that a mixture of fluorine and nitrogen trifluoride under pressure between 10 and 33 GPa forms [NF 4 ] + F − with space group R3m . This is a high-pressure oxidation. Over 33 GPa it will form a stable ionic compound with formula ([NF 4 ] + ) 2 [NF 6 ] − F − (bis(tetrafluoroammonium) hexafluoronitrate(V) fluoride) with space group I4/m . Over 151 GPa this is predicted to transform to [NF 4 ] + [NF 6 ] − (tetrafluoroammonium hexafluoronitrate(V)) with space group P4/n . [ 8 ] A NF 5 molecular compound is not stable under any pressure conditions.
For a NF 5 molecule to form, five fluorine atoms have to be arranged around a nitrogen atom. There is insufficient space to do this at typical nitrogen–fluorine covalent-bond lengths, so at least some bonds are forced to be longer. Calculations show that fragmentation to form NF 4 and F radicals would have a transition state barrier of around 66–84 kJ/mol (15.8–20.0 kcal/mol) and that this process is thermodynamically favourable ( exothermic ) by 38 kJ/mol (9 kcal/mol). [ 9 ] Nitrogen pentafluoride also violates the octet rule in which compounds with eight outer shell electrons are particularly stable. [ 10 ] | https://en.wikipedia.org/wiki/Nitrogen_pentafluoride |
Nitrogen pentahydride , also known as ammonium hydride is a hypothetical compound with the chemical formula NH 5 . There are two theoretical structures of nitrogen pentahydride. One structure is trigonal bipyramidal molecular geometry type NH 5 molecule. Its nitrogen atom and hydrogen atoms are covalently bounded, and its symmetry group is D 3h . [ 1 ] Another predicted structure of nitrogen pentahydride is an ionic compound , composed of an ammonium ion and a hydride ion (NH 4 + H − ). Until now, no one has synthesized this substance, or proved its existence, and related experiments have not directly observed nitrogen pentahydride. It is only speculated that it may be a reactive intermediate based on reaction products. Theoretical calculations show this molecule is thermodynamically unstable. [ 4 ] The reason might be similar to the instability of nitrogen pentafluoride , [ 5 ] so the possibility of its existence is low. However, nitrogen pentahydride might exist in special conditions or high pressure. Nitrogen pentahydride was considered for use as a solid rocket fuel for research in 1966. [ 6 ]
Some studies believe that nitrogen pentahydride may exist in the formation of other metal atoms crystal lattice , such as mercury [ 7 ] [ 8 ] and lithium . There are also related studies to explore the possibility of a substitution reaction with ammonium halide. [ 9 ] There are also attempts to react ammonium and deuterium to produce the pentahydride, however some experiments show that it may only be a reactive intermediate, which will immediately decompose into ammonia and hydrogen, [ 10 ] [ 1 ] and the same is true for experiments using deuterium. [ 2 ] [ 1 ] However, all the studies above are only theoretical calculations, the existence of nitrogen pentahydride has not been observed, and this substance has not been shown to exist.
An experimental attempted to do a displacement reaction between ammonium trifluoroacetate and lithium hydride in the molten state, in order to study the possibility of the existence of nitrogen pentahydride: [ 10 ]
In the reaction between ammonium trifluoroacetate and lithium deuteride, the product ammonia contains 85% of ordinary ammonia and 15% of monodeuterated ammonia. The product hydrogen contains 66% of hydrogen deuteride , 21% of hydrogen gas and 13% of deuterium gas. In the product collected using tetradeuterated ammonium trifluoroacetate and lithium hydride, ammonia contains ND 3 , NHD 2 and NH 2 D, while hydrogen contains 68% of hydrogen deuteride, 18% of hydrogen gas and 14% of deuterium gas. Therefore, it is speculated that the reaction may have two routes: one is to directly decompose into ammonia and hydrogen, the other is to first generate ammonium deuteride reactive intermediates, partly by forming deuterium anions and hydrogen cations to form deuterated hydrogen and ammonia and by the formation of hydride ions or deuterium cations to decompose into hydrogen or deuterium gas. [ 1 ]
But it immediately decomposed into hydrogen and ammonia, and it was impossible to prove its existence. Experiments with deuterium still get the same results: [ 2 ]
Several papers have conducted theoretical calculations on nitrogen pentahydride, and believe that nitrogen pentahydride is unlikely to form ionic crystals of hydride and ammonium ions. However, it is possible that hydrogen is connected to one of the hydrogen atoms of ammonium. [ 1 ] It may also be similar to nitrogen pentafluoride , forming a three-center two-electron bond similar to carbonium ions , or those five hydrogen atoms are arranged in a triangular bipyramid structure around the nitrogen atom. [ 1 ]
A compound that is similar to nitrogen pentahydride is the theoretical nitrogen pentafluoride . Its structure is assumed to be tetrafluoroammonium fluoride (NF 4 + F − ). [ 11 ] Similarly to nitrogen pentahydride, it is a compound of nitrogen and five of the same atom, but nitrogen pentafluoride is also a hypothetical compound, still never synthesized and only theoretical research exist. [ 12 ] Other pnictogen pentahydrides are theoretically more stable, such as phosphorus pentahydride (PH 4 H) which is more stable than nitrogen pentahydride but still unstable to decomposition to phosphine and hydrogen gas. Its organic derivatives ( phosphoranes ) are more stable, such as stable pentaphenylphosphorus (Ph 5 P). [ 13 ] Other heavier pnictogen pentahydrides are more likely to exist, such as the theoretical arsenic pentahydride . [ 14 ] [ better source needed ] | https://en.wikipedia.org/wiki/Nitrogen_pentahydride |
A nitrogen rejection unit (NRU) selectively removes nitrogen from a gas. The name can be applied to any system that removes nitrogen from natural gas .
For high flow-rate applications, typically above 420 thousand cubic metres (15 million cubic feet ) per day at standard pressure , cryogenic processing is the norm. [ 1 ] This is a distillation process which utilizes the different volatilities of methane ( boiling point of −161.6 °C) and nitrogen (boiling point of −195.69 °C) to achieve separation. In this process, a system of compression and distillation columns drastically reduces the temperature of the gas mixture to a point where methane is liquified and the nitrogen is not. For smaller applications, a series of heat exchangers may be used as an alternative to distillation columns.
For smaller volumes of gas, a system utilizing pressure swing adsorption (PSA) is a more typical method of separation. In PSA, methane and nitrogen can be separated by using an adsorbent with an aperture size very close to the molecular diameter of the larger species, in this case methane (3.8 angstroms ). This means nitrogen is able to diffuse through the adsorbent, filling adsorption sites, whilst methane is not. This results in a purified natural gas stream that fits pipeline specifications. The adsorbent can then be regenerated, leaving a highly pure nitrogen stream. PSA is a flexible method for nitrogen rejection, being applied to both small and large flow rates.
The operating conditions of various PSA units are quite variable. Depending on the vendor, high degrees of pretreatment of the gas stream (removal of water vapor and heavy hydrocarbons) may be necessary for the system to operate optimally and without damage to the adsorbent material. Moreover, the degree of hydrocarbon recoveries (75% vs 95%) and purities can vary considerably. The economic viability of any PSA unit will be highly dependent on such factors.
An estimated 25% of the US natural gas reserves contain unacceptably large quantities of nitrogen. Nitrogen is inert and lowers the energy value per volume of natural gas. It also takes up capacity in pipelines that could be used for valuable methane.
Pipeline specifications for nitrogen are extremely variable, though no more than 4% nitrogen is a typical specification. [ citation needed ] | https://en.wikipedia.org/wiki/Nitrogen_rejection_unit |
The nitrogen rule states that organic compounds containing exclusively hydrogen , carbon , nitrogen , oxygen , silicon , phosphorus , sulfur , and the halogens either have (1) an odd nominal mass that indicates an odd number of nitrogen atoms are present or (2) an even nominal mass that indicates an even number of nitrogen atoms in the molecular formula of the neutral compound. [ 1 ] [ 2 ] The nitrogen rule is not a rule as much as a general principle which may prove useful when attempting to solve organic mass spectrometry structures.
This rule is derived from the fact that, perhaps coincidentally, for the most common chemical elements in neutral organic compounds (hydrogen, carbon, nitrogen, oxygen, silicon, phosphorus, sulfur, and the halogens), elements with even numbered nominal masses form even numbers of covalent bonds , while elements with odd numbered nominal masses form odd numbers of covalent bonds, with the exception of nitrogen, which has a nominal (or integer ) mass of 14, but has a valency of 3.
The nitrogen rule is only true for neutral structures in which all of the atoms in the molecule have a number of covalent bonds equal to their standard valency (counting each sigma bond and pi bond as a separate covalent bond for the purposes of the calculation). Therefore, the rule is typically only applied to the molecular ion signal in the mass spectrum .
Mass spectrometry generally operates by measuring the mass of ions . If the measured ion is generated by creating or breaking a single covalent bond (such as protonating an amine to form an ammonium center or removing a hydride from a molecule to leave a positively charged ion) then the nitrogen rule becomes reversed (odd numbered masses indicate even numbers of nitrogens and vice versa). However, for each consecutive covalent bond that is broken or formed, the nitrogen rule again reverses.
Therefore, a more rigorous definition of the nitrogen rule for organic compounds containing exclusively hydrogen, carbon, nitrogen, oxygen, silicon, phosphorus, sulfur, and the halogens would be as follows:
An even nominal mass indicates that a net even number of covalent bonds have been broken or formed and an even number of nitrogen atoms are present, or that a net odd number of covalent bonds have been broken or formed and an odd number of nitrogen atoms are present. An odd nominal mass indicates that a net even number of covalent bonds have been broken or formed and an odd number of nitrogen atoms are present, or that a net odd number of covalent bonds have been broken or formed and an even number of nitrogen atoms are present.
Inorganic molecules do not necessarily follow the rule. For example, the nitrogen oxides NO and NO 2 have an odd number of nitrogens but even masses of 30 and 46, respectively. | https://en.wikipedia.org/wiki/Nitrogen_rule |
The nitrogen solubility index (NSI) is a measure of the solubility of the protein in a substance. It is typically used as a quick measure of the functionality of a protein, for example to predict the ability of the protein to stabilise foams, emulsions or gels. [ 1 ] [ 2 ] To determine the NSI, the sample is dried, dispersed in a 0.1 M salt solution, centrifuged and filtered. The NSI is the amount of Nitrogen in this filtered solution divided by the nitrogen in the initial sample, as measured by the Kjeldahl method . [ 3 ]
The relevance of the NSI is based on the fact that proteins are the major biological source of Nitrogen: for various types of protein, there are empirical formulas which correlate the nitrogen content to the protein content. Other related measures of protein solubility are the Protein Solubility Index (PSI), the Protein Dispersibility index (PDI). These are based on a specific protein assay, rather than a nitrogen assay, [ 4 ] and the dispersibility index differs from the solubility index, in that the sample is dispersed with a high-shear mixer and then strained through a screen instead of being centrifuged and filtered. [ 5 ] | https://en.wikipedia.org/wiki/Nitrogen_solubility_index |
Nitrogen trichloride , also known as trichloramine , is the chemical compound with the formula NCl 3 . This yellow, oily, and explosive liquid is most commonly encountered as a product of chemical reactions between ammonia -derivatives and chlorine (for example, in swimming pools ). Alongside monochloramine and dichloramine , trichloramine is responsible for the distinctive 'chlorine smell' associated with swimming pools, where the compound is readily formed as a product from hypochlorous acid reacting with ammonia and other nitrogenous substances in the water, such as urea from urine . [ 1 ]
The compound is generated by treatment of ammonium chloride with calcium hypochlorite . When prepared in an aqueous-dichloromethane mixture, the trichloramine is extracted into the nonaqueous phase. [ 2 ] Intermediates in this conversion include monochloramine and dichloramine , NH 2 Cl and NHCl 2 , respectively.
Nitrogen trichloride, trademarked as Agene , was at one time used to bleach flour , [ 3 ] but this practice was banned in the United States in 1949 due to safety concerns.
Like ammonia, NCl 3 is a pyramidal molecule . The N-Cl distances are 1.76 Å, and the Cl-N-Cl angles are 107°. [ 4 ]
Nitrogen trichloride can form in small amounts when public water supplies are disinfected with monochloramine , and in swimming pools by disinfecting chlorine reacting with urea in urine and sweat from bathers.
The chemistry of NCl 3 has been well explored. [ 5 ] It is moderately polar with a dipole moment of 0.6 D. The nitrogen center is basic but much less so than ammonia. It is hydrolyzed by hot water to release ammonia and hypochlorous acid .
Concentrated samples of NCl 3 can explode to give N 2 and chlorine gas . [ citation needed ]
In the presence of aluminium trichloride , NCl 3 react with some branch hydrocarbon to produce, after a hydrolysis step, amines . [ 2 ]
Nitrogen trichloride can irritate mucous membranes — it is a lachrymatory agent , but has never been used as such. [ 6 ] [ 7 ] The compound (rarely encountered) is a dangerous explosive, being sensitive to light, heat, even moderate shock, and organic compounds. Pierre Louis Dulong first prepared it in 1812, and lost several fingers and an eye in two explosions. [ 8 ] In 1813, an NCl 3 explosion blinded Sir Humphry Davy temporarily, inducing him to hire Michael Faraday as a co-worker. They were both injured in another NCl 3 explosion shortly thereafter. [ 9 ] | https://en.wikipedia.org/wiki/Nitrogen_trichloride |
Nitrogen trifluoride is the inorganic compound with the formula ( NF 3 ). It is a colorless, non- flammable , toxic gas with a slightly musty odor. In contrast with ammonia, it is nonbasic. It finds increasing use within the manufacturing of flat-panel displays , photovoltaics , LEDs and other microelectronics . [ 6 ] NF 3 is a greenhouse gas , with a global warming potential (GWP) 17,200 times greater than that of CO 2 when compared over a 100-year period. [ 7 ] [ 8 ] [ 9 ]
Nitrogen trifluoride can be prepared from the elements in the presence of an electric discharge. [ 10 ] In 1903, Otto Ruff prepared nitrogen trifluoride by the electrolysis of a molten mixture of ammonium fluoride and hydrogen fluoride . [ 11 ] It is far less reactive than the other nitrogen trihalides nitrogen trichloride , nitrogen tribromide , and nitrogen triiodide , all of which are explosive. Alone among the nitrogen trihalides it has a negative enthalpy of formation . It is prepared in modern times both by direct reaction of ammonia and fluorine and by a variation of Ruff's method. [ 6 ] It is supplied in pressurized cylinders.
NF 3 is slightly soluble in water without undergoing chemical reaction. It is nonbasic with a low dipole moment of 0.2340 D. By contrast, ammonia is basic and highly polar (1.47 D). [ 12 ] This contrast reflects the differing electronegativities of H vs F.
Similar to dioxygen , NF 3 is a potent yet sluggish oxidizer. [ 6 ] It oxidizes hydrogen chloride to chlorine: [ citation needed ]
However, it only attacks (explosively) organic compounds at high temperatures. Consequently it is compatible under standard conditions with several plastics, as well as steel and Monel . [ 6 ]
Above 200-300 °C, NF 3 reacts with metals, carbon, and other reagents to give tetrafluorohydrazine : [ 13 ]
NF 3 reacts with fluorine and antimony pentafluoride to give the tetrafluoroammonium salt: [ 6 ]
NF 3 and B 2 H 6 react vigorously even at cryogenic temperatures to give nitrogen gas , boron trifluoride , and hydrofluoric acid . [ 14 ]
High-volume applications such as DRAM computer memory production, the manufacturing of flat panel displays and the large-scale production of thin-film solar cells use NF 3 . [ 15 ] [ 16 ]
Nitrogen trifluoride is primarily used to remove silicon and silicon-compounds during the manufacturing of semiconductor devices such as LCD displays , some thin-film solar cells , and other microelectronics. In these applications NF 3 is initially broken down within a plasma . The resulting fluorine radicals are the active agents that attack polysilicon , silicon nitride and silicon oxide . They can be used as well to remove tungsten silicide , tungsten , and certain other metals. In addition to serving as an etchant in device fabrication, NF 3 is also widely used to clean PECVD chambers.
NF 3 dissociates more readily within a low-pressure discharge in comparison to perfluorinated compounds (PFCs) and sulfur hexafluoride ( SF 6 ). The greater abundance of negatively-charged free radicals thus generated can yield higher silicon removal rates, and provide other process benefits such as less residual contamination and a lower net charge stress on the device being fabricated. As a somewhat more thoroughly consumed etching and cleaning agent, NF 3 has also been promoted as an environmentally preferable substitute for SF 6 or PFCs such as hexafluoroethane . [ 17 ]
The utilization efficiency of the chemicals applied in plasma processes varies widely between equipment and applications. A sizeable fraction of the reactants are wasted into the exhaust stream and can ultimately be emitted into Earth's atmosphere. Modern abatement systems can substantially decrease atmospheric emissions. [ 18 ] NF 3 has not been subject to significant use restrictions. The annual reporting of NF 3 production, consumption, and waste emissions by large manufacturers has been required in many industrialized countries as a response to the observed atmospheric growth and the international Kyoto Protocol . [ 19 ]
Highly toxic fluorine gas (F 2 , diatomic fluorine ) is a climate neutral replacement for nitrogen trifluoride in some manufacturing applications. It requires more stringent handling and safety precautions, especially to protect manufacturing personnel. [ 20 ]
Nitrogen trifluoride is also used in hydrogen fluoride and deuterium fluoride lasers , which are types of chemical lasers . There it is also preferred to fluorine gas due to its more convenient handling properties
The GWP of NF 3 is second only to SF 6 in the group of Kyoto-recognised greenhouse gases, and NF 3 was included in that grouping with effect from 2013 and the commencement of the second commitment period of the Kyoto Protocol. It has an estimated atmospheric lifetime of 740 years, [ 7 ] although other work suggests a slightly shorter lifetime of 550 years (and a corresponding GWP of 16,800). [ 15 ]
Since 1992, when less than 100 tons were produced, production grew to an estimated 4000 tons in 2007 and is projected to increase significantly. [ 15 ] World production of NF 3 is expected to reach 8000 tons a year by 2010. By far the world's largest producer of NF 3 is the US industrial gas and chemical company Air Products & Chemicals . An estimated 2% of produced NF 3 is released into the atmosphere. [ 23 ] [ 24 ] Robson projected that the maximum atmospheric concentration is less than 0.16 parts per trillion (ppt) by volume, which will provide less than 0.001 Wm −2 of IR forcing. [ 25 ] The mean global tropospheric concentration of NF 3 has risen from about 0.02 ppt (parts per trillion, dry air mole fraction) in 1980, to 0.86 ppt in 2011, with a rate of increase of 0.095 ppt yr −1 , or about 11% per year, and an interhemispheric gradient that is consistent with emissions occurring overwhelmingly in the Northern Hemisphere, as expected. This rise rate in 2011 corresponds to about 1200 metric tons/y NF 3 emissions globally, or about 10% of the NF 3 global production estimates. This is a significantly higher percentage than has been estimated by industry, and thus strengthens the case for inventorying NF 3 production and for regulating its emissions. [ 26 ] One study co-authored by industry representatives suggests that the contribution of the NF 3 emissions to the overall greenhouse gas budget of thin-film Si-solar cell manufacturing is clear. [ 27 ]
The UNFCCC , within the context of the Kyoto Protocol, decided to include nitrogen trifluoride in the second Kyoto Protocol compliance period, which begins in 2012 and ends in either 2017 or 2020. Following suit, the WBCSD/WRI GHG Protocol is amending all of its standards (corporate, product and Scope 3) to also cover NF 3 . [ 28 ]
Skin contact with NF 3 is not hazardous, and it is a relatively minor irritant to mucous membranes and eyes. It is a pulmonary irritant with a toxicity considerably lower than nitrogen oxides , and overexposure via inhalation causes the conversion of hemoglobin in blood to methemoglobin , which can lead to the condition methemoglobinemia . [ 29 ] The National Institute for Occupational Safety and Health (NIOSH) specifies that the concentration that is immediately dangerous to life or health (IDLH value) is 1,000 ppm. [ 30 ] | https://en.wikipedia.org/wiki/Nitrogen_trifluoride |
Nitrogen triiodide is an inorganic compound with the formula N I 3 . It is an extremely sensitive contact explosive : small quantities explode with a loud, sharp snap when touched even lightly, releasing a purple cloud of iodine vapor; it can even be detonated by alpha radiation . NI 3 has a complex structural chemistry that is difficult to study because of the instability of the derivatives.
Nitrogen triiodide was first characterized by Raman spectroscopy in 1990, when it was prepared by an ammonia-free route. Boron nitride reacts with iodine monofluoride in trichlorofluoromethane at −30 °C to produce pure NI 3 in low yield: [ 3 ]
NI 3 is pyramidal (C 3v molecular symmetry ), as are the other nitrogen trihalides and ammonia . [ 4 ]
The material that is usually called "nitrogen triiodide" is prepared by the reaction of iodine with ammonia . When this reaction is conducted at low temperatures in anhydrous ammonia, the initial product is NI 3 · (NH 3 ) 5 , but this material loses some ammonia upon warming to give the 1:1 adduct NI 3 · NH 3 . This adduct was first reported by Bernard Courtois in 1812, and its formula was finally determined in 1905 by Oswald Silberrad . [ 5 ] Its solid state structure consists of chains of -NI 2 -I-NI 2 -I-NI 2 -I-. [ 6 ] Ammonia molecules are situated between the chains. When kept cold in the dark and damp with ammonia, NI 3 · NH 3 is stable.
The instability of NI 3 and NI 3 · NH 3 can be attributed to the large steric strain caused by the three large iodine atoms being held in proximity to each other around the relatively tiny nitrogen atom. This results in a very low activation energy for its decomposition, a reaction made even more favorable due to the great stability of N 2 . Nitrogen triiodide has no practical commercial value due to its extreme shock sensitivity, making it impossible to store, transport, and utilize for controlled explosions. Whereas pure nitroglycerin is powerful and also greatly shock-sensitive (although not nearly as much so as nitrogen triiodide, which can be set off with the touch of a feather), it was only due to phlegmatizers that nitroglycerin's shock sensitivity was reduced and it became safer to handle and transport in the form of dynamite .
The decomposition of NI 3 proceeds as follows to give nitrogen gas and iodine:
However, the dry material is a contact explosive, decomposing approximately as follows: [ 4 ]
Consistent with this equation, these explosions leave orange-to-purple stains of iodine, which can be removed with sodium thiosulfate solution. An alternate method of stain removal is to simply allow the iodine time to sublime.
Small amounts of nitrogen triiodide are sometimes synthesized as a demonstration to high school chemistry students or as an act of "chemical magic." [ 7 ] To highlight the sensitivity of the compound, it is usually detonated by touching it with a feather, but even the slightest air current, laser light, or other movement can cause detonation . Nitrogen triiodide is also notable for being the only known chemical explosive that detonates when exposed to alpha particles and nuclear fission products. [ 8 ] | https://en.wikipedia.org/wiki/Nitrogen_triiodide |
The nitrogen–phosphorus detector ( NPD ) is also known as thermionic specific detector ( TSD ) is a detector commonly used with gas chromatography , in which thermal energy is used to ionize an analyte . [ 1 ] [ 2 ] It is a type of flame thermionic detector (FTD), the other being the alkali flame-ionization detector (AFID also known as AFD).
With this method , nitrogen and phosphorus can be selectively detected with a sensitivity that is 10 4 times greater than that for carbon . [ citation needed ]
A concentration of hydrogen gas is used such that it is just below the minimum required for ignition. A rubidium or cesium bead, which is mounted over the nozzle , ignites the hydrogen (by acting catalytically), and forms a cold plasma . Excitation of the alkali metal results in ejection of electrons, which in turn are detected as a current flow between an anode and cathode in the chamber. As nitrogen or phosphorus analytes exit the column, they cause a reduction in the work function of the metal bead, resulting in an increase in current. Since the alkali metal bead is consumed over time, it must be replaced regularly .
This article related to chromatography is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitrogen–phosphorus_detector |
Nitroglycerin ( NG ) (alternative spelling nitroglycerine), also known as trinitroglycerol ( TNG ), nitro , glyceryl trinitrate ( GTN ), or 1,2,3-trinitroxypropane , is a dense, colorless or pale yellow, oily, explosive liquid most commonly produced by nitrating glycerol with white fuming nitric acid under conditions appropriate to the formation of the nitric acid ester . Chemically, the substance is a nitrate ester rather than a nitro compound , but the traditional name is retained. Discovered in 1846 by Ascanio Sobrero , [ 4 ] nitroglycerin has been used as an active ingredient in the manufacture of explosives, namely dynamite , and as such it is employed in the construction , demolition , and mining industries. It is combined with nitrocellulose to form double-based smokeless powder , used as a propellant in artillery and firearms since the 1880s.
As is the case for many other explosives, nitroglycerin becomes more and more prone to exploding (i.e. spontaneous decomposition ) as the temperature is increased. Upon exposure to heat above 218 °C at sea-level atmospheric pressure , nitroglycerin becomes extremely unstable and tends to explode. When placed in vacuum, it has an autoignition temperature of 270 °C instead. [ 5 ] With a melting point of 12.8 °C, the chemical is almost always encountered as a thick and viscous fluid, changing to a crystalline solid when frozen. [ 5 ] [ 6 ] Although the pure compound itself is colorless, in practice the presence of nitric oxide impurities left over during production tends to give it a slight yellowish tint.
Due to its high boiling point and consequently low vapor pressure (0.00026 mmHg at 20 °C), [ 5 ] pure nitroglycerin has practically no odor at room temperature, with a sweet and burning taste when ingested. Unintentional detonation may ensue when dropped, shaken, lit on fire, rapidly heated, exposed to sunlight and ozone, subjected to sparks and electrical discharges, or roughly handled. [ 7 ] Its sensitivity to exploding is responsible for numerous devastating industrial accidents throughout its history. The chemical's characteristic reactivity may be reduced through the addition of desensitizing agents, which makes it less likely to explode. Clay ( diatomaceous earth ) is an example of such an agent, forming dynamite, a much more easily handled composition. Addition of other desensitizing agents give birth to the various formulations of dynamite.
Nitroglycerin has been used for over 130 years in medicine as a potent vasodilator (causing dilation of the vascular system) to treat heart conditions, such as angina pectoris and chronic heart failure . Though it was previously known that these beneficial effects are due to nitroglycerin being converted to nitric oxide , a potent venodilator, the enzyme for this conversion was only discovered to be mitochondrial aldehyde dehydrogenase ( ALDH2 ) in 2002. [ 8 ] Nitroglycerin is available in sublingual tablets , sprays, ointments, and patches. [ 9 ]
Nitroglycerin was the first practical explosive produced that was stronger than black powder . It was synthesized by the Italian chemist Ascanio Sobrero in 1846, working under Théophile-Jules Pelouze at the University of Turin . [ 10 ] Sobrero initially called his discovery "pyroglycerin" and warned vigorously against its use as an explosive. [ 11 ]
Nitroglycerin was adopted as a commercially useful explosive by Alfred Nobel , who experimented with safer ways to handle the dangerous compound after his younger brother, Emil Oskar Nobel , and several factory workers were killed in an explosion at the Nobels' armaments factory in 1864 in Heleneborg , Sweden. [ 12 ]
One year later, Nobel founded Alfred Nobel and Company in Germany and built an isolated factory in the Krümmel hills of Geesthacht near Hamburg . This business exported a liquid combination of nitroglycerin and gunpowder called "Blasting Oil", but this was extremely unstable and difficult to handle, as evidenced in numerous catastrophes. [ 13 ] The buildings of the Krümmel factory were destroyed twice. [ 14 ]
In April 1866, several crates of nitroglycerin were shipped to California , three of which were destined for the Central Pacific Railroad , which planned to experiment with it as a blasting explosive to expedite the construction of the 1,659-foot-long (506 m) Summit Tunnel through the Sierra Nevada Mountains . One of the remaining crates exploded, destroying a Wells Fargo company office in San Francisco and killing 15 people. This led to a complete ban on the transportation of liquid nitroglycerin in California. The on-site manufacture of nitroglycerin was thus required for the remaining hard-rock drilling and blasting required for the completion of the First transcontinental railroad in North America. [ 15 ]
On Christmas Day 1867, an attempt to dispose of nine canisters of Blasting Oil that had been illegally stored at the White Swan Inn in the centre of Newcastle upon Tyne resulted in an explosion on the Town Moor that killed eight people. In June 1869, two one-ton wagons loaded with nitroglycerin, then known locally as Powder-Oil, exploded in the road at the North Wales village of Cwm-y-glo . The explosion led to the loss of six lives, many injuries and much damage to the village. Little trace was found of the two horses. The UK Government was so alarmed at the damage caused and what could have happened in a city location (these two tons were part of a larger load coming from Germany via Liverpool) that they soon passed the Nitro-Glycerine Act of 1869. [ 16 ] Liquid nitroglycerin was widely banned elsewhere, as well, and these legal restrictions led to Alfred Nobel and his company's developing dynamite in 1867. This was made by mixing nitroglycerin with diatomaceous earth (" Kieselguhr " in German) found in the Krümmel hills. Similar mixtures, such as "dualine" (1867), "lithofracteur" (1869), and " gelignite " (1875), were formed by mixing nitroglycerin with other inert absorbents, and many combinations were tried by other companies in attempts to get around Nobel's tightly held patents for dynamite.
Dynamite mixtures containing nitrocellulose , which increases the viscosity of the mix, are commonly known as "gelatins".
Following the discovery that amyl nitrite helped alleviate chest pain, the physician William Murrell experimented with the use of nitroglycerin to alleviate angina pectoris and to reduce the blood pressure . He began treating his patients with small diluted doses of nitroglycerin in 1878, and this treatment was soon adopted into widespread use after Murrell published his results in The Lancet in 1879. [ 17 ] [ 18 ] A few months before his death in 1896, Alfred Nobel was prescribed nitroglycerin for this heart condition, writing to a friend: "Isn't it the irony of fate that I have been prescribed nitro-glycerin, to be taken internally! They call it Trinitrin, so as not to scare the chemist and the public." [ 19 ] The medical establishment also used the name "glyceryl trinitrate" for the same reason.
Large quantities of nitroglycerin were manufactured during World War I and World War II for use as military propellants and in military engineering work. During World War I, HM Factory, Gretna , the largest propellant factory in the United Kingdom , produced about 800 tonnes of cordite RDB per week. This amount required at least 336 tonnes of nitroglycerin per week (assuming no losses in production). The Royal Navy had its own factory at the Royal Navy Cordite Factory, Holton Heath , in Dorset , England. A large cordite factory was also built in Canada during World War I. The Canadian Explosives Limited cordite factory at Nobel, Ontario , was designed to produce 1,500,000 lb (680 t) of cordite per month, requiring about 286 tonnes of nitroglycerin per month.
In its undiluted form, nitroglycerin is a contact explosive , meaning physical shock causes it to explode. If it has not been adequately purified during manufacture it can degrade over time to even more unstable forms. This makes nitroglycerin highly dangerous to transport or use. In its undiluted form, it is one of the world's most powerful explosives, comparable to the more recently developed RDX and PETN .
Early in its history, liquid nitroglycerin was found to be " desensitized " by freezing it at a temperature below 45 to 55 °F (7 to 13 °C) depending on its purity. [ 20 ] Its sensitivity to shock while frozen is somewhat unpredictable: "It is more insensitive to the shock from a fulminate cap or a rifle ball when in that condition but on the other hand it appears to be more liable to explode on breaking, crushing, tamping, etc." [ 21 ] Frozen nitroglycerin is much less energetic than liquid, and so must be thawed before use. [ 22 ] Thawing it out can be extremely sensitizing, especially if impurities are present or the warming is too rapid. [ 23 ] Ethylene glycol dinitrate or another polynitrate may be added to lower the melting point and thereby avoid the necessity of thawing frozen explosive. [ 24 ]
Chemically "desensitizing" nitroglycerin is possible to a point where it can be considered about as "safe" as modern high explosives , such as by the addition of ethanol , acetone , or dinitrotoluene . [ 25 ] The nitroglycerin may have to be extracted from the desensitizer chemical to restore its effectiveness before use, for example by adding water to draw off ethanol used as a desensitizer. [ 25 ]
When nitroglycerin explodes, the products after cooling are given by:
The heat released can be calculated from the heats of formation. Using −371 kJ/ mol for the heat of formation of condensed phase nitroglycerin [ 26 ] gives 1414 kJ/mol released if forming water vapor, and 1524 if forming liquid water.
The detonation velocity of nitroglycerin is 7820 meters per second, which is about 113% the speed of TNT . Accordingly, nitroglycerin is considered to be a high- brisance explosive, which is to say, it has excellent shattering ability. The heat liberated during detonation raises the temperature of the gaseous byproducts to about 5,000 °C (9,000 °F). [ 24 ] With a standard enthalpy of explosive decomposition of −1414 kJ/ mol and a molecular weight of 227.0865 g/mol, nitroglycerin has a specific explosive energy density of 1.488 kilocalories per gram, or 6.23 kJ/g, making nitroglycerin 49% more energetic on a mass basis than the standard definitional value assigned to TNT (precisely 1 kcal/g).
Nitroglycerin can be produced by acid-catalyzed nitration of glycerol (glycerin). [ 30 ]
The industrial manufacturing process often reacts glycerol with a nearly 1:1 mixture of concentrated sulfuric acid and concentrated nitric acid . This can be produced by mixing white fuming nitric acid —a quite expensive pure nitric acid in which the oxides of nitrogen have been removed, as opposed to red fuming nitric acid , which contains nitrogen oxides —and concentrated sulfuric acid . More often, this mixture is attained by the cheaper method of mixing fuming sulfuric acid , also known as oleum — sulfuric acid containing excess sulfur trioxide —and azeotropic nitric acid (consisting of about 70% nitric acid , with the rest being water). [ 31 ]
The sulfuric acid produces protonated nitric acid species, which are attacked by glycerol 's nucleophilic oxygen atoms. The nitro group is thus added as an ester C−O−NO 2 and water is produced. This is different from an electrophilic aromatic substitution reaction in which nitronium ions are the electrophile .
The addition of glycerol results in an exothermic reaction (i.e., heat is produced), as usual for mixed-acid nitrations. If the mixture becomes too hot, it results in a runaway reaction, a state of accelerated nitration accompanied by the destructive oxidation of organic materials by the hot nitric acid and the release of poisonous nitrogen dioxide gas at high risk of an explosion. Thus, the glycerin mixture is added slowly to the reaction vessel containing the mixed acid (not acid to glycerin). The nitrator is cooled with cold water or some other coolant mixture and maintained throughout the glycerin addition at about 22 °C (72 °F), hot enough for esterification to occur at a fast rate but cold enough to avoid runaway reaction. The nitrator vessel, often constructed of iron or lead and generally stirred with compressed air , has an emergency trap door at its base, which hangs over a large pool of very cold water and into which the whole reaction mixture (called the charge) can be dumped to prevent an explosion, a process referred to as drowning. If the temperature of the charge exceeds about 30 °C (86 °F) (actual value varying by country) or brown fumes are seen in the nitrator's vent, then it is immediately drowned.
Nitroglycerin is an oily liquid that explodes when subjected to heat, shock, or flame. The main use of nitroglycerin, by tonnage , is in explosives such as dynamite and in propellants as an ingredient. However, its sensitivity has limited the usefulness of nitroglycerin as a military explosive; less sensitive explosives such as TNT , RDX , and HMX have largely replaced it in munitions.
Alfred Nobel developed the use of nitroglycerin as a blasting explosive by mixing nitroglycerin with inert absorbents , particularly " Kieselgur ", or diatomaceous earth . He named this explosive dynamite and patented it in 1867. [ 32 ] It was supplied ready for use in the form of sticks, individually wrapped in greased waterproof paper. Dynamite and similar explosives were widely adopted for civil engineering tasks, such as in drilling highway and railroad tunnels , for mining , for clearing farmland of stumps, in quarrying , and in demolition work . Likewise, military engineers have used dynamite for construction and demolition work.
Nitroglycerin has been used in conjunction with hydraulic fracturing , a process used to recover oil and gas from shale formations. The technique involves displacing and detonating nitroglycerin in natural or hydraulically induced fracture systems, or displacing and detonating nitroglycerin in hydraulically induced fractures followed by wellbore shots using pelletized TNT . [ 33 ]
Nitroglycerin has an advantage over some other high explosives that on detonation it produces practically no visible smoke. Therefore, it is useful as an ingredient in the formulation of various kinds of smokeless powder . [ 34 ]
Alfred Nobel then developed ballistite , by combining nitroglycerin and guncotton . He patented it in 1887. Ballistite was adopted by a number of European governments, as a military propellant. Italy was the first to adopt it. The British government and the Commonwealth governments adopted cordite instead, which had been developed by Sir Frederick Abel and Sir James Dewar of the United Kingdom in 1889. The original Cordite Mk I consisted of 58% nitroglycerin, 37% guncotton, and 5.0% petroleum jelly . Ballistite and cordite were both manufactured in the form of "cords".
Smokeless powders were originally developed using nitrocellulose as the sole explosive ingredient. Therefore, they were known as single-base propellants. A range of smokeless powders that contains both nitrocellulose and nitroglycerin, known as double-base propellants, were also developed. Smokeless powders were originally supplied only for military use, but they were also soon developed for civilian use and were quickly adopted for sports. Some are known as sporting powders. Triple-base propellants contain nitrocellulose, nitroglycerin, and nitroguanidine , but are reserved mainly for extremely high-caliber ammunition rounds such as those used in tank cannons and naval artillery . Blasting gelatin, also known as gelignite , was invented by Nobel in 1875, using nitroglycerin, wood pulp , and sodium or potassium nitrate . This was an early, low-cost, flexible explosive.
Nitroglycerin belongs to a group of drugs called nitrates, which includes many other nitrates like isosorbide dinitrate (Isordil) and isosorbide mononitrate (Imdur, Ismo, Monoket). [ 35 ] These agents all exert their effect by being converted to nitric oxide in the body by mitochondrial aldehyde dehydrogenase ( ALDH2 ), [ 8 ] and nitric oxide is a potent natural vasodilator.
In medicine , nitroglycerin is probably most commonly prescribed for angina pectoris , a painful symptom of ischemic heart disease caused by inadequate flow of blood and oxygen to the heart and as a potent antihypertensive agent. Nitroglycerin corrects the imbalance between the flow of oxygen and blood to the heart and the heart's energy demand. [ 35 ] There are many formulations on the market at different doses. At low doses, nitroglycerin dilates veins more than arteries, thereby reducing preload (volume of blood in the heart after filling); this is thought to be its primary mechanism of action. By decreasing preload, the heart has less blood to pump, which decreases oxygen requirement since the heart does not have to work as hard. Additionally, having a smaller preload reduces the ventricular transmural pressure (pressure exerted on the walls of the heart), which decreases the compression of heart arteries to allow more blood to flow through the heart. At higher doses, it also dilates arteries, thereby reducing afterload (decreasing the pressure against which the heart must pump). [ 35 ] An improved ratio of myocardial oxygen demand to supply leads to the following therapeutic effects during episodes of angina pectoris: subsiding of chest pain, decrease of blood pressure , increase of heart rate, and orthostatic hypotension . Patients experiencing angina when doing certain physical activities can often prevent symptoms by taking nitroglycerin 5 to 10 minutes before the activity. Overdoses may generate methemoglobinemia . [ 36 ] [ 37 ]
Nitroglycerin is available in tablets, ointment, solution for intravenous use, transdermal patches , or sprays administered sublingually . Some forms of nitroglycerin last much longer in the body than others. Nitroglycerin as well as the onset and duration of action of each form is different. The sublingual or tablet spray of nitroglycerin has a two minute onset and twenty five minute duration of action. The oral formulation of nitroglycerin has a thirty five minute onset and a duration of action of 4–8 hours. The transdermal patch has an onset of thirty minutes and a duration of action of ten to twelve hours. Continuous exposure to nitrates has been shown to cause the body to stop responding normally to this medicine. Experts recommend that the patches be removed at night, allowing the body a few hours to restore its responsiveness to nitrates. Shorter-acting preparations of nitroglycerin can be used several times a day with less risk of developing tolerance. [ 38 ] Nitroglycerin was first used by William Murrell to treat angina attacks in 1878, with the discovery published that same year. [ 18 ] [ 39 ]
Infrequent exposure to high doses of nitroglycerin can cause severe headaches known as "NG head" or "bang head". These headaches can be severe enough to incapacitate some people; however, humans develop a tolerance to and dependence on nitroglycerin after long-term exposure. Although rare, withdrawal can be fatal; [ 40 ] symptoms include chest pain and other heart problems. These symptoms may be relieved with re-exposure to nitroglycerin or other suitable organic nitrates. [ 41 ]
For workers in nitroglycerin (NTG) manufacturing facilities, the effects of withdrawal sometimes include "Sunday heart attacks" in those experiencing regular nitroglycerin exposure in the workplace, leading to the development of tolerance for the venodilating effects. Over the weekend, the workers lose the tolerance, and when they are re-exposed on Monday, the drastic vasodilation produces a fast heart rate , dizziness, and a headache. This is referred to as "Monday disease." [ 42 ] [ 43 ]
People can be exposed to nitroglycerin in the workplace by breathing it in, skin absorption, swallowing it, or eye contact. The Occupational Safety and Health Administration has set the legal limit ( permissible exposure limit ) for nitroglycerin exposure in the workplace as 0.2 ppm (2 mg/m 3 ) skin exposure over an 8-hour workday. The National Institute for Occupational Safety and Health has set a recommended exposure limit of 0.1 mg/m 3 skin exposure over an 8-hour workday. At levels of 75 mg/m 3 , nitroglycerin is immediately dangerous to life and health . [ 44 ] | https://en.wikipedia.org/wiki/Nitroglycerin |
Nitroguanidine - sometimes abbreviated NGu - is a colorless, crystalline solid that melts at 257 °C and decomposes at 254 °C. Nitroguanidine is an extremely insensitive but powerful high explosive. Wetting it with > 20 wt.-% water effects desensitization from HD 1.1 down to HD 4.1 (flammable solid). [ 2 ] Nitroguanidine is used as an energetic material, i.e., propellant or high explosive, precursor for insecticides, and for other purposes.
Nitroguanidine is produced worldwide on a large scale starting with the reaction of dicyandiamide (DCD) with ammonium nitrate to afford the salt guanidinium nitrate , which is then nitrated by treatment with concentrated sulfuric acid at low temperature. [ 3 ]
The guanidinium nitrate intermediate may also be produced via the Boatright–Mackay–Roberts (BMR) process, in which molten urea is reacted with molten ammonium nitrate in the presence of silica gel . [ 3 ] [ 4 ] This process had been commercialized because of its attractive economic features.
Nitroguanidine has been in use since the 1930s as an ingredient in triple-base gun propellants in which it reduces flame temperature, muzzle flash, and erosion of the gun barrel but preserves chamber pressure due to high nitrogen content. Its extreme insensitivity combined with low cost has made it a popular ingredient in insensitive high explosive formulations (e.g AFX-453, AFX-760, IMX-101 , AL-IMX-101, IMX-103, etc.). [ 5 ]
The first triple-base propellant, featuring 20-25% of nitroguanidine and 30-45% nitroglycerine, was developed at the Dynami Nobel factory at Avigliana and patented by its director Dr. Modesto Abelli (1859-1911) in 1905. [ 6 ] [ 7 ]
Nitroguanidine's explosive decomposition is given by the following equation:
H 4 N 4 CO 2 (s) → 2 H 2 O (g) + 2 N 2 (g) + C (s)
Nitroguanidine derivatives are used as insecticides , having a comparable effect to nicotine . Derivatives include clothianidin , dinotefuran , imidacloprid , and thiamethoxam .
The nitrosoylated derivative, nitrosoguanidine, is often used to mutagenize bacterial cells for biochemical studies.
Following several decades of debate, it could be confirmed by NMR spectroscopy , and both x-ray and neutron diffraction that nitroguanidine exclusively exists as the nitroimine tautomer both in solid state and solution. [ 8 ] [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Nitroguanidine |
Nitrolic acids are organic compounds with the functional group RC(NO 2 )=NOH. They are prepared by the reaction of nitroalkanes with base and nitrite sources: [ 1 ]
The conversion was first demonstrated by Victor Meyer using nitroethane . [ 2 ] The reaction proceeds via the intermediacy of the nitronate anion.
Most nitrolic acids are laboratory curiosities. One exception is the compound HO 2 C(CH 2 ) 4 C(NO 2 )=NOH, which is produced by the oxidation of cyclohexanone with nitric acid . [ 3 ] This species decomposes to adipic acid and nitrous oxide :
This conversion is thought to be the largest anthropogenic route to N 2 O, which, on a molecule-to-molecule basis, has 298 times the atmospheric heat-trapping ability of carbon dioxide. [ 4 ] Adipic acid is a precursor to many nylon polymers. In the end, nitrous oxide is produced in about one to one mole ratio to the adipic acid. [ 5 ] | https://en.wikipedia.org/wiki/Nitrolic_acid |
Nitrolite is an older form of powdery high explosive with an ammonium nitrate base, mixed with a smaller amount of TNT and nitroglycerin etc. [ 1 ] [ 2 ] [ 3 ] [ 4 ] It is used for mining, construction as well as military purposes. During World War II it came to be a budget replacement for more expensive TNT. [ 2 ]
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitrolite |
Nitrolysis is a chemical reaction involving cleavage ("lysis") of a chemical bond concomitant with installation of a nitro group (NO 2 ). Typical reagents for effecting this conversion are nitric acid and acetyl nitrate . A commercially important nitrolysis reaction is the conversion of hexamine to nitramide . Nitrolysis of hexamine is also used to produce RDX , (O 2 NNCH 2 ) 3 , a tri nitramide widely used as an explosive . [ 1 ] | https://en.wikipedia.org/wiki/Nitrolysis |
Nitromethane , sometimes shortened to simply "nitro", is an organic compound with the chemical formula CH 3 NO 2 . It is the simplest organic nitro compound . It is a polar liquid commonly used as a solvent in a variety of industrial applications such as in extractions, as a reaction medium, and as a cleaning solvent. As an intermediate in organic synthesis , it is used widely in the manufacture of pesticides, explosives, fibers, and coatings. [ 12 ] Nitromethane is used as a fuel additive in various motorsports and hobbies, e.g. Top Fuel drag racing and miniature internal combustion engines in radio control , control line and free flight model aircraft.
Nitromethane is produced industrially by combining propane and nitric acid in the gas phase at 350–450 °C (662–842 °F). This exothermic reaction produces the four industrially significant nitroalkanes: nitromethane, nitroethane , 1-nitropropane , and 2-nitropropane . The reaction involves free radicals, including the alkoxyl radicals of the type CH 3 CH 2 CH 2 O, which arise via homolysis of the corresponding nitrite ester . These alkoxy radicals are susceptible to C—C fragmentation reactions, which explains the formation of a mixture of products. [ 12 ]
It can also be prepared by other methods that are of instructional value. The reaction of sodium chloroacetate with sodium nitrite in aqueous solution produces this compound: [ 13 ]
The dominant use of the nitromethane is as a precursor reagent. A major derivative is chloropicrin ( CCl 3 NO 2 ), a widely used pesticide. It condenses with formaldehyde ( Henry reaction ) to eventually give tris(hydroxymethyl)aminomethane ("tris"), a widely used buffer and ingredient in alkyd resins . [ 12 ]
The major application is as a stabilizer in chlorinated solvents. As an organic solvent, nitromethane has an unusual combination of properties: highly polar (ε r = 36 at 20 °C and μ = 3.5 Debye) but aprotic and weakly basic. This combination makes it useful for dissolving positively charged, strongly electrophilic species. It is a solvent for acrylate monomers , such as cyanoacrylates (more commonly known as "super-glues"). [ 12 ]
Although a minor application in terms of volume, [ 12 ] nitromethane also is used as a fuel or fuel additive for sports and hobby. For some applications, it is mixed with methanol in racing cars, boats, and model engines.
Nitromethane is used as a fuel in motor racing, particularly drag racing , as well as for radio-controlled model power boats, cars , planes and helicopters . In this context, nitromethane is commonly referred to as "nitro fuel" or simply "nitro", and is the principal ingredient for fuel used in the " Top Fuel " category of drag racing. [ 14 ]
The oxygen content of nitromethane enables it to burn with much less atmospheric oxygen than conventional fuels. [ 15 ] During nitromethane combustion, nitric oxide (NO) is one of the major emission products along with CO 2 and H 2 O. [ 16 ] Nitric oxide contributes to air pollution, acid rain, and ozone layer depletion. Recent (2020) studies [ 17 ] suggest the correct stoichiometric equation for the burning of nitromethane is:
The amount of air required to burn 1 kg (2.2 lb) of gasoline is 14.7 kg (32 lb), but only 1.7 kg (3.7 lb) of air is required for 1 kg of nitromethane. Since an engine's cylinder can only contain a limited amount of air on each stroke, 8.6 times as much nitromethane as gasoline can be burned in one stroke. Nitromethane, however, has a lower specific energy: gasoline provides about 42–44 MJ /kg, whereas nitromethane provides only 11.3 MJ/kg. [ citation needed ] This analysis indicates that nitromethane generates about 2.3 times the power of gasoline when combined with a given amount of oxygen. [ citation needed ]
Nitromethane can also be used as a monopropellant , i.e., a propellant that decomposes to release energy without added oxygen. It was first tested as rocket monopropellant in 1930s by Luigi Crocco [ it ] fom Italian Rocket Society. [ 18 ] [ 19 ] There is a renewed interest in nitromethane as safer replacement of hydrazine monopropellant. [ 20 ] The following equation describes this process:
Nitromethane has a laminar combustion velocity of approximately 0.5 m/s, somewhat higher than gasoline, thus making it suitable for high-speed engines. It also has a somewhat higher flame temperature of about 2,400 °C (4,350 °F). The high heat of vaporization of 0.56 MJ/kg together with the high fuel flow provides significant cooling of the incoming charge (about twice that of methanol), resulting in reasonably low temperatures. [ citation needed ]
Nitromethane is usually used with rich air–fuel mixtures because it provides power even in the absence of atmospheric oxygen. When rich air–fuel mixtures are used, hydrogen and carbon monoxide are two of the combustion products. These gases often ignite, sometimes spectacularly, as the normally very rich mixtures of the still burning fuel exits the exhaust ports. Very rich mixtures are necessary to reduce the temperature of combustion chamber hot parts in order to control pre-ignition and subsequent detonation. Operational details depend on the particular mixture and engine characteristics. [ citation needed ]
A small amount of hydrazine blended in nitromethane can increase the power output even further. With nitromethane, hydrazine forms an explosive salt that is again a monopropellant. This unstable mixture poses a severe safety hazard. The National Hot Rod Association and Academy of Model Aeronautics do not permit its use in competitions. [ 21 ]
In model aircraft and car glow fuel , the primary ingredient is generally methanol with some nitromethane (0% to 65%, but rarely over 30%, and 10–20% lubricants (usually castor oil and/or synthetic oil )). Even moderate amounts of nitromethane tend to increase the power created by the engine (as the limiting factor is often the air intake), making the engine easier to tune (adjust for the proper air/fuel ratio).
It formerly was used in the explosives industry as a component in a binary explosive formulation with ammonium nitrate and in shaped charges, and it was used as a chemical stabilizer to prevent decomposition of various halogenated hydrocarbons. [ 22 ]
It can be used as an explosive, when gelled with several percent of gelling agent. This type of mixture is called PLX . Other mixtures include ANNM and ANNMAl – explosive mixtures of ammonium nitrate, nitromethane and aluminium powder.
A YouTuber posted a video that demonstrated that burning nitromethane will give off a very unusually colored flame. [ 23 ] The flame actually appears to be black and white. He has used methanol to start the fire in the mentioned video.
Nitromethane is a relatively acidic carbon acid . It has a pK a of 17.2 in DMSO solution. This value indicates an aqueous pK a of about 11. [ 24 ] It is so acidic because the anion admits an alternate, stabilizing resonance structure:
The acid deprotonates only slowly. Protonation of the conjugate base O 2 NCH 2 − , which is nearly isosteric with nitrate , occurs initially at oxygen. [ 25 ]
In organic synthesis nitromethane is employed as a one carbon building block . [ 26 ] [ 27 ] Its acidity allows it to undergo deprotonation, enabling condensation reactions analogous to those of carbonyl compounds. Thus, under base catalysis, nitromethane adds to aldehydes in 1,2-addition in the nitroaldol reaction . Some important derivatives include the pesticides chloropicrin (Cl 3 CNO 2 ), beta-nitrostyrene , and tris(hydroxymethyl)nitromethane, ((HOCH 2 ) 3 CNO 2 ). Reduction of the latter gives tris(hydroxymethyl)aminomethane, (HOCH 2 ) 3 CNH 2 , better known as tris , a widely used buffer . In more specialized organic synthesis , nitromethane serves as a Michael donor, adding to α,β-unsaturated carbonyl compounds via 1,4-addition in the Michael reaction .
Nitromethane is a popular solvent in organic and electroanalytical chemistry. It can be purified by cooling below its freezing point, washing the solid with cold diethyl ether , followed by distillation. [ 28 ]
Nitromethane has a modest acute toxicity. LD50 (oral, rats) is 1210±322 mg/kg. [ 12 ]
Nitromethane is "reasonably anticipated to be a human carcinogen" according to a U.S. government report. [ 29 ]
Nitromethane was not known to be a high explosive until a railroad tank car loaded with it exploded on June 1, 1958 . [ 30 ] After much testing [ citation needed ] , it was realized that nitromethane was a more energetic high explosive than TNT [ citation needed ] , although TNT has a higher velocity of detonation (VoD) and brisance [ citation needed ] . Both of these explosives are oxygen-poor, and some benefits are gained from mixing with an oxidizer , such as ammonium nitrate . Pure nitromethane is an insensitive explosive with a VoD of approximately 6,400 m/s (21,000 ft/s), but even so inhibitors may be used to reduce the hazards. The tank car explosion was speculated [ citation needed ] to be due to adiabatic compression, a hazard common to all liquid explosives. This is when small entrained air bubbles compress and superheat with rapid rises in pressure. It was thought that an operator rapidly snapped shut a valve creating a " hammer-lock " pressure surge. [ citation needed ]
If mixed with ammonium nitrate , which is used as an oxidizer, it forms an explosive mixture known as ANNM .
Nitromethane is used as a model explosive, along with TNT. It has several advantages as a model explosive over TNT, namely its uniform density and lack of solid post-detonation species that complicate the determination of equation of state and further calculations.
Nitromethane reacts with solutions of sodium hydroxide or methoxide in alcohol to produce an insoluble salt of nitromethane. This substance is a sensitive explosive which reverts to nitromethane under acidic conditions and decomposes in water to form another explosive compound, sodium methazonate, which has a reddish-brown color:
Nitromethane's reaction with solid sodium hydroxide is hypergolic . | https://en.wikipedia.org/wiki/Nitromethane |
This page provides supplementary chemical data on nitromethane .
The handling of this chemical may incur notable safety precautions. MSDS is available from Mallinckrodt Baker. [ 1 ]
Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. | https://en.wikipedia.org/wiki/Nitromethane_(data_page) |
A nitronate ( IUPAC : azinate ) in organic chemistry is an anion with the general structure R 1 R 2 C = N + (− O − ) 2 , containing the =N + (−O − ) 2 functional group , [ 1 ] [ 2 ] where R can be hydrogen , halogen , organyl group or other groups. It is the anion of nitronic acid R 1 R 2 C=N + (−O − )−OH (sometimes also called an aci -nitro compound, [ 3 ] or an azinic acid [ 4 ] ), a tautomeric form of a nitro compound. Just as aldehydes and ketones can exist in equilibrium with their enol tautomer, nitro compounds exist in equilibrium with their nitronate tautomer under basic conditions . In practice they are formed by the deprotonation of the α - carbon , the p K a of which is typically around 17.
Nitronates are formed as intermediates in the Henry reaction , Hass–Bender oxidation and Nef reaction , the latter of which also demonstrates the instability of the nitronic acid form. The nitronate has two different resonance structures , one with a negative charge on the α-carbon and a double bond between the nitrogen and one of the oxygens , and another resonance structure with a double bond between the nitrogen and the α-carbon, and single bonds between the nitrogen and the oxygens.
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitronate |
In organic chemistry , a nitrone is a functional group consisting of an N -oxide of an imine . The general structure is R 1 R 2 C=N + (−O − )(−R 3 ) , where R 3 is not a hydrogen . Their primary application is intermediates in chemical synthesis . A nitrone is a 1,3-dipole used in cycloadditions , and a carbonyl mimic.
Nitrones, as a tetrasubstituted double bond , admit cis – trans isomerism . [ 1 ] : 474
Typical nitrone sources are hydroxylamine oxidation or condensation with carbonyl compounds . Secondary hydroxylamines oxidize to nitrones in air over a timescale of several weeks, a process cupric salts accelerate. [ 1 ] : 476 [ 2 ] : 332–333 The most general reagent used for the oxidation of hydroxylamines is aqueous mercuric oxide : [ 1 ] : 476 [ 3 ]
However, a hydroxylamine with two α hydrogens may unsaturate on either side. Carbonyl condensation avoids this ambiguity... [ 4 ]
...but is inhibited if both ketone substituents are bulky. [ 1 ] : 477
In principle, N - alkylation could produce nitrones from oximes , but in practice electrophiles typically perform a mixture of N - and O -attack. [ 1 ] : 479 [ 2 ] : 334
Some nitrones oligomerize: [ 1 ] : 483 [ 2 ] : 334,337-338 [ 5 ]
Syntheses with nitrone precursors obviate the issue with increased temperature, to exaggerate entropic factors; or with a nitrone excess.
Like many other unsaturated functional groups, nitrones activate the α and β carbons towards reaction. The α carbon is an electrophile and the β carbon a nucleophile; that is, nitrones polarize like carbonyls and nitriles but unlike nitro compounds and vinyl sulfur derivatives. [ 1 ] : 483 [ 2 ] : 338–340
Nitrones hydrolyze extremely easily to the corresponding carbonyl and N-hydroxylamine. [ 1 ] : 491 [ 2 ] : 344
As 1,3‑dipoles , nitrones perform [3+2] cycloadditions . [ 6 ] For example, a dipolarophilic alkene combines to form isoxazolidine :
Other ring-closing reactions are known, [ 7 ] including formal [3+3] and [5+2] cycloadditions . [ 6 ]
Deoxygenating reagents , light , or heat all catalyze rearrangement to the amide . Acids catalyze rearrangement to the oxime ether . [ 1 ] : 489–490 [ 2 ] : 345–347
Hydrides add to give hydroxylamines . Reducing Lewis acids (e.g. metals , SO 2 ) deoxygenate to the imine instead. [ 1 ] : 490 [ 2 ] : 343 | https://en.wikipedia.org/wiki/Nitrone |
The nitronium ion , [ N O 2 ] + , is a cation . It is an onium ion because its nitrogen atom has +1 charge, similar to ammonium ion [NH 4 ] + . It is created by the removal of an electron from the paramagnetic nitrogen dioxide molecule NO 2 , or the protonation of nitric acid HNO 3 (with removal of H 2 O ). [ 2 ]
It is stable enough to exist in normal conditions, but it is generally reactive and used extensively as an electrophile in the nitration of other substances. The ion is generated in situ for this purpose by mixing concentrated sulfuric acid and concentrated nitric acid according to the equilibrium :
The nitronium ion is isoelectronic with carbon dioxide and has the same linear structure and bond angle of 180°. For this reason it has a similar vibrational spectrum to carbon dioxide. Historically, the nitronium ion was detected by Raman spectroscopy , because its symmetric stretch is Raman-active but infrared-inactive. The Raman-active symmetrical stretch was first used to identify the ion in nitrating mixtures. [ 3 ]
A few stable nitronium salts with anions of weak nucleophilicity can be isolated. These include nitronium perchlorate [NO 2 ] + [ClO 4 ] − , nitronium tetrafluoroborate [NO 2 ] + [BF 4 ] − , nitronium hexafluorophosphate [NO 2 ] + [PF 6 ] − , nitronium hexafluoroarsenate [NO 2 ] + [AsF 6 ] − , and nitronium hexafluoroantimonate [NO 2 ] + [SbF 6 ] − . These are all very hygroscopic compounds. [ 4 ]
The solid form of dinitrogen pentoxide , N 2 O 5 , actually consists of nitronium and nitrate ions, so it is an ionic compound , nitronium nitrate [NO 2 ] + [NO 3 ] − , not a molecular solid . However, dinitrogen pentoxide in liquid or gaseous state is molecular and does not contain nitronium ions. [ 2 ] [ 5 ]
The compounds nitryl fluoride , NO 2 F , and nitryl chloride , NO 2 Cl , are not nitronium salts but molecular compounds, as shown by their low boiling points (−72 °C and −6 °C respectively) and short nitrogen–halogen bond lengths (N–F 135 pm, N–Cl 184 pm). [ 6 ]
Addition of one electron forms the neutral nitryl radical , NO 2 • ; in fact, this is fairly stable and known as the compound nitrogen dioxide .
The related negatively charged species is NO − 2 , the nitrite ion. | https://en.wikipedia.org/wiki/Nitronium_ion |
Nitronium perchlorate , NO 2 ClO 4 , also known as nitryl perchlorate and nitroxyl perchlorate , is an inorganic chemical , the salt of the perchlorate anion and the nitronium cation. It forms colorless monoclinic crystals. It is hygroscopic , and is a strong oxidizing and nitrating agent. It may become hypergolic in contact with organic materials.
Nitronium perchlorate was investigated as an oxidizer in solid rocket propellants . Thomas N. Scortia filed for patent on such propellant in 1963, [ 3 ] however, its reactivity and incompatibility with many materials hindered such use. Coating of nitronium perchlorate particles with ammonium nitrate , prepared in situ by passing of dry ammonia gas over the particles, was investigated, and a patent was awarded. [ 4 ]
The decomposition rate of nitronium perchlorate can be altered by doping with multivalent cations. [ 5 ]
Nitronium perchlorate and ammonium perchlorate do not produce smoke when stoichiometrically burned with non-metallic fuels. Potassium perchlorate and other metal perchlorates generate smoke, as the metal chlorides are solid materials creating aerosols of their particles. Of all the perchlorates, nitronium perchlorate is the most powerful oxidizer. It can be easily detonated . [ 6 ] | https://en.wikipedia.org/wiki/Nitronium_perchlorate |
The nitrophosphate process (also known as the Odda process ) is a method for the industrial production of nitrogen fertilizers invented by Erling Johnson in the municipality of Odda, Norway around 1927.
The process involves acidifying phosphate rock with dilute nitric acid to produce a mixture of phosphoric acid and calcium nitrate .
The mixture is cooled to below 0 °C, where the calcium nitrate crystallizes and can be separated from the phosphoric acid.
The resulting calcium nitrate produces nitrogen fertilizer. The filtrate is composed mainly of phosphoric acid with some nitric acid and traces of calcium nitrate, and this is neutralized with ammonia to produce a compound fertilizer.
If potassium chloride or potassium sulfate is added, the result will be NPK fertilizer. The process was an innovation for requiring neither the expensive sulfuric acid nor producing gypsum waste (known in the context of phosphate production as phosphogypsum ).
The calcium nitrate mentioned before, can as said be worked up as calcium nitrate fertilizer but often it is converted into ammonium nitrate and calcium carbonate using carbon dioxide and ammonia.
Both products can be worked up together as straight nitrogen fertilizer.
Although Johnson created the process while working for the Odda Smelteverk , his company never employed it. Instead, it licensed the process to Norsk Hydro , BASF , Hoechst , and DSM. Each of these companies used the process, introduced variations, and licensed it to other companies. Today, only a few companies (e.g. Yara (Norsk Hydro), Acron , EuroChem , Borealis Agrolinz Melamine GmbH , Omnia, GNFC ) still use the Odda process. Due to the alterations of the process by the various companies who employed it, the process is now generally referred to as the nitrophosphate process. | https://en.wikipedia.org/wiki/Nitrophosphate_process |
Sodium nitroprusside ( SNP ), sold under the brand name Nitropress among others, is a medication used to lower blood pressure . [ 3 ] This may be done if the blood pressure is very high and resulting in symptoms , in certain types of heart failure , and during surgery to decrease bleeding . [ 3 ] It is used by continuous injection into a vein . [ 3 ] Onset is nearly immediate and effects last for up to ten minutes. [ 3 ]
It is available as a generic medication . [ 5 ]
Common side effects include low blood pressure and cyanide toxicity . [ 3 ] Other serious side effects include methemoglobinemia . [ 3 ] It is not generally recommended during pregnancy due to concerns of side effects. [ 6 ] High doses are not recommended for more than ten minutes. [ 7 ] It works by increasing nitric oxide levels in the blood, which increases cGMP levels in cells, and causes dilation of blood vessels . [ 8 ] [ 3 ]
Sodium nitroprusside was discovered as early as 1850 and found to be useful in medicine in 1928. [ 8 ] [ 9 ] It is on the World Health Organization's List of Essential Medicines . [ 10 ] [ 11 ] Sodium nitroprusside is light sensitive, so it needs to be shielded from light to prevent degradation. [ 12 ]
Sodium nitroprusside is intravenously infused in cases of acute hypertensive crises . [ 13 ] [ 14 ] Its effects are usually seen within a few minutes. [ 4 ]
Nitric oxide reduces both total peripheral resistance and venous return, thus decreasing both preload and afterload . So, it can be used in severe congestive heart failure where this combination of effects can act to increase cardiac output . In situations where cardiac output is normal, the effect is to reduce blood pressure . [ 13 ] [ 15 ] It is sometimes also used to induce hypotension (to reduce bleeding) for surgical procedures (for which it is also FDA , TGA , and MHRA labelled). [ 13 ] [ 14 ] [ 16 ]
The medication is extremely beneficial for use in medical patients because the effects of the medication will directly stop the second that it stops being infused. This is due to the metabolism of the drug, and the rapid inactivation to thiocyanate once conversion of the drug stops.
This compound has also been used as a treatment for aortic valve stenosis , [ 17 ] oesophageal varices , [ 18 ] myocardial infarction , [ 19 ] pulmonary hypertension , [ 20 ] [ 21 ] [ 22 ] respiratory distress syndrome in the newborn , [ 23 ] [ 24 ] shock , [ 24 ] and ergot toxicity . [ 25 ]
Adverse effects by incidence and severity [ 13 ] [ 15 ] [ 26 ]
Common
Unknown frequency
Serious
Sodium nitroprusside should not be used for compensatory hypertension (e.g. due to an arteriovenous stent or coarctation of the aorta). [ 15 ] It should not be used in patients with inadequate cerebral circulation or in patients who are near death. It should not be used in patients with vitamin B 12 deficiency, anaemia, severe renal disease, or hypovolaemia. [ 15 ] Patients with conditions associated with a higher cyanide/thiocyanate ratio (e.g. congenital (Leber's) optic atrophy, tobacco amblyopia) should only be treated with sodium nitroprusside with great caution. [ 15 ] Its use in patients with acute congestive heart failure associated with reduced peripheral resistance is also not recommended. [ 15 ] Its use in hepatically impaired individuals is also not recommended, as is its use in cases of pre-existing hypothyroidism . [ 13 ]
Its use in pregnant women is advised against, although the available evidence suggests it may be safe, provided maternal pH and cyanide levels are closely monitored. [ 15 ] [ 27 ] Some evidence suggests sodium nitroprusside use in critically ill children may be safe, even without monitoring of cyanide level. [ 28 ]
The only known drug interactions are pharmacodynamic in nature, that is it is possible for other antihypertensive drugs to reduce the threshold for dangerous hypotensive effects to be seen. [ 15 ]
Due to its cyanogenic nature, overdose may be particularly dangerous. Treatment of sodium nitroprusside overdose includes the following: [ 15 ] [ 29 ]
Haemodialysis is ineffective for removing cyanide from the body but it can be used to remove most of the thiocyanate produced from the above procedure. [ 15 ]
The cyanide can be detoxified by reaction with a sulfur -donor such as thiosulfate , catalysed by the enzyme rhodanese . [ 30 ] In the absence of sufficient thiosulfate, cyanide ions can quickly reach toxic levels. [ 30 ] Hydroxocobalamin can be administered to reduce the risk of thiocyanate toxicity induced by nitroprusside. [ 31 ]
As a result of its breakdown to nitric oxide (NO), sodium nitroprusside has potent vasodilating effects on arterioles and venules (arterial more than venous), whereas other nitrates exhibit more selectivity for veins (e.g. nitroglycerin ). [ 13 ] [ 15 ] [ 26 ] [ 33 ]
Sodium nitroprusside breaks down in circulation to release nitric oxide (NO). [ 8 ] It does this by binding to oxyhaemoglobin to release cyanide, methaemoglobin and nitric oxide. [ 8 ] NO activates guanylate cyclase in vascular smooth muscle and increases intracellular production of cGMP . cGMP activates protein kinase G which activates phosphatases which inactivate myosin light chains. [ 34 ] Myosin light chains are involved in smooth muscle contraction. The result is vascular smooth muscle relaxation, which allow vessels to dilate. [ 34 ] This mechanism is similar to that of phosphodiesterase 5 (PDE5) inhibitors such as sildenafil (Viagra) and tadalafil (Cialis), which elevate cGMP concentration by inhibiting its degradation by PDE5. [ 35 ]
A role for NO in various common psychiatric disorders including schizophrenia , [ 36 ] [ 37 ] [ 38 ] [ 39 ] bipolar disorder [ 40 ] [ 41 ] [ 42 ] and major depressive disorder [ 43 ] [ 44 ] [ 45 ] has been proposed and supported by several clinical findings. These findings may also implicate the potential of drugs that alter NO signalling such as SNP in their treatment. [ 38 ] [ 44 ] Such a role is also supported by the findings of the recent SNP clinical trial. [ 46 ]
Nitroprusside is an inorganic compound with the chemical formula Na 2 [Fe(CN) 5 NO], usually encountered as the dihydrate , Na 2 [Fe(CN) 5 NO]·2H 2 O. [ 47 ] This red-colored sodium salt dissolves in water or ethanol to give solutions containing the free complex dianion [Fe(CN) 5 NO] 2− .
Nitroprusside is a complex anion that features an octahedral iron(II) centre surrounded by five tightly bound cyanide ligands and one linear nitric oxide ligand (Fe-N-O angle = 176.2° [ 48 ] ). The anion possesses idealized C 4v symmetry .
Due to the linear Fe-N-O angle, the relatively short N-O distance of 113 pm [ 48 ] and the relatively high stretching frequency of 1947 cm −1 , the complex is formulated as containing an NO + ligand. [ 49 ] Consequently, iron is assigned an oxidation state of +2. The iron center has a diamagnetic low-spin d 6 electron configuration, although a paramagnetic long-lived metastable state has been observed by EPR spectroscopy . [ 50 ]
The chemical reactions of sodium nitroprusside are mainly associated with the NO ligand. [ 51 ] For example, addition of S 2− ion to [Fe(CN) 5 (NO)] 2− produces the violet colour [Fe(CN) 5 (NOS)] 4− ion, which is the basis for a sensitive test for S 2− ions. An analogous reaction also exists with OH − ions, giving [Fe(CN) 5 (NO 2 )] 4− . [ 49 ] Roussin's red salt (K 2 [Fe 2 S 2 (NO) 4 ]) and Roussin's black salt (NaFe 4 S 3 (NO) 7 ) are related iron nitrosyl complexes. The former was first prepared by treating nitroprusside with sulfur. [ 52 ]
Sodium nitroprusside can be synthesized by digesting a solution of potassium ferrocyanide in water with nitric acid , followed by neutralization with sodium carbonate : [ 53 ]
Alternatively, the nitrosyl ligand can be introduced using nitrite : [ 49 ]
Sodium nitroprusside is often used as a reference compound for the calibration of Mössbauer spectrometers . [ 54 ] Sodium nitroprusside crystals are also of interest for optical storage. For this application, sodium nitroprusside can be reversibly promoted to a metastable excited state by blue-green light, and de-excited by heat or red light. [ 55 ]
In physiology research, sodium nitroprusside is frequently used to test endothelium-independent vasodilation. Iontophoresis , for example, allows local administration of the drug, preventing the systemic effects listed above but still inducing local microvascular vasodilation. Sodium nitroprusside is also used in microbiology, where it has been linked with the dispersal of Pseudomonas aeruginosa biofilms by acting as a nitric oxide donor. [ 56 ] [ 57 ]
Sodium nitroprusside is also used as an analytical reagent under the name sodium nitroferricyanide for the detection of methyl ketones , amines , and thiols. It is also used as a catalyst in the quantitative determination of ammonia in water samples via the phenate method. [ 58 ]
The nitroprusside reaction is used for the identification of ketones in urine testing. [ 59 ] Sodium nitroprusside was found to give a reaction with acetone or creatine under basic conditions in 1882. Rothera refined this method by the use of ammonia in place of sodium or potassium hydroxide. The reaction was now specific for methyl ketones. Addition of ammonium salts (e.g. ammonium sulfate) improved the sensitivity of the test, too. [ 60 ]
In this test, known as Rothera's test, methyl ketones (CH 3 C(=O)-) under alkaline conditions give bright red coloration (see also iodoform test ). Rothera's test was initially applied to detecting ketonuria (a symptom of diabetes ) in urine samples. This reaction is now exploited in the form of urine test strips (e.g. "Ketostix"). [ 61 ]
The nitroprusside reaction is a chemical test used to detect the presence of thiol groups of cysteine in proteins. Proteins with the free thiol group give a red colour when added to a solution of sodium nitroprusside in aqueous ammonia . Some proteins test positive when denatured, indicating that thiol groups are liberated. [ 62 ] [ 63 ] [ 64 ]
Sodium nitroprusside is used in a separate urinalysis test known as the cyanide nitroprusside test or Brand's test. In this test, sodium cyanide is added first to urine and let stand for about 10 minutes. In this time, disulfide bonds will be broken by the released cyanide. The destruction of disulfide bonds liberates cysteine from cystine as well as homocysteine from homocystine . Next, sodium nitroprusside is added to the solution and it reacts with the newly freed sulfhydryl groups. The test will turn a red/purple colour if the test is positive, indicating significant amounts of amino acids were in the urine ( aminoaciduria ). Cysteine, cystine, homocysteine, and homocystine all react when present in the urine when this test is performed. This test can indicate inborn errors of amino acid transporters such as cystinuria , which results from pathology in the transport of dibasic amino acids. [ 65 ]
Sodium nitroprusside is also used to detect amines , including those in illicit drugs. This compound is thus used as a stain to indicate amines in thin layer chromatography . [ 66 ] Sodium nitroprusside is similarly used as a presumptive test for the presence of alkaloids (amine-containing natural products ) common in illicit substances. [ 67 ] The test, called Simon's test , is performed by adding 1 volume of a solution of sodium nitroprusside and acetaldehyde in deionized water to a suspected drug, followed by the addition of 2 volumes of an aqueous sodium carbonate solution. The test turns blue for some secondary amines . The most common secondary amines encountered in forensic chemistry include 3,4-methylenedioxymethamphetamine ( MDMA , the main component in ecstasy) and phenethylamines such as methamphetamine . Sodium nitroprusside is also useful in the identification the mercaptans (thiol groups) in the nitroprusside reaction.
Sodium nitroprusside is primarily used as a vasodilator. It was first used in human medicine in 1928. [ 8 ] By 1955, data on its safety during short-term use in people with severe hypertension had become available. [ 8 ] Despite this, due to difficulties in its chemical preparation, it was not finally approved by the US FDA until 1974 for the treatment of severe hypertension. [ 8 ] By 1993, its popularity had grown such that total sales in the US had totalled US$ 2 million. [ 8 ] | https://en.wikipedia.org/wiki/Nitroprusside_reaction |
Nitrosamines (or more formally N -nitrosamines ) are organic compounds produced by industrial processes. [ 1 ]
The chemical structure is R 2 N−N=O , where R is usually an alkyl group . [ 2 ] Nitrosamines have a nitroso group ( NO + ) that are "probable human carcinogens", [ 3 ] bonded to a deprotonated amine . Most nitrosamines are carcinogenic in animals. [ 4 ] A 2006 systematic review supports a "positive association between nitrite and nitrosamine intake and gastric cancer , between meat and processed meat intake and gastric cancer and oesophageal cancer , and between preserved fish, vegetable and smoked food intake and gastric cancer, but is not conclusive". [ 5 ]
The organic chemistry of nitrosamines is well developed with regard to their syntheses, their structures, and their reactions. [ 7 ] [ 8 ] They usually are produced by the reaction of nitrous acid ( HNO 2 ) and secondary amines, although other nitrosyl sources (e.g. N 2 O 4 , NOCl , RONO ) have the same effect: [ 9 ]
The nitrous acid usually arises from protonation of a nitrite . This synthesis method is relevant to the generation of nitrosamines under some biological conditions. [ 10 ] The nitrosation is also reversible, particularly in acidic solutions of nucleophiles . [ 11 ] Aryl nitrosamines rearrange to give a para -nitroso aryl amine in the Fischer-Hepp rearrangement . [ 12 ]
With regards to structure, the C 2 N 2 O core of nitrosamines is planar, as established by X-ray crystallography . The N-N and N-O distances are 132 and 126 pm, respectively in dimethylnitrosamine , [ 13 ] one of the simplest members of a large class of N-nitrosamines.
Nitrosamines are not directly carcinogenic. Metabolic activation is required to convert them to the alkylating agents that modify bases in DNA, inducing mutations. The specific alkylating agents vary with the nitrosamine, but all are proposed to feature alkyldiazonium centers. [ 14 ] [ 6 ]
In 1956, two British scientists, John Barnes and Peter Magee, reported that a simple member of the large class of N-nitrosamines, dimethylnitrosamine , produced liver tumours in rats. Subsequent studies showed that approximately 90% of the 300 nitrosamines tested were carcinogenic in a wide variety of animals. [ 15 ]
A common way ordinary consumers are exposed to nitrosamines is through tobacco use and cigarette smoke. [ 14 ] Tobacco-specific nitrosamines also can be found in American dip snuff , chewing tobacco , and to a much lesser degree, snus (127.9 ppm for American dip snuff compared to 2.8 ppm in Swedish snuff or snus). [ 16 ]
Nitroso compounds react with primary amines in acidic environments to form nitrosamines , which human metabolism converts to mutagenic diazo compounds . Small amounts of nitro and nitroso compounds form during meat curing ; the toxicity of these compounds preserves the meat against bacterial infection . After curing completes, the concentration of these compounds appears to degrade over time. Their presence in finished products has been tightly regulated since several food-poisoning cases in the early 20th century, [ 17 ] but consumption of large quantities of processed meats can still cause a slight elevation in gastric and oesophageal cancer risk today. [ 18 ] [ 19 ] [ 20 ] [ 21 ]
For example, during the 1970s, certain Norwegian farm animals began exhibiting elevated levels of liver cancer . These animals had been fed herring meal preserved with sodium nitrite . The sodium nitrite had reacted with dimethylamine in the fish and produced dimethylnitrosamine . [ 22 ]
The effects of nitroso compounds vary dramatically across the gastrointestinal tract, and with diet. Nitroso compounds present in stool do not induce nitrosamine formation, because stool has neutral pH . [ 23 ] [ 24 ] Stomach acid catalyzes nitrosamine compound formation and is the main location of the reaction during digestion. [ 25 ]
The formation process is inhibited when amine concentration is low (e.g. a low-protein diet or no fermented food). The process may also be inhibited in the case of high vitamin C (ascorbic acid) or erythorbic acid [ 26 ] concentration (e.g. high-fruit diet). [ 27 ] [ 28 ] [ 29 ] However, when 10% of the meal is fat, the effect reverses, and ascorbic acid markedly increases nitrosamine formation. [ 25 ] [ 30 ] Vitamin C and erythorbic acid are already commonly used in the meat industry because they enhance the binding of nitrite to myoglobin, encouraging the formation of the desired pink color. [ 31 ]
There have been recalls for various medications due to the presence of nitrosamine impurities. There have been recalls for angiotensin II receptor blockers , ranitidine , valsartan , duloxetine, and others.
The US Food and Drug Administration published guidance about the control of nitrosamine impurities in medicines. [ 32 ] [ 33 ] Health Canada published guidance about nitrosamine impurities in medications [ 34 ] and a list of established acceptable intake limits of nitrosamine impurities in medications. [ 35 ] | https://en.wikipedia.org/wiki/Nitrosamine |
Nitrosation and nitrosylation are two names for the process of converting organic compounds or metal complexes [ 1 ] into nitroso derivatives, i.e., compounds containing the R−NO functionality. The synonymy arises because the R-NO functionality can be interpreted two different ways, depending on the physico-chemical environment:
There are multiple chemical mechanisms by which this can be achieved, including enzymes and chemical synthesis.
The biological functions of nitric oxide include S-nitrosylation , the conjugation of NO to cysteine thiols in proteins, which is an important part of cell signalling . [ 2 ]
Nitrosation is typically performed with nitrous acid , formed from acidification of a sodium nitrite solution. Nitrous acid is unstable, and high yields require a rapid reaction rate. NO + synthon transfer is catalyzed by a strong nucleophile, such as (in order of increasing efficacy) chloride , bromide , thiocyanate , or thiourea . Indeed, (meta)stable nitrosation products ( alkyl nitrites or nitrosamines ) can also nitrosate under such conditions; and the equilibria can be driven in any desired direction. Absent a driving force, thionitrosos form out of nitrosamines, which form out of nitrite esters, which form out of nitrous acid. [ 3 ]
Some form of Lewis acid also enhances the electrophilicity of NO + carriers, but the acid need not be Brønsted: nitroprusside , for example, nitrosates best in neutral-to-basic conditions. Roussin's salts may react similarly, but it is unclear if they release NO + or NO • . [ 4 ]
In general, nitric oxide is a poor nitrosant, Traube-type reactions notwithstanding. But atmospheric oxygen can oxidize nitric oxide to nitrogen dioxide , which does nitrosate. Alternatively cupric ions catalyze disproportionation into NO + and NO − . [ 5 ]
Nitroso compounds , such as nitrosobenzene , are typically prepared by oxidation of hydroxylamines :
In principle, NO + can substitute directly onto an aromatic ring, but the ring must be substantially activated, because NO + is about 14 bel less electrophilic than NO + 2 . [ 6 ] Unusually for electrophilic aromatic substitution , proton release to the solvent is typically rate-limiting, and the reaction can be suppressed in superacidic conditions. [ 7 ]
Excess NO + typically oxidizes the initially-nitroso product to a nitro compound or diazonium salt. [ 8 ]
S -nitrosothiols are typically prepared by condensation of a thiol and nitrous acid : [ 9 ]
They are liable to disproportionate to the disulfide and nitrogen oxides . [ 10 ]
Although such cations have not been isolated, nitrosating reagents likely coordinate to sulfides with no hydrogen substituent . [ 11 ]
Sulfinates and sulfinic acids add twice to nitrous acid , so that the initial nitroso product (from the first addition) is reduced to a disulfonyl hydroxylamine. A variant on this process with bisulfite is Raschig's hydroxylamine production technique . [ 12 ]
O - Nitroso compounds are similar to S -nitroso compounds, but are less reactive because the oxygen atom is less nucleophilic than the sulfur atom. The formation of an alkyl nitrite from an alcohol and nitrous acid is a common example: [ 13 ]
N - Nitrosamines arise from the reaction of nitrite sources with amino compounds . Typically, this reaction occurs when the nucleophilic nitrogen of a secondary amine attacks the nitrogen of the electrophilic nitrosonium ion: [ 14 ]
If the amine is secondary, then the product is stable, but primary amines decompose in acid to the corresponding diazonium cation , and then attack any nearby nucleophile. Nitrosation of a primary amine is thus sometimes referred to as deamination . [ 15 ]
The stable secondary nitrosamines are carcinogens in rodents. The compounds are believed to nitrosate primary amines during the acid environment of the stomach, and the resulting diazonium ions alkylate DNA, leading to cancer. | https://en.wikipedia.org/wiki/Nitrosation_and_nitrosylation |
In organic chemistry , nitroso refers to a functional group in which the nitric oxide ( −N=O ) group is attached to an organic moiety . As such, various nitroso groups can be categorized as C -nitroso compounds (e.g., nitroso alkanes ; R−N=O ), S -nitroso compounds ( nitrosothiols ; RS−N=O ), N -nitroso compounds (e.g., nitrosamines , RN(−R’)−N=O ), and O -nitroso compounds ( alkyl nitrites ; RO−N=O ).
Nitroso compounds can be prepared by the reduction of nitro compounds [ 1 ] or by the oxidation of hydroxylamines . [ 2 ] Ortho-nitrosophenols may be produced by the Baudisch reaction . In the Fischer–Hepp rearrangement , aromatic 4-nitrosoanilines are prepared from the corresponding nitrosamines .
Nitrosoarenes typically participate in a monomer–dimer equilibrium . The azobenzene N , N'- dioxide (Ar( – O)N + = + N(O – )Ar) dimers, which are often pale yellow, are generally favored in the solid state, whereas the deep-green monomers are favored in dilute solution or at higher temperatures. They exist as cis and trans isomers . [ 4 ] The central "double bond" in the dimer in fact has a bond order of about 1.5. [ 5 ]
When stored in protic media , primary and secondary nitrosoalkanes isomerize to oximes . [ 6 ] Some tertiary nitrosoalkanes also isomerize to oximes through C-C bond fission, particularly if the bond is electron-poor . [ 7 ] Nitrosophenols and naphthols isomerize to the oxime quinone in solution, but reversibly; nitrosophenol ethers typically dealkylate to facilitate the isomerization. Nitroso tertiary anilines generally do not dealkylate in that way. [ 8 ]
Due to the stability of the nitric oxide free radical , nitroso organyls tend to have very low C–N bond dissociation energies : nitrosoalkanes have BDEs on the order of 30–40 kcal/mol (130–170 kJ/mol), while nitrosoarenes have BDEs on the order of 50–60 kcal/mol (210–250 kJ/mol). As a consequence, they are generally heat- and light-sensitive. Compounds containing O–(NO) or N–(NO) bonds generally have even lower bond dissociation energies. For instance, N -nitrosodiphenylamine , Ph 2 N–N=O, has a N–N bond dissociation energy of only 23 kcal/mol (96 kJ/mol). [ 9 ]
Organonitroso compounds serve as a ligands giving transition metal nitroso complexes . [ 10 ]
Many reactions make use of an intermediate nitroso compound, such as the Barton reaction and Davis–Beirut reaction , as well as the synthesis of indoles , for example: Baeyer–Emmerling indole synthesis , Bartoli indole synthesis . In the Saville reaction , mercury is used to replace a nitrosyl from a thiol group.
C -nitroso compounds are used in organic synthesis as synthons in some well-documented chemical reactions such as hetero Diels-Alder (HDA), nitroso-ene and nitroso-aldol reactions. [ 11 ]
Nitrosyls are non-organic compounds containing the NO group, for example directly bound to the metal via the N atom, giving a metal–NO moiety. Alternatively, a nonmetal example is the common reagent nitrosyl chloride ( Cl−N=O ). Nitric oxide is a stable radical , having an unpaired electron. Reduction of nitric oxide gives the nitrosyl anion , NO − :
Oxidation of NO yields the nitrosonium cation , NO + :
Nitric oxide can serve as a ligand forming metal nitrosyl complexes or just metal nitrosyls. These complexes can be viewed as adducts of NO + , NO − , or some intermediate case.
Nitroso compounds react with primary amines in acidic environments to form nitrosamines , which human metabolism converts to mutagenic diazo compounds . Small amounts of nitro and nitroso compounds form during meat curing ; the toxicity of these compounds preserves the meat against bacterial infection . After curing completes, the concentration of these compounds appears to degrade over time. Their presence in finished products has been tightly regulated since several food-poisoning cases in the early 20th century, [ 12 ] but consumption of large quantities of processed meats can still cause a slight elevation in gastric and oesophageal cancer risk today. [ 13 ] [ 14 ] [ 15 ] [ 16 ]
For example, during the 1970s, certain Norwegian farm animals began exhibiting elevated levels of liver cancer . These animals had been fed herring meal preserved with sodium nitrite . The sodium nitrite had reacted with dimethylamine in the fish and produced dimethylnitrosamine . [ 17 ]
The effects of nitroso compounds vary dramatically across the gastrointestinal tract, and with diet. Nitroso compounds present in stool do not induce nitrosamine formation, because stool has neutral pH . [ 18 ] [ 19 ] Stomach acid catalyzes nitrosamine compound formation and is the main location of the reaction during digestion. [ 20 ]
The formation process is inhibited when amine concentration is low (e.g. a low-protein diet or no fermented food). The process may also be inhibited in the case of high vitamin C (ascorbic acid) or erythorbic acid [ 21 ] concentration (e.g. high-fruit diet). [ 22 ] [ 23 ] [ 24 ] However, when 10% of the meal is fat, the effect reverses, and ascorbic acid markedly increases nitrosamine formation. [ 20 ] [ 25 ] Vitamin C and erythorbic acid are already commonly used in the meat industry because they enhance the binding of nitrite to myoglobin, encouraging the formation of the desired pink color. [ 26 ] | https://en.wikipedia.org/wiki/Nitroso |
Nitrosomonas is a genus of Gram-negative bacteria belonging to the class Betaproteobacteria . It is one of the five genera of ammonia-oxidizing bacteria [ 8 ] and, as an obligate chemolithoautotroph , [ 9 ] uses ammonia ( NH 3 {\displaystyle {\ce {NH3}}} ) as an energy source and carbon dioxide ( CO 2 {\displaystyle {\ce {CO2}}} ) as a carbon source in the presence of oxygen.
Nitrosomonas are important in the global biogeochemical nitrogen cycle , [ 10 ] since they increase the bioavailability of nitrogen to plants and in the denitrification , which is important for the release of nitrous oxide , a powerful greenhouse gas . [ 11 ] This microbe is photophobic , and usually generate a biofilm matrix, or form clumps with other microbes, to avoid light. [ 12 ] Nitrosomonas can be divided into six lineages: the first one includes the species Nitrosomonas europea , Nitrosomonas eutropha , Nitrosomonas halophila , and Nitrosomonas mobilis . The second lineage presents the species Nitrosomonas communis , N. sp. I and N. sp. II. The third lineage includes only Nitrosomonas nitrosa . The fourth lineage includes the species Nitrosomonas ureae and Nitrosomonas oligotropha . T he fifth and sixth lineages include the species Nitrosomonas marina , N. sp. III, Nitrosomonas estuarii , and Nitrosomonas cryotolerans . [ 13 ]
All species included in this genus have ellipsoidal or rod-shaped cells which have extensive intracytoplasmic membranes displaying as flattened vesicles. [ 8 ]
Most species are motile with a flagellum located in the polar region of the cell. Three basic morphological types of Nitrosomonas were studied, which are: short rods Nitrosomonas , rods Nitrosomonas, and Nitrosomonas with pointed ends. Nitrosomonas species cells have different criteria of size and shape: [ 13 ]
Genome sequencing of Nitrosomonas species has been important to understand the ecological role of these bacteria. [ 11 ]
Among the various species of Nitrosomonas that are known today, the complete genomes of N. ureae strain Nm10 and N. europaea , N.sp. Is79 have been sequenced. [ 14 ]
The presence of the genes for ammonia oxidation characterizes all these species. The first enzyme involved in the ammonia oxidation is ammonia monooxygenase (AMO), which is encoded by the amoCAB operon . The AMO enzyme catalyzes the oxidation from NH 3 {\displaystyle {\ce {NH3}}}
( ammonia ) to NH 2 OH {\displaystyle {\ce {NH2OH}}} ( hydroxylamine ). The amoCAB operon contains three different genes: amoA , amoB and amoC . While N. europaea presents two copies of the genes, N . sp. Is79 and N. ureae strain Nm10 have three copies of these genes. [ 15 ] [ 16 ]
The second enzyme involved in the ammonia oxidation is hydroxylamine oxidoreductase (HAO), encoded by the hao operon. This enzyme catalyzes the oxidation from NH 2 OH {\displaystyle {\ce {NH2OH}}} to NO {\displaystyle {\ce {NO}}} , [ 17 ] a highly reactive radical intermediate that can be partitioned into both of the main AOB products: N 2 O {\displaystyle {\ce {N2O}}} , a potent greenhouse gas, and NO 2 − {\displaystyle {\ce {NO2-}}} , a form of nitrogen more bioavailable for crops, but that conversely washes away from fields faster. [ 18 ] The hao operon contains different genes such as the haoA , which encodes for the functional cytochrome c subunit, the cycA which encodes for cytochrome c554, and cycB that encodes for quinone reductase. [ 15 ] These genes are present in different copies in various species; for instance, in Nitrosomonas sp. Is79 there are only three copies, while in N. ureae there are four. [ 19 ]
The discovery of genes that encode for enzymes involved in the denitrification process includes the first gene nirK which encodes for a nitrite reductase with copper . This enzyme catalyzes the reduction form NO 2 {\displaystyle {\ce {NO2}}} ( nitrite ) to NO {\displaystyle {\ce {NO}}} ( nitric oxide ). While in N. europaea , N. eutropha , and N. cryotolerans, nirK is included in a multigenetic cluster; [ 20 ] in Nitrosomonas sp. Is79 and N. sp. AL212, it is present as a single gene. [ 21 ] A high expression of the nirK gene was found in N.ureae and this has been explained with the hypothesis that the NirK enzyme is also involved in the oxidation of NH 2 OH {\displaystyle {\ce {NH2OH}}} in this species. [ 22 ] The second gene involved in denitrification is norCBQD which encodes a nitric-oxide reductase that catalyze the reduction from NO {\displaystyle {\ce {NO}}} (nitric oxide) to N 2 O {\displaystyle {\ce {N2O}}} ( nitrous oxide ). These genes are present in N. sp. AL212, N.cryotolerans, and N. communis strain Nm2 . In Nitrosomonas europaea , these genes are included in a cluster. [ 23 ] These genes are absent in N. sp. Is79 and N. ureae . [ 15 ] Recently, it was found that the norSY gene encodes for a nitric-oxide reductase with copper in N. communis strain Nm2 and Nitrosomonas AL212. [ 24 ] [ 25 ]
Nitrosomonas uses the Calvin-Benson cycle as a pathway for Carbon fixation . For this reason, all of the species have an operon that encodes for the RuBisCO enzyme. [ 21 ] A peculiarity is found in N. sp Is79 in which the two copies of the operon encode for two different forms of the RuBisCO enzyme: the IA form and the IC form, where the first one has a major affinity with the Carbon dioxide . Other species present different copies of this operon that encodes only for the IA form. [ 15 ] In N. europaea, an operon is characterized by five genes ( ccbL , ccbS , ccbQ , ccbO, and ccbN ) that encode for the RuBisCO enzyme. ccbL encodes for the major subunit while ccbS encodes for the minor subunit; these genes are also the most expressed within the operon. ccbQ and ccbO genes encode for a number of proteins involved in the mechanisms of processing, folding, assembling, activation, and regulation of the RuBisCO enzyme. Instead, ccbN encodes for a protein of 101 amino acids, whose function is not known yet. A putative regulatory gene, cbbR , was found 194 bases upstream of the start codon of cbbL and is transcribed in the opposite direction of other genes). [ 26 ]
Since Nitrosomonas are part of the ammonia-oxidizing bacteria (AOB) , ammonia carriers are important to them. Bacteria adapted to high concentrations of ammonia can absorb it passively by simple diffusion . Indeed, N. eutropha, that is adapted to high levels of ammonia, does not present genes that encode for an ammonia transporter. [ 27 ] Bacteria adapted to low concentrations of ammonia have a transporter ( transmembrane protein ) for this substrate. In Nitrosomonas, two different carriers for ammonia have been identified, differing in structure and function. The first transporter is the Amt protein (amtB type) encoded by amt genes and was found in Nitrosomonas sp. Is79 . [ 15 ] The activity of this ammonia carrier depends on the membrane potential . [ 27 ] The second was found in N. europaea , wherein the rh1 gene encodes an Rh-type ammonia carrier. Its activity is independent from the membrane potential. [ 27 ] Recent research has also linked the Rh transmembrane proteins with CO 2 {\displaystyle {\ce {CO2}}} transport, but this is not clear yet. [ 28 ]
Nitrosomonas is one of the genera included in AOB and use ammonia as an energy source and carbon dioxide as the main source of carbon. [ 29 ] The oxidation of ammonia is a rate-limiting step in nitrification and plays a fundamental role in the nitrogen cycle, because it transforms ammonia, which is usually extremely volatile , into less volatile forms of nitrogen. [ 29 ]
Nitrosomonas oxidizes ammonia into nitrite in a metabolic process, known as nitritation (a step of nitrification). This process occurs with the accompanying reduction of an oxygen molecule to water (which requires four electrons), and the release of energy. [ 30 ] The oxidation of ammonia to hydroxylamine is catalyzed by ammonia monooxygenase (AMO), which is a membrane-bound, multisubstrate enzyme . In this reaction, two electrons are required to reduce an oxygen atom to water: [ 31 ]
Since an ammonia molecule only releases two electrons when oxidized, it has been assumed that the other two necessary electrons come from the oxidation of hydroxylamine to nitrite, [ 32 ] which occurs in the periplasm and it is catalyzed by hydroxylamine oxidoreductase (HAO), a periplasm associated enzymes. [ 32 ]
Two of the four electrons released by the reaction, return to the AMO to convert the ammonia in hydroxylamine. [ 32 ] 1,65 of the two remaining electrons are available for the assimilation of nutrients and the generation of the proton gradient . [ 30 ] They pass through the cytochrome c552 to the cytochrome caa3, then to O 2 , which is the terminal acceptor; here they are reduced to form water. [ 13 ] The remaining 0,35 electrons are used to reduce NAD+ to NADH, to generate the proton gradient. [ 13 ]
Nitrite is the major nitrogen oxide produced in the process, but it has been observed that, when oxygen concentrations are low, [ 13 ] nitrous oxide and nitric oxide can also form, as by-products from the oxidation of hydroxylamine to nitrite. [ 30 ]
The species N. europaea has been identified as being able to degrade a variety of halogenated compounds including trichloroethylene , benzene , and vinyl chloride . [ 33 ]
Nitrosomonas is generally found in highest numbers in all habitats in which there is abundance of ammonia (environment with plentiful protein decomposition or in wastewater treatment ), thrive in a pH range of 6.0–9.0, and a temperature range of 20–30 °C (68–86 °F). Some species can live and proliferate on a monuments’ surface or on stone buildings’ walls, contributing to erosion of those surfaces. [ 12 ]
It is usually found in all types of waters, globally distributed in both eutrophic and oligotrophic freshwater and saltwater, emerging especially in shallow coastal sediments and under the upwelling zones, such as the Peruvian coast and the Arabian Sea, [ 34 ] [ 35 ] but can also be found in fertilized soils. [ 21 ]
Some Nitrosomonas species, such as N.europaea , possess the enzyme urease (which catalyzes the conversion of urea into ammonia and carbon dioxide) and have been shown to assimilate the carbon dioxide released by the reaction to make biomass via the Calvin cycle , and harvest energy by oxidizing ammonia (the other product of urease ) to nitrite. This feature may explain enhanced growth of AOB in the presence of urea in acidic environments. [ 36 ]
In agriculture, nitrification made by Nitrosomonas represents a problem because the oxidized nitrite by ammonia can persist in the soil, leaching and making it less available for plants. [ 37 ]
Nitrification can be slowed down by some inhibitors that are able to slow down the oxidation process of ammonia to nitrites by inhibiting the activity of Nitrosomonas and other ammonia-oxidizing bacteria thereby minimizing or preventing the loss of nitrate. [ 37 ] [ 38 ] (Read more about inhibitors in the section 'Inhibitors of nitrification' on this page Nitrification )
Nitrosomonas is used in activated sludge in aerobic wastewater treatment; the reduction of nitrogen compounds in the water is given by nitrification treatment in order to avoid environmental issues, such as ammonia toxicity and groundwater contamination. Nitrogen, if present in high quantities can cause algal development, leading to eutrophication with degradation of oceans and lakes. [ 39 ]
Employing as wastewater treatment, biological removal of nitrogen is obtained at a lower economic expense and with less damage caused to the environment compared to physical-chemical treatments. [ 39 ]
Nitrosomonas has also a role in biofilter systems, typically in association and collaboration with other microbes, to consume compounds such as NH 4 + {\displaystyle {\ce {NH4+}}} or CO 2 {\displaystyle {\ce {CO2}}} and recycle nutrients. These systems are used for various purposes but mainly for the elimination of odors from waste treatment. [ 29 ]
N. europaea is a non-pathogenic bacteria studied in connection with probiotic therapies. In this context, it may give aesthetic benefits in terms of reducing the appearance of wrinkles. [ 40 ] The effectiveness of probiotic products has been studied to explore why N. eutropha , which is a highly mobile bacterium, has become extinct from the normal flora of our skin. It has been studied in connection with the idea of having benefits through the repopulation and reintroduction of N. eutropha to the normal flora of human skin. [ 41 ] | https://en.wikipedia.org/wiki/Nitrosomonas |
Nitrososphaera is a mesophilic genus of ammonia-oxidizing Crenarchaeota. [ 1 ] [ 2 ] The first Nitrososphaera organism was discovered in garden soils at the University of Vienna leading to the categorization of a new genus, family, order and class of Archaea. [ 3 ] This genus is contains three distinct species: N. viennensis , Ca. N. gargensis , and Ca N. evergladensis . [ 1 ] Nitrososphaera are chemolithoautotrophs and have important biogeochemical roles as nitrifying organisms. [ 4 ]
The Nitrososphaera genus contains one of the first discovered ammonia-oxidizing archaea ( N. viennensis) . Only three distinct species of this genus have been identified. Both Ca. N. gargensis , and Ca N. Evergladensis are known as Candidatus , which have been discovered and analyzed but have yet been studied in pure culture in a lab. The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) [ 2 ] and National Center for Biotechnology Information (NCBI) Cladogram was taken from GTDB release 07-RS207 (8 April 2022).
" Ca. N. gargensis " Hatzenpichler et al. 2008
" Ca. N. evergladensis " Zhainina et al. 2014
N. viennensis Stieglmeier et al. 2014
The 16S rRNA gene of all Nitrososphaera sp. are nearly identical as they are neighboring within the phylogentic tree. N. viennensis has a 3% divergence from Ca. N. gargensis, while Ca. N evergladensis has a 97% similarity to Ca. N. gargensis within the 16S rRNA gene. [ 5 ] The Nitrososphaera sp. use ammonia monooxygenase ( amo A) genes to oxidize ammonium to nitrite. [ 6 ]
All three species contain genes for urease , urea , and ammonia . [ 6 ] Nitrososphaera have a cell membrane composed of crenarchaeol , its isomer , and a glycerol dialkyl glycerol tetraether (GDGT), all of which are used for identifying ammonia-oxidizing archaea. [ 7 ] N. viennensis has a cell diameter of 0.6–0.9 μm and is an irregular spherical coccus . [ 1 ] [ 6 ] Ca. N. gargensis is non- pathogenic presents a diameter of approximately 0.9 ± 0.3 μm with a relatively small coccus. [ 8 ] Ca. N evergladensis has yet to be properly analyzed and described for morphological characteristics.
Ammonia-oxidizing archaea have been found in various environments and habitats around the world. N. viennensis was first discovered in garden soils. [ 3 ] The preferred growth conditions are 35 °C - 42 °C and pH of 7.5. [ 1 ] Ca. N. gargensis was found in hot springs and is commonly found in heavy metal containing habitats with a growth temperature of ~ 46 °C. [ 9 ] Ca. N evergladensis was first discovered in the humid region of the Everglades in Florida. Other relatives of Nitrososphaera sp. have also been detected in swamps, microbial mats, freshwater sediments, deep sea marine sediments, and regions with high levels of nitrogen and ammonia sources to allow for the oxidation process of the lipids and nutrients for the optimal survival of these microbes. [ 4 ]
The discovery of Nitrososphaera capable of ammonia oxidation indicated that both archaea and bacteria were capable of ammonia oxidation . [ 10 ] Ammonia-oxidizing archaea have been comparable to ammonia-oxidizing bacteria . [ 2 ] It was not until recent discovery and analysis, scientists believed that only ammonia-oxidizing bacteria were capable of oxidizing ammonia within the soils. However, ammonia-oxidizing archaea and ammonia-oxidizing bacteria work together in the nitrogen cycle. Ammonia-oxidizing archaea, including Nitrososphaera, are abundant in warm and humid soils, along with ammonia-oxidizing bacteria. Both microbes play a significant role in the nitrification of soils. [ 1 ] [ 2 ]
Nitrososphaera utilize ammonia from the environment to generate ATP by oxidizing ammonia (NH 3 ) into nitrite (NO 2 − ). [ 11 ] Ammonia oxidation leads to the disaggregation of other chemical compounds, providing important nutrients for plant survival. [ 1 ] One of the chemical compounds that forms from nitrogen cycling is nitrous oxide (N 2 O), a greenhouse gas . [ 4 ] [ 6 ] Nitrous oxide has a 216 times higher radiative efficiency than CO 2 . [ 12 ] These ammonia-oxidizing archaea are a key component in soils, which emit more than 65% of the Earth's atmospheric nitrous oxide concentrations. [ 13 ] | https://en.wikipedia.org/wiki/Nitrososphaera |
Nitrospinota is a bacterial phylum. Despite only few described species, members of this phylum are major nitrite-oxidizing bacteria in surface waters in oceans. By oxidation of nitrite to nitrate they are important in the process of nitrification in marine environments. [ 3 ]
Although the genus Nitrospina is an aerobic bacterium, it was shown to oxidize nitrite also in oxygen minimum zone of the ocean. Depletion of oxygen in such zones leads to preference of anaerobic processes such as denitrification and nitrogen loss through anammox . Nitrospina thus outweigh nitrogen loss by nitrification also in these oxygen depleted zones. [ 4 ] [ 5 ]
Among the cultivated isolates within the genus Nitrospina are Nitrospina gracilis [ 6 ] [ 3 ] and Nitrospina watsonii . [ 7 ] Further genomes were resolved by culture-independent metagenome binning . [ 5 ] The two Nitrospina species are, however, distantly related to environmentally abundant uncultured Nitrospinota. [ 8 ] The two other strains were cultivated in 2020 each in the binary culture with alphaproteobacterial heterotroph . They are called " Candidatus Nitrohelix vancouverensis " and " Candidatus Nitronauta litoralis ". " Nitrohelix vancouverensis " is closely related to uncultivated environmentally abundant Nitrospinota clades 1 and 2. [ 8 ]
" Ca. Nitrohelix vancouverensis "
" Ca. Nitromaritima "
" Ca. Nitronauta litoralis "
N. gracilis
" N. watsonii "
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) [ 12 ] and National Center for Biotechnology Information (NCBI) [ 13 ] | https://en.wikipedia.org/wiki/Nitrospinota |
Nitrostarch is a secondary explosive [ 1 ] similar to nitrocellulose . Much like starch , it is made up of two components, nitrated amylose and nitrated amylopectin . Nitrated amylopectin generally has a greater solubility than amylose; however, it is less stable than nitrated amylose. [ 2 ]
The solubility, detonation velocity, and impact sensitivity depend heavily on the level of nitration. [ 2 ]
Nitrostarch is made by dissolving starch in red fuming nitric acid . It is then precipitated by adding the solution to concentrated sulfuric acid . [ 2 ]
Nitrostarch can be stabilized by refluxing it in ethanol to drive off the left over nitric acid. [ 2 ]
Nitrostarch was first discovered by French chemist and pharmacist Henri Braconnot . [ 3 ]
After stabilizers (such as ammonium oxalate ) were devised in the early 1900s to prolong its shelf life, it was started to be used as an industrial explosive. [ 4 ]
During World War I , it was used as a filler in hand grenades . [ 5 ]
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitrostarch |
Nitrosyl- O -hydroxide (molecular formula H O O N ) is an isomer of nitrous acid , which has been experimentally observed in the gas phase. [ 2 ] HOON contains the longest oxygen-oxygen bond thus far observed in any known molecule, measured to be 1.9149 angstroms. There had been speculation about the existence of this molecule, and ab initio calculations have suggested that it might have a stable chemically bonded structure. [ 3 ]
The HOON structure was generated by the McCarthy group in a pulsed supersonic expansion of a gaseous mixture of nitric oxide and water vapor diluted with neon . The molecule was detected using Fourier transform microwave spectroscopy. The equilibrium structure of nitrosyl- O -hydroxide in the gas-phase was determined to be a planar structure, adopting a trans conformation. The structure shown below is a semi-empirical structure derived from a combination of experimental data and theoretically derived vibration-rotation constants.
Early theoretical work had suggested the HOON structure should be extremely unstable, decomposing with no significant activation barrier into hydroxyl radical and nitric oxide : [ 4 ] | https://en.wikipedia.org/wiki/Nitrosyl-O-hydroxide |
Nitrotriazolone ( NTO ) is a heterocyclic semicarbazide -derived high explosive first identified in 1905, but research into its explosive properties was not conducted until the 1980s. [ 2 ] NTO is currently being used by the US Army in munitions, specifically Insensitive munitions replacing those made with legacy explosives. [ 3 ]
Nitrotriazolone is getting progressively adopted in novel explosive formulations, such as IMX-101 , a new, safer alternative to TNT specially devised in 2010 by BAE Systems , where it is combined with 2,4-dinitroanisole (DNAN) and nitroguanidine . As such, NTO is found in the vast majority of IMX formulations. The Picatinny Arsenal has also adopted the implementation of NTO and DNAN in many of their likewise newly developed insensitive explosive mixtures, which share many of the same applications of the IMXs. [ 4 ]
Nitrotriazolone shows keto–enol tautomerism through proton transfer reactions. The keto form shows significantly different stability to heat, friction, and impact. [ 5 ]
Nitrotriazolone can form either a mono or dihydrate. [ 5 ]
NTO was first made in 1905 [ 6 ] in a two step process. Semicarbazide hydrochloride is condensed with formic acid to produce 1,2,4-triazol-3-one, which is nitrated with nitric acid to form nitrotriazolone. [ 7 ] [ 5 ]
In vivo studies showed the nitrotriazolone is absorbed through the skin and gastrointestinal tract . In the kidneys , NTO is broken down into 5-amino-1,2,4-triazol-3-one, which undergoes oxidative denitrification and forms urazoles and nitrites in rats. [ 8 ]
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitrotriazolone |
Nitrourea is a strong high explosive compound [ 1 ] synthesized by the nitration of urea or by way of a dehydration reaction of urea nitrate with sulfuric acid at 0 degrees. [ 2 ]
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitrourea |
Nitrous oxide (dinitrogen oxide or dinitrogen monoxide), commonly known as laughing gas , nitrous , or factitious air , among others, [ 4 ] is a chemical compound , an oxide of nitrogen with the formula N 2 O . At room temperature, it is a colourless non-flammable gas , and has a slightly sweet scent and taste. [ 4 ] At elevated temperatures, nitrous oxide is a powerful oxidiser similar to molecular oxygen. [ 4 ]
Nitrous oxide has significant medical uses , especially in surgery and dentistry , for its anaesthetic and pain-reducing effects, [ 5 ] and it is on the World Health Organization's List of Essential Medicines . [ 6 ] Its colloquial name, "laughing gas", coined by Humphry Davy , describes the euphoric effects upon inhaling it, which cause it to be used as a recreational drug inducing a brief " high ". [ 5 ] [ 7 ] When abused chronically, it may cause neurological damage through inactivation of vitamin B 12 . It is also used as an oxidiser in rocket propellants and motor racing fuels, and as a frothing gas for whipped cream.
Nitrous oxide is also an atmospheric pollutant , with a concentration of 333 parts per billion (ppb) in 2020, increasing at 1 ppb annually. [ 8 ] [ 9 ] It is a major scavenger of stratospheric ozone , with an impact comparable to that of CFCs . [ 10 ] About 40% of human-caused emissions are from agriculture , [ 11 ] [ 12 ] as nitrogen fertilisers are digested into nitrous oxide by soil micro-organisms. [ 13 ] As the third most important greenhouse gas , nitrous oxide substantially contributes to global warming . [ 14 ] [ 15 ] Reduction of emissions is an important goal in the politics of climate change . [ 16 ]
The gas was first synthesised in 1772 by English natural philosopher and chemist Joseph Priestley who called it dephlogisticated nitrous air (see phlogiston theory ) [ 17 ] or inflammable nitrous air . [ 18 ] Priestley published his discovery in the book Experiments and Observations on Different Kinds of Air (1775) , where he described how to produce the preparation of "nitrous air diminished", by heating iron filings dampened with nitric acid . [ 19 ]
The first important use of nitrous oxide was made possible by Thomas Beddoes and James Watt , who worked together to publish the book Considerations on the Medical Use and on the Production of Factitious Airs (1794) . This book was important for two reasons. First, James Watt had invented a novel machine to produce " factitious airs " (including nitrous oxide) and a novel "breathing apparatus" to inhale the gas. Second, the book also presented the new medical theories by Thomas Beddoes, that tuberculosis and other lung diseases could be treated by inhalation of "Factitious Airs". [ 20 ]
The machine to produce "Factitious Airs" had three parts: a furnace to burn the needed material, a vessel with water where the produced gas passed through in a spiral pipe (for impurities to be "washed off"), and finally the gas cylinder with a gasometer where the gas produced, "air", could be tapped into portable air bags (made of airtight oily silk). The breathing apparatus consisted of one of the portable air bags connected with a tube to a mouthpiece. With this new equipment being engineered and produced by 1794, the way was paved for clinical trials , [ clarification needed ] which began in 1798 when Thomas Beddoes established the " Pneumatic Institution for Relieving Diseases by Medical Airs" in Hotwells ( Bristol ). In the basement of the building, a large-scale machine was producing the gases under the supervision of a young Humphry Davy, who was encouraged to experiment with new gases for patients to inhale. [ 20 ] The first important work of Davy was examination of the nitrous oxide, and the publication of his results in the book: Researches, Chemical and Philosophical (1800) . In that publication, Davy notes the analgesic effect of nitrous oxide at page 465 and its potential to be used for surgical operations at page 556. [ 21 ] Davy coined the name "laughing gas" for nitrous oxide. [ 22 ]
Despite Davy's discovery that inhalation of nitrous oxide could relieve a conscious person from pain, another 44 years elapsed before doctors attempted to use it for anaesthesia . The use of nitrous oxide as a recreational drug at "laughing gas parties", primarily arranged for the British upper class , became an immediate success beginning in 1799. While the effects of the gas generally make the user appear stuporous, dreamy and sedated, some people also "get the giggles" in a state of euphoria, and frequently erupt in laughter. [ 23 ]
One of the earliest commercial producers in the U.S. was George Poe , cousin of the poet Edgar Allan Poe , who also was the first to liquefy the gas. [ 24 ]
The first time nitrous oxide was used as an anaesthetic drug in the treatment of a patient was when dentist Horace Wells , with assistance by Gardner Quincy Colton and John Mankey Riggs , demonstrated insensitivity to pain from a dental extraction on 11 December 1844. [ 25 ] In the following weeks, Wells treated the first 12 to 15 patients with nitrous oxide in Hartford, Connecticut , and, according to his own record, only failed in two cases. [ 26 ] In spite of these convincing results having been reported by Wells to the medical society in Boston in December 1844, this new method was not immediately adopted by other dentists. The reason for this was most likely that Wells, in January 1845 at his first public demonstration to the medical faculty in Boston, had been partly unsuccessful, leaving his colleagues doubtful regarding its efficacy and safety. [ 27 ] The method did not come into general use until 1863, when Gardner Quincy Colton successfully started to use it in all his "Colton Dental Association" clinics, that he had just established in New Haven and New York City . [ 20 ] Over the following three years, Colton and his associates successfully administered nitrous oxide to more than 25,000 patients. [ 28 ] Today, nitrous oxide is used in dentistry as an anxiolytic , as an adjunct to local anaesthetic .
Nitrous oxide was not found to be a strong enough anaesthetic for use in major surgery in hospital settings, however. Instead, diethyl ether , being a stronger and more potent anaesthetic, was demonstrated and accepted for use in October 1846, along with chloroform in 1847. [ 20 ] When Joseph Thomas Clover invented the "gas-ether inhaler" in 1876, however, it became a common practice at hospitals to initiate all anaesthetic treatments with a mild flow of nitrous oxide, and then gradually increase the anaesthesia with the stronger ether or chloroform. Clover's gas-ether inhaler was designed to supply the patient with nitrous oxide and ether at the same time, with the exact mixture being controlled by the operator of the device. It remained in use by many hospitals until the 1930s. [ 28 ] Although hospitals today use a more advanced anaesthetic machine , these machines still use the same principle launched with Clover's gas-ether inhaler, to initiate the anaesthesia with nitrous oxide, before the administration of a more powerful anaesthetic.
Colton's popularisation of nitrous oxide led to its adoption by a number of less than reputable quacksalvers , who touted it as a cure for consumption , scrofula , catarrh and other diseases of the blood, throat and lungs. Nitrous oxide treatment was administered and licensed as a patent medicine by the likes of C. L. Blood and Jerome Harris in Boston and Charles E. Barney of Chicago. [ 29 ] [ 30 ]
Nitrous oxide is a colourless gas with a faint, sweet odour.
Nitrous oxide supports combustion by releasing the dipolar bonded oxygen radical, and can thus relight a glowing splint .
N 2 O is inert at room temperature and has few reactions. At elevated temperatures, its reactivity increases. For example, nitrous oxide reacts with NaNH 2 at 187 °C (369 °F) to give NaN 3 :
This reaction is the route adopted by the commercial chemical industry to produce azide salts, which are used as detonators. [ 31 ]
The pharmacological mechanism of action of inhaled N 2 O is not fully known. However, it has been shown to directly modulate a broad range of ligand-gated ion channels , which likely plays a major role. It moderately blocks NMDAR and β 2 -subunit -containing nACh channels , weakly inhibits AMPA , kainate , GABA C and 5-HT 3 receptors , and slightly potentiates GABA A and glycine receptors . [ 32 ] [ 33 ] It also has been shown to activate two-pore-domain K + channels . [ 34 ] While N 2 O affects several ion channels, its anaesthetic, hallucinogenic and euphoriant effects are likely caused mainly via inhibition of NMDA receptor-mediated currents. [ 32 ] [ 35 ] In addition to its effects on ion channels, N 2 O may act similarly to nitric oxide (NO) in the central nervous system. [ 35 ] Nitrous oxide is 30 to 40 times more soluble than nitrogen.
The effects of inhaling sub-anaesthetic doses of nitrous oxide may vary unpredictably with settings and individual differences; [ 36 ] [ 37 ] however, Jay (2008) [ 38 ] suggests that it reliably induces the following states and sensations:
A minority of users also experience uncontrolled vocalisations and muscular spasms. These effects generally disappear minutes after removal of the nitrous oxide source. [ 38 ]
In behavioural tests of anxiety , a low dose of N 2 O is an effective anxiolytic . This anti-anxiety effect is associated with enhanced activity of GABA A receptors, as it is partially reversed by benzodiazepine receptor antagonists . Mirroring this, animals that have developed tolerance to the anxiolytic effects of benzodiazepines are partially tolerant to N 2 O . [ 39 ] Indeed, in humans given 30% N 2 O , benzodiazepine receptor antagonists reduced the subjective reports of feeling "high", but did not alter psychomotor performance. [ 40 ] [ 41 ]
The analgesic effects of N 2 O are linked to the interaction between the endogenous opioid system and the descending noradrenergic system. When animals are given morphine chronically, they develop tolerance to its pain-killing effects, and this also renders the animals tolerant to the analgesic effects of N 2 O . [ 42 ] Administration of antibodies that bind and block the activity of some endogenous opioids (not β-endorphin ) also block the antinociceptive effects of N 2 O . [ 43 ] Drugs that inhibit the breakdown of endogenous opioids also potentiate the antinociceptive effects of N 2 O . [ 43 ] Several experiments have shown that opioid receptor antagonists applied directly to the brain block the antinociceptive effects of N 2 O , but these drugs have no effect when injected into the spinal cord .
Apart from an indirect action, nitrous oxide, like morphine [ 44 ] also interacts directly with the endogenous opioid system by binding at opioid receptor binding sites. [ 45 ] [ 46 ]
Conversely, α 2 -adrenoceptor antagonists block the pain-reducing effects of N 2 O when given directly to the spinal cord, but not when applied directly to the brain. [ 47 ] Indeed, α 2B -adrenoceptor knockout mice or animals depleted in norepinephrine are nearly completely resistant to the antinociceptive effects of N 2 O . [ 48 ] Apparently N 2 O -induced release of endogenous opioids causes disinhibition of brainstem noradrenergic neurons, which release norepinephrine into the spinal cord and inhibit pain signalling. [ 49 ] Exactly how N 2 O causes the release of endogenous opioid peptides remains uncertain.
Various methods of producing nitrous oxide are used. [ 50 ]
Nitrous oxide is prepared on an industrial scale by carefully heating ammonium nitrate [ 50 ] at about 250 °C, which decomposes into nitrous oxide and water vapour. [ 51 ]
The addition of various phosphate salts favours formation of a purer gas at slightly lower temperatures. This reaction may be difficult to control, resulting in detonation . [ 52 ]
The decomposition of ammonium nitrate is also a common laboratory method for preparing the gas. Equivalently, it can be obtained by heating a mixture of sodium nitrate and ammonium sulfate : [ 53 ]
Another method involves the reaction of urea, nitric acid and sulfuric acid: [ 54 ]
Direct oxidation of ammonia with a manganese dioxide - bismuth oxide catalyst has been reported: [ 55 ] cf. Ostwald process .
Hydroxylammonium chloride reacts with sodium nitrite to give nitrous oxide. If the nitrite is added to the hydroxylamine solution, the only remaining by-product is salt water. If the hydroxylamine solution is added to the nitrite solution (nitrite is in excess), however, then toxic higher oxides of nitrogen also are formed:
Treating HNO 3 with SnCl 2 and HCl also has been demonstrated:
Hyponitrous acid decomposes to N 2 O and water with a half-life of 16 days at 25 °C at pH 1–3. [ 56 ]
Nitrous oxide is a minor component of Earth's atmosphere and is an active part of the planetary nitrogen cycle . Based on analysis of air samples gathered from sites around the world, its concentration surpassed 330 ppb in 2017. [ 8 ] The growth rate of about 1 ppb per year has also accelerated during recent decades. [ 9 ] Nitrous oxide's atmospheric abundance has grown more than 20% from a base level of about 270 ppb in 1750. [ 58 ] Important atmospheric properties of N 2 O are summarized in the following table:
In 2022 the IPCC reported that: "The human perturbation of the natural nitrogen cycle through the use of synthetic fertilizers and manure, as well as nitrogen deposition resulting from land-based agriculture and fossil fuel burning has been the largest driver of the increase in atmospheric N2O of 31.0 ± 0.5 ppb (10%) between 1980 and 2019." [ 61 ]
17.0 (12.2 to 23.5) million tonnes total annual average nitrogen in N 2 O was emitted in 2007–2016. [ 61 ] About 40% of N 2 O emissions are from humans and the rest are part of the natural nitrogen cycle . [ 62 ] The N 2 O emitted each year by humans has a greenhouse effect equivalent to about 3 billion tonnes of carbon dioxide: for comparison humans emitted 37 billion tonnes of actual carbon dioxide in 2019, and methane equivalent to 9 billion tonnes of carbon dioxide. [ 63 ]
Most of the N 2 O emitted into the atmosphere, from natural and anthropogenic sources, is produced by microorganisms such as denitrifying bacteria and fungi in soils and oceans. [ 64 ] Soils under natural vegetation are an important source of nitrous oxide, accounting for 60% of all naturally produced emissions. Other natural sources include the oceans (35%) and atmospheric chemical reactions (5%). [ 65 ] Wetlands can also be emitters of nitrous oxide . [ 66 ] [ 67 ] Emissions from thawing permafrost may be significant, but as of 2022 this is not certain. [ 61 ]
The main components of anthropogenic emissions are fertilised agricultural soils and livestock manure (42%), runoff and leaching of fertilisers (25%), biomass burning (10%), fossil fuel combustion and industrial processes (10%), biological degradation of other nitrogen-containing atmospheric emissions (9%) and human sewage (5%). [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] Agriculture enhances nitrous oxide production through soil cultivation, the use of nitrogen fertilisers and animal waste handling. [ 73 ] These activities stimulate naturally occurring bacteria to produce more nitrous oxide. Nitrous oxide emissions from soil can be challenging to measure as they vary markedly over time and space, [ 74 ] and the majority of a year's emissions may occur when conditions are favorable during "hot moments" [ 75 ] [ 76 ] and/or at favorable locations known as "hotspots". [ 77 ]
Among industrial emissions, the production of nitric acid and adipic acid are the largest sources of nitrous oxide emissions. The adipic acid emissions specifically arise from the degradation of the nitrolic acid intermediate derived from the nitration of cyclohexanone . [ 68 ] [ 78 ] [ 79 ]
Microbial processes that generate nitrous oxide may be classified as nitrification and denitrification . Specifically, they include:
These processes are affected by soil chemical and physical properties such as the availability of mineral nitrogen and organic matter , acidity and soil type, as well as climate-related factors such as soil temperature and water content.
The emission of the gas to the atmosphere is limited greatly by its consumption inside the cells, by a process catalysed by the enzyme nitrous oxide reductase . [ 80 ]
Nitrous oxide may be used as an oxidiser in a rocket motor. Compared to other oxidisers, it is much less toxic and more stable at room temperature, making it easier to store and safer to carry on a flight. Its high density and low storage pressure (when maintained at low temperatures) make it highly competitive with stored high-pressure gas systems. [ 81 ]
In a 1914 patent, American rocket pioneer Robert Goddard suggested nitrous oxide and gasoline as possible propellants for a liquid-fuelled rocket. [ 82 ] Nitrous oxide has been the oxidiser of choice in several hybrid rocket designs (using solid fuel with a liquid or gaseous oxidiser). The combination of nitrous oxide with hydroxyl-terminated polybutadiene fuel has been used by SpaceShipOne and others. It also is notably used in amateur and high power rocketry with various plastics as the fuel.
Nitrous oxide may also be used as a monopropellant . In the presence of a heated catalyst at a temperature of 577 °C (1,071 °F), N 2 O decomposes exothermically into nitrogen and oxygen. [ 83 ] Because of the large heat release, the catalytic action rapidly becomes secondary, as thermal autodecomposition becomes dominant. In a vacuum thruster, this may provide a monopropellant specific impulse ( I sp ) up to 180 s. While noticeably less than the I sp available from hydrazine thrusters (monopropellant, or bipropellant with dinitrogen tetroxide ), the decreased toxicity makes nitrous oxide a worthwhile option.
The ignition of nitrous oxide depends critically on pressure. It deflagrates at approximately 600 °C (1,112 °F) at a pressure of 309 psi (21 atmospheres). [ 84 ] At 600 psi , the required ignition energy is only 6 joules, whereas at 130 psi a 2,500-joule ignition energy input is insufficient. [ 85 ] [ 86 ]
In vehicle racing , nitrous oxide (often called " nitrous ") increases engine power by providing more oxygen during combustion, thus allowing the engine to burn more fuel. It is an oxidising agent roughly equivalent to hydrogen peroxide, and much stronger than molecular oxygen. Nitrous oxide is not flammable at low pressure/temperature, but at about 300 °C (572 °F), its breakdown delivers more oxygen than atmospheric air. It often is mixed with another fuel that is easier to deflagrate.
Nitrous oxide is stored as a compressed liquid. In an engine intake manifold , the evaporation and expansion of the liquid causes a large drop in intake charge temperature, resulting in a denser charge and allowing more air/fuel mixture to enter the cylinder. Sometimes nitrous oxide is injected into (or prior to) the intake manifold, whereas other systems directly inject it just before the cylinder (direct port injection).
The technique was used during World War II by Luftwaffe aircraft with the GM-1 system to boost the power output of aircraft engines . Originally meant to provide the Luftwaffe standard aircraft with superior high-altitude performance, technological considerations limited its use to extremely high altitudes. Accordingly, it was only used by specialised planes such as high-altitude reconnaissance aircraft , high-speed bombers and high-altitude interceptor aircraft . It sometimes could be found on Luftwaffe aircraft also fitted with another engine-boost system, MW 50 , a form of water injection for aviation engines that used methanol for its boost capabilities.
One of the major problems of nitrous oxide oxidant in a reciprocating engine is excessive power: if the mechanical structure of the engine is not properly reinforced, it may be severely damaged or destroyed. It is important with nitrous oxide augmentation of petrol engines to maintain proper and evenly spread operating temperatures and fuel levels to prevent pre-ignition (also called detonation or spark knock). [ 87 ] However, most problems associated with nitrous oxide come not from excessive power but from excessive pressure, since the gas builds up a much denser charge in the cylinder. The increased pressure and temperature can melt, crack, or warp the piston, valve, and cylinder head.
Automotive-grade liquid nitrous oxide differs slightly from medical-grade. A small amount of sulfur dioxide ( SO 2 ) is added to prevent substance abuse. [ 88 ]
The gas is approved for use as a food additive ( E number : E942), specifically as an aerosol spray propellant . It is commonly used in aerosol whipped cream canisters and cooking sprays .
The gas is extremely soluble in fatty compounds. In pressurised aerosol whipped cream, it is dissolved in the fatty cream until it leaves the can, when it becomes gaseous and thus creates foam. This produces whipped cream four times the volume of the liquid, whereas whipping air into cream only produces twice the volume. Unlike air, nitrous oxide inhibits rancidification of the butterfat. Carbon dioxide cannot be used for whipped cream because it is acidic in water, which would curdle the cream and give it a seltzer-like "sparkle".
Extra-frothed whipped cream produced with nitrous oxide is unstable, and will return to liquid within half an hour to one hour. [ 89 ] Thus, it is not suitable for decorating food that will not be served immediately.
In December 2016, there was a shortage of aerosol whipped cream in the United States, with canned whipped cream use at its peak during the Christmas and holiday season , due to an explosion at the Air Liquide nitrous oxide facility in Florida in late August. The company prioritized the remaining supply of nitrous oxide to medical customers rather than to food manufacturing. [ 90 ]
Also, cooking spray, made from various oils with lecithin emulsifier , may use nitrous oxide propellant , or alternatively food-grade alcohol or propane .
Nitrous oxide has been used in dentistry and surgery, as an anaesthetic and analgesic, since 1844. [ 20 ] In the early days, the gas was administered through simple inhalers consisting of a breathing bag made of rubber cloth. [ 28 ] Today, the gas is administered in hospitals by means of an automated relative analgesia machine , with an anaesthetic vaporiser and a medical ventilator , that delivers a precisely dosed and breath-actuated flow of nitrous oxide mixed with oxygen in a 2:1 ratio.
Nitrous oxide is a weak general anaesthetic , and so is generally not used alone in general anaesthesia, but used as a carrier gas (mixed with oxygen) for more powerful general anaesthetic drugs such as sevoflurane or desflurane . It has a minimum alveolar concentration of 105% and a blood/gas partition coefficient of 0.46. The use of nitrous oxide in anaesthesia can increase the risk of postoperative nausea and vomiting. [ 91 ] [ 92 ] [ 93 ]
Dentists use a simpler machine which only delivers an N 2 O / O 2 mixture for the patient to inhale while conscious but must still be a recognised purpose designed dedicated relative analgesic flowmeter with a minimum 30% of oxygen at all times and a maximum upper limit of 70% nitrous oxide. The patient is kept conscious throughout the procedure, and retains adequate mental faculties to respond to questions and instructions from the dentist. [ 94 ]
Inhalation of nitrous oxide is used frequently to relieve pain associated with childbirth , trauma , oral surgery and acute coronary syndrome (including heart attacks). Its use during labour has been shown to be a safe and effective aid for birthing women. [ 95 ] Its use for acute coronary syndrome is of unknown benefit. [ 96 ]
In Canada and the UK, Entonox and Nitronox are used commonly by ambulance crews (including unregistered practitioners) as rapid and highly effective analgesic gas.
Fifty percent nitrous oxide can be considered for use by trained non-professional first aid responders in prehospital settings, given the relative ease and safety of administering 50% nitrous oxide as an analgesic. The rapid reversibility of its effect would also prevent it from precluding diagnosis. [ 97 ]
Recreational inhalation of nitrous oxide , to induce euphoria and slight hallucinations , began with the British upper class in 1799 in gatherings known as "laughing gas parties". [ 98 ]
From the 19th century, the widespread availability of the gas for medical and culinary purposes allowed for recreational use to greatly expand globally. In the UK as of 2014, nitrous oxide was estimated to be used by almost half a million young people at nightspots, festivals and parties. [ 99 ]
Widespread recreational use of the drug throughout the UK was featured in the 2017 Vice documentary Inside The Laughing Gas Black Market , in which journalist Matt Shea met with dealers of the drug who stole it from hospitals. [ 100 ]
A significant issue cited in London's press is the effect of nitrous oxide canister littering, which is highly visible and causes significant complaints from communities. [ 101 ]
Prior to 8 November 2023 in the UK, nitrous oxide was subject to the Psychoactive Substances Act 2016, making it illegal to produce, supply, import or export nitrous oxide for recreational use. The updated law prohibited possession of nitrous oxide, classifying it as a Class C drug under the Misuse of Drugs Act 1971. [ 102 ]
While nitrous oxide is understood by most recreational users to give a "safe high", many are unaware that excessive consumption may cause neurological harm which, if left untreated, can cause permanent neurological damage. [ 103 ] In Australia, recreation use became a public health concern following a rise in reports of neurotoxicity and emergency room admissions. In the state of South Australia, legislation was passed in 2020 to restrict canister sales. [ 104 ]
In 2024, under the street name "Galaxy Gas", nitrous oxide has exploded in popularity among young people for recreational use. Most of the popularity has been fostered through TikTok . [ 105 ]
Nitrous oxide is a significant occupational hazard for surgeons, dentists and nurses. Because the gas is minimally metabolised in humans (with a rate of 0.004%), it retains its potency when exhaled into the room by the patient, and can intoxicate the clinic staff if the room is poorly ventilated, with potential chronic exposure. A continuous-flow fresh-air ventilation system or N 2 O scavenger system may be needed to prevent waste-gas buildup. [ citation needed ] The National Institute for Occupational Safety and Health recommends that workers' exposure to nitrous oxide should be controlled during the administration of anaesthetic gas in medical, dental and veterinary operators. [ 106 ] It set a recommended exposure limit (REL) of 25 ppm (46 mg/m 3 ) to escaped anaesthetic. [ 107 ]
Exposure to nitrous oxide causes short-term impairment of cognition, audiovisual acuity, and manual dexterity, as well as spatial and temporal disorientation, [ 108 ] putting the user at risk of accidental injury. [ 38 ]
Nitrous oxide is neurotoxic , and medium or long-term habitual consumption of significant quantities can cause neurological harm with the potential for permanent damage if left untreated. [ 104 ] [ 103 ] It is believed that, like other NMDA receptor antagonists , N 2 O produces Olney's lesions in rodents upon prolonged (several hour) exposure. [ 109 ] [ 110 ] [ 111 ] [ 112 ] However, because it is normally expelled from the body rapidly, it is less likely to be neurotoxic than other NMDAR antagonists. [ 113 ] In rodents, short-term exposure results in only mild injury that is rapidly reversible, and neuronal death occurs only after constant and sustained exposure. [ 109 ] Nitrous oxide may also cause neurotoxicity after extended exposure because of hypoxia . This is especially true of non-medical formulations such as whipped-cream chargers ("whippits" or "nangs"), [ 114 ] which contain no oxygen gas. [ 115 ]
In reports to poison control centers, heavy users (≥400 g or ≥200 L of N 2 O gas in one session) or frequent users (regular, i.e., daily or weekly) have developed signs of peripheral neuropathy : ataxia (gait abnormalities) or paresthesia (perception of sensations such as tingling, numbness, or prickling, mostly in the extremities). Such early signs of neurological damage indicate chronic toxicity . [ 116 ]
Nitrous oxide might have therapeutic use in treating stroke . In a rodent model, nitrous oxide at 75% by volume reduced ischemia-induced neuronal death induced by occlusion of the middle cerebral artery, and decreased NMDA-induced Ca 2+ influx in neuronal cell cultures, a cause of excitotoxicity . [ 113 ]
Occupational exposure to ambient nitrous oxide has been associated with DNA damage, due to interruptions in DNA synthesis. [ 117 ] This correlation is dose-dependent [ 118 ] [ 119 ] and does not appear to extend to casual recreational use; however, further research is needed to confirm the level of exposure needed to cause damage.
Inhalation of pure nitrous oxide causes oxygen deprivation, resulting in low blood pressure, fainting, and even heart attacks. This can occur if the user inhales large quantities continuously, as with a strap-on mask connected to a gas canister or other inhalation system, or prolonged breath-holding. [ citation needed ]
Long-term exposure to nitrous oxide may cause vitamin B 12 deficiency . This can cause serious neurotoxicity if the user has preexisting vitamin B 12 deficiency. [ 120 ] It inactivates the cobalamin form of vitamin B 12 by oxidation. Symptoms of vitamin B 12 deficiency, including sensory neuropathy , myelopathy and encephalopathy , may occur within days or weeks of exposure to nitrous oxide anaesthesia in people with subclinical vitamin B 12 deficiency. Symptoms are treated with high doses of vitamin B 12 , but recovery can be slow and incomplete. [ 121 ] People with normal vitamin B 12 levels have stores to make the effects of nitrous oxide insignificant, unless exposure is repeated and prolonged (nitrous oxide abuse). Vitamin B 12 levels should be checked in people with risk factors for vitamin B 12 deficiency prior to using nitrous oxide anaesthesia. [ 122 ]
Several experimental studies in rats indicate that chronic exposure of pregnant females to nitrous oxide may have adverse effects on the developing fetus. [ 123 ] [ 124 ] [ 125 ]
At room temperature (20 °C [68 °F]) the saturated vapour pressure is 50.525 bar, rising up to 72.45 bar at 36.4 °C (97.5 °F)—the critical temperature . The pressure curve is thus unusually sensitive to temperature. [ 126 ] As with many strong oxidisers, contamination of parts with fuels have been implicated in rocketry accidents, where small quantities of nitrous/fuel mixtures explode due to " water hammer "-like effects (sometimes called "dieseling"—heating due to adiabatic compression of gases can reach decomposition temperatures). [ 127 ] Some common building materials such as stainless steel and aluminium can act as fuels with strong oxidisers such as nitrous oxide, as can contaminants that may ignite due to adiabatic compression. [ 128 ] There also have been incidents where nitrous oxide decomposition in plumbing has led to the explosion of large tanks. [ 84 ]
Global accounting of N 2 O sources and sinks over the decade ending 2016 indicates that about 40% of the average 17 TgN/yr ( teragrams , or million metric tons, of nitrogen per year) of emissions originated from human activity, and shows that emissions growth chiefly came from expanding agriculture . [ 11 ] [ 12 ]
Nitrous oxide has significant global warming potential as a greenhouse gas . On a per-molecule basis, considered over a 100-year period, nitrous oxide has 265 times the atmospheric heat-trapping ability of carbon dioxide ( CO 2 ). [ 60 ] However, because of its low concentration (less than 1/1,000 of that of CO 2 ), its contribution to the greenhouse effect is less than one third that of carbon dioxide, and also less than methane . [ 129 ] On the other hand, since about 40% of the N 2 O entering the atmosphere is the result of human activity, [ 68 ] control of nitrous oxide is part of efforts to curb greenhouse gas emissions. [ 130 ]
Most human caused nitrous oxide released into the atmosphere is a greenhouse gas emission from agriculture , when farmers add nitrogen-based fertilizers onto the fields, and through the breakdown of animal manure. Reduction of emissions can be a hot topic in the politics of climate change . [ 131 ]
Nitrous oxide is also released as a by-product of burning fossil fuel, though the amount released depends on which fuel was used. It is also emitted through the manufacture of nitric acid , which is used in the synthesis of nitrogen fertilizers. The production of adipic acid, a precursor to nylon and other synthetic clothing fibres, also releases nitrous oxide. [ 132 ]
A rise in atmospheric nitrous oxide concentrations has been implicated as a possible contributor to the extremely intense global warming during the Cenomanian-Turonian boundary event . [ 133 ]
Nitrous oxide has also been implicated in thinning the ozone layer . A 2009 study suggested that N 2 O emission was the single most important ozone-depleting emission and it was expected to remain the largest throughout the 21st century. [ 10 ] [ 134 ]
In India transfer of nitrous oxide from bulk cylinders to smaller, more transportable E-type, 1,590-litre-capacity tanks [ 135 ] is legal when intended for medical anaesthesia.
The New Zealand Ministry of Health has warned that nitrous oxide is a prescription medicine whose sale or possession without a prescription is an offense under the Medicines Act. [ 136 ] This would seemingly prohibit all non-medicinal uses of nitrous oxide, although it is implied that only recreational use will be targeted.
In August 2015, the Council of the London Borough of Lambeth ( UK ) banned the use of the drug for recreational purposes, making offenders liable to an on-the-spot fine of up to £1,000. [ 137 ] In September 2023, the UK Government announced that nitrous oxide would be made illegal by the end of the year, with possession potentially carrying up to a two-year prison sentence or an unlimited fine. [ 138 ]
Possession of nitrous oxide is legal under United States federal law and is not subject to DEA purview. [ 139 ] It is, however, regulated by the Food and Drug Administration under the Food Drug and Cosmetics Act; prosecution is possible under its "misbranding" clauses, prohibiting the sale or distribution of nitrous oxide for the purpose of human consumption without a proper medical license. Many states have laws regulating the possession, sale and distribution of nitrous oxide. Such laws usually ban distribution to minors or limit the amount that may be sold without special license. [ citation needed ] For example, in California, possession for recreational use is prohibited and qualifies as a misdemeanor. [ 140 ] | https://en.wikipedia.org/wiki/Nitrous_oxide |
Hydrogen oxonitrate(I) Hyponitrous acid monomer Nitronous oxide
Nitroxyl (common name) or azanone (IUPAC name) [ 2 ] is the chemical compound HNO. It is well known in the gas phase. [ 3 ] [ 4 ] Nitroxyl can be formed as a short-lived intermediate in solution. Its conjugate base, NO − , the nitroxide anion, is the reduced form of nitric oxide (NO) and is isoelectronic with dioxygen . The bond dissociation energy of H−NO is 49.5 kcal/mol (207 kJ/mol), which is unusually weak for a bond to the hydrogen atom.
Nitroxyl is produced from the reagents Angeli's salt (Na 2 N 2 O 3 ) and Piloty's acid (PhSO 2 NHOH). [ 5 ] Other notable studies on the production of HNO exploit cycloadducts of acyl nitroso species, which are known to decompose via hydrolysis to HNO and acyl acid. Upon photolysis these compounds release the acyl nitroso species which then further decompose. [ 6 ] HNO is generated via organic oxidation of cyclohexanone oxime with lead tetraacetate to form 1-nitrosocyclohexyl acetate: [ 7 ]
This compound can be hydrolyzed under basic conditions in a phosphate buffer to HNO, acetic acid , and cyclohexanone .
Dichloramine reacts with the hydroxide ion , which is always present in water, to yield nitroxyl and the chloride ion . [ 8 ]
Alkali metals react with nitric oxide to give salts of the form MNO (M = metal) . [ 9 ] However, generation of the (unstable) free acid from these salts is not entirely straightforward (see below).
Nitroxyl is a weak acid , with p K a of about 11, the conjugate base being the triplet state of NO − , sometimes called nitroxide . Nitroxyl itself, however, is a singlet ground state. Thus, deprotonation of nitroxyl uniquely involves the forbidden spin crossing from the singlet state starting material to triplet state product:
Due to the spin-forbidden nature of deprotonation, proton abstraction is many orders of magnitude slower ( k = 4.9 × 10 4 M −1 s −1 for deprotonation by OH − ) than what one would expect for a heteroatom proton-transfer process (processes that are so fast that they are sometimes diffusion-controlled ).
The K a of starting from or ending with the electronic excited states has also been determined. When process of deprotonating singlet state HNO to obtain singlet state NO − has a p K a is about 23. On the other hand, when deprotonating triplet HNO to obtain triplet NO − , the p K a is about −1.8. [ 10 ] [ 11 ]
Nitroxyl rapidly decomposes by a bimolecular pathway to nitrous oxide ( k at 298 K = 8 × 10 6 M s ): [ 10 ]
The reaction proceeds via dimerization to hyponitrous acid , H 2 N 2 O 2 , which subsequently undergoes dehydration. Therefore, HNO is generally prepared in situ as described above.
Nitroxyl is very reactive towards nucleophiles, including thiols . The initial adduct rearranges to a sulfinamide : [ 11 ]
In biological samples, nitroxyl can be detected using fluorescent sensors, many of which are based on the reduction of copper(II) to copper(I) with concomitant increase in fluorescence. [ 12 ]
Nitroxyl donors, known as nitroso compounds, show potential in the treatment of heart failure and ongoing research is focused on finding new molecules for this task. [ citation needed ] | https://en.wikipedia.org/wiki/Nitroxyl |
Nitryl is the nitrogen dioxide (NO 2 ) moiety when it occurs in a larger compound as a univalent fragment. Examples include nitryl fluoride (NO 2 F) and nitryl chloride (NO 2 Cl). [ 1 ]
Like nitrogen dioxide, the nitryl moiety contains a nitrogen atom with two bonds to the two oxygen atoms, and a third bond shared equally between the nitrogen and the two oxygen atoms. The nitrogen-centred radical is then free to form a bond with another univalent fragment (X) to produce an N−X bond, where X can be F, Cl, OH, etc.
In organic nomenclature, the nitryl moiety is known as the nitro group . For instance, nitryl benzene is normally called nitrobenzene (PhNO 2 ). [ 2 ]
This article about chemical compounds is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nitryl |
In Indian astronomy, yoga (also called nityayoga ) is a period of time, of varying lengths, during which the sum of the nirayana longitudes of the Sun and the Moon increases by an amount of 13 degrees 20 minutes (or, equivalently, 800 minutes). [ 1 ] While considering the sum, when the sum is 360 degrees or more, then 360 degrees is subtracted from the sum to make the sum an angle between 0 degree and 360 minutes. Consider a moment T 1 when the sum of the longitudes of the Sun and the Moon is 0 degree and let T 2 be the next immediate moment when the sum of the longitudes of the Sun and the Moon is 13 degree 20 minutes. The duration of time between the moments T 1 and T 2 is the first yoga . Similarly, let the next immediate moment when the sum of the longitudes of the Sun and Moon is 26 degrees 40 minutes. The duration of time between the moments T 2 and T 3 is the second yoga . The third, fourth and higher yoga -s are defined in a similar way. Since 27 X 13 degrees 20 minutes = 360 degrees, at the end-moment of the 27th yoga , the sum of the nirayana longitudes of the Sun and Moon would be 0 degree. The numbering of the yoga -s then starts afresh from that point. It appears that the astronomical yoga -s are in no way related to any astronomical phenomena. [ 2 ] S. B. Dikshit in his Bhāratīya Jyotiṣ Śāstra observes: "It is not known what planetary position in the sky is indicated by yoga , and it is useful only in astrology." [ 3 ]
In Indian astrology, the term yoga has been used to indicate luni-solar distances and planetary situations, associations, and combinations. When one planet or house is related to another by placement, aspect or conjunction in a particular way then it is said that the planets and houses are in a particular yoga .
In the traditional Indian calendars or almanacs, that is in Pañcāṅg -s, Yoga or Nityayoga is one of the five elements or organs or limbs that constitute the Pañcāṅg -s, the "five organs" in the literary meaning of the term Pañcāṅg . The other four elements are Nakṣatra , Tithi , Vāra and Karaṇa .
The names of the 27 nitayoga are:
Nityayoga or yoga has a prominent place in traditional Indian almanac known as Pañcāṅg . It is one of the five elements that constitutes the pañcāṅg -s, that is, the five elements that define a Pañcāṅg . However, the yoga -s entered the Pañcāṅg calculations only several centuries after the other four elements became parts of the Indian alamanac. Pancha-siddhantika , a text on astronomy composed around 505 CE by Varāhamihira gives the methods of calculating nakṣatra -s and tithi -s but does not give any method for calculating yoga -s. Similarly, Bṛhat Saṃhitā , a work on astrology also by Varāhamihira has long discussions on the effects of nakṣatra -s but is silent on the effects of yoga -s. These facts indicate that the concept of yoga -s did not exist at the time of Varāhamihira. The currently available Brāhmasphuṭasiddhānta composed by Brahmagupta in c.628 CE has just one verse containing a reference to yoga , but all internal evidences point to the possibility of the verse being a much later interpolation. Khaṇḍakhādyaka , another treatise composed by Brahmagupta in c.665 CE has a couplet of verses referring to yoga . These verses have also been determined as later interpolations. All these point to the fact that the concept of yoga in astronomy arose post Brahmagupta. Lalla (c. 720–790 CE) in his Śiṣyadhīvṛddhidatantra mentions the yoga -s in detail. Surya Siddhanta , the founding text of the Saura-pakṣa in Indian astronomy, of undetermined authorship believed to have been composed in the 4th-5th century CE but again believed to have undergone a substantial revision in around 800 CE presents the list of all the 27 yoga -s as they are used in modern Pañcāṅg -s and also methods of calculating the yoga -s. All these evidences suggest that the concept of yoga arose sometime around 700 CE and became an integral part of the Pañcāṅg -s only after around 700 CE. [ 3 ]
The word vyātīpāta occurs in two verses in Brāhmasphuṭasiddhānta , but from the context of the occurrence of the word, it is clear that it is not referring to the vyātīpāta that occurs as the 17th yoga in the list of 27 yoga -s. It is referring to one of two mahāpāta -s which occur when the Sun and the Moon are in parallel declination and this happens when the sum of the longitudes of the Sun and Moon is 180°. There are two moments in every lunar month when this happens. One of them is called the vyātīpāta and other vaidhṛti . In order to find these mahāpāta -s one has find the sum of the longitudes of the Sun and the Moon. This must have led to the idea of finding yoga -s by finding the sum of longitudes just as tithi is determined by the difference of longitudes. [ 3 ]
There is another theory regarding the origin of the yoga concept in Indian astronomy. According this view, the astronomical yoga came into being in attempts to predict the phenomena of eclipses. [ 4 ]
Robert Sewell's The Indian Calendar contains a section which explains in meticulous detail how the Yoga at sunrise on a day specified by a date in the Common Era can be determined. The procedure also explains how to find how much time has elapsed at the moment of sunrise since the beginning of the Yoga . [ 5 ]
The lengths of the various yoga -s varies from yoga to yoga . The following table gives the mean length, the greatest length and the least length of the yoga -s. [ 6 ] It follows that the total length of a yoga -cycle consisting of 27 yoga -s is 26 days 10 hours 12 minutes 47 seconds.
There is a different system of yoga -s in use in India. This system consists of 28 yoga -s, in contrast to 27 yoga -s in the system already explained, and the names and the rules for the determination of these yoga -s are different from the ones given earlier. In this system, the succession of the yoga -s depends the day of the week. Hence it has absolutely no connection whatsoever with any astronomical phenomena as the week has no definable relation to the motion of the moon or the sun. This system of yoga -s do not find any mention in Sūrya-sddhānta . In some Hindu calendars yoga -s of this system are also given for each day of the month. But these yogas are only of astrological interest.
The names as well as the rules for the determination of the 28 yoga -s as given in Śrīpati 's Jyotiṡa Ratnamāla are given below. [ 7 ] [ 8 ]
The rule assumes a cycle of 28 nakṣatra -s which includes the 28th nakṣatra , namely, Abhijit . The 28 yoga -s are assigned as follows: [ 7 ] | https://en.wikipedia.org/wiki/Nityayoga |
In number theory , Niven's constant , named after Ivan Niven , is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H (1) = 1 and H ( n ) = the largest exponent appearing in the unique prime factorization of a natural number n > 1, then Niven's constant is given by
where ζ is the Riemann zeta function . [ 1 ]
In the same paper Niven also proved that
where h (1) = 1, h ( n ) = the smallest exponent appearing in the unique prime factorization of each natural number n > 1, o is little o notation , and the constant c is given by
and consequently that
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Niven's_constant |
In mathematics , Niven's theorem , named after Ivan Niven , states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: [ 1 ]
In radians , one would require that 0° ≤ x ≤ π /2 , that x / π be rational, and that sin( x ) be rational. The conclusion is then that the only such values are sin(0) = 0 , sin( π /6) = 1/2 , and sin( π /2) = 1 .
The theorem appears as Corollary 3.12 in Niven's book on irrational numbers . [ 2 ]
The theorem extends to the other trigonometric functions as well. [ 2 ] For rational values of θ , the only rational values of the sine or cosine are 0 , ±1/2 , and ±1 ; the only rational values of the secant or cosecant are ±1 and ±2 ; and the only rational values of the tangent or cotangent are 0 and ±1 . [ 3 ]
Niven's proof of his theorem appears in his book Irrational Numbers . Earlier, the theorem had been proven by D. H. Lehmer and J. M. H. Olmstead. [ 2 ] In his 1933 paper, Lehmer proved the theorem for the cosine by proving a more general result. Namely, Lehmer showed that for relatively prime integers k and n with n > 2 , the number 2 cos(2 πk / n ) is an algebraic number of degree φ ( n )/2 , where φ denotes Euler's totient function . Because rational numbers have degree 1, we must have n ≤ 2 or φ ( n ) = 2 and therefore the only possibilities are n = 1,2,3,4,6 . Next, he proved a corresponding result for the sine using the trigonometric identity sin( θ ) = cos( θ − π /2) . [ 4 ] In 1956, Niven extended Lehmer's result to the other trigonometric functions. [ 2 ] Other mathematicians have given new proofs in subsequent years. [ 3 ] | https://en.wikipedia.org/wiki/Niven's_theorem |
In nonmonotonic reasoning , the Nixon diamond is a scenario in which default assumptions lead to mutually inconsistent conclusions. The scenario is:
Since Nixon is a Quaker, one could assume that he is a pacifist; since he is Republican, however, one could also assume he is not a pacifist. The problem is how a formal logic of nonmonotonic reasoning should deal with such cases. Two approaches can be adopted:
The credulous approach can allow proving both something and its contrary. For this reason, the sceptical approach is often preferred. Another solution to this problem is to attach priorities to default assumptions; for example, the fact that “usually, Republicans are not pacifist” can be assumed more likely than “usually, Quakers are pacifist”, leading to the conclusion that Nixon is not pacifist.
The name "diamond" comes from the fact that such a scenario, when expressed as a belief network , forms a diamond shape . This example is mentioned for the first time by Reiter and Criscuolo in a slightly different form where the person that is both a Republican and a Quaker is a John instead of Richard Nixon. | https://en.wikipedia.org/wiki/Nixon_diamond |
Niyazi Serdar Sarıçiftçi (born 1961 in Konya , Turkey ) is a Turkish-Austrian physicist. He is professor for physical chemistry at the Johannes Kepler University (JKU) Linz . There, he leads the Institut for Physical Chemistry as well as the Institut for Organic Solar Cells (LIOS).
Niyazi Serdar Sarıçiftçi graduated from the Austrian St. George's College in Istanbul. He also studied classical piano at the Music Conservatory in Istanbul (1970–1980).
Then he began studying physics at the University of Vienna (1980–1989). After obtaining the doctorate (1989), he conducted research on the 2nd Physical Institute of the University of Stuttgart , Germany (1989–1992). In 1992 he received the academic teaching license (venia docendi) by the Central Interuniversitary Commission (YÖK) in Ankara , Turkey. He then went to the Institute for Polymers & Organic Solids at the University of California , Santa Barbara, California , United States, where he worked for four years and, together with Alan J. Heeger ( Nobel Prize in Chemistry , 2000) discovered and investigated the polymeric organic solar cells has (1992–1996). In April 1996, he accepted the appointment as Chair of Physical Chemistry at the Johannes Kepler University Linz.
Since 1996 he gives lectures as a full professor at the JKU and is the head of the Institute for Physical Chemistry. In 2000 he was appointed founding director of the Linz Institute for Organic Solar Cells (LIOS) at JKU. Between 2003 and 2009 he was elected to the City Council of the City of Linz (SPÖ Group). Furthermore, Sarıçiftçi is a founding member of the Linz Circle. He is also a member of various associations and societies: Fellow of the Royal Society of Chemistry (FRSC), American Chemical Society (ACS), Materials Research Society (MRS), Austrian Physical Society (ÖPG), Austrian Chemical Society (GÖCH) and Fellow of SPIE . 2014, he was elected a corresponding member of the Austrian Academy of Sciences (AAS).
Sarıçiftçi specializes in the field of organic semiconductors and their applications. In particular, he has worked in the field of organic solar cells. Chemical energy storage of solar energy by means of CO 2 recycling recycling is in its research increasingly important.
Sarıçiftçi has published more than 500 scientific publications in scientific journals. He is one of the most cited scientists in his field. In a global ranking of the best materials scientists Sarıçiftçi was classified as 14th. [ 1 ] | https://en.wikipedia.org/wiki/Niyazi_Serdar_Sarıçiftçi |
In paleoecology and ecological forecasting , a no-analog [ 1 ] community or climate is one that is compositionally different from a (typically modern) baseline for measurement. [ 2 ] [ 3 ] Alternative naming conventions to describe no-analog communities and climates may include novel, emerging, mosaic, disharmonious and intermingled. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
Modern climates, communities and ecosystems are often studied in an attempt to understand no-analogs that have happened in the past and those that may occur in the future. [ 3 ] This use of a modern analog to study the past draws on the concept of uniformitarianism . Along with the use of these modern analogs, actualistic studies and taphonomy are additional tools that are used in understanding no-analogs. [ 7 ] Statistical tools are also used to identify no-analogs and their baselines, often through the use of dissimilarity analyses or analog matching [ 8 ] Study of no-analog fossil remains are often carefully evaluated as to rule out mixing of fossils in an assemblage due to erosion, animal activity or other processes. [ 3 ]
Conditions that are considered no-analog climates are those that have no modern analog, such as the climate during the last glaciation . [ 3 ] Glacial climates varied from current climates in seasonality and temperature, having an overall more steady climate without as many extreme temperatures as today's climate. [ 6 ]
Climates with no modern analog may be used to infer species range shifts, biodiversity changes, ecosystem arrangements and help in understanding species fundamental niche space. [ 10 ] Past climates are often studied to understand how changes in a species' fundamental niche may lead to the formation of no analog communities. [ 3 ] Seasonality and temperatures that are outside the climates at present provide opportunity for no-analog communities to arise, as is seen in the late Holocene plant communities. [ 3 ] Evidence of deglacial temperature controls having significant effects on the formation of no-analog communities in the midwestern United States provides example of how intertwined climate and species assemblage are when studying no-analogs. [ 11 ]
No-analog communities are defined by the existence of extant species in groupings that are not currently seen in modern biomes , or populations that have history of species assemblages that are no longer seen in the modern world. [ 3 ] Formation of no-analog communities can be due to multiple factors, including climate conditions, environmental changes, human action, disease or species interactions. [ 3 ] [ 4 ] [ 6 ] Migrations of species causes displacement and colonization into areas that may have been outside of what was known to be their fundamental niche, such as northern species moving south and mountain fauna being removed entirely or isolated to the peaks. [ 12 ] [ 6 ]
Quaternary fossil records from the Pleistocene present a developed history of no-analogs. Records of plants , mammals , coleopterans , mollusks and foraminifera with no modern analogs are abundant in the fossil record. [ 3 ] In the last glacial maximum, species aggregations were different from previous time periods due to a unique set of climate conditions. [ 6 ] The development of no-analog plant and mammal communities is often interconnected, and also tied to occurrence of no-analog climates. [ 3 ] [ 13 ] Changes in plant community compositions may also lead to no-analog conditions with addition of biotic pressures such as competition and disease, or enhanced fire regimes.
The North American pollen record provides examples of detailed no-analog plant assemblages from the late quaternary. Pollen assemblages that contain no modern analog are present from many late glacial and early Holocene records, and extend from 14,000 to 12,000 years ago. [ 7 ] [ 13 ] Pollen is a commonly used proxy in studying plant no-analogs. These assemblages are marked by high abundances of taxa such as Betula , the co-occurrence of now allopatric species such as Fraxinus and Picea , and the low abundance of taxa that are now modernly abundant, such as Pinus . [ 3 ] These associations are evident across Alaska, eastern North America, Europe and the southwestern US. [ 3 ]
The environmental conditions during the Pleistocene offered a climate that was more productive for plant species than climate conditions that exist today. [ 13 ] This is evident through extensive records of high abundances of broadleaved trees Ulmus , Ostrya , Fraxinus and Quercus mixed with boreal conifers such as Picea and Larix during the late Holocene . [ 13 ] [ 12 ] New evidence states that deglacial temperatures are now hypothesized to be a major contributor to the formation of no-analog plant communities in the Midwestern US. [ 11 ] Christensen bog fauna during this time period also represent a significant example of no-analog assemblages from the Pleistocene. [ 6 ] It is also possible that these plant assemblages formed due to influence from megafaunal extinctions during the late quaternary, and there is also evidence that shows connection between novel plant assemblages and new fire regimes . [ 13 ]
Pleistocene mammal assemblages had high levels of diversity and abundance of megafauna . During the late quaternary extinction there was a loss of many megafauna. [ 14 ] This extinction has led to the creation of a no-analog for modern ecosystems, which are lacking high diversity or abundance of large herbivores.
These no-analog mammal assemblages and the loss of megafauna coincides with no-analog plant community rise. The shifts in these groups has been hypothesized to have direct relationship to one another, with the possibility of a release from herbivory pressures causing the bloom in novel plant assemblages during the late quaternary. [ 13 ]
Modern ecologists looking to study future climates and ecosystem assemblages use modern analogs to understand how species distributions will change and how to infer management of ecosystems with climate change. Along with modern analogs, studying past climates and how they've changed is being used to understand future novel climates due to climate changes. Species distribution models are currently being tested with no-analog climates to get more predictive estimates of species range shifts and biodiversity loss . [ 10 ]
Examples of modern conditions that are considered no-analogs are also present. Accelerated tree growth due to environmental conditions and pollutants that are present today provide no analog to past conditions of tree growth. [ 15 ]
The concept of emerging ecosystems originated from the discussion of the ecological and economical fate of agricultural land once it is no longer in use. Similarly to the definition of a no-analog, emerging ecosystems are considered as those that have species composition and abundances that are not seen in modern analogs. Emerging ecosystems not only encompass the understanding of ecological consequences, but also those social, economic and cultural associations. These ecosystems may provide opportunities for species to colonize new niche space. [ 5 ]
Projections of future no-analog communities based on two climate models and two species-distribution-model algorithms indicate that by 2070 over half of California could be occupied by novel assemblages of bird species, implying the potential for dramatic community reshuffling and altered patterns of species interactions [ 16 ] | https://en.wikipedia.org/wiki/No-analog_(ecology) |
The no-observed-adverse-effect level ( NOAEL ) denotes the level of exposure of an organism , found by experiment or observation , at which there is no biologically or statistically significant increase in the frequency or severity of any adverse effects of the tested protocol. In drug development, the NOAEL of a new drug is assessed in laboratory animals, such as mice , prior to initiation of human trials in order to establish a safe clinical starting dose in humans. The OECD publishes guidelines for Preclinical Safety Assessments , in order to help scientists discover the NOAEL. [ 1 ]
Some adverse effects in the exposed population when compared to its appropriate control might include alteration of morphology , functional capacity, growth , development or life span. The NOAEL is determined or proposed by qualified personnel, often a pharmacologist or a toxicologist . [ citation needed ]
The NOAEL could be defined as "the highest experimental point that is without adverse effect," meaning that under laboratory conditions, it is the level where there are no side-effects . It either does not provide the effects of drug with respect to duration and dose, or it does not address the interpretation of risk based on toxicologically relevant effects. [ 2 ]
In toxicology it is specifically the highest tested dose or concentration of a substance (i.e. a drug or chemical) or agent (e.g. radiation), at which no such adverse effect is found in exposed test organisms where higher doses or concentrations resulted in an adverse effect. [ 3 ] [ 4 ] [ 5 ]
The NOAEL level may be used in the process of establishing a dose-response relationship , [ 6 ] a fundamental step in most risk assessment methodologies. [ 5 ]
The NOAEL is also known as NOEL (no-observed-effect level) as well as NEC (no-effect concentration) and NOEC (no-observed-effect concentration). [ 7 ] [ 8 ]
The United States Environmental Protection Agency defines NOAEL as 'an exposure level at which there are no statistically or biologically significant increases in the frequency or severity of adverse effects between the exposed population and its appropriate control; some effects may be produced at this level, but they are not considered as adverse, or as precursors to adverse effects. [ 5 ] In an experiment with several NOAELs, the regulatory focus is primarily on the highest one, leading to the common usage of the term NOAEL as the highest exposure without adverse effects.' [ 9 ]
This toxicology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/No-observed-adverse-effect_level |
In fluid dynamics , the no-slip condition is a boundary condition which enforces that at a solid boundary, a viscous fluid attains zero bulk velocity . This boundary condition was first proposed by Osborne Reynolds , who observed this behaviour while performing his influential pipe flow experiments. [ 1 ] The form of this boundary condition is an example of a Dirichlet boundary condition .
In the majority of fluid flows relevant to fluids engineering, the no-slip condition is generally utilised at solid boundaries. [ 2 ] This condition often fails for systems which exhibit non-Newtonian behaviour . Fluids which this condition fails includes common food-stuffs which contain a high fat content, such as mayonnaise or melted cheese. [ 3 ]
The no-slip condition is an empirical assumption that has been useful in modelling many macroscopic experiments. It was one of three alternatives that were the subject of contention in the 19th century, with the other two being the stagnant-layer (a thin layer of stationary fluid on which the rest of the fluid flows) and the partial slip (a finite relative velocity between solid and fluid) boundary conditions. However, by the start of the 20th century it became generally accepted that slip, if it did exist, was too small to be measured. The stagnant layer was deemed too thin, and the partial slip was considered to have negligible effect on the macroscopic scale. [ 4 ]
While not derived from first principles, two possible mechanisms have been offered to explain the no-slip behaviour, with one or the other being dominant under different conditions. [ 5 ] The first contends that the surface roughness is responsible for bringing the fluid to rest through viscous dissipation past the surface irregularities. The second is related to the attraction of fluid molecules to the surface. Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion . At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (adhesive forces) is greater than that between the fluid particles (cohesive forces). This force imbalance causes the fluid velocity to be zero adjacent to the solid surface, with the velocity approaching that of the stream as distance from the surface increases.
When a fluid is at rest, its molecules move constantly with a random velocity. When the fluid begins to flow, an average flow velocity, sometimes called the bulk velocity, is added to the random motion. At the boundary between the fluid and a solid surface, the attraction between the fluid molecules and the surface atoms is strong enough to slow the bulk velocity to zero. Consequently, the bulk velocity of the fluid decreases from its value away from the wall to zero at the wall. [ 6 ]
As the no-slip condition was an empirical observation, there are physical scenarios in which it fails. For sufficiently rarefied flows , including flows of high altitude atmospheric gases [ 7 ] and for microscale flows, the no-slip condition is inaccurate. [ 8 ] For such examples, this change is driven by an increasing Knudsen number , which implies increasing rarefaction, and gradual failure of the continuum approximation . The first-order expression, which is often used to model fluid slip, is expressed as (also known as the Navier slip boundary condition) u − u Wall = C ℓ ∂ u ∂ n , {\displaystyle u-u_{\text{Wall}}=C\ell {\frac {\partial u}{\partial n}},} where n {\displaystyle n} is the coordinate normal to the wall, ℓ {\displaystyle \ell } is the mean free path and C {\displaystyle C} is some constant known as the slip coefficient, which is approximately of order 1. Alternatively, one may introduce β = C ℓ {\displaystyle \beta =C\ell } as the slip length. [ 9 ] Some highly hydrophobic surfaces, such as carbon nanotubes with added radicals, have also been observed to have a nonzero but nanoscale slip length. [ 10 ]
While the no-slip condition is used almost universally in modeling of viscous flows, it is sometimes neglected in favor of the 'no-penetration condition' (where the fluid velocity normal to the wall is set to the wall velocity in this direction, but the fluid velocity parallel to the wall is unrestricted) in elementary analyses of inviscid flow , where the effect of boundary layers is neglected.
The no-slip condition poses a problem in viscous flow theory at contact lines : places where an interface between two fluids meets a solid boundary. Here, the no-slip boundary condition implies that the position of the contact line does not move, which is not observed in reality. Analysis of a moving contact line with the no slip condition results in infinite stresses that can't be integrated over. The rate of movement of the contact line is believed to be dependent on the angle the contact line makes with the solid boundary, but the mechanism behind this is not yet fully understood. | https://en.wikipedia.org/wiki/No-slip_condition |
In quantum information theory , the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits (or even an infinite number of such bits); nor can such bits be used to reconstruct the original state, thus "teleporting" it by merely moving classical bits around. Put another way, it states that the unit of quantum information , the qubit , cannot be exactly, precisely converted into classical information bits. This should not be confused with quantum teleportation , which does allow a quantum state to be destroyed in one location, and an exact replica to be created at a different location.
In crude terms, the no-teleportation theorem stems from the Heisenberg uncertainty principle and the EPR paradox : although a qubit | ψ ⟩ {\displaystyle |\psi \rangle } can be imagined to be a specific direction on the Bloch sphere , that direction cannot be measured precisely, for the general case | ψ ⟩ {\displaystyle |\psi \rangle } ; if it could, the results of that measurement would be describable with words, i.e. classical information.
The no-teleportation theorem is implied by the no-cloning theorem : if it were possible to convert a qubit into classical bits, then a qubit would be easy to copy (since classical bits are trivially copyable).
The term quantum information refers to information stored in the state of a quantum system. Two quantum states ρ 1 and ρ 2 are identical if the measurement results of any physical observable have the same expectation value for ρ 1 and ρ 2 . Thus measurement can be viewed as an information channel with quantum input and classical output, that is, performing measurement on a quantum system transforms quantum information into classical information. On the other hand, preparing a quantum state takes classical information to quantum information.
In general, a quantum state is described by a density matrix . Suppose one has a quantum system in some mixed state ρ . Prepare an ensemble, of the same system, as follows:
The no-teleportation theorem states that the result will be different from ρ , irrespective of how the preparation procedure is related to measurement outcome. A quantum state cannot be determined via a single measurement. In other words, if a quantum channel measurement is followed by preparation, it cannot be the identity channel. Once converted to classical information, quantum information cannot be recovered.
In contrast, perfect transmission is possible if one wishes to convert classical information to quantum information then back to classical information. For classical bits, this can be done by encoding them in orthogonal quantum states, which can always be distinguished.
Among other no-go theorems in quantum information are:
With the aid of shared entanglement , quantum states can be teleported, see | https://en.wikipedia.org/wiki/No-teleportation_theorem |
In financial economics , the no-trade theorem states that if
then even though some traders may possess private information, none of them will be in a position to profit from it. The assumptions are deliberately unrealistic, but the theorem may nonetheless be pertinent to debates over inside information .
It was demonstrated by Paul Milgrom and Nancy Stokey in their 1982 paper, "Information, trade and common knowledge". [ 1 ]
The idea behind the proof of the no-trade theorem is that if there is common knowledge about the structure of a market, then any bid or offer (i.e. attempt to initiate a trade) will reveal the bidder's private knowledge and will be incorporated into market prices even before anyone accepts the bid or offer, so no profit will result. Another way to put it is: all the traders in the market are rational, and thus they know that all the prices are rational/efficient; therefore, anyone who makes an offer to them must have special knowledge, else why would they be making the offer? Accepting the offer would make them a loser . All the traders will reason the same way, and thus will not accept any offers.
This economics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/No-trade_theorem |
In mathematics , the no-wandering-domain theorem is a result on dynamical systems , proven by Dennis Sullivan in 1985.
The theorem states that a rational map f : Ĉ → Ĉ with deg( f ) ≥ 2 does not have a wandering domain , where Ĉ denotes the Riemann sphere . More precisely, for every component U in the Fatou set of f , the sequence
will eventually become periodic. Here, f n denotes the n -fold iteration of f , that is,
The theorem does not hold for arbitrary maps; for example, the transcendental map f ( z ) = z + 2 π sin ( z ) {\displaystyle f(z)=z+2\pi \sin(z)} has wandering domains. However, the result can be generalized to many situations where the functions naturally belong to a finite-dimensional parameter space, most notably to transcendental entire and meromorphic functions with a finite number of singular values.
This chaos theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/No-wandering-domain_theorem |
A no-win situation or lose–lose situation is an outcome of a negotiation , conflict or challenging circumstance in which all parties are worse off. It is an alternative to a win–win or outcome in which one party wins . Arbitration or mediation may be used to avoid no-win outcomes and find more satisfactory results. [ citation needed ]
In game theory , a "no-win" situation is a circumstance in which no player benefits from any outcome, hence ultimately losing the match. This may be because of any or all of the following:
A variation of a no-win situation found in video gaming is a softlock , a scenario where the game remains playable (as opposed to a 'hard lock', which typically involves the game crashing or otherwise becoming unplayable), but where further progress is rendered impossible. [ 1 ] Softlocks may occur due to an unnoticed design flaw or oversight during game development , or they may occur deliberately as a consequence of glitches, sequence breaking , or other intentional actions carried out by players to render the game impossible to win. [ 2 ]
Carl von Clausewitz 's advice never to launch a war that one has not already won characterizes war as a no-win situation. A similar example is the Pyrrhic victory in which a military victory is so costly that the winning side actually ends up worse off than before it started. Looking at the victory as a part of a larger situation, the situation could either be no-win, or more of a win for the other side than the one that won the "victory", or victory at such cost that the gains are outweighed by the cost and are no longer a source of joy.
For example, the "victorious" side may have accomplished their objective, which may have been worthless; it may also lose a strategic advantage in manpower or positioning. For example, the British Empire was one of the victorious powers of the Second World War but was so weakened by the war that it could no longer maintain its status as a great power in a world that became dominated by the United States and the Soviet Union .
A related concept is sometimes described as "winning the battle but losing the war", where a lesser objective is won, but the greater objective beyond it is not well-pursued and is lost.
In the past in Europe , women accused of being witches were sometimes bound and then thrown or dunked in water to test their innocence. A witch would float (by calling upon the devil to save her from drowning), and then be executed, but a non-witch would drown (proving her innocence but causing her death). [ 3 ]
A different form of a no-win situation is where a person or government will look bad no matter what they or it does. Sometimes such is described as a situation destined for failure, expressed by the phrase "damned if you do, damned if you don't." [ 4 ]
A no-win situation is a dilemma where no matter what one does, the outcome will be negative. [ 5 ] | https://en.wikipedia.org/wiki/No-win_situation |
The No.1 -class patrol boat ( 第一号型哨戒特務艇, , Dai Ichi Gō -gata Shōkai-Tokumutei ) was a class of auxiliary patrol boat (picket boat) of the Imperial Japanese Navy (IJN), serving during World War II . 280 vessels were planned under the Maru Sen Programme (Ship # 2121–2400), however, only 27 vessels were completed before the end of the war. | https://en.wikipedia.org/wiki/No.1-class_patrol_boat_(1945) |
No7 is a beauty brand of anti-ageing creams , skincare and cosmetic products developed by Boots in the United Kingdom . [ 1 ] The brand No7 was launched by Boots in 1935 [ 2 ] as a selection of eleven skincare products and was expanded in 1937 with some colour cosmetics. [ 3 ] [ 4 ] Since its introduction, the brand has undergone eight redesigns. [ 3 ] In 2007, Boots expanded the range to incorporate body products, foundation, creams and men's skincare. [ 3 ]
In 2021, Walgreens Boots Alliance (WBA), the company owning the brand, launched No7 as a separate company. [ 5 ] [ 6 ]
No7's products and services are available in over 20,000 stores and online, in 29 markets worldwide. [ 7 ]
This product article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/No._7_(brand) |
In mathematical folklore , the " no free lunch " ( NFL ) theorem (sometimes pluralized) of David Wolpert and William Macready , alludes to the saying " no such thing as a free lunch ", that is, there are no easy shortcuts to success. It appeared in the 1997 "No Free Lunch Theorems for Optimization". [ 1 ] Wolpert had previously derived no free lunch theorems for machine learning (statistical inference). [ 2 ]
In 2005, Wolpert and Macready themselves indicated that the first theorem in their paper "state[s] that any two optimization algorithms are equivalent when their performance is averaged across all possible problems". [ 3 ]
The "no free lunch" (NFL) theorem is an easily stated and easily understood consequence of theorems Wolpert and Macready actually prove. It is objectively weaker than the proven theorems, and thus does not encapsulate them. Various investigators have extended the work of Wolpert and Macready substantively. In terms of how the NFL theorem is used in the context of the research area, the no free lunch in search and optimization is a field that is dedicated for purposes of mathematically analyzing data for statistical identity, particularly search [ 4 ] and optimization. [ 1 ]
While some scholars argue that NFL conveys important insight, others argue that NFL is of little relevance to machine learning research. [ 5 ] [ 6 ] [ 7 ]
Posit a toy universe that exists for exactly two days and on each day contains exactly one object: a square or a triangle. The universe has exactly four possible histories:
Any prediction strategy that succeeds for history #2, by predicting a square on day 2 if there is a square on day 1, will fail on history #1, and vice versa. If all histories are equally likely, then any prediction strategy will score the same, with the same accuracy rate of 0.5. [ 8 ]
Wolpert and Macready give two NFL theorems that are closely related to the folkloric theorem. In their paper, they state:
We have dubbed the associated results NFL theorems because they demonstrate that if an algorithm performs well on a certain class of problems then it necessarily pays for that with degraded performance on the set of all remaining problems. [ 1 ]
The first theorem hypothesizes objective functions that do not change while optimization is in progress, and the second hypothesizes objective functions that may change. [ 1 ]
Theorem — For any algorithms a 1 and a 2 , at iteration step m ∑ f P ( d m y ∣ f , m , a 1 ) = ∑ f P ( d m y ∣ f , m , a 2 ) , {\displaystyle \sum _{f}P(d_{m}^{y}\mid f,m,a_{1})=\sum _{f}P(d_{m}^{y}\mid f,m,a_{2}),} where d m y {\displaystyle d_{m}^{y}} denotes the ordered set of size m {\displaystyle m} of the cost values y {\displaystyle y} associated to input values x ∈ X {\displaystyle x\in X} , f : X → Y {\displaystyle f:X\rightarrow Y} is the function being optimized and P ( d m y ∣ f , m , a ) {\displaystyle P(d_{m}^{y}\mid f,m,a)} is the conditional probability of obtaining a given sequence of cost values from algorithm a {\displaystyle a} run m {\displaystyle m} times on function f {\displaystyle f} .
The theorem can be equivalently formulated as follows:
Theorem — Given a finite set V {\displaystyle V} and a finite set S {\displaystyle S} of real numbers , assume that f : V → S {\displaystyle f:V\to S} is chosen at random according to uniform distribution on the set S V {\displaystyle S^{V\!}} of all possible functions from V {\displaystyle V} to S {\displaystyle S} . For the problem of optimizing f {\displaystyle f} over the set V {\displaystyle V} , then no algorithm performs better than blind search.
Here, blind search means that at each step of the algorithm, the element v ∈ V {\displaystyle v\in V} is chosen at random with uniform probability distribution from the elements of V {\displaystyle V} that have not been chosen previously.
In essence, this says that when all functions f are equally likely, the probability of observing an arbitrary sequence of m values in the course of optimization does not depend upon the algorithm. In the analytic framework of Wolpert and Macready, performance is a function of the sequence of observed values (and not e.g. of wall-clock time), so it follows easily that all algorithms have identically distributed performance when objective functions are drawn uniformly at random, and also that all algorithms have identical mean performance. But identical mean performance of all algorithms does not imply Theorem 1, and thus the folkloric theorem is not equivalent to the original theorem.
Theorem 2 establishes a similar, but "more subtle", NFL result for time-varying objective functions. [ 1 ]
The NFL theorems were explicitly not motivated by the question of what can be inferred (in the case of NFL for machine learning) or found (in the case of NFL for search) when the "environment is uniform random". Rather uniform randomness was used as a tool, to compare the number of environments for which algorithm A outperforms algorithm B to the number of environments for which B outperforms A. NFL tells us that (appropriately weighted) [ clarification needed ] there are just as many environments in both of those sets.
This is true for many definitions of what precisely an "environment" is. In particular, there are just as many prior distributions (appropriately weighted) in which learning algorithm A beats B (on average) as vice versa. [ citation needed ] This statement about sets of priors is what is most important about NFL, not the fact that any two algorithms perform equally for the single, specific prior distribution that assigns equal probability to all environments.
While the NFL is important to understand the fundamental limitation for a set of problems, it does not state anything about each particular instance of a problem that can arise in practice. That is, the NFL states what is contained in its mathematical statements and it is nothing more than that. For example, it applies to the situations where the algorithm is fixed a priori and a worst-case problem for the fixed algorithm is chosen a posteriori. Therefore, if we have a "good" problem in practice or if we can choose a "good" learning algorithm for a given particular problem instance, then the NFL does not mention any limitation about this particular problem instance. Though the NFL might seem contradictory to results from other papers suggesting generalization of learning algorithms or search heuristics, it is important to understand the difference between the exact mathematical logic of the NFL and its intuitive interpretation. [ 9 ]
To illustrate one of the counter-intuitive implications of NFL, suppose we fix two supervised learning algorithms, C and D. We then sample a target function f to produce a set of input-output pairs, d . The question is how should we choose whether to train C or D on d , in order to make predictions for what output would be associated with a point lying outside of d.
It is common in almost all of science and statistics to answer this question – to choose between C and D – by running cross-validation on d with those two algorithms. In other words, to decide whether to generalize from d with either C or D , we see which of them has better out-of-sample performance when tested within d .
Since C and D are fixed, this use of cross-validation to choose between them is itself an algorithm, i.e., a way of generalizing from an arbitrary dataset. Call this algorithm A. (Arguably, A is a simplified model of the scientific method itself.)
We could also use anti -cross-validation to make our choice. In other words, we could choose between C and D based on which has worse out-of-sample performance within d . Again, since C and D are fixed, this use of anti-cross-validation is itself an algorithm. Call that algorithm B.
NFL tells us (loosely speaking) that B must beat A on just as many target functions (and associated datasets d ) as A beats B. In this very specific sense, the scientific method will lose to the "anti" scientific method just as readily as it wins. [ 10 ]
NFL only applies if the target function is chosen from a uniform distribution of all possible functions. If this is not the case, and certain target functions are more likely to be chosen than others, then A may perform better than B overall. The contribution of NFL is that it tells us that choosing an appropriate algorithm requires making assumptions about the kinds of target functions the algorithm is being used for. With no assumptions, no "meta-algorithm", such as the scientific method, performs better than random choice.
While some scholars argue that NFL conveys important insight, others argue that NFL is of little relevance to machine learning research. [ 5 ] [ 6 ] [ 7 ] If Occam's razor is correct, for example if sequences of lower Kolmogorov complexity are more probable than sequences of higher complexity, then (as is observed in real life) some algorithms, such as cross-validation, perform better on average on practical problems (when compared with random choice or with anti-cross-validation). [ 11 ]
However, there are major formal challenges in using arguments based on Kolmogorov complexity to establish properties of
the real world, since it is uncomputable, and undefined up to an arbitrary additive constant. Partly in recognition of these challenges,
it has recently been argued that there are ways to circumvent the no free lunch theorems without invoking
Turing machines, by using "meta-induction". [ 12 ] [ 13 ] Moreover, the Kolmogorov complexity of machine learning models can be upper bounded through compressions of their data labeling, and it is possible to produce non-vacuous cross-domain generalization bounds via Kolmogorov complexity. [ 7 ] | https://en.wikipedia.org/wiki/No_free_lunch_theorem |
The general prohibition sign , [ 1 ] also known informally as the no symbol , ' do not' sign , circle-backslash symbol , nay , interdictory circle , prohibited symbol , is a red circle with a 45-degree diagonal line inside the circle from upper-left to lower-right. It is typically overlaid on a pictogram to warn that an activity is not permitted, or has accompanying text to describe what is prohibited. It is a mechanism in graphical form to assert 'drawn norms', i.e. to qualify behaviour without the use of words. [ 2 ]
According to the ISO standard (and also under a UK Statutory Instrument ), the red area must take up at least 35 percent of the total area of the sign within the outer circumference of the "prohibition sign". Under the UK rules the width of a "no symbol" is 80 percent the height of the printed area.
For computer display and printing, the symbol is supported in Unicode by combining elements rather than with individual code points ( see below ).
The "prohibition" symbol is used on traffic signs , so that drivers can interpret traffic laws quickly while driving. For example:
The symbol's use is not limited to informing drivers of motorized vehicles, and is commonly used for other forms of traffic:
The symbol is used for non-traffic purposes to warn or prohibit certain activities:
It is also used on packages sent through the mail and sealed boxes of merchandise that are sold in stores. Using a graphical symbol is useful to convey important warnings regardless of language. For example:
In product documentation, the symbol may be accompanied by drawings of the product being threatened by the prohibited items: for instance, a cartoon of a floppy disk being menaced by horseshoe magnets.
It is also used on clothing, linens, and other household products to indicate the care, treatment or cleaning of the item. For example:
Some companies use the "prohibition sign" when describing the services they offer, e.g. an insect deterrent spray brand symbol showing the "prohibition sign" over a mosquito. The Ghostbusters logo is a fictional example of this, although it uses a mirror image of the symbol with the slash going from upper right down to lower left.
It can also be used as a symbol of opposition, to strike out the unwanted item, as in "no airport here!" with a No symbol superimposed on an aeroplane symbol.
The official prohibition sign design characteristics are governed by regional and international standards. The symbol's canonical definition comes from the International Organization for Standardization which published ISO 3864-1 in 2002, a revision of a standard first published in 1984. The current version was published in 2011. [ 3 ]
ISO 3864-1 sets the rules for the color, shape, and dimensions of safety signage. The regulations include the incorporation of text and pictograms, with reference to materials used, sign size, and viewing conditions. The introduction includes language on the need for using as few words as possible to convey information.
The 3864 standard defines the color and design for the prohibition symbol. The verbal definition reads "circle with diagonal bar" with a red safety color, a white contrast color, and black for the graphical symbol [ 4 ] (i.e. the pictogram).
The symbol is defined as a circle, with the circular band having a thickness of 10% of the outer diameter of the circle. The inner diagonal line has a thickness of 8% of the outer diameter of the circle (i.e. 80% of the circle's line width). The diagonal is centered in the circle and at a 45-degree angle going from upper left to lower right. It is recommended to have a white outside border that is 2.5% to 5% of the outer diameter of the circle.
The circle and line are red, the background is white, and the pictogram or descriptive text is black.
The standard defines the range of CIE x,y chromacity coordinates for the color red to be used, relative to the CIE 1931 2° standard observer. They also list equivalent colors for various common color systems such as Munsell , defining red as Munsell 7,5R 4/14.
Relative to CSS colors for the web and sRGB , and assuming a white background of #ffffff , the red color should be no lighter than #f80000 , and no darker than #a00000 , with #b00000 being a useful choice in terms of good contrast and color.
Despite the fact that the ISO standard is freely available, [ 5 ] it is not uncommon for graphic artists to improvise on the particular color and dimensions. As a result, there is a wide variation of the symbol in common use, for instance using a lower-contrast red than specified in the standard or using the same width for the diagonal line as the circle (the standard specifies the diagonal width is 80% as wide as the circle).
For example, compare (a non-conforming example) with (drawn using the ISO standard).
Circles with red borders and no slanted or diagonal line are used under the Vienna Convention on Road Signs and Signals to indicate "No entry to vehicles with the following characteristics" (often defined on a plate beneath) such as height, width, mass, or speed. The European Vienna Convention prohibits a diagonal line in the symbol for any sign other than no turning signs. An alternative use for red bordered circles is as a Mandatory Action Symbol type B. [ 6 ]
In many jurisdictions ( such as Germany ), 'no entry' is indicated by a solid red disc with white horizontal bar. See the general article on Prohibitory traffic signs .
A blue filled circle with an illustration or legend means that a lane is restricted to a particular class of users (such as buses, cyclists, pedestrians) as shown, and no other traffic may use it. In contrast, a blue filled circle without a diagonal line through it is used as a Mandatory Action Symbol , indicating that the activity represented inside the circle is mandatory and must be executed. [ 7 ]
The Unicode code point for the prohibition sign is U+1F6C7 🛇 PROHIBITED SIGN .
There is also U+20E0 ◌⃠ COMBINING ENCLOSING CIRCLE BACKSLASH , which also represents prohibition. It is a combining character , which means that it appears on top of the character immediately before it.
Example: Putting W⃠ in html will display the letter W inside the prohibition sign: W⃠ (if the user's system handles it correctly, which is not always the case).
There are also several prohibition sign emojis and related unicode characters: [ 8 ] [ 9 ]
The symbol appears in a number of different computer fonts , such as Arial Unicode MS , and in dingbat fonts such Webdings and Wingdings 2 . These are not necessarily "combining characters." In the case of Webdings and Wingdings 2, the character encoding does not match the Unicode standard, so if these fonts are not present on the user's system, the symbol may not render correctly. [ 10 ] This is particularly an issue in webpages. If the page designer wishes to use Webdings for instance, it is important to provide the font resource via the CSS @import font-face command.
There are Unicode code points for other glyphs that look very similar to the 'prohibited' symbol, but which may be available in more font repertoires:
Other glyphs exist but are incorrectly oriented, for example
All of these are spacing characters , which means that they cannot readily be used in combination with a symbol for the action to be prohibited. | https://en.wikipedia.org/wiki/No_symbol |
No value added ( NVA ) is a management term loosely related to the lean manufacturing movement as codified in the 1980s by a landmark MIT study [ 1 ] of the automobile industry , which explained lean production for the first time.
No Value Added programs can be formal or whimsical. Generally, they involved seeking input and opinion from every level of the organization about rules, processes or process elements which are said to be "no value added".
In one form, the proponent of an activity accused of being NVA must defend it, or suspend it.
In a milder form, the proponent (or process owner ) of an activity accused of being NVA is simply informed that it is seen in that light. Oddly, this milder form is often effective because in a large organization, the original reason for an activity can be long forgotten, similar to cabooses which came into use in the 1830s, [ 2 ] but eventually had no useful purpose and became NVA.
Some claim that this NVA is a jibe at Net Value Added accounting methods , which were held in low esteem by some Lean advocates, and high esteem by others. | https://en.wikipedia.org/wiki/No_value_added |
This page provides supplementary data about the noble gases , which were excluded from the main article to conserve space and preserve focus. Oganesson mostly not included due to the amount of research known about it.
Radon is available only in very small quantities, and due to its short half-life, is generally produced by a radium-226 source in secular equilibrium. [ 22 ] Oganesson is almost impossible to produce and with a very short half life, it is generally not readily available for purchase. | https://en.wikipedia.org/wiki/Noble_gas_(data_page) |
A noble metal is ordinarily regarded as a metallic element that is generally resistant to corrosion and is usually found in nature in its raw form . Gold , platinum , and the other platinum group metals ( ruthenium , rhodium , palladium , osmium , iridium ) are most often so classified. Silver , copper , and mercury are sometimes included as noble metals, but each of these usually occurs in nature combined with sulfur .
In more specialized fields of study and applications the number of elements counted as noble metals can be smaller or larger. It is sometimes used for the three metals copper , silver, and gold which have filled d-bands , while it is often used mainly for silver and gold when discussing surface-enhanced Raman spectroscopy involving metal nanoparticles . It is sometimes applied more broadly to any metallic or semimetallic element that does not react with a weak acid and give off hydrogen gas in the process. This broader set includes copper, mercury , technetium , rhenium , arsenic , antimony , bismuth , polonium , gold, the six platinum group metals , and silver.
Many of the noble metals are used in alloys for jewelry or coinage. In dentistry , silver is not always considered a noble metal because it is subject to corrosion when present in the mouth. All the metals are important heterogeneous catalysts .
While lists of noble metals can differ, they tend to cluster around gold and the six platinum group metals : ruthenium, rhodium, palladium, osmium, iridium, and platinum.
In addition to this term's function as a compound noun , there are circumstances where noble is used as an adjective for the noun metal . A galvanic series is a hierarchy of metals (or other electrically conductive materials, including composites and semimetals ) that runs from noble to active, and allows one to predict how materials will interact in the environment used to generate the series. In this sense of the word, graphite is more noble than silver and the relative nobility of many materials is highly dependent upon context, as for aluminium and stainless steel in conditions of varying pH . [ 5 ]
The term noble metal can be traced back to at least the late 14th century [ 6 ] and has slightly different meanings in different fields of study and application.
Prior to Mendeleev's publication in 1869 of the first (eventually) widely accepted periodic table, Odling published a table in 1864, in which the "noble metals" rhodium, ruthenium, palladium; and platinum, iridium, and osmium were grouped together, [ 7 ] and adjacent to silver and gold.
The noble metals are siderophiles (iron-lovers). They tend to sink into the Earth's core because they dissolve readily in iron either as solid solutions or in the molten state. Most siderophile elements have practically no affinity whatsoever for oxygen: indeed, oxides of gold are thermodynamically unstable with respect to the elements.
Copper, silver, gold, and the six platinum group metals are the only native metals that occur naturally in relatively large amounts. [ citation needed ]
Noble metals tend to be resistant to oxidation and other forms of corrosion, and this corrosion resistance is often considered to be a defining characteristic. Some exceptions are described below.
Copper is dissolved by nitric acid and aqueous potassium cyanide .
Ruthenium can be dissolved in aqua regia , a highly concentrated mixture of hydrochloric acid and nitric acid , only when in the presence of oxygen, while rhodium must be in a fine pulverized form. Palladium and silver are soluble in nitric acid , while silver's solubility in aqua regia is limited by the formation of silver chloride precipitate. [ 8 ]
Rhenium reacts with oxidizing acids , and hydrogen peroxide , and is said to be tarnished by moist air. Osmium and iridium are chemically inert in ambient conditions. [ 9 ] Platinum and gold can be dissolved in aqua regia. [ 10 ] Mercury reacts with oxidising acids. [ 9 ]
In 2010, US researchers discovered that an organic "aqua regia" in the form of a mixture of thionyl chloride SOCl 2 and the organic solvent pyridine C 5 H 5 N achieved "high dissolution rates of noble metals under mild conditions, with the added benefit of being tunable to a specific metal" for example, gold but not palladium or platinum. [ 11 ]
However, Gold can be dissolved in selenic acid (H 2 SeO 4 ).
The noble elements gold and platinum also have a comparatively high electronegativity for a metallic element, thus allowing them to exist as single-metallic anions.
For example:
Cs + Au -> CsAu ( Caesium auride , a yellow crystalline salt with the Au − ion). [ citation needed ] Platinum also exhibits similar properties with
BaPt, BaPt 2 , Cs 2 Pt (Barium and Caesium Platinides, which are reddish salts). [ 12 ] [ 13 ]
The expression noble metal is sometimes confined to copper, silver, and gold since their full d-subshells can contribute to their noble character. [ 14 ] There are also known to be significant contributions from how readily there is overlap of the d-electron states with the orbitals of other elements, particularly for gold. [ 15 ] Relativistic contributions are also important, [ 16 ] playing a role in the catalytic properties of gold. [ 17 ]
The elements to the left of gold and silver have incompletely filled d-bands, which is believed to play a role in their catalytic properties. A common explanation is the d-band filling model of Hammer and Jens Nørskov , [ 18 ] [ 19 ] where the total d-bands are considered, not just the unoccupied states.
The low-energy plasmon properties are also of some importance, particularly those of silver and gold nanoparticles for surface-enhanced Raman spectroscopy , localized surface plasmons and other plasmonic properties. [ 20 ] [ 21 ]
Standard reduction potentials in aqueous solution are also a useful way of predicting the non-aqueous chemistry of the metals involved. Thus, metals with high negative potentials, such as sodium, or potassium, will ignite in air, forming the respective oxides. These fires cannot be extinguished with water, which also react with the metals involved to give hydrogen, which is itself explosive. Noble metals, in contrast, are disinclined to react with oxygen and, for that reason (as well as their scarcity) have been valued for millennia, and used in jewellery and coins. [ 22 ]
The adjacent table lists standard reduction potential in volts; [ 23 ] electronegativity (revised Pauling); and electron affinity values (kJ/mol), for some metals and metalloids.
The simplified entries in the reaction column can be read in detail from the Pourbaix diagrams of the considered element in water. Noble metals have large positive potentials; [ 24 ] elements not in this table have a negative standard potential or are not metals.
Electronegativity is included since it is reckoned to be, "a major driver of metal nobleness and reactivity". [ 3 ]
The black tarnish commonly seen on silver arises from its sensitivity to sulphur containing gases such as hydrogen sulfide :
Rayner-Canham [ 4 ] contends that, "silver is so much more chemically-reactive and has such a different chemistry, that it should not be considered as a 'noble metal'." In dentistry , silver is not regarded as a noble metal due to its tendency to corrode in the oral environment. [ 25 ]
The relevance of the entry for water is addressed by Li et al. [ 26 ] in the context of galvanic corrosion. Such a process will only occur when:
The superheavy elements from hassium (element 108) to livermorium (116) inclusive are expected to be "partially very noble metals"; chemical investigations of hassium has established that it behaves like its lighter congener osmium, and preliminary investigations of nihonium and flerovium have suggested but not definitively established noble behavior. [ 27 ] Copernicium 's behaviour seems to partly resemble both its lighter congener mercury and the noble gas radon . [ 28 ]
As long ago as 1890, Hiorns observed as follows:
Smith, writing in 1946, continued the theme:
Such nobility is mainly associated with the relatively high electronegativity values of the noble metals, resulting in only weakly polar covalent bonding with oxygen. [ 3 ] The table lists the melting points of the oxides of the noble metals, and for some of those of the non-noble metals, for the elements in their most stable oxidation states.
All the noble metals can act as catalysts. For example, platinum is used in catalytic converters , devices which convert toxic gases produced in car engines, such as the oxides of nitrogen, into non-polluting substances. [ citation needed ]
Gold has many industrial applications; it is used as a catalyst in hydrogenation and the water gas shift reaction. [ citation needed ] | https://en.wikipedia.org/wiki/Noble_metal |
Noboru Tokita (February 20, 1923 - October 31, 2014) was a Uniroyal and later Cabot scientist known for his work on the processing of elastomers. [ 1 ]
Tokita was born in Sapporo, Japan in 1923. He met his wife Noriko while on an exchange program at Duke University. They married and decided to stay in the United States. He was a close colleague of 2009 Charles Goodyear Medal winner James White , introducing White to his future wife Yoko Masaki. [ 2 ]
Tokita completed BS degree at Tokyo University in 1948, and his Ph.D. in physics and chemistry in 1957 at the University of Hokkaido . [ 3 ]
He began his professional career in 1954 as a professor of Applied Physics at Waseda University in Tokyo. He held this position until 1960 when he came to the United States on an exchange program with Duke University . At Duke, he taught polymer rheology. In the early 1960s Tokita joined the U. S. Rubber Company in New Jersey, later Uniroyal, working there for 30 years on elastomer processing. He later joined Uniroyal Goodrich Tire Company in Akron in a research role. He joined Cabot Corporation in Billerica in 1990. During his career he produced 9 U.S. Patents. His most cited scientific article treated the subject of morphology formation in elastomer blends. [ 4 ] | https://en.wikipedia.org/wiki/Noboru_Tokita |
A nocebo effect is said to occur when a patient's expectations for a treatment cause the treatment to have a worse effect than it otherwise would have. [ 1 ] [ 2 ] For example, when a patient anticipates a side effect of a medication, they can experience that effect even if the "medication" is actually an inert substance. [ 1 ] The complementary concept, the placebo effect, is said to occur when expectations improve an outcome.
More generally, the nocebo effect is falling ill simply by consciously or subconsciously anticipating a harmful event. This definition includes anticipated events other than medical treatment. It has been applied to Havana syndrome , where purported victims were anticipating attacks by foreign adversaries. [ 3 ] [ 4 ] [ 5 ] This definition also applies to cases of electromagnetic hypersensitivity .
Both placebo and nocebo effects are presumably psychogenic but can induce measurable changes in the body. [ 1 ] One article that reviewed 31 studies on nocebo effects reported a wide range of symptoms that could manifest as nocebo effects, including nausea, stomach pains, itching, bloating, depression, sleep problems, loss of appetite, sexual dysfunction , and severe hypotension . [ 1 ]
Walter Kennedy coined the term nocebo ( Latin nocēbō , "I shall harm", from noceō , "I harm") [ 6 ] in 1961 to denote the counterpart of placebo (Latin placēbō , "I shall please", from placeō , "I please"), [ 7 ] a substance that may produce a beneficial, healthful, pleasant, or desirable effect. Kennedy emphasized that his use of the term nocebo refers strictly to a subject-centered response, a quality "inherent in the patient rather than in the remedy". [ 8 ] That is, he rejected the use of the term for pharmacologically induced negative side effects such as the ringing in the ears caused by quinine . [ 8 ] That is not to say that the patient's psychologically induced response may not include physiological effects. For example, an expectation of pain may induce anxiety, which in turn causes the release of cholecystokinin , which facilitates pain transmission. [ 9 ]
In the narrowest sense, a nocebo response occurs when a drug-trial subject's symptoms are worsened by the administration of an inert, sham, [ 10 ] or dummy ( simulator ) treatment, called a placebo . Placebos contain no chemicals (or any other agents) that could cause any of the observed worsening in the subject's symptoms, so any change for the worse must be due to some subjective factor. Adverse expectations can also cause anesthetic medications' analgesic effects to disappear. [ 11 ]
The worsening of the subject's symptoms or reduction of beneficial effects is a direct consequence of their exposure to the placebo, but the placebo has not chemically generated those symptoms. Because this generation of symptoms entails a complex of "subject-internal" activities, we can never speak in the strictest sense in terms of simulator-centered "nocebo effects", but only in terms of subject-centered "nocebo responses". Some observers attribute nocebo responses (or placebo responses) to a subject's gullibility , but there is no evidence that someone who manifests a nocebo/placebo response to one treatment will manifest a nocebo/placebo response to any other treatment; i.e., there is no fixed nocebo/placebo-responding trait or propensity. [ 12 ]
Based on a biosemiotic model (2022), Goli explains how harm and/or healing expectations lead to a multimodal image and form transient allostatic or homeostatic interoceptive feelings, demonstrating how repetitive experiences of a potential body induce epigenetic changes and form new attractors, such as nocebos and placeboes, in the actual body. [ 13 ]
It has been shown that, due to the nocebo effect, warning patients about drugs' side effects can contribute to the causation of such effects, whether the drug is real or not. [ 14 ] [ 15 ] This effect has been observed in clinical trials: according to a 2013 review, the dropout rate among placebo-treated patients in a meta-analysis of 41 clinical trials of Parkinson's disease treatments was 8.8%. [ 16 ] A 2013 review found that nearly 1 out of 20 patients receiving a placebo in clinical trials for depression dropped out due to adverse events, which were believed to have been caused by the nocebo effect. [ 17 ]
In January 2022, a systematic review and meta-analysis concluded that nocebo responses accounted for 72% of adverse effects after the first COVID-19 vaccine dose and 52% after the second dose. [ 18 ] [ 19 ]
Many studies show that the formation of nocebo responses are influenced by inappropriate health education, media work, and other discourse makers who induce health anxiety and negative expectations. [ 20 ]
Researchers studying the side effects of statins in UK determined that a large proportion of reported side effects were related not to any pharmacological cause but to the nocebo effect. In the UK, publicity in 2013 about the apparent side effects caused hundreds of thousands of patients to stop taking statins, leading to an estimated 2,000 additional cardiovascular events in the subsequent years. [ 3 ]
Evidence suggests that the symptoms of electromagnetic hypersensitivity are caused by the nocebo effect. [ 21 ] [ 22 ]
Verbal suggestion can cause hyperalgesia (increased sensitivity to pain) and allodynia (perception of a tactile stimulus as painful) as a result of the nocebo effect. [ 23 ] Nocebo hyperalgesia is believed to involve the activation of cholecystokinin receptors. [ 24 ]
Stewart-Williams and Podd argue that using the contrasting terms "placebo" and "nocebo" for inert agents that produce pleasant, health-improving, or desirable outcomes and unpleasant, health-diminishing, or undesirable outcomes (respectively) is extremely counterproductive. [ 25 ] For example, precisely the same inert agents can produce analgesia and hyperalgesia, the first of which, on this definition, would be a placebo, and the second a nocebo. [ 26 ]
A second problem is that the same effect, such as immunosuppression , may be desirable for a subject with an autoimmune disorder , but undesirable for most other subjects. Thus, in the first case, the effect would be a placebo, and in the second a nocebo. [ 25 ] A third problem is that the prescriber does not know whether the relevant subjects consider the effects they experience desirable or undesirable until some time after the drugs have been administered. [ 25 ] A fourth is that the same phenomena are generated in all the subjects, and generated by the same drug, which is acting in all of the subjects through the same mechanism. Yet because the phenomena in question have been subjectively considered desirable to one group but not the other, the phenomena are now being labeled in two mutually exclusive ways (i.e., placebo and nocebo), giving the false impression that the drug in question has produced two different phenomena. [ 25 ]
Some people maintain that belief can kill (e.g., voodoo death : Cannon in 1942 describes a number of instances from a variety of different cultures) and or heal (e.g., faith healing ). [ 27 ] A self-willed death (due to voodoo hex , evil eye , pointing the bone procedure, [ 28 ] [ 29 ] etc.) is an extreme form of a culture-specific syndrome or mass psychogenic illness that produces a particular form of psychosomatic or psychophysiological disorder resulting in psychogenic death. Rubel in 1964 spoke of "culture-bound" syndromes, those "from which members of a particular group claim to suffer and for which their culture provides an etiology, diagnosis, preventive measures, and regimens of healing". [ 30 ]
Certain anthropologists, such as Robert Hahn and Arthur Kleinman , have extended the placebo/nocebo distinction into this realm to allow a distinction to be made between rituals, such as faith healing, performed to heal, cure, or bring benefit (placebo rituals) and others, such as "pointing the bone", performed to kill, injure or bring harm (nocebo rituals). As the meaning of the two interrelated and opposing terms has extended, we now find anthropologists speaking, in various contexts, of nocebo or placebo (harmful or helpful) rituals: [ 31 ]
Yet it may become even more terminologically complex, for as Hahn and Kleinman indicate, there can also be cases of paradoxical nocebo outcomes from placebo rituals and placebo outcomes from nocebo rituals (see also unintended consequences ). [ 31 ] In 1973, writing from his extensive experience of treating cancer (including more than 1,000 melanoma cases) at Sydney Hospital , Milton warned of the impact of the delivery of a prognosis , and how many of his patients, upon receiving their prognosis, gave up hope and died a premature death: "there is a small group of patients in whom the realization of impending death is a blow so terrible that they are quite unable to adjust to it, and they die rapidly before the malignancy seems to have developed enough to cause death. This problem of self-willed death is in some ways analogous to the death produced in primitive peoples by witchcraft ('pointing the bone')". [ 32 ]
Some researchers have pointed out that the harm caused by communicating with patients about potential treatment adverse events raises an ethical issue. To respect their autonomy , one must inform a patient about harms a treatment may cause. Yet the way in which potential harms are communicated could cause additional harm, which may violate the ethical principle of non-maleficence . [ 33 ] It is possible that nocebo effects can be reduced while respecting autonomy using different models of informed consent , including the use of a framing effect [ 34 ] and the authorized concealment. | https://en.wikipedia.org/wiki/Nocebo |
Nocodazole is an antineoplastic agent which exerts its effect in cells by interfering with the polymerization of microtubules . [ 1 ] Microtubules are one type of fibre which constitutes the cytoskeleton , and the dynamic microtubule network has several important roles in the cell, including vesicular transport, forming the mitotic spindle and in cytokinesis . Several drugs including vincristine and colcemid are similar to nocodazole in that they interfere with microtubule polymerization.
Nocodazole has been shown to decrease the oncogenic potential of cancer cells via another microtubules-independent mechanisms. Nocodazole stimulates the expression of LATS2 which potently inhibits the Wnt signaling pathway by abrogating the interaction between the Wnt-dependent transcriptional co-factors beta-catenin and BCL9 . [ 2 ]
It is related to mebendazole by replacement of the left most benzene ring by thiophene .
As nocodazole affects the cytoskeleton, it is often used in cell biology experiments as a control: for example, some dominant negative Rho small GTPases cause a similar effect as nocodazole, and constitutively activated mutants often reverse or negate the effect.
Nocodazole is frequently used in cell biology laboratories to synchronize the cell division cycle . Cells treated with nocodazole arrest with a G2 - or M -phase DNA content when analyzed by flow cytometry . Microscopy of nocodazole-treated cells shows that they do enter mitosis but cannot form metaphase spindles because microtubules (of which the spindles are made) cannot polymerise. The absence of microtubule attachment to kinetochores activates the spindle assembly checkpoint , causing the cell to arrest in prometaphase . For cell synchronization experiments, nocodazole is usually used at a concentration of 40–100 ng/mL of culture medium for a duration of 12–18 hours. Prolonged arrest of cells in mitosis due to nocodazole treatment typically results in cell death by apoptosis .
Another standard cell biological application of nocodazole is to induce the formation of Golgi ministacks in eukaryotic cells. The perinuclear structural organization of the Golgi apparatus in eukaryotes is dependent on microtubule trafficking, but disrupting the trafficking of Golgi elements from the endoplasmic reticulum treatment with nocodazole (33 μ M for 3 hours) induces numerous Golgi elements to form adjacent to ER exit sites. These functional Golgi ministacks remain distributed about the cell, unable to track forward to form a perinuclear Golgi since nocodazole has depolymerized the microtubules.
Also used with Mad2p protein as an anti-microtubule drug. | https://en.wikipedia.org/wiki/Nocodazole |
A nocturnal is an instrument used to determine the local time based on the position of a star in the night sky relative to the pole star . As a result of the Earth's rotation , any fixed star makes a full revolution around the pole star in 23 hours and 56 minutes and therefore can be used as an hour hand . The 4-minute difference between the solar day and sidereal day requires a correction of this giant clock based on the date of observation, and nocturnal helps to apply this correction. [ 1 ]
Sometimes called a horologium nocturnum (time instrument for night) or nocturlabe (in French and occasionally used by English writers), it is related to the astrolabe and sundial . Knowing the time is important in piloting for calculating tides and some nocturnals incorporate tide charts for important ports.
The actual horologium nocturnum , a precursor for the later nocturnal instruments, was invented in the 9th century by Pacificus of Verona . [ 2 ]
Even if the nightly course of the stars has been known since antiquity, mentions of a dedicated instrument for its measurement are not found before the Middle Ages. The earliest image presenting the use of a nocturnal is in a manuscript dated from the 12th century. [ 3 ] Raymond Lull repeatedly described the use of a sphaera horarum noctis or astrolabium nocturnum . [ 4 ]
With Martín Cortés de Albacar 's book Arte de Navegar , published in 1551 the name and the instrument gained a larger popularity. [ 5 ]
It was described also c. 1530 by Petrus Apianus in his Cosmographicus Liber , republished later by Gemma Frisius with a widely circulated illustration of the instrument while being used by an observer.
Nocturnals have been most commonly constructed of wood or brass .
A nocturnal will have an outer disc marked with the months of the year, and an inner disc marked with hours (and perhaps half hours, or quarter hours on the largest instruments) as well as locations for one or more reference stars. It will also have a pointer rotating on the same axis as the discs, sometimes extended beyond the rim. The axis, or pivot point, must be such that a star can be sighted through it; usually a hollow rivet is used. Since the instrument is used at night, markings may be exaggerated or raised. Often the inner disc has a diagram of the necessary constellations and stars, to aid in locating them.
A nocturnal is a simple analog computer , made of two or more dials, that will provide the local time based on the time of year and a sighting of Polaris , the North Star, and one or more other stars. In the northern hemisphere , all stars will appear to rotate about the North Star during the night, and their positions, like the progress of the sun , can be used to determine the time. The positions of the stars will change based on the time of year.
The most commonly used reference stars are the pointer stars from the Big Dipper ( Ursa Major ) or Kochab from the Little Dipper (Ursa Minor). The star Schedar in Cassiopeia may also be used, since it is on the opposite side of the sky from Ursa Major.
The inner disc is rotated so that the mark for the chosen reference star points to the current date on the outer disc. The north star is sighted through the center of the device, and the pointer arm is rotated to point at the chosen reference star. The intersection of the pointer arm with the hour markings on the inner disc indicates the time. The instrument must be held upright, and should have a handle or similar hint as to which direction is down.
It is not possible to convert the local time to a standard time such as UTC without accurate knowledge of the observer's longitude . Similarly, it is not possible to determine longitude unless the observer also knows the standard time from a chronometer . | https://en.wikipedia.org/wiki/Nocturnal_(instrument) |
The nocturnal bottleneck hypothesis is an evolutionary biology hypothesis to explain the origin of several mammalian traits. In 1942, Gordon Lynn Walls described this concept which states that placental mammals were mainly or even exclusively nocturnal through most of their evolutionary history, from their origin 225 million years ago during the Late Triassic to after the Cretaceous–Paleogene extinction event , 66 million years ago . [ 1 ] While some mammalian groups later adapted to diurnal (daytime) lifestyles to fill niches newly vacated by the extinction of non-avian dinosaurs , the approximately 160 million years spent as nocturnal animals has left a lasting legacy on basal mammalian anatomy and physiology , and most mammals are still nocturnal. [ 2 ]
Mammals evolved from cynodonts , a group of superficially dog-like therapsid synapsids that survived the Permian–Triassic mass extinction . The emerging archosaurian sauropsids , including pseudosuchians , pterosaurs and dinosaurs and their ancestors, flourished after the Early Triassic Smithian–Spathian boundary event and competitively displaced the larger therapsids into extinction, leaving only the smaller burrowing cynodonts. [ 3 ] The surviving cynodonts could only succeed in leftover niches with minimal competitions from the more dominant , diurnal dinosaurs, evolving into the nocturnal, small-bodied, insectivorous and granivorous dwellers of the forest undergrowths . [ 4 ] While the early mammals continued to develop into several probably quite common groups of animals during the Mesozoic , they all remained relatively small and nocturnal.
Mammals experienced a significant radiation from the angiosperm revolution during the Middle/Late Cretaceous , but only with the massive end-Cretaceous extinction event did the dinosaurs' demise leave the stage open for the establishment of new mammalian faunae . Despite this, mammals continued to be small-bodied for millions of years. [ 5 ] While all the largest animals alive today are mammals, the majority of mammals are still small nocturnal animals. [ 6 ]
Numerous features of mammalian physiology, especially features relating to the sensory organs, appear to be adaptations to a nocturnal lifestyle. These include: | https://en.wikipedia.org/wiki/Nocturnal_bottleneck |
Nocturnality is a behavior in some non-human animals characterized by being active during the night and sleeping during the day . The common adjective is " nocturnal ", versus diurnal meaning the opposite.
Nocturnal creatures generally have highly developed senses of hearing , smell , and specially adapted eyesight . [ 1 ] Some animals, such as cats and ferrets , have eyes that can adapt to both low-level and bright day levels of illumination (see metaturnal ). Others, such as bushbabies and (some) bats , can function only at night. Many nocturnal creatures including tarsiers and some owls have large eyes in comparison with their body size to compensate for the lower light levels at night. More specifically, they have been found to have a larger cornea relative to their eye size than diurnal creatures to increase their visual sensitivity : in the low-light conditions. [ 2 ] Nocturnality helps wasps , such as Apoica flavissima , avoid hunting in intense sunlight.
Diurnal animals, including humans (except for night owls ), squirrels and songbirds, are active during the daytime. Crepuscular species, such as rabbits , skunks , tigers and hyenas , are often erroneously referred to as nocturnal. Cathemeral species, such as fossas and lions , are active both in the day and at night.
While it is difficult to say which came first, nocturnality or diurnality, a hypothesis in evolutionary biology , the nocturnal bottleneck theory, postulates that in the Mesozoic , many ancestors of modern-day mammals evolved nocturnal characteristics in order to avoid contact with the numerous diurnal predators. [ 3 ] A recent study attempts to answer the question as to why so many modern day mammals retain these nocturnal characteristics even though they are not active at night. The leading answer is that the high visual acuity that comes with diurnal characteristics is not needed anymore due to the evolution of compensatory sensory systems, such as a heightened sense of smell and more astute auditory systems. [ 4 ] In a recent study, recently extinct elephant birds and modern day nocturnal kiwi bird skulls were examined to recreate their likely brain and skull formation. They indicated that olfactory bulbs were much larger in comparison to their optic lobes , indicating they both have a common ancestor who evolved to function as a nocturnal species, decreasing their eyesight in favor of a better sense of smell. [ 4 ] The anomaly to this theory were anthropoids , who appeared to have the most divergence from nocturnality of all organisms examined. While most mammals did not exhibit the morphological characteristics expected of a nocturnal creature, reptiles and birds fit in perfectly. A larger cornea and pupil correlated well with whether these two classes of organisms were nocturnal or not. [ 2 ]
Being active at night is a form of niche differentiation , where a species' niche is partitioned not by the amount of resources but by the amount of time (i.e. temporal division of the ecological niche ). Hawks and owls can hunt the same field or meadow for the same rodents without conflict because hawks are diurnal and owls are nocturnal. [ 5 ] This means they are not in competition for each other's prey. Another niche that being nocturnal lessens competition within is pollination - nocturnal pollinators such as moths, beetles, thrips, and bats have a lower risk of being seen by predators, and the plants evolved temporal scent production and ambient heat to attract nocturnal pollination. [ 6 ] Like with predators hunting the same prey, some plants such as apples can be pollinated both during the day and at night. [ 7 ]
Nocturnality is a form of crypsis , an adaptation to avoid or enhance predation . Although lions are cathemeral , and may be active at any time of day or night, they prefer to hunt at night because many of their prey species ( zebra , antelope , impala, wildebeest , etc.) have poor night vision . Many species of small rodents, such as the Large Japanese Field Mouse , are active at night because most of the dozen or so birds of prey that hunt them are diurnal. There are many diurnal species that exhibit some nocturnal behaviors. For example, many seabirds and sea turtles only gather at breeding sites or colonies at night to reduce the risk of predation to themselves and/or their offspring. Nocturnal species take advantage of the night time to prey on species that are used to avoiding diurnal predators. Some nocturnal fish species will use the moonlight to prey on zooplankton species that come to the surface at night. [ 8 ] Some species have developed unique adaptations that allow them to hunt in the dark. Bats are famous for using echolocation to hunt down their prey, using sonar sounds to capture them in the dark.
Another reason for nocturnality is avoiding the heat of the day. This is especially true in arid biomes like deserts , where nocturnal behavior prevents creatures from losing precious water during the hot, dry daytime. This is an adaptation that enhances osmoregulation . [ 9 ] One of the reasons that ( cathemeral ) lions prefer to hunt at night is to conserve water. Hamilton's frog , found on Stephens and Maud islands, stays hidden for most of the day when temperatures are warmer and is mainly active at night. They will only come out during the day if there are humid and cool conditions.
Many plant species native to arid biomes have adapted so that their flowers only open at night when the sun's intense heat cannot wither and destroy their moist, delicate blossoms. These flowers are pollinated by bats, another creature of the night.
Climate change has led to an increasing number of diurnal species to push their activity patterns closer towards crepuscular or fully nocturnal behavior. This adaptive measure allows species to avoid the day's heat, without having to leave that particular habitat. [ 10 ]
The exponential increase in human expansion and technological advances in the last few centuries has had a major effect on nocturnal animals, as well as diurnal species. The causes of these can be traced to distinct, sometimes overlapping areas: light pollution and spatial disturbance.
Light pollution is a major issue for nocturnal species, and the impact continues to increase as electricity reaches parts of the world that previously had no access. [ 11 ] Species in the tropics are generally more affected by this due to the change in their relatively constant light patterns, but temperate species relying on day-night triggers for behavioral patterns are also affected as well. Many diurnal species see the benefit of a "longer day", allowing for a longer hunting period which is detrimental to their nocturnal prey trying to avoid them. [ 8 ]
Light pollution can disorient species that are used to darkness, as their adaptive eyes are not as used to the artificial lighting. Insects are the most obvious example, who are attracted by the lighting and are usually killed by either the heat or electrical current. [ 12 ] Some species of frogs are blinded by the quick changes in light, while nocturnal migratory birds may be disoriented, causing them to lose direction, tire out, or be captured by predators. [ 8 ] Sea turtles are particularly affected by this, adding to a number of threats to the different endangered species. Adults are likely to stay away from artificially lit beaches that they might prefer to lay eggs on, as there is less cover against predators. [ 8 ] [ 12 ] Additionally, baby sea turtles that hatch from eggs on artificially lit beaches often get lost, heading towards the light sources as opposed to the ocean. [ 12 ]
Rhythmic behaviors are affected by light pollution both seasonally and daily patterns. Migrating birds or mammals might have issues with the timing of their movement for example. [ 12 ] On a day-to-day basis, species can see significant changes in their internal temperatures, their general movement, feeding and body mass. [ 13 ] These small scale changes can eventually lead to a population decline, as well as hurting local trophic levels and interconnecting species. [ 13 ] Some typically diurnal species have even become crepuscular or nocturnal as a result of light pollution and general human disturbance. [ 13 ]
There have been documented effects of light pollution on reproductive cycles and factors in different species. It can affect mate choice , migration to breeding grounds, and nest site selection. [ 8 ] In male green frogs , artificial light causes a decrease in mate calls and continued to move around instead of waiting for a potential mate to arrive. [ 14 ] This hurts the overall fitness of the species, which is concerning considering the overall decrease in amphibian populations. [ 14 ]
Predation
Some nocturnal predator-prey relationships are interrupted by artificial lighting. Bats that are fast-moving are often at an advantage with insects being drawn to light; they are fast enough to escape any predators also attracted to the light, leaving slow-moving bats at a disadvantage. [ 8 ] Another example is harbor seals eating juvenile salmon that moved down a river lit by nearby artificial lighting. Once the lights were turned off, predation levels decreased. [ 8 ] Many diurnal prey species forced into being nocturnal are susceptible to nocturnal predators and those species with poor nocturnal eyesight often bear the brunt of the cost. [ 13 ]
The increasing amount of habitat destruction worldwide as a result of human expansion has given both advantages and disadvantages to different nocturnal animals. As a result of peak human activity in the daytime, more species are likely to be active at night in order to avoid the new disturbance in their habitat. [ 15 ] Carnivorous predators however are less timid of the disturbance, feeding on human waste and keeping a relatively similar spatial habitat as they did before. [ 15 ] In comparison, herbivorous prey tend to stay in areas where human disturbance is low, limiting both resources and their spatial habitat. This leads to an imbalance in favor of predators, who increase in population and come out more often at night. [ 15 ]
In zoos , nocturnal animals are usually kept in special night-illumination enclosures to invert their normal sleep-wake cycle and to keep them active during the hours when visitors will be there to see them.
Hedgehogs and sugar gliders are just two of the many nocturnal species kept as ( exotic ) pets. Cats have adapted to domestication so that each individual, whether stray alley cat or pampered housecat, can change their activity level at will, becoming nocturnal or diurnal in response to their environment or the routine of their owners. Cats normally demonstrate crepuscular behavior, bordering nocturnal, being most active in hunting and exploration at dusk and dawn. [ 16 ] | https://en.wikipedia.org/wiki/Nocturnality |
Nod factors ( nodulation factors or NF ), are signaling molecules produced by soil bacteria known as rhizobia in response to flavonoid exudation from plants under nitrogen limited conditions. Nod factors initiate the establishment of a symbiotic relationship between legumes and rhizobia by inducing nodulation. Nod factors produce the differentiation of plant tissue in root hairs into nodules where the bacteria reside and are able to fix nitrogen from the atmosphere for the plant in exchange for photosynthates and the appropriate environment for nitrogen fixation. [ 1 ] One of the most important features provided by the plant in this symbiosis is the production of leghemoglobin , which maintains the oxygen concentration low and prevents the inhibition of nitrogenase activity.
Nod factors structurally are lipochitooligosaccharides (LCOs) that consist of an N -acetyl- D -glucosamine chain linked through β-1,4 linkage with a fatty acid of variable identity attached to a non reducing nitrogen in the backbone with various functional group substitutions at the terminal or non-terminal residues. [ 2 ]
Nod factors are produced in complex mixtures differing in the following characteristics: [ 3 ]
Nod gene expression is induced by the presence of certain flavonoids in the soil, which are secreted by the plant and act as an attractant to bacteria and induce Nod factor production. Flavonoids activate NodD, a LysR family transcription factor, which binds to the nod box and initiates the transcription of the nod genes which encode the proteins necessary for the production of a wide range of LCOs. [ 4 ]
Nod factors are potentially recognized by plant receptors made of two histidine kinases with extracellular LysM domain , which have been identified in L. japonicus , soybean , and M. truncatula [ 5 ] . Binding of Nod factors to these receptors depolarizes the plasma membrane of root hairs via an influx of Ca +2 which induce the expression of early nodulin (ENOD) genes and swelling of the root hairs. In M. truncatula, the signal transduction initiates by the activation of dmi1, dmi2 , and dmi3 which lead to the deformation of root hairs, early nodulin expression, cortical cell division and bacterial infection. Additionally, nsp and hcl genes are recruited later and aid in the process of early nodulation expression, cortical cell division, and infection. [ 6 ] Genes dmi1, dmi2, and dmi3 have also been found to aid in the establishment of interactions between M. truncatula and arbuscular mycorrhiza , indicating that the two very different symbioses may share some common mechanisms. [ 7 ] The end result is the nodule, the structure in which nitrogen is fixed. Nod factors act by inducing changes in gene expression in the legume, most notable the nodulin genes, which are needed for nodule organogenesis. [ 8 ]
Rhizobia bind to host specific lectins present in root hairs which together with Nod factors lead to the formation of nodulation. Nod factors are recognized by a specific class of receptor kinases that have LysM domains in their extracellular domains. The two LysM (lysin motif) receptor kinases ( NFR1 and NFR5 ) that appear to make up the Nod factor receptor were first isolated in the model legume Lotus japonicus in 2003. They now have been isolated also from soybean and the model legume Medicago truncatula . NFR5 lacks the classical activation loop in the kinase domain. The NFR5 gene lacks introns . First the cell membrane is depolarized and the root hairs start to swell and cell division stops. Nod factor cause the fragmentation and rearrangement of actin network, which coupled with the reinstitution of cell growth lead to the curling of the root hair around the bacteria. This is followed by the localized breakdown of the cell wall and the invagination of the plant cell membrane, allowing the bacterium to form an infection thread. As the infection thread grows the rhizobia travel down its length towards the site of the nodule. During this process the pericycle cells in plants become activated and cells in the inner cortex start growing and become the nodule primordium where the rhizobia infect and differentiate into bacteroids and fix nitrogen. Activation of adjacent middle cortex cells leads to the formation of nodule meristem. [ 5 ] | https://en.wikipedia.org/wiki/Nod_factor |
In power engineering , nodal admittance matrix (or just admittance matrix ) is an N x N matrix describing a linear power system with N buses . It represents the nodal admittance of the buses in a power system. In realistic systems which contain thousands of buses, the admittance matrix is quite sparse. Each bus in a real power system is usually connected to only a few other buses through the transmission lines . [ 1 ] The nodal admittance matrix is used in the formulation of the power flow problem .
The nodal admittance matrix of a power system is a form of Laplacian matrix of the nodal admittance diagram of the power system, which is derived by the application of Kirchhoff's laws to the admittance diagram of the power system. Starting from the single line diagram of a power system, the nodal admittance diagram is derived by:
Consider an admittance graph with N {\displaystyle N} buses. The vector of bus voltages , V {\displaystyle V} , is an N × 1 {\displaystyle N\times 1} vector where V k {\displaystyle V_{k}} is the voltage of bus k {\displaystyle k} , and vector of bus current injections , I {\displaystyle I} , is an N × 1 {\displaystyle N\times 1} vector where I k {\displaystyle I_{k}} is the cumulative current injected at bus k {\displaystyle k} by all loads and sources connected to the bus. The admittance between buses k {\displaystyle k} and i {\displaystyle i} is a complex number y k i {\displaystyle y_{ki}} , and is the sum of the admittance of all lines connecting busses k {\displaystyle k} and i {\displaystyle i} . The admittance between the bus i {\displaystyle i} and ground is y k {\displaystyle y_{k}} , and is the sum of the admittance of all the loads connected to bus k {\displaystyle k} .
Consider the current injection , I k {\displaystyle I_{k}} , into bus k {\displaystyle k} . Applying Kirchhoff's current law
where I k i {\displaystyle I_{ki}} is the current from bus k {\displaystyle k} to bus i {\displaystyle i} for k ≠ i {\displaystyle k\neq i} and I k k {\displaystyle I_{kk}} is the current from bus k {\displaystyle k} to ground through the bus load. Applying Ohm's law to the admittance diagram, the bus voltages and the line and load currents are linked by the relation
Therefore,
This relation can be written succinctly in matrix form using the admittance matrix. The nodal admittance matrix Y {\displaystyle Y} is a N × N {\displaystyle N\times N} matrix such that bus voltage and current injection satisfy Ohm's law
in vector format. The entries of Y {\displaystyle Y} are then determined by the equations for the current injections into buses, resulting in
As an example, consider the admittance diagram of a fully connected three bus network of figure 1. The admittance matrix derived from the three bus network in the figure is:
The diagonal entries Y 11 , Y 22 , . . . , Y n n {\displaystyle Y_{11},Y_{22},...,Y_{nn}} are called the self-admittances of the network nodes. The non-diagonal entries are the mutual admittances of the nodes corresponding to the subscripts of the entry. The admittance matrix Y {\displaystyle Y} is typically a symmetric matrix as Y k i = Y i k {\displaystyle Y_{ki}=Y_{ik}} . However, extensions of the line model may make Y {\displaystyle Y} asymmetrical. For instance, modeling phase-shifting transformers, results in a Hermitian admittance matrix. [ 2 ]
The admittance matrix is most often used in the formulation of the power flow problem . [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Nodal_admittance_matrix |
In electric circuit analysis, nodal analysis (also referred to as node-voltage analysis or the branch current method ) is a method of determining the voltage between nodes (points where elements or branches connect) in an electrical circuit in terms of the branch currents.
Nodal analysis is essentially a systematic application of Kirchhoff's current law (KCL) for circuit analysis . Similarly, mesh analysis is a systematic application of Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node specifying that the branch currents incident at a node must sum to zero (using KCL). The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, I branch = V branch * G, where G (=1/R) is the admittance (conductance) of the resistor.
Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs (e.g., SPICE ) use nodal analysis as a basis. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis , can be used.
The only unknown voltage in this circuit is V 1 {\displaystyle V_{1}} . There are three connections to this node and consequently three currents to consider. The direction of the currents in calculations is chosen to be away from the node.
With Kirchhoff's current law, we get:
V 1 − V S R 1 + V 1 R 2 − I S = 0 {\displaystyle {\frac {V_{1}-V_{S}}{R_{1}}}+{\frac {V_{1}}{R_{2}}}-I_{S}=0}
This equation can be solved with respect to V 1 :
V 1 = ( V S R 1 + I S ) ( 1 R 1 + 1 R 2 ) {\displaystyle V_{1}={\frac {\left({\frac {V_{S}}{R_{1}}}+I_{S}\right)}{\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)}}}
Finally, the unknown voltage can be solved by substituting numerical values for the symbols. Any unknown currents are easy to calculate after all the voltages in the circuit are known.
V 1 = ( 5 V 100 Ω + 20 mA ) ( 1 100 Ω + 1 200 Ω ) = 14 3 V {\displaystyle V_{1}={\frac {\left({\frac {5{\text{ V}}}{100\,\Omega }}+20{\text{ mA}}\right)}{\left({\frac {1}{100\,\Omega }}+{\frac {1}{200\,\Omega }}\right)}}={\frac {14}{3}}{\text{ V}}}
In this circuit, we initially have two unknown voltages, V 1 and V 2 . The voltage at V 3 is already known to be V B because the other terminal of the voltage source is at ground potential.
The current going through voltage source V A cannot be directly calculated. Therefore, we cannot write the current equations for either V 1 or V 2 . However, we know that the same current leaving node V 2 must enter node V 1 . Even though the nodes cannot be individually solved, we know that the combined current of these two nodes is zero. This combining of the two nodes is called the supernode technique, and it requires one additional equation: V 1 = V 2 + V A .
The complete set of equations for this circuit is:
{ V 1 − V B R 1 + V 2 − V B R 2 + V 2 R 3 = 0 V 1 = V 2 + V A {\displaystyle {\begin{cases}{\frac {V_{1}-V_{\text{B}}}{R_{1}}}+{\frac {V_{2}-V_{\text{B}}}{R_{2}}}+{\frac {V_{2}}{R_{3}}}=0\\V_{1}=V_{2}+V_{\text{A}}\\\end{cases}}}
By substituting V 2 = ( R 1 + R 2 ) R 3 V B − R 2 R 3 V A ( R 1 + R 2 ) R 3 + R 1 R 2 {\displaystyle V_{2}={\frac {(R_{1}+R_{2})R_{3}V_{\text{B}}-R_{2}R_{3}V_{\text{A}}}{(R_{1}+R_{2})R_{3}+R_{1}R_{2}}}}
In general, for a circuit with N {\displaystyle N} nodes, the node-voltage equations obtained by nodal analysis can be written in a matrix form as derived in the following.
For any node k {\displaystyle k} , KCL states ∑ j ≠ k G j k ( v k − v j ) = 0 {\textstyle \sum _{j\neq k}G_{jk}(v_{k}-v_{j})=0} where G k j = G j k {\displaystyle G_{kj}=G_{jk}} is the negative of the sum of the conductances between nodes k {\displaystyle k} and j {\displaystyle j} , and v k {\displaystyle v_{k}} is the voltage of node k {\displaystyle k} .
This implies 0 = ∑ j ≠ k G j k ( v k − v j ) = ∑ j ≠ k G j k v k − ∑ j ≠ k G j k v j = G k k v k − ∑ j ≠ k G j k v j {\textstyle 0=\sum _{j\neq k}G_{jk}(v_{k}-v_{j})=\sum _{j\neq k}G_{jk}v_{k}-\sum _{j\neq k}G_{jk}v_{j}=G_{kk}v_{k}-\sum _{j\neq k}G_{jk}v_{j}} where G k k {\displaystyle G_{kk}} is the sum of conductances connected to node k {\displaystyle k} .
We note that the first term contributes linearly to the node k {\displaystyle k} via G k k {\displaystyle G_{kk}} , while the second term contributes linearly to each node j {\displaystyle j} connected to the node k {\displaystyle k} via G j k {\displaystyle G_{jk}} with a minus sign.
If an independent current source/input i k {\displaystyle i_{k}} is also attached to node k {\displaystyle k} , the above expression is generalized to i k = G k k v k − ∑ j ≠ k G j k v j {\textstyle i_{k}=G_{kk}v_{k}-\sum _{j\neq k}G_{jk}v_{j}} .
It is readily shown that one can combine the above node-voltage equations for all N {\displaystyle N} nodes, and write them down in the following matrix form
( G 11 G 12 ⋯ G 1 N G 21 G 22 ⋯ G 2 N ⋮ ⋮ ⋱ ⋮ G N 1 G N 2 ⋯ G N N ) ( v 1 v 2 ⋮ v N ) = ( i 1 i 2 ⋮ i N ) {\displaystyle {\begin{pmatrix}G_{11}&G_{12}&\cdots &G_{1N}\\G_{21}&G_{22}&\cdots &G_{2N}\\\vdots &\vdots &\ddots &\vdots \\G_{N1}&G_{N2}&\cdots &G_{NN}\end{pmatrix}}{\begin{pmatrix}v_{1}\\v_{2}\\\vdots \\v_{N}\end{pmatrix}}={\begin{pmatrix}i_{1}\\i_{2}\\\vdots \\i_{N}\end{pmatrix}}} or simply G v = i . {\textstyle \mathbf {Gv} =\mathbf {i} .}
The matrix G {\displaystyle \mathbf {G} } on the left hand side of the equation is singular since it satisfies G 1 = 0 {\displaystyle \mathbf {G1} =0} where 1 {\displaystyle \mathbf {1} } is an N × 1 {\displaystyle N\times 1} column matrix containing only 1s. This corresponds to the fact of current conservation, namely, ∑ k i k = 0 {\textstyle \sum _{k}i_{k}=0} , and the freedom to choose a reference node (ground). In practice, the voltage at the reference node is taken to be 0. Consider it is the last node, v N = 0 {\displaystyle v_{N}=0} . In this case, it is straightforward to verify that the resulting equations for the other N − 1 {\displaystyle N-1} nodes remain the same, and therefore one can simply discard the last column as well as the last line of the matrix equation. This procedure results in a ( N − 1 ) × ( N − 1 ) {\displaystyle (N-1)\times (N-1)} dimensional non-singular matrix equation with the definitions of all the elements stay unchanged. | https://en.wikipedia.org/wiki/Nodal_analysis |
Nodamuvirales is an order of positive-strand RNA viruses which infect eukaryotes . [ 1 ] The name of the group is a contraction of " Nodamu ra virus " and - virales which is the suffix for a virus order . [ 2 ]
The following families are recognized:
This virus -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nodamuvirales |
In physics and geometry , the nodary is the curve that is traced by the focus of a hyperbola as it rolls without slipping along the axis, a roulette curve . [ 1 ]
The differential equation of the curve is: y 2 + 2 a y 1 + y ′ 2 = b 2 {\displaystyle y^{2}+{\frac {2ay}{\sqrt {1+y'^{2}}}}=b^{2}} .
Its parametric equation is:
where k = cos ( tan − 1 ( b / a ) ) {\displaystyle k=\cos(\tan ^{-1}(b/a))} is the elliptic modulus and E ( u , k ) {\displaystyle E(u,k)} is the incomplete elliptic integral of the second kind and sn, cn and dn are Jacobi's elliptic functions . [ 1 ]
The surface of revolution is the nodoid constant mean curvature surface .
This physics -related article is a stub . You can help Wikipedia by expanding it .
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nodary |
A node is a point along a standing wave where the wave has minimum amplitude . For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets , the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an antinode , a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes. [ 1 ]
Standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. [ 2 ] They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line , and particularly when waves are confined in a resonator at resonance , bouncing back and forth between two boundaries, such as in an organ pipe or guitar string .
In a standing wave the nodes are a series of locations at equally spaced intervals where the wave amplitude (motion) is zero (see animation above). At these points the two waves add with opposite phase and cancel each other out. They occur at intervals of half a wavelength (λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes . At these points the two waves add with the same phase and reinforce each other.
In cases where the two opposite wave trains are not the same amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero but merely a minimum. This occurs when the reflection at the boundary is imperfect. This is indicated by a finite standing wave ratio (SWR), the ratio of the amplitude of the wave at the antinode to the amplitude at the node.
In resonance of a two dimensional surface or membrane, such as a drumhead or vibrating metal plate, the nodes become nodal lines, lines on the surface where the surface is motionless, dividing the surface into separate regions vibrating with opposite phase. These can be made visible by sprinkling sand on the surface, and the intricate patterns of lines resulting are called Chladni figures .
In transmission lines a voltage node is a current antinode, and a voltage antinode is a current node.
Nodes are the points of zero displacement, not the points where two constituent waves intersect.
Where the nodes occur in relation to the boundary reflecting the waves depends on the end conditions or boundary conditions . Although there are many types of end conditions, the ends of resonators are usually one of two types that cause total reflection:
A sound wave consists of alternating cycles of compression and expansion of the wave medium. During compression, the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure and density.
The number of nodes in a specified length is directly proportional to the frequency of the wave.
Occasionally on a guitar, violin, or other stringed instrument, nodes are used to create harmonics . When the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created (in addition to the bridge and nut ) and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, although they are quieter. With the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, which is an octave above the fundamental note which would be played, had the harmonic not been sounded. When two additional nodes divide the string into thirds, this creates an octave and a perfect fifth (twelfth). When three additional nodes divide the string into quarters, this creates a double octave. When four additional nodes divide the string into fifths, this creates a double-octave and a major third (17th). The octave, major third and perfect fifth are the three notes present in a major chord.
The characteristic sound that allows the listener to identify a particular instrument is largely due to the relative magnitude of the harmonics created by the instrument.
In two dimensional standing waves, nodes are curves (often straight lines or circles when displayed on simple geometries.) For example, sand collects along the nodes of a vibrating Chladni plate to indicate regions where the plate is not moving. [ 3 ]
In chemistry, quantum mechanical waves, or " orbitals ", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes and antinodes as well. The number and position of these nodes and antinodes give rise to many of the properties of an atom or covalent bond . Atomic orbitals are classified according to the number of radial and angular nodes. A radial node for the hydrogen atom is a sphere that occurs where the wavefunction for an atomic orbital is equal to zero, while the angular node is
a flat plane. [ 4 ]
Molecular orbitals are classified according to bonding character. Molecular orbitals with an antinode between nuclei are very stable, and are known as "bonding orbitals" which strengthen the bond. In contrast, molecular orbitals with a node between nuclei will not be stable due to electrostatic repulsion and are known as "anti-bonding orbitals" which weaken the bond. Another such quantum mechanical concept is the particle in a box where the number of nodes of the wavefunction can help determine the quantum energy state—zero nodes corresponds to the ground state, one node corresponds to the 1st excited state, etc. In general, [ 5 ] If one arranges the eigenstates in the order of increasing energies, ϵ 1 , ϵ 2 , ϵ 3 , . . . {\displaystyle \epsilon _{1},\epsilon _{2},\epsilon _{3},...} , the eigenfunctions likewise fall in the order of increasing number of nodes; the n th eigenfunction has n−1 nodes, between each of which the following eigenfunctions have at least one node . | https://en.wikipedia.org/wiki/Node_(physics) |
In graph theory and network analysis , node influence metrics are measures that rank or quantify the influence of every node (also called vertex) within a graph. They are related to centrality indices . Applications include measuring the influence of each person in a social network , understanding the role of infrastructure nodes in transportation networks , the Internet , or urban networks , and the participation of a given node in disease dynamics.
The traditional approach to understanding node importance is via centrality indicators . Centrality indices are designed to produce a ranking which accurately identifies the most influential nodes. Since the mid 2000s, however, social scientists and network physicists have begun to question the suitability of centrality indices for understanding node influence. Centralities may indicate the most influential nodes, but they are rather less informative for the vast majority of nodes which are not highly influential.
Borgatti and Everett's 2006 review article [ 1 ] showed that the accuracy of centrality indices is highly dependent on network topology .
This finding has been repeatedly observed since then. (e.g. [ 2 ] [ 3 ] ).
In 2012, Bauer and colleagues reminded us that centrality indices only rank nodes but do not quantify the difference between them. [ 4 ] In 2013, Sikic and colleagues presented strong evidence that centrality indices considerably underestimate the power of non-hub nodes. [ 5 ] The reason is quite clear. The accuracy of a centrality measure depends on network topology, but complex networks have heterogeneous topology. Hence a centrality measure which is appropriate for identifying highly influential nodes will most likely be inappropriate for the remainder of the network. [ 3 ]
This has inspired the development of novel methods designed to measure the influence of all network nodes. The most general of these are
the accessibility , which uses the diversity of random walks to measure how accessible the rest of the network is from a given start node, [ 6 ] and the expected force , derived from the expected value of the force of infection generated by a node. [ 3 ] Both of these measures can be meaningfully computed from the structure of the network alone.
The Accessibility is derived from the theory of random walks. It measures the diversity of self-avoiding walks which start from a given node. A walk on a network is a sequence of adjacent vertices; a self-avoiding walk visits (lists) each vertex at most once.
The original work used simulated walks of length 60 to characterize the network of urban streets in a Brazilian city. [ 6 ] It was later formalized as a modified form of hierarchical degree which controls for both transmission probabilities and the diversity of walks of a given fixed length. [ 7 ]
The hierarchical degree measures the number of nodes reachable from a start node by performing walks of length h {\displaystyle h} . For a fixed h {\displaystyle h} and walk type, each of these neighbors is reached with a (potentially different) probability p j ( h ) {\displaystyle p_{j}^{(h)}} .
Given a vector of such probabilities, the accessibility of node i {\displaystyle i} at scale h {\displaystyle h} is defined
The probabilities can be based on uniform-probability random walks, or additionally modulated by edge weights and/or explicit (per edge) transmission probabilities. [ 7 ]
The accessibility has been shown to reveal community structure in urban networks, [ 6 ] corresponds to the number of nodes which can be visited in a defined time period, [ 7 ] and is predictive of the outcome of epidemiological SIR model spreading processes on networks with large diameter and low density . [ 2 ]
The expected force measures node influence from an epidemiological perspective. It is the expected value of the force of infection generated by the node after two transmissions.
The expected force of a node i {\displaystyle i} is given by
where the sum is taken over the set J {\displaystyle J} of all possible transmission clusters resulting from two transmissions starting from i {\displaystyle i} . That is, node i {\displaystyle i} and two of its neighbors or i {\displaystyle i} , one of its neighbors (called infected) and a neighbor of the infected neighbor. J {\displaystyle J} contains all possible orderings of the transmission events, so two clusters may contain the same nodes if they got infected in a different order. d j {\displaystyle d_{j}} is the normalized cluster degree of cluster j ∈ J {\displaystyle j\in J} , that is, the number of edges with exactly one endpoint in cluster j {\displaystyle j} .
The definition naturally extends to directed networks by limiting the enumeration J {\displaystyle J} by edge direction.
Likewise, extension to weighted networks , or networks with heterogeneous transmission probabilities, is a matter of adjusting the normalization of d j {\displaystyle d_{j}} to include the probability that that cluster forms.
It is also possible to use more than two transmissions to define the set J {\displaystyle J} . [ 3 ]
The expected force has been shown to strongly correlate with SI, SIS, and SIR epidemic outcomes over a broad range of network topologies, both simulated and empirical. [ 3 ] [ 8 ] It has also been used to measure the pandemic potential of world airports, [ 9 ] and mentioned in the context of
digital payments, [ 10 ] ecology, [ 11 ] fitness, [ 12 ] and project management. [ 13 ]
Others suggest metrics which explicitly encode the dynamics of a specified process unfolding on the network.
The dynamic influence is the proportion of infinite walks starting from each node, where walk steps are scaled such that the linear dynamics of the system are expected to converge to a non-null steady state. [ 14 ] The Impact sums, over increasing walk lengths, the probability of transmission to the end node of the walk and that the end node has not been previously visited by a shorter walk. [ 4 ] While both measures well predict the outcome of the dynamical systems they encode, in each case the authors admit that results from one dynamic do not translate to other dynamics. | https://en.wikipedia.org/wiki/Node_influence_metric |
Nodes of Ranvier ( / ˈ r ɑː n v i eɪ / RAHN -vee-ay ), [ 1 ] [ 2 ] also known as myelin-sheath gaps , occur along a myelinated axon where the axolemma is exposed to the extracellular space . Nodes of Ranvier are uninsulated axonal domains that are high in sodium and potassium ion channels complexed with cell adhesion molecules , allowing them to participate in the exchange of ions required to regenerate the action potential . [ 3 ] Nerve conduction in myelinated axons is referred to as saltatory conduction (from Latin saltus ' leap, jump ' ) due to the manner in which the action potential seems to "jump" from one node to the next along the axon. This results in faster conduction of the action potential. The nodes of Ranvier are present in both the peripheral and central nervous systems.
The nodes are primarily composed of sodium and potassium voltage-gated ion channels; CAMs such as neurofascin-186 and NrCAM ; and cytoskeletal adaptor proteins such as ankyrin-G and spectrinβIV . [ 4 ] Many vertebrate axons are surrounded by a myelin sheath, allowing rapid and efficient saltatory ("jumping") propagation of action potentials. The contacts between neurons and glial cells display a very high level of spatial and temporal organization in myelinated fibers. The myelinating glial cells - oligodendrocytes in the central nervous system (CNS), and Schwann cells in the peripheral nervous system (PNS) - are wrapped around the axon, leaving the axolemma relatively uncovered at the regularly spaced nodes of Ranvier.
The internodal glial membranes are fused to form compact myelin , whereas the cytoplasm-filled paranodal loops of myelinating cells are spirally wrapped around the axon at both sides of the nodes. This organization demands a tight developmental control and the formation of a variety of specialized zones of contact between different areas of the myelinating cell membrane. Each node of Ranvier is flanked by paranodal regions where helicoidally wrapped glial loops are attached to the axonal membrane by a septate-like junction.
The segment between nodes of Ranvier is termed as the internode , and its outermost part that is in contact with paranodes is referred to as the juxtaparanodal region. The nodes are encapsulated by microvilli stemming from the outer aspect of the Schwann cell membrane in the PNS, or by perinodal extensions from astrocytes in the CNS.
The internodes are the myelin segments and the gaps between are referred to as nodes. The size and the spacing of the internodes vary with the fiber diameter in a curvilinear relationship that is optimized for maximal conduction velocity. [ 5 ] The size of the nodes span from 1–2 μm whereas the internodes can be up to (and occasionally even greater than)1.5 millimetres long, depending on the axon diameter and fiber type.
The structure of the node and the flanking paranodal regions are distinct from the internodes under the compact myelin sheath, but are very similar in CNS and PNS. The axon is exposed to the extra-cellular environment at the node and is constricted in its diameter. The decreased axon size reflects a higher packing density of neurofilaments in this region, which are less heavily phosphorylated and are transported more slowly. [ 6 ] Vesicles and other organelles are also increased at the nodes, which suggest that there is a bottleneck of axonal transport in both directions as well as local axonal-glial signaling.
When a longitudinal section is made through a myelinating Schwann cell at the node, three distinctive segments are represented: the stereotypic internode , the paranodal region, and the node itself. In the internodal region, the Schwann cell has an outer collar of cytoplasm, a compact myelin sheath, and inner collar of cytoplasm, and the axolemma. At the paranodal regions, the paranodal cytoplasm loops contact thickenings of the axolemma to form septate –like junctions. In the node alone, the axolemma is contacted by several Schwann microvilli and contains a dense cytoskeletal undercoating.
Although freeze fracture studies have revealed that the nodal axolemma in both the CNS and PNS is enriched in intra-membranous particles (IMPs) compared to the internode, there are some structural differences reflecting their cellular constituents. [ 6 ] In the PNS, specialized microvilli project from the outer collar of Schwann cells and come very close to nodal axolemma of large fibers. The projections of the Schwann cells are perpendicular to the node and are radiating from the central axons. However, in the CNS, one or more of the astrocytic processes come in close vicinity of the nodes. Researchers declare that these processes stem from multi-functional astrocytes, as opposed to from a population of astrocytes dedicated to contacting the node. On the other hand, in the PNS, the basal lamina that surrounds the Schwann cells is continuous across the node. A study suggests that in the CNS, nerve cells individually alter the size of the nodes to tune conduction speeds, leading node length to vary much more across different axons than within one. [ 7 ]
The nodes of Ranvier Na+/Ca2+ exchangers and high density of voltage-gated Na+ channels that generate action potentials. A sodium channel consists of a pore-forming α subunit and two accessory β subunits, which anchor the channel to extra-cellular and intra-cellular components. The nodes of Ranvier in the central and peripheral nervous systems mostly consist of αNaV1.6 and β1 subunits. [ 8 ] The extra-cellular region of β subunits can associate with itself and other proteins, such as tenascin R and the cell-adhesion molecules neurofascin and contactin. Contactin is also present at nodes in the CNS and interaction with this molecule enhances the surface expression of Na+ channels.
Ankyrin has been found to be bounded to βIV spectrin, a spectrin isoform enriched at nodes of Ranvier and axon initial segments. The PNS nodes are surrounded by Schwann cell microvilli, which contain ERMs and EBP50 that may provide a connection to actin microfilaments. Several extracellular matrix proteins are enriched at nodes of Ranvier, including tenascin-R , Bral-1 , and proteoglycan NG2, as well as phosphacan and versican V2. At CNS nodes, the axonal proteins also include contactin; however, different from the PNS, Schwann cell microvilli are replaced by astrocyte perinodal extensions.
The molecular organization of the nodes corresponds to their specialized function in impulse propagation. The level of sodium channels in the node versus the internode suggests that the number IMPs corresponds to sodium channels. Potassium channels are essentially absent in the nodal axolemma, whereas they are highly concentrated in the paranodal axolemma and Schwann cell membranes at the node. [ 6 ] The exact function of potassium channels have not quite been revealed, but it is known that they may contribute to the rapid repolarization of the action potentials or play a vital role in buffering the potassium ions at the nodes. This highly asymmetric distribution of voltage-gated sodium and potassium channels is in striking contrast to their diffuse distribution in unmyelinated fibers. [ 6 ] [ 9 ]
The filamentous network subjacent to the nodal membrane contains cytoskeletal proteins called spectrin and ankyrin . The high density of ankyrin at the nodes may be functionally significant because several of the proteins that are populated at the nodes share the ability to bind to ankyrin with extremely high affinity. All of these proteins, including ankyrin, are enriched in the initial segment of axons which suggests a functional relationship. Now the relationship of these molecular components to the clustering of sodium channels at the nodes is still not known. Although some cell-adhesion molecules have been reported to be present at the nodes inconsistently; however, a variety of other molecules are known to be highly populated at the glial membranes of the paranodal regions where they contribute to its organization and structural integrity.
The complex changes that the Schwann cell undergoes during the process of myelination of peripheral nerve fibers have been observed and studied by many. The initial envelopment of the axon occurs without interruption along the entire extent of the Schwann cell. This process is sequenced by the in-folding of the Schwann cell surface so that a double membrane of the opposing faces of the in-folded Schwann cell surface is formed. This membrane stretches and spirally wraps itself over and over as the in-folding of the Schwann cell surface continues. As a result, the increase in the thickness of the extension of the myelin sheath in its cross-sectional diameter is easily ascertained. It is also evident that each of the consecutive turns of the spiral increases in size along the length of the axon as the number of turns increase. However, it is not clear whether or not the increase in length of the myelin sheath can be accounted solely by the increase in length of axon covered by each successive turn of the spiral, as previously explained.
At the junction of two Schwann cells along an axon, the directions of the lamellar overhang of the myelin endings are of opposite sense. [ 10 ] This junction, adjacent of the Schwann cells, constitutes the region designated as the node of Ranvier.
Researchers prove that in the developing CNS, Nav1.2 is initially expressed at all forming nodes of Ranvier. [ 11 ] Upon maturation, nodal Nav1.2 is down-regulated and replaced by Nav1.6. Nav1.2 is also expressed during PNS node formation, which suggests that the switching of Nav-channel subtypes is a general phenomenon in the CNS and PNS. In this same investigation, it was shown that Nav1.6 and Nav1.2 colocalize at many nodes of Ranvier during early myelination. This also led to the suggestion that early clusters of Nav1.2 and Nav1.6 channels are destined to later become nodes of Ranvier. Neurofascin is also reported to be one of the first proteins to accumulate at newly forming nodes of Ranvier. They are also found to provide the nucleation site for attachment of ankyrin G, Nav channels, and other proteins. [ 12 ] The recent identification of the Schwann cell microvilli protein gliomedin as the likely binding partner of axonal neurofascin brings forward substantial evidence for the importance of this protein in recruiting Nav channels to the nodes of Ranvier. Furthermore, Lambert et al. and Eshed et al. also indicates that neurofascin accumulates before Nav channels and is likely to have crucial roles in the earliest events associated with node of Ranvier formation. Thus, multiple mechanisms may exist and work synergistically to facilitate clustering of Nav channels at nodes of Ranvier.
The first event appears to be the accumulation of cell adhesion molecules such as NF186 or NrCAM. The intra-cellular regions of these cell-adhesion molecules interact with ankyrin G, which serves as an anchor for sodium channels. In the PNS, this interaction has been elucidated. The Ig superfamily membrane protein NrCAM acts as a pioneer molecule in the formation of the nodes by recruiting ankyrin-G, a mediator protein in the connection of actin-spectrin cytoskeleton to the ion gated channels present at the node. [ 13 ] [ 14 ] At the same time, the periaxonal extension of the glial cell wraps around the axon, giving rise to the paranodal regions. This movement along the axon contributes significantly to the overall formation of the nodes of Ranvier by permitting heminodes formed at the edges of neighboring glial cells to fuse into complete nodes.
Septate-like junctions form at the paranodes with the enrichment of NF155 in glial paranodal loops.
Immediately following the early differentiation of the nodal and paranodal regions, potassium channels, Caspr2 and TAG1 accumulate in the juxta-paranodal regions. This accumulation coincides directly with the formation of compact myelin. In mature nodal regions, interactions with the intracellular proteins appear vital for the stability of all nodal regions. In the CNS, oligodendrocytes do not possess microvilli, but appear capable to initiate the clustering of some axonal proteins through secreted factors. The combined effects of such factors with the subsequent movements generated by the wrapping of oligodendrocyte periaxonal extension could account for the organization of CNS nodes of Ranvier.
An action potential is a spike of both positive and negative ionic discharge that travels along the membrane of a cell. [ 15 ] The creation and conduction of action potentials represents a fundamental means of communication in the nervous system. Action potentials represent rapid reversals in voltage across the plasma membrane of axons. These rapid reversals are mediated by voltage-gated ion channels found in the plasma membrane .
The action potential travels from one location in the cell to another, but ion flow across the membrane occurs only at the nodes of Ranvier. As a result, the action potential signal jumps along the axon, from node to node, rather than propagating smoothly, as they do in axons that lack a myelin sheath. The clustering of voltage-gated sodium and potassium ion channels at the nodes permits this behavior.
Since an axon can be unmyelinated or myelinated, the action potential has two methods to travel down the axon. These methods are referred to as continuous conduction for unmyelinated axons, and saltatory conduction for myelinated axons. Saltatory conduction is defined as an action potential moving in discrete jumps down a myelinated axon.
This process is outlined as the charge passively spreading to the next node of Ranvier to depolarize it to threshold which will then trigger an action potential in this region which will then passively spread to the next node and so on.
Saltatory conduction provides one advantage over conduction that occurs along an axon without myelin sheaths. This is that the increased speed afforded by this mode of conduction assures faster interaction between neurons. On the other hand, depending on the average firing rate of the neuron, calculations show that the energetic cost of maintaining the resting potential of oligodendrocytes can outweigh the energy savings of action potentials. [ 16 ] So, axon myelination does not necessarily save energy.
Mitochondria and other membranous organelles are normally enriched in the PNP region of peripheral myelinated axons, especially those large caliber axons. [ 17 ] The actual physiological role of this accumulation and factors that regulate it are not understood; however, it is known that mitochondria are usually present in areas of the cell that expresses a high energy demand. In these same regions, they are also understood to contain growth cones, synaptic terminals , and sites of action potential initiation and regeneration, such as the nodes of Ranvier. In the synaptic terminals, mitochondria produce the ATP needed to mobilize vesicles for neurotransmission. In the nodes of Ranvier, mitochondria serve as an important role in impulse conduction by producing the ATP that is essential to maintain the activity of energy-demanding ion pumps. Supporting this fact, about five times more mitochondria are present in the PNP axoplasm of large peripheral axons than in the corresponding internodal regions of these fibers. [ 17 ]
Saltatory conduction in myelinated axons requires organization of the nodes of Ranvier, whereas voltage-gated sodium channels are highly populated. Studies show that αII-Spectrin, a component of the cytoskeleton is enriched at the nodes and paranodes at early stages and as the nodes mature, the expression of this molecule disappears. [ 18 ] It is also proven that αII-Spectrin in the axonal cytoskeleton is absolutely vital for stabilizing sodium channel clusters and organizing the mature node of Ranvier.
It has been shown previously that OMgp (oligodendrocyte myelin glycoprotein) clusters at nodes of Ranvier and may regulate paranodal architecture, node length and axonal sprouting at nodes. [ 19 ] However, a follow-up study showed that the antibody used previously to identify OMgp at nodes crossreacts with another node-enriched component versican V2 and that OMgp is not required for the integrity of nodes and paranodes, arguing against the previously reported localization and proposed functions of OMgp at nodes. [ 20 ]
The proteins in these excitable domains of neuron when injured may result in cognitive disorders and various neuropathic ailments.
The myelin sheath of long nerves was discovered and named by German pathological anatomist Rudolf Virchow [ 21 ] in 1854. [ 22 ] French pathologist and anatomist Louis-Antoine Ranvier later discovered the nodes, or gaps, in the myelin sheath that now bear his name. Born in Lyon , Ranvier was one of the most prominent histologists of the late 19th century. Ranvier abandoned pathological studies in 1867 and became an assistant of physiologist Claude Bernard . He was the chairman of General Anatomy at the Collège de France in 1875.
Ranvier discovered the nodes in 1878. [ 23 ] Using staining techniques developed by Ludwig Mauthner , he noticed that myelinated axons were only stained at regular intervals, leading to the discovery of the nodes. Reportedly, he dismissed the idea of nodes in the CNS although their existence was proven later. [ 24 ]
His refined histological techniques and his work on both injured and normal nerve fibers became world-renowned. His observations on fiber nodes and the degeneration and regeneration of cut fibers had a great influence on Parisian neurology at the Salpêtrière . Soon afterwards, he discovered gaps in sheaths of nerve fibers, which were later called the Nodes of Ranvier. This discovery later led Ranvier to careful histological examination of myelin sheaths and Schwann cells. [ 25 ] | https://en.wikipedia.org/wiki/Node_of_Ranvier |
In differential geometry , a nodoid is a surface of revolution with constant nonzero mean curvature obtained by rolling a hyperbola along a fixed line, tracing the focus , and revolving the resulting nodary curve around the line. [ 1 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Nodoid |
Noel Fitzpatrick is an Irish veterinary surgeon , based in Eashing , Surrey , who came to prominence through the television programme The Supervet .
Originally from Ballyfin , in County Laois , Ireland, he moved to Guildford , Surrey , in 1993, [ 2 ] where he is director and managing clinician at Fitzpatrick Referrals. [ 3 ] His veterinary practice includes two hospitals specialising in orthopaedics and neurosurgery in Eashing, [ 4 ] Surrey, and another specialising in oncology and soft tissue surgery in Guildford . [ 5 ] He is director of a number of biotechnology companies spun off from his practice. [ 6 ]
Fitzpatrick obtained his Bachelor of Veterinary Medicine from University College Dublin , in 1990. [ 7 ]
In November 2014, he was awarded the UCD Alumni Award for veterinary medicine. [ 7 ] He was awarded an honorary doctorate by the University of Surrey for the concept of One Medicine: the advancement of human and animal treatments in tandem. [ 8 ] He is an Associate Professor at the University of Florida School of Veterinary Medicine [ 9 ] and Professor and founding member of Orthopaedics in the School of Veterinary Medicine at the University of Surrey . [ 10 ]
In 2017, he was presented with the Blaine Award by British Small Animal Veterinary Association for outstanding contributions to the advancement of small animal veterinary medicine and surgery. [ 11 ] The award acknowledges him as the creator of more than 30 new techniques in the field. [ 12 ]
In 2009, he became the first veterinary surgeon in the world to successfully apply an amputation prosthesis (PerFiTS [ 13 ] ) to a cat named Oscar who had lost both hind feet in an accident. In 2014, Fitzpatrick was recognised by Guinness World Records for being the first veterinary surgeon to conduct that operation. [ 14 ]
Fitzpatrick and his team at Fitzpatrick Referrals have been the subject of television series, including The Bionic Vet and The Supervet . [ 15 ] Fitzpatrick has also appeared on The One Show , [ 16 ] Graham Norton 's BBC Radio 2 show, [ 17 ] Steve Wright in the Afternoon , [ 18 ] Heartbeat and The Chris Evans Breakfast Show . [ 19 ] In October 2018, Fitzpatrick was the subject of BBC Radio 4's The Life Scientific , discussing his life and work with the programme's presenter, Jim Al-Khalili . [ 20 ]
The 2010 BBC documentary television series The Bionic Vet followed the work of vet Fitzpatrick and his team at Fitzpatrick Referrals. The series saw Fitzpatrick develop new methods and techniques to help pets with unique problems.
In 2014, Fitzpatrick and his practice became the subject of the Channel 4 television series The Supervet . It continues to run, and Series 12 was being broadcast in September 2018.
Outside of his veterinary career, Fitzpatrick has a keen interest in acting. He has been cast in two episodes of ITV's Heartbeat as vet Andrew Lawrence, first broadcast in November 2002, and as sheep rustler Gabriel broadcast in January 2000. He appeared in an episode of the BBC medical drama Casualty (2005), around the same time he appeared in the documentary TV series Wildlife SOS , resulting in the BBC receiving complaints that the latter show included an actor who was pretending to be a vet. [ 21 ] He has appeared in the ITV series London's Burning (2001), and two episodes of ITV's The Bill .
Fitzpatrick's first film appearance was in the horror film The Devil's Tattoo (2003). He took the lead role in the film Live for the Moment (2004) in which he starred as David Fowler, and starred as Inspector Beckett in the film Framed (2008). | https://en.wikipedia.org/wiki/Noel_Fitzpatrick |
In mathematics and theoretical physics , Noether's second theorem relates symmetries of an action functional with a system of differential equations . [ 1 ] The theorem is named after its discoverer, Emmy Noether .
The action S of a physical system is an integral of a so-called Lagrangian function L , from which the system's behavior can be determined by the principle of least action . Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by k arbitrary functions and their derivatives up to order m , then the functional derivatives of L satisfy a system of k differential equations.
Noether's second theorem is sometimes used in gauge theory . Gauge theories are the basic elements of all modern field theories of physics, such as the prevailing Standard Model .
Suppose that we have a dynamical system specified in terms of m {\textstyle m} independent variables x = ( x 1 , … , x m ) {\textstyle x=(x^{1},\dots ,x^{m})} , n {\textstyle n} dependent variables u = ( u 1 , … , u n ) {\textstyle u=(u^{1},\dots ,u^{n})} , and a Lagrangian function L ( x , u , u ( 1 ) … , u ( r ) ) {\textstyle L(x,u,u_{(1)}\dots ,u_{(r)})} of some finite order r {\textstyle r} . Here u ( k ) = ( u i 1 . . . i k σ ) = ( d i 1 … d i k u σ ) {\textstyle u_{(k)}=(u_{i_{1}...i_{k}}^{\sigma })=(d_{i_{1}}\dots d_{i_{k}}u^{\sigma })} is the collection of all k {\textstyle k} th order partial derivatives of the dependent variables. As a general rule, latin indices i , j , k , … {\textstyle i,j,k,\dots } from the middle of the alphabet take the values 1 , … , m {\textstyle 1,\dots ,m} , greek indices take the values 1 , … , n {\textstyle 1,\dots ,n} , and the summation convention apply to them. Multiindex notation for the latin indices is also introduced as follows. A multiindex I {\textstyle I} of length k {\textstyle k} is an ordered list I = ( i 1 , … , i k ) {\displaystyle I=(i_{1},\dots ,i_{k})} of k {\textstyle k} ordinary indices. The length is denoted as | I | = k {\textstyle \left|I\right|=k} . The summation convention does not directly apply to multiindices since the summation over lengths needs to be displayed explicitly, e.g. ∑ | I | = 0 r f I g I = f g + f i g i + f i j g i j + ⋯ + f i 1 . . . i r g i 1 . . . i r . {\displaystyle \sum _{|I|=0}^{r}f_{I}g^{I}=fg+f_{i}g^{i}+f_{ij}g^{ij}+\dots +f_{i_{1}...i_{r}}g^{i_{1}...i_{r}}.} The variation of the Lagrangian with respect to an arbitrary variation δ u σ {\textstyle \delta u^{\sigma }} of the dependent variables is δ L = ∂ L ∂ u σ δ u σ + ∂ L ∂ u i σ δ u i σ + ⋯ + ∂ L ∂ u i 1 . . . i r σ δ u i 1 . . . i r σ = ∑ | I | = 0 r ∂ L ∂ u I σ δ u I σ , {\displaystyle \delta L={\frac {\partial L}{\partial u^{\sigma }}}\delta u^{\sigma }+{\frac {\partial L}{\partial u_{i}^{\sigma }}}\delta u_{i}^{\sigma }+\dots +{\frac {\partial L}{\partial u_{i_{1}...i_{r}}^{\sigma }}}\delta u_{i_{1}...i_{r}}^{\sigma }=\sum _{|I|=0}^{r}{\frac {\partial L}{\partial u_{I}^{\sigma }}}\delta u_{I}^{\sigma },} and applying the inverse product rule of differentiation we get δ L = E σ δ u σ + d i ( ∑ | I | = 0 r − 1 P σ i I δ u I σ ) {\displaystyle \delta L=E_{\sigma }\delta u^{\sigma }+d_{i}\left(\sum _{|I|=0}^{r-1}P_{\sigma }^{iI}\delta u_{I}^{\sigma }\right)} where E σ = ∂ L ∂ u σ − d i ∂ L ∂ u i σ + ⋯ + ( − 1 ) r d i 1 … d i r ∂ L ∂ u i 1 . . . i r σ = ∑ | I | = 0 r ( − 1 ) | I | d I ∂ L ∂ u I σ {\displaystyle E_{\sigma }={\frac {\partial L}{\partial u^{\sigma }}}-d_{i}{\frac {\partial L}{\partial u_{i}^{\sigma }}}+\dots +(-1)^{r}d_{i_{1}}\dots d_{i_{r}}{\frac {\partial L}{\partial u_{i_{1}...i_{r}}^{\sigma }}}=\sum _{|I|=0}^{r}(-1)^{|I|}d_{I}{\frac {\partial L}{\partial u_{I}^{\sigma }}}} are the Euler-Lagrange expressions of the Lagrangian, and the coefficients P σ I {\textstyle P_{\sigma }^{I}} (Lagrangian momenta) are given by P σ I = ∑ | J | = 0 r − | I | ( − 1 ) | J | d J ∂ L ∂ u I J σ {\displaystyle P_{\sigma }^{I}=\sum _{|J|=0}^{r-|I|}(-1)^{|J|}d_{J}{\frac {\partial L}{\partial u_{IJ}^{\sigma }}}}
A variation δ u σ = X σ ( x , u , u ( 1 ) , … ) {\textstyle \delta u^{\sigma }=X^{\sigma }(x,u,u_{(1)},\dots )} is an infinitesimal symmetry of the Lagrangian L {\textstyle L} if δ L = 0 {\textstyle \delta L=0} under this variation. It is an infinitesimal quasi-symmetry if there is a current K i = K i ( x , u , … ) {\textstyle K^{i}=K^{i}(x,u,\dots )} such that δ L = d i K i {\textstyle \delta L=d_{i}K^{i}} .
It should be remarked that it is possible to extend infinitesimal (quasi-)symmetries by including variations with δ x i ≠ 0 {\displaystyle \delta x^{i}\neq 0} as well, i.e. the independent variables are also varied. However such symmetries can always be rewritten so that they act only on the dependent variables. Therefore, in the sequel we restrict to so-called vertical variations where δ x i = 0 {\displaystyle \delta x^{i}=0} .
For Noether's second theorem, we consider those variational symmetries (called gauge symmetries ) which are parametrized linearly by a set of arbitrary functions and their derivatives. These variations have the generic form δ λ u σ = R a σ λ a + R a σ , i λ i a + ⋯ + R a σ , i 1 . . . i s λ i 1 . . . i s a = ∑ | I | = 0 s R a σ , I λ I a , {\displaystyle \delta _{\lambda }u^{\sigma }=R_{a}^{\sigma }\lambda ^{a}+R_{a}^{\sigma ,i}\lambda _{i}^{a}+\dots +R_{a}^{\sigma ,i_{1}...i_{s}}\lambda _{i_{1}...i_{s}}^{a}=\sum _{|I|=0}^{s}R_{a}^{\sigma ,I}\lambda _{I}^{a},} where the coefficients R a σ , I {\displaystyle R_{a}^{\sigma ,I}} can depend on the independent and dependent variables as well as the derivatives of the latter up to some finite order, the λ a = λ a ( x ) {\displaystyle \lambda ^{a}=\lambda ^{a}(x)} are arbitrarily specifiable functions of the independent variables, and the latin indices a , b , … {\displaystyle a,b,\dots } take the values 1 , … , q {\displaystyle 1,\dots ,q} , where q {\displaystyle q} is some positive integer.
For these variations to be (exact, i.e. not quasi-) gauge symmetries of the Lagrangian, it is necessary that δ λ L = 0 {\displaystyle \delta _{\lambda }L=0} for all possible choices of the functions λ a ( x ) {\displaystyle \lambda ^{a}(x)} . If the variations are quasi-symmetries, it is then necessary that the current also depends linearly and differentially on the arbitrary functions, i.e. then δ λ L = d i K λ i {\displaystyle \delta _{\lambda }L=d_{i}K_{\lambda }^{i}} , where K λ i = K a i λ a + K a i , j λ j a + K a i , j 1 j 2 λ j 1 j 2 a … {\displaystyle K_{\lambda }^{i}=K_{a}^{i}\lambda ^{a}+K_{a}^{i,j}\lambda _{j}^{a}+K_{a}^{i,j_{1}j_{2}}\lambda _{j_{1}j_{2}}^{a}\dots } For simplicity, we will assume that all gauge symmetries are exact symmetries, but the general case is handled similarly.
The statement of Noether's second theorem is that whenever given a Lagrangian L {\textstyle L} as above that admits gauge symmetries δ λ u σ {\displaystyle \delta _{\lambda }u^{\sigma }} parametrized linearly by q {\displaystyle q} arbitrary functions and their derivatives, then there exist q {\displaystyle q} linear differential relations between the Euler-Lagrange equations of L {\textstyle L} .
Combining the first variation formula together with the fact that the variations δ λ u σ {\textstyle \delta _{\lambda }u^{\sigma }} are symmetries, we get 0 = E σ δ λ u σ + d i W λ i , W λ i = ∑ | I | = 0 r P σ i I δ λ u σ , {\displaystyle 0=E_{\sigma }\delta _{\lambda }u^{\sigma }+d_{i}W_{\lambda }^{i},\quad W_{\lambda }^{i}=\sum _{|I|=0}^{r}P_{\sigma }^{iI}\delta _{\lambda }u^{\sigma },} where on the first term proportional to the Euler-Lagrange expressions, further integrations by parts can be performed as E σ δ λ u σ = ∑ | I | = 0 s E σ R a σ , I λ I a = Q a λ a + d i ( ∑ | I | = 0 s − 1 Q a i I λ I a ) , {\displaystyle E_{\sigma }\delta _{\lambda }u^{\sigma }=\sum _{|I|=0}^{s}E_{\sigma }R_{a}^{\sigma ,I}\lambda _{I}^{a}=Q_{a}\lambda ^{a}+d_{i}\left(\sum _{|I|=0}^{s-1}Q_{a}^{iI}\lambda _{I}^{a}\right),} where Q a I = ∑ | J | = 0 s − | I | ( − 1 ) | J | d J ( E σ R a σ , I J ) , {\displaystyle Q_{a}^{I}=\sum _{|J|=0}^{s-|I|}(-1)^{|J|}d_{J}\left(E_{\sigma }R_{a}^{\sigma ,IJ}\right),} in particular for | I | = 0 {\textstyle |I|=0} , Q a = E σ R a σ − d i ( E σ R a σ , i ) + ⋯ + ( − 1 ) s d i 1 … d i s ( E σ R a σ , i 1 . . . i s ) = ∑ | I | = 0 s ( − 1 ) | I | d I ( E σ R a σ , I ) . {\displaystyle Q_{a}=E_{\sigma }R_{a}^{\sigma }-d_{i}\left(E_{\sigma }R_{a}^{\sigma ,i}\right)+\dots +(-1)^{s}d_{i_{1}}\dots d_{i_{s}}\left(E_{\sigma }R_{a}^{\sigma ,i_{1}...i_{s}}\right)=\sum _{|I|=0}^{s}(-1)^{|I|}d_{I}\left(E_{\sigma }R_{a}^{\sigma ,I}\right).} Hence, we have an off-shell relation 0 = Q a λ a + d i S λ i , {\displaystyle 0=Q_{a}\lambda ^{a}+d_{i}S_{\lambda }^{i},} where S λ i = H λ i + W λ i , {\textstyle S_{\lambda }^{i}=H_{\lambda }^{i}+W_{\lambda }^{i},} with H λ i = ∑ | I | = 0 s − 1 Q a i I λ I a {\textstyle H_{\lambda }^{i}=\sum _{|I|=0}^{s-1}Q_{a}^{iI}\lambda _{I}^{a}} . This relation is valid for any choice of the gauge parameters λ a ( x ) {\textstyle \lambda ^{a}(x)} . Choosing them to be compactly supported, and integrating the relation over the manifold of independent variables, the integral total divergence terms vanishes due to Stokes' theorem . Then from the fundamental lemma of the calculus of variations , we obtain that Q a ≡ 0 {\displaystyle Q_{a}\equiv 0} identically as off-shell relations (in fact, since the Q a {\displaystyle Q_{a}} are linear in the Euler-Lagrange expressions, they necessarily vanish on-shell). Inserting this back into the initial equation, we also obtain the off-shell conservation law d i S λ i = 0 {\displaystyle d_{i}S_{\lambda }^{i}=0} .
The expressions Q a {\displaystyle Q_{a}} are differential in the Euler-Lagrange expressions, specifically we have Q a = D a [ E ] = ∑ | I | = 0 s ( − 1 ) | I | d I ( E σ R a σ , I ) = ∑ | I | = 0 s F a σ , I d I E σ , {\displaystyle Q_{a}={\mathcal {D}}_{a}[E]=\sum _{|I|=0}^{s}(-1)^{|I|}d_{I}\left(E_{\sigma }R_{a}^{\sigma ,I}\right)=\sum _{|I|=0}^{s}F_{a}^{\sigma ,I}d_{I}E_{\sigma },} where F a σ , I = ∑ | J | = 0 s − | I | ( | I | + | J | | I | ) ( − 1 ) | I | + | J | d J R a σ , I J . {\displaystyle F_{a}^{\sigma ,I}=\sum _{|J|=0}^{s-|I|}{\binom {|I|+|J|}{|I|}}(-1)^{|I|+|J|}d_{J}R_{a}^{\sigma ,IJ}.} Hence, the equations 0 = D a [ E ] {\displaystyle 0={\mathcal {D}}_{a}[E]} are q {\textstyle q} differential relations to which the Euler-Lagrange expressions are subject to, and therefore the Euler-Lagrange equations of the system are not independent.
A converse of the second Noether them can also be established. Specifically, suppose that the Euler-Lagrange expressions E σ {\displaystyle E_{\sigma }} of the system are subject to q {\displaystyle q} differential relations 0 = D a [ E ] = ∑ | I | = 0 s F a σ , I d I E σ . {\displaystyle 0={\mathcal {D}}_{a}[E]=\sum _{|I|=0}^{s}F_{a}^{\sigma ,I}d_{I}E_{\sigma }.} Letting λ = ( λ 1 , … , λ q ) {\textstyle \lambda =(\lambda ^{1},\dots ,\lambda ^{q})} be an arbitrary q {\textstyle q} -tuple of functions, the formal adjoint of the operator D a {\textstyle {\mathcal {D}}_{a}} acts on these functions through the formula E σ ( D + ) σ [ λ ] − λ a D a [ E ] = d i B λ i , {\displaystyle E_{\sigma }({\mathcal {D}}^{+})^{\sigma }[\lambda ]-\lambda ^{a}{\mathcal {D}}_{a}[E]=d_{i}B_{\lambda }^{i},} which defines the adjoint operator ( D + ) σ {\displaystyle ({\mathcal {D}}^{+})^{\sigma }} uniquely. The coefficients of the adjoint operator are obtained through integration by parts as before, specifically ( D + ) σ [ λ ] = ∑ | I | = 0 s R a σ , I λ I a , {\displaystyle ({\mathcal {D}}^{+})^{\sigma }[\lambda ]=\sum _{|I|=0}^{s}R_{a}^{\sigma ,I}\lambda _{I}^{a},} where R a σ , I = ∑ | J | = 0 s − | I | ( − 1 ) | I | + | J | ( | I | + | J | | I | ) d J F a σ , I J . {\displaystyle R_{a}^{\sigma ,I}=\sum _{|J|=0}^{s-|I|}(-1)^{|I|+|J|}{\binom {|I|+|J|}{|I|}}d_{J}F_{a}^{\sigma ,IJ}.} Then the definition of the adjoint operator together with the relations 0 = D a [ E ] {\displaystyle 0={\mathcal {D}}_{a}[E]} state that for each q {\textstyle q} -tuple of functions λ {\displaystyle \lambda } , the value of the adjoint on the functions when contracted with the Euler-Lagrange expressions is a total divergence, viz. E σ ( D + ) σ [ λ ] = d i B λ i , {\displaystyle E_{\sigma }({\mathcal {D}}^{+})^{\sigma }[\lambda ]=d_{i}B_{\lambda }^{i},} therefore if we define the variations δ λ u σ := ( D + ) σ [ λ ] = ∑ | I | = 0 s R a σ , I λ I a , {\displaystyle \delta _{\lambda }u^{\sigma }:=({\mathcal {D}}^{+})^{\sigma }[\lambda ]=\sum _{|I|=0}^{s}R_{a}^{\sigma ,I}\lambda _{I}^{a},} the variation δ λ L = E σ δ λ u σ + d i W λ i = d i ( B λ i + W λ i ) {\displaystyle \delta _{\lambda }L=E_{\sigma }\delta _{\lambda }u^{\sigma }+d_{i}W_{\lambda }^{i}=d_{i}\left(B_{\lambda }^{i}+W_{\lambda }^{i}\right)} of the Lagrangian is a total divergence, hence the variations δ λ u σ {\textstyle \delta _{\lambda }u^{\sigma }} are quasi-symmetries for every value of the functions λ a {\displaystyle \lambda ^{a}} .
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Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law . This is the first of two theorems (see Noether's second theorem ) published by the mathematician Emmy Noether in 1918. [ 1 ] The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action . This theorem applies to continuous and smooth symmetries of physical space . Noether's formulation is quite general and has been applied across classical mechanics, high energy physics, and recently statistical mechanics. [ 2 ]
Noether's theorem is used in theoretical physics and the calculus of variations . It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g., systems with a Rayleigh dissipation function ). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law. [ citation needed ]
As an illustration, if a physical system behaves the same regardless of how it is oriented in space (that is, it is invariant ), its Lagrangian is symmetric under continuous rotation: from this symmetry, Noether's theorem dictates that the angular momentum of the system be conserved, as a consequence of its laws of motion. [ 3 ] : 126 The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. It is the laws of its motion that are symmetric.
As another example, if a physical process exhibits the same outcomes regardless of place or time, then its Lagrangian is symmetric under continuous translations in space and time respectively: by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively. [ 4 ] : 23 [ 5 ] : 261
Noether's theorem is important, both because of the insight it gives into conservation laws, and also as a practical calculational tool. It allows investigators to determine the conserved quantities (invariants) from the observed symmetries of a physical system. Conversely, it allows researchers to consider whole classes of hypothetical Lagrangians with given invariants, to describe a physical system. [ 3 ] : 127 As an illustration, suppose that a physical theory is proposed which conserves a quantity X . A researcher can calculate the types of Lagrangians that conserve X through a continuous symmetry. Due to Noether's theorem, the properties of these Lagrangians provide further criteria to understand the implications and judge the fitness of the new theory.
There are numerous versions of Noether's theorem, with varying degrees of generality. There are natural quantum counterparts of this theorem, expressed in the Ward–Takahashi identities . Generalizations of Noether's theorem to superspaces also exist. [ 6 ]
All fine technical points aside, Noether's theorem can be stated informally as:
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time. [ 7 ]
A more sophisticated version of the theorem involving fields states that:
To every continuous symmetry generated by local actions there corresponds a conserved current and vice versa.
The word "symmetry" in the above statement refers more precisely to the covariance of the form that a physical law takes with respect to a one-dimensional Lie group of transformations satisfying certain technical criteria. The conservation law of a physical quantity is usually expressed as a continuity equation .
The formal proof of the theorem utilizes the condition of invariance to derive an expression for a current associated with a conserved physical quantity. In modern terminology, the conserved quantity is called the Noether charge , while the flow carrying that charge is called the Noether current . The Noether current is defined up to a solenoidal (divergenceless) vector field.
In the context of gravitation, Felix Klein 's statement of Noether's theorem for action I stipulates for the invariants: [ 8 ]
If an integral I is invariant under a continuous group G ρ with ρ parameters, then ρ linearly independent combinations of the Lagrangian expressions are divergences.
The main idea behind Noether's theorem is most easily illustrated by a system with one coordinate q {\displaystyle q} and a continuous symmetry φ : q ↦ q + δ q {\displaystyle \varphi :q\mapsto q+\delta q} (gray arrows on the diagram).
Consider any trajectory q ( t ) {\displaystyle q(t)} (bold on the diagram) that satisfies the system's laws of motion . That is, the action S {\displaystyle S} governing this system is stationary on this trajectory, i.e. does not change under any local variation of the trajectory. In particular it would not change under a variation that applies the symmetry flow φ {\displaystyle \varphi } on a time segment [ t 0 , t 1 ] and is motionless outside that segment. To keep the trajectory continuous, we use "buffering" periods of small time τ {\displaystyle \tau } to transition between the segments gradually.
The total change in the action S {\displaystyle S} now comprises changes brought by every interval in play. Parts where variation itself vanishes, i.e outside [ t 0 , t 1 ] {\displaystyle [t_{0},t_{1}]} , bring no Δ S {\displaystyle \Delta S} . The middle part does not change the action either, because its transformation φ {\displaystyle \varphi } is a symmetry and thus preserves the Lagrangian L {\displaystyle L} and the action S = ∫ L {\textstyle S=\int L} . The only remaining parts are the "buffering" pieces. In these regions both the coordinate q {\displaystyle q} and velocity q ˙ {\displaystyle {\dot {q}}} change, but q ˙ {\displaystyle {\dot {q}}} changes by δ q / τ {\displaystyle \delta q/\tau } , and the change δ q {\displaystyle \delta q} in the coordinate is negligible by comparison since the time span τ {\displaystyle \tau } of the buffering is small (taken to the limit of 0), so δ q / τ ≫ δ q {\displaystyle \delta q/\tau \gg \delta q} . So the regions contribute mostly through their "slanting" q ˙ → q ˙ ± δ q / τ {\displaystyle {\dot {q}}\rightarrow {\dot {q}}\pm \delta q/\tau } .
That changes the Lagrangian by Δ L ≈ ( ∂ L / ∂ q ˙ ) Δ q ˙ {\displaystyle \Delta L\approx {\bigl (}\partial L/\partial {\dot {q}}{\bigr )}\Delta {\dot {q}}} , which integrates to Δ S = ∫ Δ L ≈ ∫ ∂ L ∂ q ˙ Δ q ˙ ≈ ∫ ∂ L ∂ q ˙ ( ± δ q τ ) ≈ ± ∂ L ∂ q ˙ δ q = ± ∂ L ∂ q ˙ φ . {\displaystyle \Delta S=\int \Delta L\approx \int {\frac {\partial L}{\partial {\dot {q}}}}\Delta {\dot {q}}\approx \int {\frac {\partial L}{\partial {\dot {q}}}}\left(\pm {\frac {\delta q}{\tau }}\right)\approx \ \pm {\frac {\partial L}{\partial {\dot {q}}}}\delta q=\pm {\frac {\partial L}{\partial {\dot {q}}}}\varphi .}
These last terms, evaluated around the endpoints t 0 {\displaystyle t_{0}} and t 1 {\displaystyle t_{1}} , should cancel each other in order to make the total change in the action Δ S {\displaystyle \Delta S} be zero, as would be expected if the trajectory is a solution. That is ( ∂ L ∂ q ˙ φ ) ( t 0 ) = ( ∂ L ∂ q ˙ φ ) ( t 1 ) , {\displaystyle \left({\frac {\partial L}{\partial {\dot {q}}}}\varphi \right)(t_{0})=\left({\frac {\partial L}{\partial {\dot {q}}}}\varphi \right)(t_{1}),} meaning the quantity ( ∂ L / ∂ q ˙ ) φ {\displaystyle \left(\partial L/\partial {\dot {q}}\right)\varphi } is conserved, which is the conclusion of Noether's theorem. For instance if pure translations of q {\displaystyle q} by a constant are the symmetry, then the conserved quantity becomes just ( ∂ L / ∂ q ˙ ) = p {\displaystyle \left(\partial L/\partial {\dot {q}}\right)=p} , the canonical momentum.
More general cases follow the same idea:
Δ S ≈ ± ( T L + ∫ ∑ r ∂ L ∂ q ˙ r Δ q ˙ r ) ≈ ± T ( L − ∑ r ∂ L ∂ q ˙ r q ˙ r ) . {\displaystyle \Delta S\approx \pm \left(TL+\int \sum _{r}{\frac {\partial L}{\partial {\dot {q}}_{r}}}\Delta {\dot {q}}_{r}\right)\approx \pm T\left(L-\sum _{r}{\frac {\partial L}{\partial {\dot {q}}_{r}}}{\dot {q}}_{r}\right).}
A conservation law states that some quantity X in the mathematical description of a system's evolution remains constant throughout its motion – it is an invariant . Mathematically, the rate of change of X (its derivative with respect to time ) is zero,
Such quantities are said to be conserved; they are often called constants of motion (although motion per se need not be involved, just evolution in time). For example, if the energy of a system is conserved, its energy is invariant at all times, which imposes a constraint on the system's motion and may help in solving for it. Aside from insights that such constants of motion give into the nature of a system, they are a useful calculational tool; for example, an approximate solution can be corrected by finding the nearest state that satisfies the suitable conservation laws.
The earliest constants of motion discovered were momentum and kinetic energy , which were proposed in the 17th century by René Descartes and Gottfried Leibniz on the basis of collision experiments, and refined by subsequent researchers. Isaac Newton was the first to enunciate the conservation of momentum in its modern form, and showed that it was a consequence of Newton's laws of motion . According to general relativity , the conservation laws of linear momentum, energy and angular momentum are only exactly true globally when expressed in terms of the sum of the stress–energy tensor (non-gravitational stress–energy) and the Landau–Lifshitz stress–energy–momentum pseudotensor (gravitational stress–energy). The local conservation of non-gravitational linear momentum and energy in a free-falling reference frame is expressed by the vanishing of the covariant divergence of the stress–energy tensor . Another important conserved quantity, discovered in studies of the celestial mechanics of astronomical bodies, is the Laplace–Runge–Lenz vector .
In the late 18th and early 19th centuries, physicists developed more systematic methods for discovering invariants. A major advance came in 1788 with the development of Lagrangian mechanics , which is related to the principle of least action . In this approach, the state of the system can be described by any type of generalized coordinates q ; the laws of motion need not be expressed in a Cartesian coordinate system , as was customary in Newtonian mechanics. The action is defined as the time integral I of a function known as the Lagrangian L
where the dot over q signifies the rate of change of the coordinates q ,
Hamilton's principle states that the physical path q ( t )—the one actually taken by the system—is a path for which infinitesimal variations in that path cause no change in I , at least up to first order. This principle results in the Euler–Lagrange equations ,
Thus, if one of the coordinates, say q k , does not appear in the Lagrangian, the right-hand side of the equation is zero, and the left-hand side requires that
where the momentum
is conserved throughout the motion (on the physical path).
Thus, the absence of the ignorable coordinate q k from the Lagrangian implies that the Lagrangian is unaffected by changes or transformations of q k ; the Lagrangian is invariant, and is said to exhibit a symmetry under such transformations. This is the seed idea generalized in Noether's theorem.
Several alternative methods for finding conserved quantities were developed in the 19th century, especially by William Rowan Hamilton . For example, he developed a theory of canonical transformations which allowed changing coordinates so that some coordinates disappeared from the Lagrangian, as above, resulting in conserved canonical momenta. Another approach, and perhaps the most efficient for finding conserved quantities, is the Hamilton–Jacobi equation .
Emmy Noether's work on the invariance theorem began in 1915 when she was helping Felix Klein and David Hilbert with their work related to Albert Einstein 's theory of general relativity [ 9 ] : 31 By March 1918 she had most of the key ideas for the paper which would be published later in the year. [ 10 ] : 81
The essence of Noether's theorem is generalizing the notion of ignorable coordinates.
One can assume that the Lagrangian L defined above is invariant under small perturbations (warpings) of the time variable t and the generalized coordinates q . One may write
where the perturbations δt and δ q are both small, but variable. For generality, assume there are (say) N such symmetry transformations of the action, i.e. transformations leaving the action unchanged; labelled by an index r = 1, 2, 3, ..., N .
Then the resultant perturbation can be written as a linear sum of the individual types of perturbations,
where ε r are infinitesimal parameter coefficients corresponding to each:
For translations, Q r is a constant with units of length ; for rotations, it is an expression linear in the components of q , and the parameters make up an angle .
Using these definitions, Noether showed that the N quantities
are conserved ( constants of motion ).
I. Time invariance
For illustration, consider a Lagrangian that does not depend on time, i.e., that is invariant (symmetric) under changes t → t + δ t , without any change in the coordinates q . In this case, N = 1, T = 1 and Q = 0; the corresponding conserved quantity is the total energy H [ 11 ] : 401
II. Translational invariance
Consider a Lagrangian which does not depend on an ("ignorable", as above) coordinate q k ; so it is invariant (symmetric) under changes q k → q k + δq k . In that case, N = 1, T = 0, and Q k = 1; the conserved quantity is the corresponding linear momentum p k [ 11 ] : 403–404
In special and general relativity , these two conservation laws can be expressed either globally (as it is done above), or locally as a continuity equation. The global versions can be united into a single global conservation law: the conservation of the energy-momentum 4-vector. The local versions of energy and momentum conservation (at any point in space-time) can also be united, into the conservation of a quantity defined locally at the space-time point: the stress–energy tensor [ 12 ] : 592 (this will be derived in the next section).
III. Rotational invariance
The conservation of the angular momentum L = r × p is analogous to its linear momentum counterpart. [ 11 ] : 404–405 It is assumed that the symmetry of the Lagrangian is rotational, i.e., that the Lagrangian does not depend on the absolute orientation of the physical system in space. For concreteness, assume that the Lagrangian does not change under small rotations of an angle δθ about an axis n ; such a rotation transforms the Cartesian coordinates by the equation
Since time is not being transformed, T = 0, and N = 1. Taking δθ as the ε parameter and the Cartesian coordinates r as the generalized coordinates q , the corresponding Q variables are given by
Then Noether's theorem states that the following quantity is conserved,
In other words, the component of the angular momentum L along the n axis is conserved. And if n is arbitrary, i.e., if the system is insensitive to any rotation, then every component of L is conserved; in short, angular momentum is conserved.
Although useful in its own right, the version of Noether's theorem just given is a special case of the general version derived in 1915. To give the flavor of the general theorem, a version of Noether's theorem for continuous fields in four-dimensional space–time is now given. Since field theory problems are more common in modern physics than mechanics problems, this field theory version is the most commonly used (or most often implemented) version of Noether's theorem.
Let there be a set of differentiable fields φ {\displaystyle \varphi } defined over all space and time; for example, the temperature T ( x , t ) {\displaystyle T(\mathbf {x} ,t)} would be representative of such a field, being a number defined at every place and time. The principle of least action can be applied to such fields, but the action is now an integral over space and time
(the theorem can be further generalized to the case where the Lagrangian depends on up to the n th derivative, and can also be formulated using jet bundles ).
A continuous transformation of the fields φ {\displaystyle \varphi } can be written infinitesimally as
where Ψ {\displaystyle \Psi } is in general a function that may depend on both x μ {\displaystyle x^{\mu }} and φ {\displaystyle \varphi } . The condition for Ψ {\displaystyle \Psi } to generate a physical symmetry is that the action S {\displaystyle {\mathcal {S}}} is left invariant. This will certainly be true if the Lagrangian density L {\displaystyle {\mathcal {L}}} is left invariant, but it will also be true if the Lagrangian changes by a divergence,
since the integral of a divergence becomes a boundary term according to the divergence theorem . A system described by a given action might have multiple independent symmetries of this type, indexed by r = 1 , 2 , … , N , {\displaystyle r=1,2,\ldots ,N,} so the most general symmetry transformation would be written as
with the consequence
For such systems, Noether's theorem states that there are N {\displaystyle N} conserved current densities
(where the dot product is understood to contract the field indices, not the ν {\displaystyle \nu } index or r {\displaystyle r} index).
In such cases, the conservation law is expressed in a four-dimensional way
which expresses the idea that the amount of a conserved quantity within a sphere cannot change unless some of it flows out of the sphere. For example, electric charge is conserved; the amount of charge within a sphere cannot change unless some of the charge leaves the sphere.
For illustration, consider a physical system of fields that behaves the same under translations in time and space, as considered above; in other words, L ( φ , ∂ μ φ , x μ ) {\displaystyle L\left({\boldsymbol {\varphi }},\partial _{\mu }{\boldsymbol {\varphi }},x^{\mu }\right)} is constant in its third argument. In that case, N = 4, one for each dimension of space and time. An infinitesimal translation in space, x μ ↦ x μ + ε r δ r μ {\displaystyle x^{\mu }\mapsto x^{\mu }+\varepsilon _{r}\delta _{r}^{\mu }} (with δ {\displaystyle \delta } denoting the Kronecker delta ), affects the fields as φ ( x μ ) ↦ φ ( x μ − ε r δ r μ ) {\displaystyle \varphi (x^{\mu })\mapsto \varphi \left(x^{\mu }-\varepsilon _{r}\delta _{r}^{\mu }\right)} : that is, relabelling the coordinates is equivalent to leaving the coordinates in place while translating the field itself, which in turn is equivalent to transforming the field by replacing its value at each point x μ {\displaystyle x^{\mu }} with the value at the point x μ − ε X μ {\displaystyle x^{\mu }-\varepsilon X^{\mu }} "behind" it which would be mapped onto x μ {\displaystyle x^{\mu }} by the infinitesimal displacement under consideration. Since this is infinitesimal, we may write this transformation as
The Lagrangian density transforms in the same way, L ( x μ ) ↦ L ( x μ − ε r δ r μ ) {\displaystyle {\mathcal {L}}\left(x^{\mu }\right)\mapsto {\mathcal {L}}\left(x^{\mu }-\varepsilon _{r}\delta _{r}^{\mu }\right)} , so
and thus Noether's theorem corresponds [ 12 ] : 592 to the conservation law for the stress–energy tensor T μ ν , where we have used μ {\displaystyle \mu } in place of r {\displaystyle r} . To wit, by using the expression given earlier, and collecting the four conserved currents (one for each μ {\displaystyle \mu } ) into a tensor T {\displaystyle T} , Noether's theorem gives
with
(we relabelled μ {\displaystyle \mu } as σ {\displaystyle \sigma } at an intermediate step to avoid conflict). (However, the T {\displaystyle T} obtained in this way may differ from the symmetric tensor used as the source term in general relativity; see Canonical stress–energy tensor .)
The conservation of electric charge , by contrast, can be derived by considering Ψ linear in the fields φ rather than in the derivatives. [ 12 ] : 593–594 In quantum mechanics , the probability amplitude ψ ( x ) of finding a particle at a point x is a complex field φ , because it ascribes a complex number to every point in space and time. The probability amplitude itself is physically unmeasurable; only the probability p = | ψ | 2 can be inferred from a set of measurements. Therefore, the system is invariant under transformations of the ψ field and its complex conjugate field ψ * that leave | ψ | 2 unchanged, such as
a complex rotation. In the limit when the phase θ becomes infinitesimally small, δθ , it may be taken as the parameter ε , while the Ψ are equal to iψ and − iψ *, respectively. A specific example is the Klein–Gordon equation , the relativistically correct version of the Schrödinger equation for spinless particles, which has the Lagrangian density
In this case, Noether's theorem states that the conserved (∂ ⋅ j = 0) current equals
which, when multiplied by the charge on that species of particle, equals the electric current density due to that type of particle. This "gauge invariance" was first noted by Hermann Weyl , and is one of the prototype gauge symmetries of physics.
Consider the simplest case, a system with one independent variable, time. Suppose the dependent variables q are such that the action integral
I = ∫ t 1 t 2 L [ q [ t ] , q ˙ [ t ] , t ] d t {\displaystyle I=\int _{t_{1}}^{t_{2}}L[\mathbf {q} [t],{\dot {\mathbf {q} }}[t],t]\,dt}
is invariant under brief infinitesimal variations in the dependent variables. In other words, they satisfy the Euler–Lagrange equations
And suppose that the integral is invariant under a continuous symmetry. Mathematically such a symmetry is represented as a flow , φ , which acts on the variables as follows
where ε is a real variable indicating the amount of flow, and T is a real constant (which could be zero) indicating how much the flow shifts time.
The action integral flows to
which may be regarded as a function of ε . Calculating the derivative at ε = 0 and using Leibniz's rule , we get
Notice that the Euler–Lagrange equations imply
Substituting this into the previous equation, one gets
Again using the Euler–Lagrange equations we get
Substituting this into the previous equation, one gets
From which one can see that
is a constant of the motion, i.e., it is a conserved quantity. Since φ[ q , 0] = q , we get ∂ φ ∂ q = 1 {\displaystyle {\frac {\partial \varphi }{\partial \mathbf {q} }}=1} and so the conserved quantity simplifies to
To avoid excessive complication of the formulas, this derivation assumed that the flow does not change as time passes. The same result can be obtained in the more general case.
The Noether’s theorem can be seen as a consequence of the fundamental theorem of calculus (known by various names in physics such as the Generalized Stokes theorem or the Gradient theorem ): [ 13 ] for a function S {\textstyle S} analytical in a domain D {\textstyle {\cal {D}}} , ∫ P d S = 0 {\displaystyle \int _{\cal {\cal {P}}}dS=0}
where P {\textstyle {\cal {P}}} is a closed path in D {\textstyle {\cal {D}}} . Here, the function S ( q , t ) {\textstyle S(\mathbf {q} ,t)} is the action function that is computed by the integration of the Lagrangian over optimal trajectories or equivalently obtained through the Hamilton-Jacobi equation . As ∂ S / ∂ q = p {\textstyle \partial S/\partial \mathbf {q} =\mathbf {p} } (where p {\textstyle \mathbf {p} } is the momentum) and ∂ S / ∂ t = − H {\textstyle \partial S/\partial t=-H} (where H {\textstyle H} is the Hamiltonian), the differential of this function is given by d S = p d q − H d t {\textstyle dS=\mathbf {p} d\mathbf {q} -Hdt} .
Using the geometrical approach, the conserved quantity for a symmetry in Noether’s sense can be derived. The symmetry is expressed as an infinitesimal transformation: q ′ = q + ϵ ϕ q ( q , t ) t ′ = t + ϵ ϕ t ( q , t ) {\displaystyle {\begin{aligned}\mathbf {q'} &=&\mathbf {q} +\epsilon \phi _{\mathbf {q} }(\mathbf {q} ,t)\\t'&=&t+\epsilon \phi _{t}(\mathbf {q} ,t)\end{aligned}}} Let C {\textstyle {\cal {C}}} be an optimal trajectory and C ′ {\textstyle {\cal {C}}'} its image under the above transformation ( ϕ q , ϕ t ) T {\textstyle (\phi _{\mathbf {q} },\phi _{t})^{T}} (which is also an optimal trajectory). The closed path P {\textstyle {\cal {P}}} of integration is chosen as A B B ′ A ′ {\textstyle ABB'A'} , where the branches A B {\textstyle AB} and A ′ B ′ {\textstyle A'B'} are given C {\textstyle {\cal {C}}} and C ′ {\textstyle {\cal {C}}'} . By the hypothesis of Noether theorem, to the first order in ϵ {\textstyle \epsilon } , ∫ C d S = ∫ C ′ d S {\displaystyle \int _{\cal {C}}dS=\int _{{\cal {C}}'}dS} therefore, ∫ A A ′ d S = ∫ B B ′ d S {\displaystyle \int _{A}^{A'}dS=\int _{B}^{B'}dS} By definition, on the A A ′ {\textstyle AA'} branch we have d q = ϵ ϕ q ( q , t ) {\textstyle d\mathbf {q} =\epsilon \phi _{\mathbf {q} }(\mathbf {q} ,t)} and d t = ϵ ϕ t ( q , t ) {\textstyle dt=\epsilon \phi _{t}(\mathbf {q} ,t)} . Therefore, to the first order in ϵ {\textstyle \epsilon } , the quantity I = p ϕ q − H ϕ t {\displaystyle I=\mathbf {p} \phi _{\mathbf {q} }-H\phi _{t}} is conserved along the trajectory.
Noether's theorem may also be derived for tensor fields φ A {\displaystyle \varphi ^{A}} where the index A ranges over the various components of the various tensor fields. These field quantities are functions defined over a four-dimensional space whose points are labeled by coordinates x μ where the index μ ranges over time ( μ = 0) and three spatial dimensions ( μ = 1, 2, 3). These four coordinates are the independent variables; and the values of the fields at each event are the dependent variables. Under an infinitesimal transformation, the variation in the coordinates is written
whereas the transformation of the field variables is expressed as
By this definition, the field variations δ φ A {\displaystyle \delta \varphi ^{A}} result from two factors: intrinsic changes in the field themselves and changes in coordinates, since the transformed field α A depends on the transformed coordinates ξ μ . To isolate the intrinsic changes, the field variation at a single point x μ may be defined
If the coordinates are changed, the boundary of the region of space–time over which the Lagrangian is being integrated also changes; the original boundary and its transformed version are denoted as Ω and Ω’, respectively.
Noether's theorem begins with the assumption that a specific transformation of the coordinates and field variables does not change the action , which is defined as the integral of the Lagrangian density over the given region of spacetime. Expressed mathematically, this assumption may be written as
where the comma subscript indicates a partial derivative with respect to the coordinate(s) that follows the comma, e.g.
Since ξ is a dummy variable of integration, and since the change in the boundary Ω is infinitesimal by assumption, the two integrals may be combined using the four-dimensional version of the divergence theorem into the following form
The difference in Lagrangians can be written to first-order in the infinitesimal variations as
However, because the variations are defined at the same point as described above, the variation and the derivative can be done in reverse order; they commute
Using the Euler–Lagrange field equations
the difference in Lagrangians can be written neatly as
Thus, the change in the action can be written as
Since this holds for any region Ω, the integrand must be zero
For any combination of the various symmetry transformations, the perturbation can be written
where L X φ A {\displaystyle {\mathcal {L}}_{X}\varphi ^{A}} is the Lie derivative of φ A {\displaystyle \varphi ^{A}} in the X μ direction. When φ A {\displaystyle \varphi ^{A}} is a scalar or X μ , ν = 0 {\displaystyle {X^{\mu }}_{,\nu }=0} ,
These equations imply that the field variation taken at one point equals
Differentiating the above divergence with respect to ε at ε = 0 and changing the sign yields the conservation law
where the conserved current equals
Suppose we have an n -dimensional oriented Riemannian manifold , M and a target manifold T . Let C {\displaystyle {\mathcal {C}}} be the configuration space of smooth functions from M to T . (More generally, we can have smooth sections of a fiber bundle T over M .)
Examples of this M in physics include:
Now suppose there is a functional
called the action . (It takes values into R {\displaystyle \mathbb {R} } , rather than C {\displaystyle \mathbb {C} } ; this is for physical reasons, and is unimportant for this proof.)
To get to the usual version of Noether's theorem, we need additional restrictions on the action . We assume S [ φ ] {\displaystyle {\mathcal {S}}[\varphi ]} is the integral over M of a function
called the Lagrangian density , depending on φ {\displaystyle \varphi } , its derivative and the position. In other words, for φ {\displaystyle \varphi } in C {\displaystyle {\mathcal {C}}}
Suppose we are given boundary conditions , i.e., a specification of the value of φ {\displaystyle \varphi } at the boundary if M is compact , or some limit on φ {\displaystyle \varphi } as x approaches ∞. Then the subspace of C {\displaystyle {\mathcal {C}}} consisting of functions φ {\displaystyle \varphi } such that all functional derivatives of S {\displaystyle {\mathcal {S}}} at φ {\displaystyle \varphi } are zero, that is:
and that φ {\displaystyle \varphi } satisfies the given boundary conditions, is the subspace of on shell solutions. (See principle of stationary action )
Now, suppose we have an infinitesimal transformation on C {\displaystyle {\mathcal {C}}} , generated by a functional derivation , Q such that
for all compact submanifolds N or in other words,
for all x , where we set
If this holds on shell and off shell , we say Q generates an off-shell symmetry. If this only holds on shell , we say Q generates an on-shell symmetry. Then, we say Q is a generator of a one parameter symmetry Lie group .
Now, for any N , because of the Euler–Lagrange theorem, on shell (and only on-shell), we have
Since this is true for any N , we have
But this is the continuity equation for the current J μ {\displaystyle J^{\mu }} defined by: [ 14 ]
which is called the Noether current associated with the symmetry . The continuity equation tells us that if we integrate this current over a space-like slice, we get a conserved quantity called the Noether charge (provided, of course, if M is noncompact, the currents fall off sufficiently fast at infinity).
Noether's theorem is an on shell theorem: it relies on use of the equations of motion—the classical path. It reflects the relation between the boundary conditions and the variational principle. Assuming no boundary terms in the action, Noether's theorem implies that
The quantum analogs of Noether's theorem involving expectation values (e.g., ⟨ ∫ d 4 x ∂ ⋅ J ⟩ = 0 {\textstyle \left\langle \int d^{4}x~\partial \cdot {\textbf {J}}\right\rangle =0} ) probing off shell quantities as well are the Ward–Takahashi identities .
Suppose we have two symmetry derivations Q 1 and Q 2 . Then, [ Q 1 , Q 2 ] is also a symmetry derivation. Let us see this explicitly. Let us say Q 1 [ L ] ≈ ∂ μ f 1 μ {\displaystyle Q_{1}[{\mathcal {L}}]\approx \partial _{\mu }f_{1}^{\mu }} and Q 2 [ L ] ≈ ∂ μ f 2 μ {\displaystyle Q_{2}[{\mathcal {L}}]\approx \partial _{\mu }f_{2}^{\mu }}
Then, [ Q 1 , Q 2 ] [ L ] = Q 1 [ Q 2 [ L ] ] − Q 2 [ Q 1 [ L ] ] ≈ ∂ μ f 12 μ {\displaystyle [Q_{1},Q_{2}][{\mathcal {L}}]=Q_{1}[Q_{2}[{\mathcal {L}}]]-Q_{2}[Q_{1}[{\mathcal {L}}]]\approx \partial _{\mu }f_{12}^{\mu }} where f 12 = Q 1 [ f 2 μ ] − Q 2 [ f 1 μ ]. So, j 12 μ = ( ∂ ∂ ( ∂ μ φ ) L ) ( Q 1 [ Q 2 [ φ ] ] − Q 2 [ Q 1 [ φ ] ] ) − f 12 μ . {\displaystyle j_{12}^{\mu }=\left({\frac {\partial }{\partial (\partial _{\mu }\varphi )}}{\mathcal {L}}\right)(Q_{1}[Q_{2}[\varphi ]]-Q_{2}[Q_{1}[\varphi ]])-f_{12}^{\mu }.}
This shows we can extend Noether's theorem to larger Lie algebras in a natural way.
This applies to any local symmetry derivation Q satisfying QS ≈ 0, and also to more general local functional differentiable actions, including ones where the Lagrangian depends on higher derivatives of the fields. Let ε be any arbitrary smooth function of the spacetime (or time) manifold such that the closure of its support is disjoint from the boundary. ε is a test function . Then, because of the variational principle (which does not apply to the boundary, by the way), the derivation distribution q generated by q [ ε ][Φ( x )] = ε ( x ) Q [Φ( x )] satisfies q [ ε ][ S ] ≈ 0 for every ε , or more compactly, q ( x )[ S ] ≈ 0 for all x not on the boundary (but remember that q ( x ) is a shorthand for a derivation distribution , not a derivation parametrized by x in general). This is the generalization of Noether's theorem.
To see how the generalization is related to the version given above, assume that the action is the spacetime integral of a Lagrangian that only depends on φ {\displaystyle \varphi } and its first derivatives. Also, assume
Then,
for all ε {\displaystyle \varepsilon } .
More generally, if the Lagrangian depends on higher derivatives, then
Looking at the specific case of a Newtonian particle of mass m , coordinate x , moving under the influence of a potential V , coordinatized by time t . The action , S , is:
The first term in the brackets is the kinetic energy of the particle, while the second is its potential energy . Consider the generator of time translations Q = d d t {\displaystyle Q={\frac {d}{dt}}} . In other words, Q [ x ( t ) ] = x ˙ ( t ) {\displaystyle Q[x(t)]={\dot {x}}(t)} . The coordinate x has an explicit dependence on time, whilst V does not; consequently:
so we can set
Then,
The right hand side is the energy, and Noether's theorem states that d j / d t = 0 {\displaystyle dj/dt=0} (i.e. the principle of conservation of energy is a consequence of invariance under time translations).
More generally, if the Lagrangian does not depend explicitly on time, the quantity
(called the Hamiltonian ) is conserved.
Still considering 1-dimensional time, let
for N {\displaystyle N} Newtonian particles where the potential only depends pairwise upon the relative displacement.
For Q → {\displaystyle {\vec {Q}}} , consider the generator of Galilean transformations (i.e. a change in the frame of reference). In other words,
And
This has the form of d d t ∑ α m α x α i {\textstyle {\frac {d}{dt}}\sum _{\alpha }m_{\alpha }x_{\alpha }^{i}} so we can set
Then,
where P → {\displaystyle {\vec {P}}} is the total momentum, M is the total mass and x → C M {\displaystyle {\vec {x}}_{CM}} is the center of mass. Noether's theorem states:
Both examples 1 and 2 are over a 1-dimensional manifold (time). An example involving spacetime is a conformal transformation of a massless real scalar field with a quartic potential in (3 + 1)- Minkowski spacetime .
For Q , consider the generator of a spacetime rescaling. In other words,
The second term on the right hand side is due to the "conformal weight" of φ {\displaystyle \varphi } . And
This has the form of
(where we have performed a change of dummy indices) so set
Then
Noether's theorem states that ∂ μ j μ = 0 {\displaystyle \partial _{\mu }j^{\mu }=0} (as one may explicitly check by substituting the Euler–Lagrange equations into the left hand side).
If one tries to find the Ward–Takahashi analog of this equation, one runs into a problem because of anomalies .
Application of Noether's theorem allows physicists to gain powerful insights into any general theory in physics, by just analyzing the various transformations that would make the form of the laws involved invariant. For example:
In quantum field theory , the analog to Noether's theorem, the Ward–Takahashi identity , yields further conservation laws, such as the conservation of electric charge from the invariance with respect to a change in the phase factor of the complex field of the charged particle and the associated gauge of the electric potential and vector potential .
The Noether charge is also used in calculating the entropy of stationary black holes . [ 15 ] | https://en.wikipedia.org/wiki/Noether's_theorem |
In mathematics, Noether identities characterize the degeneracy of a Lagrangian system. Given a Lagrangian system and its Lagrangian L , Noether identities can be defined as a differential operator whose kernel contains a range of the Euler–Lagrange operator of L . Any Euler–Lagrange operator obeys Noether identities which therefore are separated into the trivial and non-trivial ones. A Lagrangian L is called degenerate if the Euler–Lagrange operator of L satisfies non-trivial Noether identities. In this case Euler–Lagrange equations are not independent.
Noether identities need not be independent, but satisfy first-stage Noether identities, which are subject to the second-stage Noether identities and so on. Higher-stage Noether identities also are separated into trivial and non-trivial cases. A degenerate Lagrangian is called reducible if there exist non-trivial higher-stage Noether identities. Yang–Mills gauge theory and gauge gravitation theory exemplify irreducible Lagrangian field theories.
Different variants of second Noether’s theorem state the one-to-one correspondence between the non-trivial reducible Noether identities and the non-trivial reducible gauge symmetries . Formulated in a very general setting, second Noether’s theorem associates to the Koszul–Tate complex of reducible Noether identities, parameterized by antifields , the BRST complex of reducible gauge symmetries parameterized by ghosts . This is the case of covariant classical field theory and Lagrangian BRST theory .
This article about theoretical physics is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Noether_identities |
In mathematics , the Noether inequality , named after Max Noether , is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold . It holds more generally for minimal projective surfaces of general type over an algebraically closed field.
Let X be a smooth minimal projective surface of general type defined over an algebraically closed field (or a smooth minimal compact complex surface of general type) with canonical divisor K = − c 1 ( X ), and let p g = h 0 ( K ) be the dimension of the space of holomorphic two forms, then
For complex surfaces, an alternative formulation expresses this inequality in terms of topological invariants of the underlying real oriented four manifold. Since a surface of general type is a Kähler surface, the dimension of the maximal positive subspace in intersection form on the second cohomology is given by b + = 1 + 2 p g . Moreover, by the Hirzebruch signature theorem c 1 2 ( X ) = 2 e + 3 σ , where e = c 2 ( X ) is the topological Euler characteristic and σ = b + − b − is the signature of the intersection form . Therefore, the Noether inequality can also be expressed as
or equivalently using e = 2 – 2 b 1 + b + + b −
Combining the Noether inequality with the Noether formula 12χ= c 1 2 + c 2 gives
where q is the irregularity of a surface , which leads to
a slightly weaker inequality, which is also often called the Noether inequality:
Surfaces where equality holds (i.e. on the Noether line) are called Horikawa surfaces .
It follows from the minimal general type condition that K 2 > 0. We may thus assume that p g > 1, since the inequality is otherwise automatic. In particular, we may assume there is an effective divisor D representing K . We then have an exact sequence
so p g − 1 ≤ h 0 ( K | D ) . {\displaystyle p_{g}-1\leq h^{0}(K|_{D}).}
Assume that D is smooth. By the adjunction formula D has a canonical linebundle O D ( 2 K ) {\displaystyle {\mathcal {O}}_{D}(2K)} , therefore K | D {\displaystyle K|_{D}} is a special divisor and the Clifford inequality applies, which gives
In general, essentially the same argument applies using a more general version of the Clifford inequality for local complete intersections with a dualising line bundle and 1-dimensional sections in the trivial line bundle. These conditions are satisfied for the curve D by the adjunction formula and the fact that D is numerically connected. | https://en.wikipedia.org/wiki/Noether_inequality |
In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite length. Noetherian objects are named after Emmy Noether , who was the first to study the ascending and descending chain conditions for rings. Specifically: | https://en.wikipedia.org/wiki/Noetherian |
Nofence is a Norwegian company that makes GPS collars for farm animals (cattle, sheep, and goats) that discourage them from crossing virtual fence boundaries. [ 1 ] [ 2 ]
Oscar Hovde Berntsen has been working on the idea of virtual fencing, as an alternative to fixed electric fencing , since the 1990s. [ 3 ] Nofence was incorporated in 2011. [ 3 ] In 2016, there was a pilot project in Norway with 850 goats. [ 3 ] The Norwegian Food Safety Authority approved the use of Nofence for goats in 2017, then for cattle and sheep in 2020. [ 3 ] Nofence were founded in Batnfjordsøra , Norway , and is today based in Molde , Trondheim , and Oslo in Norway, with offices in the United Kingdom , Ireland , Spain and the United States . [ 3 ]
The solar-powered collars play an audible tone when the animal reaches the pasture boundary, and if they continue, the collar delivers a small shock, similar to what an animal might receive from a fixed electric fence . [ 4 ] Farmers can use a mobile app to change boundaries and monitor the animals throughout the day, and avoid over-grazing . [ 2 ] Fenceless grazing is being supported by conservationists and farmers, particularly in sensitive areas or difficult upland areas where physical fencing would be impractical, expensive or inappropriate. [ 4 ]
In September 2020, The Times reported that trials were being conducted at six sites in the UK, including Epping Forest in Essex. [ 1 ]
In December 2020, Nofence stated that 17,000 collars were in use in Norway. [ 2 ]
By January 2025, over 150,000 collars were in use worldwide, and the number of customers had surpassed 7,000. | https://en.wikipedia.org/wiki/Nofence |
Noise, vibration, and harshness ( NVH ), also known as noise and vibration ( N&V ), is the study and modification of the noise and vibration characteristics of vehicles , particularly cars and trucks . While noise and vibration can be readily measured, harshness is a subjective quality, and is measured either via jury evaluations, or with analytical tools that can provide results reflecting human subjective impressions. The latter tools belong to the field psychoacoustics .
Interior NVH deals with noise and vibration experienced by the occupants of the cabin , while exterior NVH is largely concerned with the noise radiated by the vehicle, and includes drive-by noise testing.
NVH is mostly engineering, but often objective measurements fail to predict or correlate well with the subjective impression on human observers. For example, although the ear's response at moderate noise levels is approximated by A-weighting , two different noises with the same A-weighted level are not necessarily equally disturbing. The field of psychoacoustics is partly concerned with this correlation.
In some cases, the NVH engineer is asked to change the sound quality, by adding or subtracting particular harmonics, rather than making the vehicle quieter.
Noise, vibration, and harshness for vehicles can be distinguished easily by quantifying the frequency. Vibration is between 0.5 Hz and 50 Hz, noise is between 20 Hz and 5000 Hz, and harshness takes the coupling of noise and vibration.
The sources of noise in a vehicle can be classified as:
Many problems are generated as either vibration or noise, transmitted via a variety of paths, and then radiated acoustically into the cabin. [ 1 ] These are classified as "structure-borne" noise. Others are generated acoustically and propagated by airborne paths. Structure-borne noise is attenuated by isolation, while airborne noise is reduced by absorption or through the use of barrier materials. Vibrations are sensed at the steering wheel, the seat, armrests, or the floor and pedals. Some problems are sensed visually, such as the vibration of the rear-view mirror or header rail on open-topped cars.
NVH can be tonal such as engine noise, or broadband, such as road noise or wind noise, normally. Some resonant systems respond at characteristic frequencies, but in response to random excitation. Therefore, although they look like tonal problems on any one spectrum, their amplitude varies considerably. Other problems are self-resonant , such as whistles from antennas.
Tonal noises often have harmonics . Below is the noise spectrum of Michael Schumacher 's Ferrari at 16680 rpm, showing the various harmonics. The x- axis is given in terms of multiples of engine speed. The y- axis is logarithmic, and uncalibrated.
Typical instrumentation used to measure NVH include microphones , accelerometers , and force gauges or load cells. Many NVH facilities have semi- anechoic chambers , and rolling road dynamometers . Typically, signals are recorded directly to the hard drive via an analog-to-digital converter . In the past, magnetic or DAT tape recorders were used. The integrity of the signal chain is very important, typically each of the instruments used are fully calibrated in a laboratory once per year, and any given setup is calibrated as a whole once per day.
Laser scanning vibrometry is an essential tool for effective NVH optimization. The vibrational characteristics of a sample is acquired full-field under operational or excited conditions. The results represent the actual vibrations. No added mass is influencing the measurement, as the sensor is light itself.
Techniques used to help identify NVH include part substitution, modal analysis , rig squeak and rattle tests (complete vehicle or component/system tests), lead cladding, acoustic intensity , transfer path analysis, and partial coherence. Most NVH work is done in the frequency domain, using fast Fourier transforms to convert the time domain signals into the frequency domain. Wavelet analysis, order analysis, statistical energy analysis , and subjective evaluation of signals modified in real time are also used.
NVH analysis needs good representative prototypes of the production vehicle for testing. These are needed early in the design process as the solutions often need substantial modification to the design, forcing in engineering changes which are much less expensive when made early. These early prototypes are very expensive, so there has been great interest in computer aided predictive techniques for NVH.
One example is the modeling works for structure borne noise and vibration analysis. When the phenomenon being considered occurs below, for example, 25–30 Hz, the idle shaking of the powertrain, a multi-body model can be used. In contrast, when the phenomenon being considered occurs at relatively high frequency – for example, above 1 kHz – a statistical energy analysis (SEA) model may be a better approach.
For the mid-frequency band, various methodologies exist, such as vibro-acoustic finite element analysis , and boundary element analysis . The structure can be coupled to the interior cavity and form a fully coupled equation system. Also, other techniques exist that can mix measured data with finite element or boundary element data.
There are three principal means of improving NVH:
Deciding which of these (or what combination) to use in solving a particular problem is one of the challenges facing the NVH engineer.
Specific methods for improving NVH include the use of tuned mass dampers , subframes , balancing , modifying the stiffness or mass of structures, retuning exhausts and intakes , modifying the characteristics of elastomeric isolators, adding sound deadening or absorbing materials, and using active noise control . In some circumstances, substantial changes in vehicle architecture may be the only way to cure some problems cost-effectively.
Not-for-profit organizations such as the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) and Vibration Isolation and Seismic Control Manufacturers Association (VISCMA) provide specifications, standards, and requirements that cover a wide array of industries including electrical, mechanical, plumbing, and HVAC. | https://en.wikipedia.org/wiki/Noise,_vibration,_and_harshness |
Noise-cancelling headphones are headphones that suppress unwanted ambient sounds using active noise control ( ANC ).
Active noise cancellation makes it possible to listen to audio content without raising the volume excessively. In an aviation environment, noise-cancelling headphones increase the signal-to-noise ratio significantly more than passive noise attenuating headphones or no headphones, making hearing important information such as safety announcements easier. [ 1 ] Noise-cancelling headphones can improve listening enough to completely offset the effect of a distracting concurrent activity. [ 2 ]
To cancel the lower- frequency portions of the noise, noise-cancelling headphones use active noise control. A microphone captures the targeted ambient sounds, and a small amplifier generates sound waves that are exactly out of phase with the undesired sounds. When the sound pressure of the noise wave is high, the cancelling wave is low (and vice versa). The opposite sound waves collide and are eliminated or "cancelled" ( destructive interference ). Most noise-cancelling headsets in the consumer market generate the noise-cancelling waveform in real time with analog technology. In contrast, other active noise and vibration control products use soft real-time digital processing . According to an experiment conducted to test how lightweight earphones reduced noise as compared to commercial headphones and earphones, lightweight headphones achieved better noise reduction than normal headphones. The experiment also supported that in-ear headphones worked better at reducing noise than outer-ear headphones. [ 3 ]
Cancellation focuses on constant droning sounds like road noise and is less effective on short/sharp sounds like voices or breaking glass. It also is ineffective in eliminating higher frequency noises like the sound of spraying. Noise-cancelling headphones often combine sound isolation with ANC to maximize the sound reduction across the frequency spectrum. Noise cancellation can also be used without sound isolation to make wanted sounds (such as voices) easier to hear. Noise cancellation to eliminate ambient noise is never passive because of the circuitry required, so references to passive noise cancellation actually are referring to products featuring sound isolation.
To prevent higher-frequency noise from reaching the ear, most noise-cancelling headphones depend on sound isolation or soundproofing. Higher-frequency sound has a shorter wavelength , and cancelling this sound would require locating devices to detect and counteract it closer to the listener's eardrum than is currently technically feasible or would require digital algorithms that would complicate the headphone's electronics. [ 4 ]
Noise-cancelling headphones specify the amount of noise they can cancel in terms of decibels . This number may be useful for comparing products but does not tell the whole story, as it does not specify noise reduction at various frequencies.
By the 1950s, Lawrence J. Fogel created systems and submitted patents regarding active noise cancellation in the field of aviation . This system was designed to reduce noise for the pilots in the cockpit area and help make their communication easier and protect hearing. Fogel is considered to be the inventor of active noise cancellation, and he designed one of the first noise-cancelling headphones systems. Later on, Willard Meeker designed an active noise control model that was applied to circumaural earmuffs for advanced hearing protection. Noise-cancelling aviation headsets are now commonly available. [ 5 ] [ 6 ]
In 1989, Bose Corporation introduced its Aviation Headset Series I , which became the first commercially available ANR headset. [ 7 ]
Several airlines provide noise-cancelling headphones in their business and first-class cabins. Bose started supplying American Airlines with noise-cancelling headphones in 1999 and started offering the "Quiet Comfort" line for the general consumer in 2000. [ 7 ]
Aside from its role in communication and occupational health, ANC is used to protect wearers from lower levels of noise that still impact people sensitive to noise.
Noise-cancellation headphones have been used as sleeping aids. [ 8 ] Both passive isolating and active noise-cancellation headphones or earplugs help to achieve a reduction of ambient sounds, which is particularly helpful for people suffering from insomnia or other sleeping disorders, for whom sounds such as cars honking and snoring impact their ability to sleep. For that reason, noise-cancelling sleep headphones and earplugs are designed to cater to this segment of patients. [ 9 ]
Noise-cancelling headphones have been provided for patients in intensive care units to reduce the noise exposure they face while in a hospital environment. Active noise control technology has been shown to reduce noise exposure, which is associated with sleep disturbance, delirium, and morbidity. [ 10 ]
Many neurodivergent people, particularly autistic people or people with ADHD , are sensitive to everyday noises, and benefit from using ANC. [ 11 ] A December 2016 study from the Hong Kong Journal of Occupational Therapy found that noise-cancellation headphones helped children with autism spectrum disorder cope with behaviors related to hyper-reactivity and auditory stimuli . [ 12 ]
There is a general danger that listening to loud music in headphones can distract the listener and lead to injury and accidents. [ 13 ] [ 14 ] Noise-cancelling headphones add extra risk. Several countries and states have made it illegal to wear headphones while driving or cycling. [ 15 ]
It is not uncommon to get a pressure-like feeling when using noise-cancelling headphones initially. This is caused by the lack of low-frequency sounds being perceived as a pressure differential between the inner and outer ear. [ 16 ] [ 17 ] [ 18 ]
The active noise control requires power, usually supplied by a USB port or a battery that must occasionally be replaced or recharged . Without power, some models do not function as regular headphones. Any battery and additional electronics may increase the size and weight of the headphones compared to regular headphones. The noise-cancelling circuitry may reduce audio quality and add high-frequency hiss, although reducing the noise may result in higher perceived audio quality. [ 19 ] | https://en.wikipedia.org/wiki/Noise-cancelling_headphones |
Noise-domain reflectometry is a type of reflectometry where the reflectometer exploits existing data signals on wiring and does not have to generate any signals itself. [ 1 ] Noise-domain reflectometry, like time-domain and spread-spectrum time domain reflectometers , is most often used in identifying the location of wire faults in electrical lines.
Time-domain reflectometers work by generating a signal and then sending that signal down the wireline and examining the reflected signal . [ 2 ] Noise-domain reflectometers (NDRs) provide the benefit of locating wire faults without introducing an external signal because the NDR examines the existing signals on the line to identify wire faults. This technique is particularly useful in the testing of live wires where data integrity on the wires is critical. For example, NDRs can be used for monitoring aircraft wiring while in flight. | https://en.wikipedia.org/wiki/Noise-domain_reflectometry |
In optics the noise-equivalent flux density ( NEFD ) or noise-equivalent irradiance ( NEI ) of a system is the level of flux density required to be equivalent to the noise present in the system. [ 1 ] It is a measure used by astronomers in determining the accuracy of observations. [ 2 ]
The NEFD can be related to a light detector's noise-equivalent power for a collection area A and a photon bandwidth ν {\displaystyle \nu } by:
N E F D = η N E P A ν {\displaystyle \mathrm {NEFD} =\eta {\frac {\mathrm {NEP} }{A\nu }}} ,
where a factor η {\displaystyle \eta } (often 2, in the case of switching between measuring a source and measuring off-source) accounts for the photon statistics for the mode of operation.
External quantum efficiency
This optics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Noise-equivalent_flux_density |
Noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy ( NICE-OHMS ) is an ultra-sensitive laser-based absorption technique that utilizes laser light to assess the concentration or the amount of a species in gas phase by absorption spectrometry (AS).
The NICE-OHMS technique combines cavity enhanced absorption spectrometry (CEAS) for prolonged interaction length with the sample with frequency modulation (fm) spectrometry FMS for reduction of 1/f noise . By choosing the fm-modulation frequency equal to the free spectral range (FSR) of the cavity, all components of the spectral fm-triplet are transmitted through the cavity in an identical manner. Therefore, the cavity does not compromise the balance of the fm-triplet, which otherwise would give rise to fm-background signals. It also does not convert any fluctuations of the laser frequency with respect to the transmission mode of the cavity to intensity modulation, which would deteriorate the detectability by the introduction of intensity noise. This is referred to as "noise immunity". All this implies that FMS can be performed as if the cavity were not present, yet fully benefiting from the prolonged interaction length. [ citation needed ]
A variety of signals can be obtained by NICE-OHMS. [ citation needed ] First, due to the presence of high intensity counter-propagating beams in the cavity, both Doppler-broadened and Doppler-free signals can be obtained. The former have the advantage of being present at high intracavity pressures, which is suitable when atmospheric pressure samples are analyzed, whereas the latter provide narrow frequency features, which is of importance for frequency standard applications, but also opens up possibilities for interference-free detection. Second, due to the use of FMS, both absorption and dispersion signals can be detected (or a combination thereof). Third, to reduce the influence of low frequency noise, wavelength modulation ( wm ) can additionally be applied, which implies that the technique can be operated in either fm or wm mode. [ citation needed ]
The mode of operation to be preferred depends on the particular application of the technique and on the prevailing experimental conditions, mainly the type of noise or background signal that limits the detectability.
Frequency modulated Doppler-broadened signals can be modeled basically as ordinary fm -signals, although an extended description has to be used if the transition is optically saturated. Wavelength modulated Doppler broadened can be modeled by applying the conventional theory for wavelength modulation on the fm-signals.
Since the electrical field in NICE-OHMS consists of three modes, a carrier and two sidebands, which propagate in positive and negative directions in the cavity, up to nine sub-Doppler signals can appear; four appearing at the absorption and five at the dispersion phase. Each of these signals can, in turn, originate from interactions between several groups of molecules with various pairs of modes (e.g. carrier-carrier, sideband-carrier, sideband-sideband in various combinations). In addition, since sub-Doppler signals necessarily involve optical saturation, each of these interactions has to be modeled by a more extensive description. This implies that the situation can be complex. In fact, there are still some types of sub-Doppler signals for which there so far are no adequate theoretical description. [ citation needed ]
Some typical Doppler-broadened NICE-OHMS signals, from 13 ppb (10 μTorr, 13•10 −9 atm) of C 2 H 2 detected in a cavity with a finesse of 4800, are shown in the figure. (a) fm - and (b) wm -signal. Individual markers: measured data; Solid curves: theoretical fits.
The unique features of NICE-OHMS, in particular its high sensitivity, imply that it has a large potential for a variety of applications. First developed for frequency standard applications, [ 1 ] [ 2 ] with an astonishing detectability of 10 −14 cm −1 , it has later been used for spectroscopic investigations as well as chemical sensing and trace species detection, with detectabilities in the 10 −11 - 10 −10 cm −1 range. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] However, although the NICE-OHMS technique has shown to possess an extremely high detectability, it has so far only sparsely been developed towards trace gas analysis.
One of the biggest hurdles for implementation of the NICE-OHMS technique is indisputably the locking of the frequency of the laser to that of a cavity mode. Although the requirements for the performance of the lock are less stringent than for other direct cw-CEAS techniques (due to the noise-immune principle), the laser frequency still has to be kept locked within the cavity mode during signal acquisition, i.e. it should follow the mode while the cavity is scanned, including a possible wavelength modulation. It can be difficult to achieve these goals if the free-running linewidth of the laser is significantly larger than the cavity mode width and if the laser is prone to sudden frequency excursions due to technical noise from the surroundings. This is usually the case when working with medium- or high finesse cavities (with transmission mode widths in the low kHz range) and standard types of lasers, e.g. external cavity diode lasers (ECDLs), with free-running linewidths in the MHz range. Electronic feedback loops with high bandwidths (typically a few MHz) and high gain are then needed to couple a substantial amount of the laser power into a cavity mode and to ensure stable performance of the lock. [ citation needed ]
With the advent of narrow linewidth fiber lasers , the problems connected to laser locking can be significantly reduced. Fiber lasers with free-running linewidths as narrow as 1 kHz (measured over a fraction of a second), thus two to three orders of magnitude below those of ECDLs, are available today. Evidently, this feature simplifies the feedback electronics (bandwidths as low as 10 kHz are sufficient) and the locking procedure considerably. Moreover, the design and working principle of fiber lasers make them less affected by external disturbances, e.g. mechanical and acoustical noise, than other solid state lasers or ECDLs. In addition, the availability of integrated-optics components, such as fiber based electro-optic modulators (fiber EOMs), offers the possibility to further reduce the complexity of the setup. The first realizations of a NICE-OHMS system based upon a fiber laser and a fiber EOM have recently been demonstrated. It was shown that C 2 H 2 could be detected down to 4.5•10 −12 atm (4.5 ppt) with an instrumentation that is very sturdy. [ 12 ] It is clear that this has brought NICE-OHMS a step closer to become a practically useful technique for ultra-sensitive trace species detection! [ 13 ] | https://en.wikipedia.org/wiki/Noise-immune_cavity-enhanced_optical_heterodyne_molecular_spectroscopy |
Noise-induced order is a mathematical phenomenon appearing in the Matsumoto-Tsuda [ 1 ] model of the Belosov-Zhabotinski reaction .
In this model, adding noise to the system causes a transition from a "chaotic" behaviour to a more "ordered" behaviour; this article was a seminal paper in the area and generated a big number of citations [ 1 ] and gave birth to a line of research in applied mathematics and physics . [ 2 ] [ 3 ] This phenomenon was later observed in the Belosov-Zhabotinsky reaction. [ 4 ]
Interpolating experimental data from the Belosouv-Zabotinsky reaction, [ 5 ] Matsumoto and Tsuda introduced a one-dimensional model, a random dynamical system with uniform additive noise, driven by the map:
T ( x ) = { ( a + ( x − 1 8 ) 1 3 ) e − x + b , 0 ≤ x ≤ 0.3 c ( 10 x e − 10 x 3 ) 19 + b 0.3 ≤ x ≤ 1 {\displaystyle T(x)={\begin{cases}(a+(x-{\frac {1}{8}})^{\frac {1}{3}})e^{-x}+b,&0\leq x\leq 0.3\\c(10xe^{\frac {-10x}{3}})^{19}+b&0.3\leq x\leq 1\end{cases}}}
where
This random dynamical system is simulated with different noise amplitudes using floating-point arithmetic and the Lyapunov exponent along the simulated orbits is computed; the Lyapunov exponent of this simulated system was found to transition from positive to negative as the noise amplitude grows. [ 1 ]
The behavior of the floating point system and of the original system may differ; [ 6 ] therefore, this is not a rigorous mathematical proof of the phenomenon.
A computer assisted proof of noise-induced order for the Matsumoto-Tsuda map with the parameters above was given in 2017. [ 7 ] In 2020 a sufficient condition for noise-induced order was given for one dimensional maps: [ 8 ] the Lyapunov exponent for small noise sizes is positive, while the average of the logarithm of the derivative with respect to Lebesgue is negative. | https://en.wikipedia.org/wiki/Noise-induced_order |
A noise barrier (also called a soundwall , noise wall , sound berm , sound barrier , or acoustical barrier ) is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution . Noise barriers are the most effective method of mitigating roadway , railway, and industrial noise sources –
other than cessation of the source activity or use of source controls.
In the case of surface transportation noise, other methods of reducing the source noise intensity include encouraging the use of hybrid and electric vehicles , improving automobile aerodynamics and tire design, and choosing low-noise paving material . Extensive use of noise barriers began in the United States after noise regulations were introduced in the early 1970s.
Noise barriers have been built in the United States since the mid-twentieth century, when vehicular traffic burgeoned. I-680 in Milpitas, California was the first noise barrier. [ 1 ] In the late 1960s, analytic acoustical technology emerged to mathematically evaluate the efficacy of a noise barrier design adjacent to a specific roadway . By the 1990s, noise barriers that included use of transparent materials were being designed in Denmark and other western European countries. [ 2 ]
The best of these early computer models considered the effects of roadway geometry , topography , vehicle volumes, vehicle speeds, truck mix, road surface type, and micro- meteorology . Several U.S. research groups developed variations of the computer modeling techniques: Caltrans Headquarters in Sacramento, California ; the ESL Inc. group in Sunnyvale, California ; the Bolt, Beranek and Newman [ 3 ] group in Cambridge, Massachusetts , and a research team at the University of Florida . Possibly the earliest published work that scientifically designed a specific noise barrier was the study for the Foothill Expressway in Los Altos, California . [ 4 ]
Numerous case studies across the U.S. soon addressed dozens of different existing and planned highways. Most were commissioned by state highway departments and conducted by one of the four research groups mentioned above. The U.S. National Environmental Policy Act , enacted in 1970, effectively mandated the quantitative analysis of noise pollution from every Federal-Aid Highway Act Project in the country, propelling noise barrier model development and application. With passage of the Noise Control Act of 1972 , [ 5 ] demand for noise barrier design soared from a host of noise regulation spinoff.
By the late 1970s, more than a dozen research groups in the U.S. were applying similar computer modeling technology and addressing at least 200 different locations for noise barriers each year. As of 2006 [update] , this technology is considered a standard in the evaluation of noise pollution from highways. The nature and accuracy of the computer models used is nearly identical to the original 1970s versions of the technology.
Small and purposeful gaps exist in most noise barriers to allow firefighters to access nearby fire hydrants and pull through fire hoses , which are usually denoted by a sign indicating the nearest cross street, and a pictogram of a fire hydrant, though some hydrant gaps channel the hoses through small culvert channels beneath the wall.
The acoustical science of noise barrier design is based upon treating an airway or railway as a line source . [ dubious – discuss ] The theory is based upon blockage of sound ray travel toward a particular receptor ; however, diffraction of sound must be addressed. Sound waves bend (downward) when they pass an edge, such as the apex of a noise barrier. Barriers that block line of sight of a highway or other source will therefore block more sound. [ 6 ] Further complicating matters is the phenomenon of refraction , the bending of sound rays in the presence of an inhomogeneous atmosphere . Wind shear and thermocline produce such inhomogeneities. The sound sources modeled must include engine noise, tire noise, and aerodynamic noise, all of which vary by vehicle type and speed.
The noise barrier may be constructed on private land, on a public right-of-way , or on other public land. Because sound levels are measured using a logarithmic scale , a reduction of nine decibels is equivalent to elimination of approximately 86 percent of the unwanted sound power.
Several different materials may be used for sound barriers, including masonry, earthwork (such as earth berm ), steel, concrete, wood, plastics, insulating wool, or composites. [ 7 ] Walls that are made of absorptive material mitigate sound differently than hard surfaces. [ 8 ] It is also possible to make noise barriers with active materials such as solar photovoltaic panels to generate electricity while also reducing traffic noise. [ 9 ] [ 10 ] [ 11 ]
A wall with porous surface material and sound-dampening content material can be absorptive where little or no noise is reflected back towards the source or elsewhere. Hard surfaces such as masonry or concrete are considered to be reflective where most of the noise is reflected back towards the noise source and beyond. [ 12 ]
Noise barriers can be effective tools for noise pollution abatement, but certain locations and topographies are not suitable for use of noise barriers. Cost and aesthetics also play a role in the choice of noise barriers. In some cases, a roadway is surrounded by a noise abatement structure or dug into a tunnel using the cut-and-cover method.
Potential disadvantages of noise barriers include:
Roadside noise barriers have been shown to reduce the near-road air pollution concentration levels. Within 15–50 m from the roadside, air pollution concentration levels at the lee side of the noise barriers may be reduced by up to 50% compared to open road values. [ 13 ]
Noise barriers force the pollution plumes coming from the road to move up and over the barrier creating the effect of an elevated source and enhancing vertical dispersion of the plume. The deceleration and the deflection of the initial flow by the noise barrier force the plume to disperse horizontally. A highly turbulent shear zone characterized by slow velocities and a re-circulation cavity is created in the lee of the barrier which further enhances the dispersion; this mixes ambient air with the pollutants downwind behind the barrier. [ 14 ] | https://en.wikipedia.org/wiki/Noise_barrier |
In the design of radio receivers , a noise blanker is a circuit intended to reduce the effect of certain kinds of radio noise on a received signal. [ 1 ] It is often used on broadcast shortwave receivers or communications receivers and some types of two-way radio transceivers . [ 2 ] The noise blanker is only effective on impulse-type noise such as from lightning or from automotive ignition systems, and cannot improve performance on wideband continuous background noise, or interfering signals on the same frequency. [ 3 ] In cases where there are strong signals on frequencies near to the desired frequency, a noise blanker circuit may be ineffective and may reduce the quality of the received signal. [ 4 ]
Typically this is a network in the intermediate frequency section of the receiver; when a pulse of noise passes through the IF amplifiers , it is usually of greater amplitude than the desired signal. The noise blanker circuit momentarily reduces the gain of the IF stage during the impulse. [ 5 ] More complex noise blankers may use a secondary IF stage and have adjustable threshold and timing characteristics so as to reduce the noise passed through to the audio stages of the receiver.
A noise blanker is best applied before any narrow-bandwidth filters in the signal path, so as not to introduce "ringing" and distortion in the filtered signal. Noise blankers are most useful with amplitude modulation or single sideband signals. Frequency modulation receivers generally include a signal limiter stage which tends to reject noise pulses. | https://en.wikipedia.org/wiki/Noise_blanker |
Noise control or noise mitigation is a set of strategies to reduce noise pollution or to reduce the impact of that noise, whether outdoors or indoors.
The main areas of noise mitigation or abatement are: transportation noise control, architectural design, urban planning through zoning codes , [ 1 ] and occupational noise control. Roadway noise and aircraft noise are the most pervasive sources of environmental noise. [ 2 ] Social activities may generate noise levels that consistently affect the health of populations residing in or occupying areas, both indoor and outdoor, near entertainment venues that feature amplified sounds and music that present significant challenges for effective noise mitigation strategies.
Multiple techniques have been developed to address interior sound levels, many of which are encouraged by local building codes . In the best case of project designs, planners are encouraged to work with design engineers to examine trade-offs of roadway design and architectural design. These techniques include design of exterior walls, party walls, and floor and ceiling assemblies; moreover, there are a host of specialized means for damping reverberation from special-purpose rooms such as auditoria , concert halls , entertainment and social venues, dining areas, audio recording rooms, and meeting rooms.
Many of these techniques rely upon material science applications of constructing sound baffles or using sound-absorbing liners for interior spaces. Industrial noise control is a subset of interior architectural control of noise, with emphasis on specific methods of sound isolation from industrial machinery and for protection of workers at their task stations.
Sound masking is the active addition of noise to reduce the annoyance of certain sounds, the opposite of soundproofing .
Organizations each have their own standards, recommendations/guidelines, and directives for what levels of noise workers are permitted to be around before noise controls must be put into place.
OSHA's requirements state that when workers are exposed to noise levels above 90 A-weighted decibels (dBA) in 8-hour time-weighted averages (TWA), administrative controls and/or new engineering controls must be implemented in the workplace. OSHA also requires that impulse noises and impact noises must be controlled to prevent these noises reaching past 140 dB peak sound pressure levels (SPL). [ 3 ] [ 4 ]
MSHA requires that administrative and/or engineering controls must be implemented in the workplace when miners are exposed to levels above 90 dBA TWA. If noise levels exceed 115 dBA, miners are required to wear hearing protection. MSHA, therefore, requires that noise levels be reduced below 115 dB TWA. Measuring noise levels for noise control decision making must integrate all noises from 90 dBA to 140 dBA. [ 5 ] [ 4 ]
The FRA recommends that worker exposure to noise should be reduced when their noise exposure exceeds 90 dBA for an 8-hour TWA. Noise measurements must integrate all noises, including intermittent, continuous, impact, and impulse noises of 80 dBA to 140 dBA. [ 6 ] [ 4 ]
The Department of Defense (DoD) suggests that noise levels be controlled primarily through engineering controls. The DoD requires that all steady-state noises be reduced to levels below 85 dBA and that impulse noises be reduced below 140 dB peak SPL. TWA exposures are not considered for the DoD's requirements. [ 7 ] [ 4 ]
The European Parliament and Council directive require noise levels to be reduced or eliminated using administrative and engineering controls. This directive requires lower exposure action levels of 80 dBA for 8 hours with 135 dB peak SPL, along with upper exposure action levels of 85 dBA for 8 hours with 137 peak dBSPL. Exposure limits are 87 dBA for 8 hours with peak levels of 140 peak dBSPL. [ 8 ] [ 4 ]
An effective model for noise control is the source, path, and receiver model by Bolt and Ingard. [ 9 ] Hazardous noise can be controlled by reducing the noise output at its source, minimizing the noise as it travels along a path to the listener, and providing equipment to the listener or receiver to attenuate the noise.
A variety of measures aim to reduce hazardous noise at its source. Programs such as Buy Quiet and the National Institute for Occupational Safety and Health (NIOSH) Prevention through design promote research and design of quiet equipment and renovation and replacement of older hazardous equipment with modern technologies. [ 10 ]
The principle of noise reduction through pathway modifications applies to the alteration of direct and indirect pathways for noise. [ 4 ] Noise that travels across reflective surfaces, such as smooth floors, can be hazardous. Pathway alterations include physical materials, such as foam, absorb sound and walls to provide a sound barrier that modifies existing systems that decrease hazardous noise. Sound dampening enclosures for loud equipment and isolation chambers from which workers can remotely control equipment can also be designed. These methods prevent sound from traveling along a path to the worker or other listeners.
In the industrial or commercial setting, workers must comply with the appropriate Hearing conservation program . Administrative controls , such as the restriction of personnel in noisy areas, prevents unnecessary noise exposure. Personal protective equipment such as foam ear plugs or ear muffs to attenuate sound provide a last line of defense for the listener.
Studies on noise barriers have shown mixed results on their ability to effectively reduce noise pollution . [ 11 ] Electric and hybrid vehicles could reduce noise pollution, but only if those vehicles make up a high proportion of total vehicles on the road; even if traffic in an urban area reached a makeup of fifty percent electric vehicles, the overall noise reduction achieved would only be a few decibels and would be barely noticeable. [ 12 ] Highway noise is today less affected by motor type, since the effects in higher speed are aerodynamic and tire noise related. Other contributions to the reduction of noise at the source are: improved tire tread designs for trucks in the 1970s, better shielding of diesel stacks in the 1980s, and local vehicle regulation of unmuffled vehicles. [ 13 ]
The most fertile areas for roadway noise mitigation are in urban planning decisions, roadway design, noise barrier design, [ 14 ] speed control, surface pavement selection, and truck restrictions. Speed control is effective since the lowest sound emissions arise from vehicles moving smoothly at 30 to 60 kilometers per hour. Above that range, sound emissions double with every five miles per hour of speed. At the lowest speeds, braking and (engine) acceleration noise dominates.
Selection of road surface pavement can make a difference of a factor of two in sound levels, for the speed regime above 30 kilometers per hour. Quieter pavements are porous with a negative surface texture and use small to medium-sized aggregates; the loudest pavements have transversely-grooved surfaces, positive surface textures, and larger aggregates. Surface friction and roadway safety are important considerations as well for pavement decisions.
When designing new urban freeways or arterials, there are numerous design decisions regarding alignment and roadway geometrics. [ 15 ] Use of a computer model to calculate sound levels has become standard practice since the early 1970s. In this way exposure of sensitive receptors to elevated sound levels can be minimized. An analogous process exists for urban mass transit systems and other rail transportation decisions. Early examples of urban rail systems designed using this technology were: Boston MBTA line expansions (1970s), San Francisco BART system expansion (1981), Houston METRORail system (1982), and the MAX Light Rail system in Portland, Oregon (1983).
Noise barriers can be applied to existing or planned surface transportation projects. They are one of the most effective actions taken in retrofitting existing roadways and commonly can reduce adjacent land-use sound levels by up to ten decibels. A computer model is required to design the barrier since terrain, micrometeorology and other locale-specific factors make the endeavor a very complex undertaking. For example, a roadway in cut or strong prevailing winds can produce a setting where atmospheric sound propagation is unfavorable to any noise barrier.
As in the case of roadway noise, little progress has been made in quelling aircraft noise at the source, other than elimination of loud engine designs from the 1960s and earlier. Because of its velocity and volume, jet turbine engine exhaust noise defies reduction by any simple means.
The most promising forms of aircraft noise abatement are through land planning, flight operations restrictions and residential soundproofing . Flight restrictions can take the form of preferred runway use, departure flight path and slope, and time-of-day restrictions. These tactics are sometimes controversial since they can impact aircraft safety, flying convenience and airline economics.
In 1979, the US Congress authorized [ 16 ] the FAA to devise technology and programs to attempt to insulate homes near airports. While this obviously does not aid the exterior environment, the program has been effective for residential and school interiors. Some of the airports at which the technology was applied early on were San Francisco International Airport , [ 17 ] Seattle-Tacoma International Airport , John Wayne International Airport and San Jose International Airport [ 18 ] in California.
The underlying technology is a computer model which simulates the propagation of aircraft noise and its penetration into buildings. Variations in aircraft types, flight patterns and local meteorology can be analyzed along with benefits of alternative building retrofit strategies such as roof upgrading, window glazing improvement, fireplace baffling, caulking construction seams and other measures. The computer model allows cost-effectiveness evaluations of a host of alternative strategies.
In Canada, Transport Canada prepares noise exposure forecasts (NEF) for each airport, using a computer model similar to that used in the US. Residential land development is discouraged within high impact areas identified by the forecast. [ 19 ]
Architectural acoustics noise control practices include interior sound reverberation reduction, inter-room noise transfer mitigation, and exterior building skin augmentation.
In the case of construction of new (or remodeled) apartments , condominiums , hospitals , and hotels , many states and cities have stringent building codes with requirements of acoustical analysis, in order to protect building occupants. With regard to exterior noise, the codes usually require measurement of the exterior acoustic environment in order to determine the performance standard required for exterior building skin design. The architect can work with the acoustical scientist to arrive at the best cost-effective means of creating a quiet interior (normally 45 dBA ). The most important elements of design of the building skin are usually: glazing (glass thickness, double pane design etc.), perforated metal (used internally or externally), [ 20 ] roof material, caulking standards, chimney baffles, exterior door design, mail slots, attic ventilation ports, and mounting of through-the-wall air conditioners.
Regarding sound generated inside the building, there are two principal types of transmission. Firstly, airborne sound travels through walls or floor and ceiling assemblies and can emanate from either human activities in adjacent living spaces or from mechanical noise within the building systems. Human activities might include voice, noise from amplified sound systems, or animal noise. Mechanical systems are elevator systems, boilers , refrigeration or air conditioning systems, generators and trash compactors. Aerodynamic sources include fans, pneumatics, and combustion. Noise control for aerodynamic sources include quiet air nozzles , pneumatic silencers and quiet fan technology . Since many mechanical sounds are inherently loud, the principal design element is to require the wall or ceiling assembly to meet certain performance standards, [ 21 ] (typically Sound transmission class of 50), which allows considerable attenuation of the sound level reaching occupants.
The second type of interior sound is called Impact Insulation Class (IIC) transmission. This effect arises not from airborne transmission , but rather from the transmission of sound through the building itself. The most common perception of IIC noise is from the footfall of occupants in living spaces above. Low-frequency noise is transferred easily through the ground and buildings. This type of noise is more difficult to abate, but consideration must be given to isolating the floor assembly above or hanging the lower ceiling on resilient channel .
Both of the transmission effects noted above may emanate either from building occupants or from building mechanical systems such as elevators, plumbing systems or heating, ventilating and air conditioning units. In some cases, it is merely necessary to specify the best available quieting technology in selecting such building hardware. In other cases, shock mounting of systems to control vibration may be in order. In the case of plumbing systems, there are specific protocols developed, especially for water supply lines, to create isolation clamping of pipes within building walls. In the case of central air systems, it is important to baffle any ducts that could transmit sound between different building areas.
Designing special-purpose rooms has more exotic challenges, since these rooms may have requirements for unusual features such as concert performance, sound studio recording , lecture halls. In these cases reverberation and reflection must be analyzed in order to not only quiet the rooms, but to prevent echo effects from occurring. In these situations special sound baffles and sound absorptive lining materials may be specified to dampen unwanted effects.
Acoustical wall and ceiling panels are a common commercial and residential solution for noise control in already-constructed buildings. Acoustic panels may be constructed of a variety of materials, though commercial acoustic applications will frequently be composed of fiberglass or mineral wool-based acoustic substrates. For example, Mineral fiberboard is a commonly used acoustical substrate, and commercial thermal insulations, such as those used in the insulation of boiler tanks, are frequently repurposed for noise-controlling acoustic use based on their effectiveness at minimizing reverberations. The ideal acoustical panels are those without a face or finish material that could interfere with the performance of the acoustical infill, but aesthetic and safety concerns typically lead to fabric coverings or other finishing materials to minimize impedance. Panel finishings are occasionally made of a porous configuration of wood or metal.
The effectiveness of post-construction acoustic treatment is limited by the amount of space able to be allocated to acoustic treatment, and so on-site acoustical wall panels are frequently made to conform to the shape of the preexisting space. This is done by "framing" the perimeter track into shape, infilling the acoustical substrate and then stretching and tucking the fabric into the perimeter frame system. On-site wall panels can be constructed to work around door frames, baseboard, or any other intrusion. Large panels (generally greater than 50 feet) can be created on walls and ceilings with this method.
Double-glazed and thicker windows can also prevent sound transmission from the outdoors.
Industrial noise is traditionally associated with manufacturing settings where industrial machinery produces intense sound levels, [ 22 ] often upwards of 85 decibels. While this circumstance is the most dramatic, there are many other work environments where sound levels may lie in the range of 70 to 75 decibels, entirely composed of office equipment, music, public address systems, and even exterior noise intrusion. Either type of environment may result in noise health effects if the sound intensity and exposure time is too great.
In the case of industrial equipment, the most common techniques for noise protection of workers consist of shock mounting source equipment, creation of acrylic glass or other solid barriers, and provision of ear protection equipment . In certain cases the machinery itself can be re-designed to operate in a manner less prone to produce grating, grinding, frictional, or other motions that induce sound emissions. In recent years, Buy Quiet programs and initiatives have arisen in an effort to combat occupational noise exposures. These programs promote the purchase of quieter tools and equipment and encourage manufacturers to design quieter equipment. [ 23 ]
In the case of more conventional office environments, the techniques in architectural acoustics discussed above may apply. Other solutions may involve researching the quietest models of office equipment, particularly printers and photocopy machines. Impact printers and other equipment were often fitted with "acoustic hoods", enclosures to reduce emitted noise. One source of annoying, if not loud, sound level emissions are lighting fixtures (notably older fluorescent globes). These fixtures can be retrofitted or analyzed to see whether over-illumination is present, a common office environment issue. If over-illumination is occurring, de-lamping or reduced light bank usage may apply. Photographers can quieten noisy still cameras on a film set using sound blimps .
Reductions in cost of technology have allowed noise control technology to be used not only in performance facilities and recording studios, but also in noise-sensitive small businesses such as restaurants. [ 24 ] Acoustically absorbent materials such as fiberglass duct liner, wood fiber panels and recycled denim jeans serve as artwork-bearing canvasses in environments in which aesthetics are important. [ 24 ]
Using a combination of sound absorption materials, arrays of microphones and speakers, and a digital processor, a restaurant operator can use a tablet computer to selectively control noise levels at different places in the restaurant: the microphone arrays pick up sound and send it to the digital processor, which controls the speakers to output sound signals on command. [ 24 ]
Post-construction residential acoustic treatment throughout the 20th century was only commonly the practice of music-listening enthusiasts. However, developments in home recording technology and fidelity have led to a drastic increase in the spread and popularity of residential acoustic treatment in the pursuit of home recording fidelity and accuracy. A large secondary market of homemade and home use acoustic panels, bass trap, and similar constructed products has developed resulting from this demand, with many small companies and individuals wrapping industrial and commercial-grade insulations in fabric for use in home recording studios, theatre rooms, and music practice spaces.
Communities may use zoning codes to isolate noisy urban activities from areas that should be protected from such unhealthy exposures and to establish noise standards in areas that may not be conducive to such isolation strategies. Because low-income neighborhoods are often at greater risk of noise pollution, the establishment of such zoning codes is often an environmental justice issue. [ 25 ] Mixed-use areas present especially difficult conflicts that require special attention to the need to protect people from the harmful effects of noise pollution. Noise is generally one consideration in an environmental impact statement , if applicable (such as transportation system construction).
General: | https://en.wikipedia.org/wiki/Noise_control |
In electrical engineering , Noise margin is the maximum voltage amplitude of extraneous signal that can be algebraically added to the noise-free worst-case input level without causing the output voltage to deviate from the allowable logic voltage level. [ 1 ] It is commonly used in at least two contexts as follows:
In practice, noise margins are the amount of noise, that a logic circuit can withstand.
Noise margins are generally defined so that positive values ensure proper operation, and negative margins result in compromised operation, or outright failure. [ 3 ] | https://en.wikipedia.org/wiki/Noise_margin |
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