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Typical home loudspeakers have sensitivities of about 85 to 95 dB for 1 W @ 1 m—an efficiency of 0.5–4%. Sound reinforcement and public address loudspeakers have sensitivities of perhaps 95 to 102 dB for 1 W @ 1 m—an efficiency of 4–10%. Rock concert, stadium PA, marine hailing, etc. speakers generally have higher sensitivities of 103 to 110 dB for 1 W @ 1 m—an efficiency of 10–20%.
Since sensitivity and power handling are largely independent properties, a driver with a higher maximum power rating cannot necessarily be driven to louder levels than a lower-rated one. In the example that follows, assume (for simplicity) that the drivers being compared have the same electrical impedance, are operated at the same frequency within both driver's respective passbands, and that power compression and distortion are insignificant. A speaker 3 dB more sensitive than another produces double the sound power (is 3 dB louder) for the same electrical power input. Thus, a 100 W driver (A) rated at 92 dB for 1 W @ 1 m sensitivity puts out twice as much acoustic power as a 200 W driver (B) rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of electrical power. In this example, when driven at 100 W, speaker A produces the same SPL, or loudness as speaker B would produce with 200 W input. Thus, a 3 dB increase in the sensitivity of the speaker means that it needs half the amplifier power to achieve a given SPL. This translates into a smaller, less complex power amplifier—and often, to reduced overall system cost.
It is typically not possible to combine high efficiency (especially at low frequencies) with compact enclosure size and adequate low-frequency response. One can, for the most part, choose only two of the three parameters when designing a speaker system. So, for example, if extended low-frequency performance and small box size are important, one must accept low efficiency. This rule of thumb is sometimes called Hofmann's Iron Law (after J.A. Hofmann, the H in KLH).
Listening environment | Loudspeaker | Wikipedia | 454 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
The interaction of a loudspeaker system with its environment is complex and is largely out of the loudspeaker designer's control. Most listening rooms present a more or less reflective environment, depending on size, shape, volume, and furnishings. This means the sound reaching a listener's ears consists not only of sound directly from the speaker system, but also the same sound delayed by traveling to and from (and being modified by) one or more surfaces. These reflected sound waves, when added to the direct sound, cause cancellation and addition at assorted frequencies (e.g. from resonant room modes), thus changing the timbre and character of the sound at the listener's ears. The human brain is sensitive to small variations in reflected sound, and this is part of the reason why a loudspeaker system sounds different at different listening positions or in different rooms.
A significant factor in the sound of a loudspeaker system is the amount of absorption and diffusion present in the environment. Clapping one's hands in a typical empty room, without draperies or carpet, produces a zippy, fluttery echo due to a lack of absorption and diffusion.
Placement
In a typical rectangular listening room, the hard, parallel surfaces of the walls, floor and ceiling cause primary acoustic resonance nodes in each of the three dimensions: left-right, up-down and forward-backward. Furthermore, there are more complex resonance modes involving up to all six boundary surfaces combining to create standing waves. This is called speaker boundary interference response (SBIR). Low frequencies excite these modes the most, since long wavelengths are not much affected by furniture compositions or placement. The mode spacing is critical, especially in small and medium-sized rooms like recording studios, home theaters and broadcast studios. The proximity of the loudspeakers to room boundaries affects how strongly the resonances are excited as well as affecting the relative strength at each frequency. The location of the listener is critical, too, as a position near a boundary can have a great effect on the perceived balance of frequencies. This is because standing wave patterns are most easily heard in these locations and at lower frequencies, below the Schroeder frequency—typically around 200–300 Hz, depending on room size. | Loudspeaker | Wikipedia | 460 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Directivity
Acousticians, in studying the radiation of sound sources have developed some concepts important to understanding how loudspeakers are perceived. The simplest possible radiating source is a point source, sometimes called a simple source. An ideal point source is an infinitesimally small point radiating sound. It may be easier to imagine a tiny pulsating sphere, uniformly increasing and decreasing in diameter, sending out sound waves in all directions equally, independent of frequency.
Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources. The radiation pattern of a combination of point sources is not the same as for a single source, but depends on the distance and orientation between the sources, the position relative to them from which the listener hears the combination, and the frequency of the sound involved. Using geometry and calculus, some simple combinations of sources are easily solved; others are not.
One simple combination is two simple sources separated by a distance and vibrating out of phase, one miniature sphere expanding while the other is contracting. The pair is known as a doublet, or dipole, and the radiation of this combination is similar to that of a very small dynamic loudspeaker operating without a baffle. The directivity of a dipole is a figure 8 shape with maximum output along a vector that connects the two sources and minimums to the sides when the observing point is equidistant from the two sources, where the sum of the positive and negative waves cancel each other. While most drivers are dipoles, depending on the enclosure to which they are attached, they may radiate as monopoles, dipoles (or bipoles). If mounted on a finite baffle, and these out-of-phase waves are allowed to interact, dipole peaks and nulls in the frequency response result. When the rear radiation is absorbed or trapped in a box, the diaphragm becomes a monopole radiator. Bipolar speakers, made by mounting in-phase monopoles (both moving out of or into the box in unison) on opposite sides of a box, are a method of approaching omnidirectional radiation patterns. | Loudspeaker | Wikipedia | 449 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
In real life, individual drivers are complex 3D shapes such as cones and domes, and they are placed on a baffle for various reasons. A mathematical expression for the directivity of a complex shape, based on modeling combinations of point sources, is usually not possible, but in the far field, the directivity of a loudspeaker with a circular diaphragm is close to that of a flat circular piston, so it can be used as an illustrative simplification for discussion. As a simple example of the mathematical physics involved, consider the following:
the formula for far field directivity of a flat circular piston in an infinite baffle is
where , is the pressure on axis, is the piston radius, is the wavelength (i.e. ) is the angle off axis and is the Bessel function of the first kind.
A planar source radiates sound uniformly for low frequencies' wavelengths longer than the dimensions of the planar source, and as frequency increases, the sound from such a source focuses into an increasingly narrower angle. The smaller the driver, the higher the frequency where this narrowing of directivity occurs. Even if the diaphragm is not perfectly circular, this effect occurs such that larger sources are more directive. Several loudspeaker designs approximate this behavior. Most are electrostatic or planar magnetic designs.
Various manufacturers use different driver mounting arrangements to create a specific type of sound field in the space for which they are designed. The resulting radiation patterns may be intended to more closely simulate the way sound is produced by real instruments, or simply create a controlled energy distribution from the input signal (some using this approach are called monitors, as they are useful in checking the signal just recorded in a studio). An example of the first is a room corner system with many small drivers on the surface of a 1/8 sphere. A system design of this type was patented and produced commercially by Professor Amar Bose—the 2201. Later Bose models have deliberately emphasized production of both direct and reflected sound by the loudspeaker itself, regardless of its environment. The designs are controversial in high fidelity circles, but have proven commercially successful. Several other manufacturers' designs follow similar principles. | Loudspeaker | Wikipedia | 446 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Directivity is an important issue because it affects the frequency balance of sound a listener hears, and also the interaction of the speaker system with the room and its contents. A very directive (sometimes termed 'beamy') speaker (i.e. on an axis perpendicular to the speaker face) may result in a reverberant field lacking in high frequencies, giving the impression the speaker is deficient in treble even though it measures well on axis (e.g. flat across the entire frequency range). Speakers with very wide, or rapidly increasing directivity at high frequencies, can give the impression that there is too much treble (if the listener is on axis) or too little (if the listener is off axis). This is part of the reason why on-axis frequency response measurement is not a complete characterization of the sound of a given loudspeaker.
Other speaker designs
While dynamic cone speakers remain the most popular choice, many other speaker technologies exist.
With a diaphragm
Moving-iron loudspeakers
The original loudspeaker design was the moving iron. Unlike the newer dynamic (moving coil) design, a moving-iron speaker uses a stationary coil to vibrate a magnetized piece of metal (called the iron, reed, or armature). The metal is either attached to the diaphragm or is the diaphragm itself. This design originally appeared in the early telephone.
Moving iron drivers are inefficient and can only produce a small band of sound. They require large magnets and coils to increase force.
Balanced armature drivers (a type of moving iron driver) use an armature that moves like a see-saw or diving board. Since they are not damped, they are highly efficient, but they also produce strong resonances. They are still used today for high-end earphones and hearing aids, where small size and high efficiency are important.
Piezoelectric speakers | Loudspeaker | Wikipedia | 401 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Piezoelectric speakers are frequently used as beepers in watches and other electronic devices, and are sometimes used as tweeters in less-expensive speaker systems, such as computer speakers and portable radios. Piezoelectric speakers have several advantages over conventional loudspeakers: they are resistant to overloads that would normally destroy most high-frequency drivers, and they can be used without a crossover due to their electrical properties. There are also disadvantages: some amplifiers can oscillate when driving capacitive loads like most piezoelectrics, which results in distortion or damage to the amplifier. Additionally, their frequency response, in most cases, is inferior to that of other technologies. This is why they are generally used in single-frequency (beeper) or non-critical applications.
Piezoelectric speakers can have extended high-frequency output, and this is useful in some specialized circumstances; for instance, sonar applications in which piezoelectric variants are used as both output devices (generating underwater sound) and as input devices (acting as the sensing components of underwater microphones). They have advantages in these applications, not the least of which is simple and solid-state construction that resists seawater better than a ribbon or cone-based device would.
In 2013, Kyocera introduced piezoelectric ultra-thin medium-size film speakers with only 1 millimeter of thickness and 7 grams of weight for their 55" OLED televisions and they hope the speakers will also be used in PCs and tablets. Besides medium-size, there are also large and small sizes which can all produce relatively the same quality of sound and volume within 180 degrees. The highly responsive speaker material provides better clarity than traditional TV speakers.
Magnetostatic loudspeakers
Instead of a voice coil driving a speaker cone, a magnetostatic speaker uses an array of metal strips bonded to a large film membrane. The magnetic field produced by signal current flowing through the strips interacts with the field of permanent bar magnets mounted behind them. The force produced moves the membrane and so the air in front of it. Typically, these designs are less efficient than conventional moving-coil speakers. | Loudspeaker | Wikipedia | 442 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Magnetostrictive speakers
Magnetostrictive transducers, based on magnetostriction, have been predominantly used as sonar ultrasonic sound wave radiators, but their use has spread also to audio speaker systems. Magnetostrictive speaker drivers have some special advantages: they can provide greater force (with smaller excursions) than other technologies; low excursion can avoid distortions from large excursion as in other designs; the magnetizing coil is stationary and therefore more easily cooled; they are robust because delicate suspensions and voice coils are not required. Magnetostrictive speaker modules have been produced by Fostex and FeONIC and subwoofer drivers have also been produced.
Electrostatic loudspeakers
Electrostatic loudspeakers use a high-voltage electric field (rather than a magnetic field) to drive a thin statically charged membrane. Because they are driven over the entire membrane surface rather than from a small voice coil, they ordinarily provide a more linear and lower-distortion motion than dynamic drivers. They also have a relatively narrow dispersion pattern that can make for precise sound-field positioning. However, their optimum listening area is small and they are not very efficient speakers. They have the disadvantage that the diaphragm excursion is severely limited because of practical construction limitations—the further apart the stators are positioned, the higher the voltage must be to achieve acceptable efficiency. This increases the tendency for electrical arcs as well as increasing the speaker's attraction of dust particles. Arcing remains a potential problem with current technologies, especially when the panels are allowed to collect dust or dirt and are driven with high signal levels.
Electrostatics are inherently dipole radiators and due to the thin flexible membrane are less suited for use in enclosures to reduce low-frequency cancellation as with common cone drivers. Due to this and the low excursion capability, full-range electrostatic loudspeakers are large by nature, and the bass rolls off at a frequency corresponding to a quarter wavelength of the narrowest panel dimension. To reduce the size of commercial products, they are sometimes used as a high-frequency driver in combination with a conventional dynamic driver that handles the bass frequencies effectively. | Loudspeaker | Wikipedia | 447 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Electrostatics are usually driven through a step-up transformer that multiplies the voltage swings produced by the power amplifier. This transformer also multiplies the capacitive load that is inherent in electrostatic transducers, which means the effective impedance presented to the power amplifiers varies widely by frequency. A speaker that is nominally 8 ohms may actually present a load of 1 ohm at higher frequencies, which is challenging to some amplifier designs.
Ribbon and planar magnetic loudspeakers
A ribbon speaker consists of a thin metal-film ribbon suspended in a magnetic field. The electrical signal is applied to the ribbon, which moves with it to create the sound. The advantage of a ribbon driver is that the ribbon has very little mass; thus, it can accelerate very quickly, yielding a very good high-frequency response. Ribbon loudspeakers are often very fragile. Most ribbon tweeters emit sound in a dipole pattern. A few have backings that limit the dipole radiation pattern. Above and below the ends of the more or less rectangular ribbon, there is less audible output due to phase cancellation, but the precise amount of directivity depends on the ribbon length. Ribbon designs generally require exceptionally powerful magnets, which makes them costly to manufacture. Ribbons have a very low resistance that most amplifiers cannot drive directly. As a result, a step down transformer is typically used to increase the current through the ribbon. The amplifier sees a load that is the ribbon's resistance times the transformer turns ratio squared. The transformer must be carefully designed so that its frequency response and parasitic losses do not degrade the sound, further increasing cost and complication relative to conventional designs.
Planar magnetic speakers (having printed or embedded conductors on a flat diaphragm) are sometimes described as ribbons, but are not truly ribbon speakers. The term planar is generally reserved for speakers with roughly rectangular flat surfaces that radiate in a bipolar (i.e. front and back) manner. Planar magnetic speakers consist of a flexible membrane with a voice coil printed or mounted on it. The current flowing through the coil interacts with the magnetic field of carefully placed magnets on either side of the diaphragm, causing the membrane to vibrate more or less uniformly and without much bending or wrinkling. The driving force covers a large percentage of the membrane surface and reduces resonance problems inherent in coil-driven flat diaphragms. | Loudspeaker | Wikipedia | 499 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Bending wave loudspeakers
Bending wave transducers use a diaphragm that is intentionally flexible. The rigidity of the material increases from the center to the outside. Short wavelengths radiate primarily from the inner area, while longer waves reach the edge of the speaker. To prevent reflections from the outside back into the center, long waves are absorbed by a surrounding damper. Such transducers can cover a wide frequency range (80 Hz to 35,000 Hz) and have been promoted as being close to an ideal point sound source. This uncommon approach is being taken by only a very few manufacturers, in very different arrangements.
The Ohm Walsh loudspeakers use a unique driver designed by Lincoln Walsh, who had been a radar development engineer in WWII. He became interested in audio equipment design and his last project was a unique, one-way speaker using a single driver. The cone faced down into a sealed, airtight enclosure. Rather than move back and forth as conventional speakers do, the cone rippled and created sound in a manner known in RF electronics as a "transmission line". The new speaker created a cylindrical sound field. Lincoln Walsh died before his speaker was released to the public. The Ohm Acoustics firm has produced several loudspeaker models using the Walsh driver design since then. German Physiks, an audio equipment firm in Germany, also produces speakers using this approach.
The German firm Manger has designed and produced a bending wave driver that at first glance appears conventional. In fact, the round panel attached to the voice coil bends in a carefully controlled way to produce full-range sound. Josef W. Manger was awarded with the Rudolf-Diesel-Medaille for extraordinary developments and inventions by the German institute of inventions. | Loudspeaker | Wikipedia | 360 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Flat panel loudspeakers
There have been many attempts to reduce the size of speaker systems, or alternatively to make them less obvious. One such attempt was the development of exciter transducer coils mounted to flat panels to act as sound sources, most accurately called exciter/panel drivers. These can then be made in a neutral color and hung on walls where they are less noticeable than many speakers, or can be deliberately painted with patterns, in which case they can function decoratively. There are two related problems with flat panel techniques: first, a flat panel is necessarily more flexible than a cone shape in the same material, and therefore moves as a single unit even less, and second, resonances in the panel are difficult to control, leading to considerable distortions. Some progress has been made using such lightweight, rigid, materials such as Styrofoam, and there have been several flat panel systems commercially produced in recent years.
Heil air motion transducers
Oskar Heil invented the air motion transducer in the 1960s. In this approach, a pleated diaphragm is mounted in a magnetic field and forced to close and open under control of a music signal. Air is forced from between the pleats in accordance with the imposed signal, generating sound. The drivers are less fragile than ribbons and considerably more efficient (and able to produce higher absolute output levels) than ribbon, electrostatic, or planar magnetic tweeter designs. ESS, a California manufacturer, licensed the design, employed Heil, and produced a range of speaker systems using his tweeters during the 1970s and 1980s. Lafayette Radio, a large US retail store chain, also sold speaker systems using such tweeters for a time. There are several manufacturers of these drivers (at least two in Germany—one of which produces a range of high-end professional speakers using tweeters and mid-range drivers based on the technology) and the drivers are increasingly used in professional audio. Martin Logan produces several AMT speakers in the US and GoldenEar Technologies incorporates them in its entire speaker line.
Transparent ionic conduction speaker
In 2013, a research team introduced a transparent ionic conduction speaker which has two sheets of transparent conductive gel and a layer of transparent rubber in between to make high voltage and high actuation work to reproduce good sound quality. The speaker is suitable for robotics, mobile computing and adaptive optics fields.
Digital speakers | Loudspeaker | Wikipedia | 492 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Digital speakers have been the subject of experiments performed by Bell Labs as far back as the 1920s. The design is simple; each bit controls a driver, which is either fully 'on' or 'off'. Problems with this design have led manufacturers to abandon it as impractical for the present. First, for a reasonable number of bits (required for adequate sound reproduction quality), the physical size of a speaker system becomes very large. Secondly, due to inherent analog-to-digital conversion problems, the effect of aliasing is unavoidable, so that the audio output is reflected at equal amplitude in the frequency domain, on the other side of the Nyquist limit (half the sampling frequency), causing an unacceptably high level of ultrasonics to accompany the desired output. No workable scheme has been found to adequately deal with this.
Without a diaphragm
Plasma arc speakers
Plasma arc loudspeakers use electrical plasma as a radiating element. Since plasma has minimal mass, but is charged and therefore can be manipulated by an electric field, the result is a very linear output at frequencies far higher than the audible range. Problems of maintenance and reliability for this approach tend to make it unsuitable for mass market use. In 1978 Alan E. Hill of the Air Force Weapons Laboratory in Albuquerque, NM, designed the Plasmatronics Hill Type I, a tweeter whose plasma was generated from helium gas. This avoided the ozone and NOx produced by RF decomposition of air in an earlier generation of plasma tweeters made by the pioneering DuKane Corporation, who produced the Ionovac (marketed as the Ionofane in the UK) during the 1950s.
A less expensive variation on this theme is the use of a flame for the driver, as flames contain ionized (electrically charged) gases. | Loudspeaker | Wikipedia | 368 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
Thermoacoustic speakers
In 2008, researchers of Tsinghua University demonstrated a thermoacoustic loudspeaker (or thermophone) of carbon nanotube thin film, whose working mechanism is a thermoacoustic effect. Sound frequency electric currents are used to periodically heat the CNT and thus result in sound generation in the surrounding air. The CNT thin film loudspeaker is transparent, stretchable and flexible.
In 2013, researchers of Tsinghua University further present a thermoacoustic earphone of carbon nanotube thin yarn and a thermoacoustic surface-mounted device. They are both fully integrated devices and compatible with Si-based semiconducting technology.
Rotary woofers
A rotary woofer is essentially a fan with blades that constantly change their pitch, allowing them to easily push the air back and forth. Rotary woofers are able to efficiently reproduce subsonic frequencies, which are difficult to impossible to achieve on a traditional speaker with a diaphragm. They are often employed in movie theaters to recreate rumbling bass effects, such as explosions. | Loudspeaker | Wikipedia | 226 | 45871 | https://en.wikipedia.org/wiki/Loudspeaker | Technology | Media and communication | null |
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions.
Definitions
Probability density function
The probability density function (pdf) of an exponential distribution is
Here λ > 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval . If a random variable X has this distribution, we write .
The exponential distribution exhibits infinite divisibility.
Cumulative distribution function
The cumulative distribution function is given by
Alternative parametrization
The exponential distribution is sometimes parametrized in terms of the scale parameter , which is also the mean:
Properties
Mean, variance, moments, and median
The mean or expected value of an exponentially distributed random variable X with rate parameter λ is given by
In light of the examples given below, this makes sense; a person who receives an average of two telephone calls per hour can expect that the time between consecutive calls will be 0.5 hour, or 30 minutes.
The variance of X is given by
so the standard deviation is equal to the mean.
The moments of X, for are given by
The central moments of X, for are given by
where !n is the subfactorial of n
The median of X is given by
where refers to the natural logarithm. Thus the absolute difference between the mean and median is
in accordance with the median-mean inequality.
Memorylessness property of exponential random variable
An exponentially distributed random variable T obeys the relation
This can be seen by considering the complementary cumulative distribution function: | Exponential distribution | Wikipedia | 475 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
When T is interpreted as the waiting time for an event to occur relative to some initial time, this relation implies that, if T is conditioned on a failure to observe the event over some initial period of time s, the distribution of the remaining waiting time is the same as the original unconditional distribution. For example, if an event has not occurred after 30 seconds, the conditional probability that occurrence will take at least 10 more seconds is equal to the unconditional probability of observing the event more than 10 seconds after the initial time.
The exponential distribution and the geometric distribution are the only memoryless probability distributions.
The exponential distribution is consequently also necessarily the only continuous probability distribution that has a constant failure rate.
Quantiles
The quantile function (inverse cumulative distribution function) for Exp(λ) is
The quartiles are therefore:
first quartile: ln(4/3)/λ
median: ln(2)/λ
third quartile: ln(4)/λ
And as a consequence the interquartile range is ln(3)/λ.
Conditional Value at Risk (Expected Shortfall)
The conditional value at risk (CVaR) also known as the expected shortfall or superquantile for Exp(λ) is derived as follows:
Buffered Probability of Exceedance (bPOE)
The buffered probability of exceedance is one minus the probability level at which the CVaR equals the threshold . It is derived as follows:
Kullback–Leibler divergence
The directed Kullback–Leibler divergence in nats of ("approximating" distribution) from ('true' distribution) is given by
Maximum entropy distribution
Among all continuous probability distributions with support and mean μ, the exponential distribution with λ = 1/μ has the largest differential entropy. In other words, it is the maximum entropy probability distribution for a random variate X which is greater than or equal to zero and for which E[X] is fixed.
Distribution of the minimum of exponential random variables
Let X1, ..., Xn be independent exponentially distributed random variables with rate parameters λ1, ..., λn. Then
is also exponentially distributed, with parameter
This can be seen by considering the complementary cumulative distribution function:
The index of the variable which achieves the minimum is distributed according to the categorical distribution
A proof can be seen by letting . Then,
Note that | Exponential distribution | Wikipedia | 494 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
is not exponentially distributed, if X1, ..., Xn do not all have parameter 0.
Joint moments of i.i.d. exponential order statistics
Let be independent and identically distributed exponential random variables with rate parameter λ.
Let denote the corresponding order statistics.
For , the joint moment of the order statistics and is given by
This can be seen by invoking the law of total expectation and the memoryless property:
The first equation follows from the law of total expectation.
The second equation exploits the fact that once we condition on , it must follow that . The third equation relies on the memoryless property to replace with .
Sum of two independent exponential random variables
The probability distribution function (PDF) of a sum of two independent random variables is the convolution of their individual PDFs. If and are independent exponential random variables with respective rate parameters and then the probability density of is given by
The entropy of this distribution is available in closed form: assuming (without loss of generality), then
where is the Euler-Mascheroni constant, and is the digamma function.
In the case of equal rate parameters, the result is an Erlang distribution with shape 2 and parameter which in turn is a special case of gamma distribution.
The sum of n independent Exp(λ) exponential random variables is Gamma(n, λ) distributed. | Exponential distribution | Wikipedia | 276 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
Related distributions
If X ~ Laplace(μ, β−1), then |X − μ| ~ Exp(β).
If X ~ U(0, 1) then −log(X) ~ Exp(1).
If X ~ Pareto(1, λ), then log(X) ~ Exp(λ).
If X ~ SkewLogistic(θ), then .
If Xi ~ U(0, 1) then
The exponential distribution is a limit of a scaled beta distribution:
The exponential distribution is a special case of type 3 Pearson distribution.
The exponential distribution is the special case of a Gamma distribution with shape parameter 1.
If X ~ Exp(λ) and X ~ Exp(λ) then:
, closure under scaling by a positive factor.
1 + X ~ BenktanderWeibull(λ, 1), which reduces to a truncated exponential distribution.
keX ~ Pareto(k, λ).
e−λX ~ U(0, 1).
e−X ~ Beta(λ, 1).
e ~ PowerLaw(k, λ)
, the Rayleigh distribution
, the Weibull distribution
.
, a geometric distribution on 0,1,2,3,...
, a geometric distribution on 1,2,3,4,...
If also Y ~ Erlang(n, λ) or then
If also λ ~ Gamma(k, θ) (shape, scale parametrisation) then the marginal distribution of X is Lomax(k, 1/θ), the gamma mixture
λX − λY ~ Laplace(0, 1).
min{X1, ..., Xn} ~ Exp(λ1 + ... + λn).
If also λ = λ then:
Erlang(k, λ) = Gamma(k, λ−1) = Gamma(k, λ) (in (k, θ) and (α, β) parametrization, respectively) with an integer shape parameter k.
If , then .
X − X ~ Laplace(0, λ−1).
If also X are independent, then:
~ U(0, 1)
has probability density function . This can be used to obtain a confidence interval for .
If also λ = 1:
, the logistic distribution
μ − σ log(X) ~ GEV(μ, σ, 0).
Further if then (K-distribution) | Exponential distribution | Wikipedia | 507 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
If also λ = 1/2 then ; i.e., X has a chi-squared distribution with 2 degrees of freedom. Hence:
If and ~ Poisson(X) then (geometric distribution)
The Hoyt distribution can be obtained from exponential distribution and arcsine distribution
The exponential distribution is a limit of the κ-exponential distribution in the case.
Exponential distribution is a limit of the κ-Generalized Gamma distribution in the and cases: | Exponential distribution | Wikipedia | 89 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
Other related distributions:
Hyper-exponential distribution – the distribution whose density is a weighted sum of exponential densities.
Hypoexponential distribution – the distribution of a general sum of exponential random variables.
exGaussian distribution – the sum of an exponential distribution and a normal distribution.
Statistical inference
Below, suppose random variable X is exponentially distributed with rate parameter λ, and are n independent samples from X, with sample mean .
Parameter estimation
The maximum likelihood estimator for λ is constructed as follows.
The likelihood function for λ, given an independent and identically distributed sample x = (x1, ..., xn) drawn from the variable, is:
where:
is the sample mean.
The derivative of the likelihood function's logarithm is:
Consequently, the maximum likelihood estimate for the rate parameter is:
This is an unbiased estimator of although an unbiased MLE estimator of and the distribution mean.
The bias of is equal to
which yields the bias-corrected maximum likelihood estimator
An approximate minimizer of mean squared error (see also: bias–variance tradeoff) can be found, assuming a sample size greater than two, with a correction factor to the MLE:
This is derived from the mean and variance of the inverse-gamma distribution, .
Fisher information
The Fisher information, denoted , for an estimator of the rate parameter is given as:
Plugging in the distribution and solving gives:
This determines the amount of information each independent sample of an exponential distribution carries about the unknown rate parameter .
Confidence intervals
An exact 100(1 − α)% confidence interval for the rate parameter of an exponential distribution is given by:
which is also equal to
where is the percentile of the chi squared distribution with v degrees of freedom, n is the number of observations and x-bar is the sample average. A simple approximation to the exact interval endpoints can be derived using a normal approximation to the distribution. This approximation gives the following values for a 95% confidence interval:
This approximation may be acceptable for samples containing at least 15 to 20 elements.
Bayesian inference
The conjugate prior for the exponential distribution is the gamma distribution (of which the exponential distribution is a special case). The following parameterization of the gamma probability density function is useful:
The posterior distribution p can then be expressed in terms of the likelihood function defined above and a gamma prior: | Exponential distribution | Wikipedia | 488 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
Now the posterior density p has been specified up to a missing normalizing constant. Since it has the form of a gamma pdf, this can easily be filled in, and one obtains:
Here the hyperparameter α can be interpreted as the number of prior observations, and β as the sum of the prior observations.
The posterior mean here is:
Occurrence and applications
Occurrence of events
The exponential distribution occurs naturally when describing the lengths of the inter-arrival times in a homogeneous Poisson process.
The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. In contrast, the exponential distribution describes the time for a continuous process to change state.
In real-world scenarios, the assumption of a constant rate (or probability per unit time) is rarely satisfied. For example, the rate of incoming phone calls differs according to the time of day. But if we focus on a time interval during which the rate is roughly constant, such as from 2 to 4 p.m. during work days, the exponential distribution can be used as a good approximate model for the time until the next phone call arrives. Similar caveats apply to the following examples which yield approximately exponentially distributed variables:
The time until a radioactive particle decays, or the time between clicks of a Geiger counter
The time between receiving one telephone call and the next
The time until default (on payment to company debt holders) in reduced-form credit risk modeling
Exponential variables can also be used to model situations where certain events occur with a constant probability per unit length, such as the distance between mutations on a DNA strand, or between roadkills on a given road. | Exponential distribution | Wikipedia | 345 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
In queuing theory, the service times of agents in a system (e.g. how long it takes for a bank teller etc. to serve a customer) are often modeled as exponentially distributed variables. (The arrival of customers for instance is also modeled by the Poisson distribution if the arrivals are independent and distributed identically.) The length of a process that can be thought of as a sequence of several independent tasks follows the Erlang distribution (which is the distribution of the sum of several independent exponentially distributed variables).
Reliability theory and reliability engineering also make extensive use of the exponential distribution. Because of the memoryless property of this distribution, it is well-suited to model the constant hazard rate portion of the bathtub curve used in reliability theory. It is also very convenient because it is so easy to add failure rates in a reliability model. The exponential distribution is however not appropriate to model the overall lifetime of organisms or technical devices, because the "failure rates" here are not constant: more failures occur for very young and for very old systems.
In physics, if you observe a gas at a fixed temperature and pressure in a uniform gravitational field, the heights of the various molecules also follow an approximate exponential distribution, known as the Barometric formula. This is a consequence of the entropy property mentioned below.
In hydrology, the exponential distribution is used to analyze extreme values of such variables as monthly and annual maximum values of daily rainfall and river discharge volumes.
The blue picture illustrates an example of fitting the exponential distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.
In operating-rooms management, the distribution of surgery duration for a category of surgeries with no typical work-content (like in an emergency room, encompassing all types of surgeries).
Prediction
Having observed a sample of n data points from an unknown exponential distribution a common task is to use these samples to make predictions about future data from the same source. A common predictive distribution over future samples is the so-called plug-in distribution, formed by plugging a suitable estimate for the rate parameter λ into the exponential density function. A common choice of estimate is the one provided by the principle of maximum likelihood, and using this yields the predictive density over a future sample xn+1, conditioned on the observed samples x = (x1, ..., xn) given by | Exponential distribution | Wikipedia | 505 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
The Bayesian approach provides a predictive distribution which takes into account the uncertainty of the estimated parameter, although this may depend crucially on the choice of prior.
A predictive distribution free of the issues of choosing priors that arise under the subjective Bayesian approach is
which can be considered as
a frequentist confidence distribution, obtained from the distribution of the pivotal quantity ;
a profile predictive likelihood, obtained by eliminating the parameter λ from the joint likelihood of xn+1 and λ by maximization;
an objective Bayesian predictive posterior distribution, obtained using the non-informative Jeffreys prior 1/λ;
the Conditional Normalized Maximum Likelihood (CNML) predictive distribution, from information theoretic considerations.
The accuracy of a predictive distribution may be measured using the distance or divergence between the true exponential distribution with rate parameter, λ0, and the predictive distribution based on the sample x. The Kullback–Leibler divergence is a commonly used, parameterisation free measure of the difference between two distributions. Letting Δ(λ0||p) denote the Kullback–Leibler divergence between an exponential with rate parameter λ0 and a predictive distribution p it can be shown that
where the expectation is taken with respect to the exponential distribution with rate parameter , and is the digamma function. It is clear that the CNML predictive distribution is strictly superior to the maximum likelihood plug-in distribution in terms of average Kullback–Leibler divergence for all sample sizes .
Random variate generation
A conceptually very simple method for generating exponential variates is based on inverse transform sampling: Given a random variate U drawn from the uniform distribution on the unit interval , the variate
has an exponential distribution, where F is the quantile function, defined by
Moreover, if U is uniform on (0, 1), then so is 1 − U. This means one can generate exponential variates as follows:
Other methods for generating exponential variates are discussed by Knuth and Devroye.
A fast method for generating a set of ready-ordered exponential variates without using a sorting routine is also available. | Exponential distribution | Wikipedia | 438 | 45906 | https://en.wikipedia.org/wiki/Exponential%20distribution | Mathematics | Statistics and probability | null |
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions:
The probability distribution of the number of Bernoulli trials needed to get one success, supported on ;
The probability distribution of the number of failures before the first success, supported on .
These two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of ); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.
The geometric distribution gives the probability that the first occurrence of success requires independent trials, each with success probability . If the probability of success on each trial is , then the probability that the -th trial is the first success is
for
The above form of the geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success:
for
The geometric distribution gets its name because its probabilities follow a geometric sequence. It is sometimes called the Furry distribution after Wendell H. Furry.
Definition
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support. When supported on , the probability mass function iswhere is the number of trials and is the probability of success in each trial.
The support may also be , defining . This alters the probability mass function intowhere is the number of failures before the first success.
An alternative parameterization of the distribution gives the probability mass functionwhere and .
An example of a geometric distribution arises from rolling a six-sided die until a "1" appears. Each roll is independent with a chance of success. The number of rolls needed follows a geometric distribution with .
Properties
Memorylessness
The geometric distribution is the only memoryless discrete probability distribution. It is the discrete version of the same property found in the exponential distribution. The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.
Because there are two definitions of the geometric distribution, there are also two definitions of memorylessness for discrete random variables. Expressed in terms of conditional probability, the two definitions are
and | Geometric distribution | Wikipedia | 474 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
where and are natural numbers, is a geometrically distributed random variable defined over , and is a geometrically distributed random variable defined over . Note that these definitions are not equivalent for discrete random variables; does not satisfy the first equation and does not satisfy the second.
Moments and cumulants
The expected value and variance of a geometrically distributed random variable defined over is With a geometrically distributed random variable defined over , the expected value changes intowhile the variance stays the same.
For example, when rolling a six-sided die until landing on a "1", the average number of rolls needed is and the average number of failures is .
The moment generating function of the geometric distribution when defined over and respectively isThe moments for the number of failures before the first success are given by
where is the polylogarithm function.
The cumulant generating function of the geometric distribution defined over is The cumulants satisfy the recursionwhere , when defined over .
Proof of expected value
Consider the expected value of X as above, i.e. the average number of trials until a success.
On the first trial, we either succeed with probability , or we fail with probability .
If we fail the remaining mean number of trials until a success is identical to the original mean.
This follows from the fact that all trials are independent.
From this we get the formula:
which, if solved for , gives:
The expected number of failures can be found from the linearity of expectation, . It can also be shown in the following way:
The interchange of summation and differentiation is justified by the fact that convergent power series converge uniformly on compact subsets of the set of points where they converge.
Summary statistics
The mean of the geometric distribution is its expected value which is, as previously discussed in § Moments and cumulants, or when defined over or respectively.
The median of the geometric distribution is when defined over and when defined over .
The mode of the geometric distribution is the first value in the support set. This is 1 when defined over and 0 when defined over .
The skewness of the geometric distribution is .
The kurtosis of the geometric distribution is . The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution, . Therefore, the excess kurtosis of the geometric distribution is . Since , the excess kurtosis is always positive so the distribution is leptokurtic. In other words, the tail of a geometric distribution decays faster than a Gaussian. | Geometric distribution | Wikipedia | 509 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
Entropy and Fisher's Information
Entropy (Geometric Distribution, Failures Before Success)
Entropy is a measure of uncertainty in a probability distribution. For the geometric distribution that models the number of failures before the first success, the probability mass function is:
The entropy for this distribution is defined as:
The entropy increases as the probability decreases, reflecting greater uncertainty as success becomes rarer.
Fisher's Information (Geometric Distribution, Failures Before Success)
Fisher information measures the amount of information that an observable random variable carries about an unknown parameter . For the geometric distribution (failures before the first success), the Fisher information with respect to is given by:
Proof:
The Likelihood Function for a geometric random variable is:
The Log-Likelihood Function is:
The Score Function (first derivative of the log-likelihood w.r.t. ) is:
The second derivative of the log-likelihood function is:
Fisher Information is calculated as the negative expected value of the second derivative:
Fisher information increases as decreases, indicating that rarer successes provide more information about the parameter .
Entropy (Geometric Distribution, Trials Until Success)
For the geometric distribution modeling the number of trials until the first success, the probability mass function is:
The entropy for this distribution is given by:
Entropy increases as decreases, reflecting greater uncertainty as the probability of success in each trial becomes smaller.
Fisher's Information (Geometric Distribution, Trials Until Success)
Fisher information for the geometric distribution modeling the number of trials until the first success is given by:
Proof:
The Likelihood Function for a geometric random variable is:
The Log-Likelihood Function is:
The Score Function (first derivative of the log-likelihood w.r.t. ) is:
The second derivative of the log-likelihood function is:
Fisher Information is calculated as the negative expected value of the second derivative:
General properties
The probability generating functions of geometric random variables and defined over and are, respectively, | Geometric distribution | Wikipedia | 379 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
The characteristic function is equal to so the geometric distribution's characteristic function, when defined over and respectively, is
The entropy of a geometric distribution with parameter is
Given a mean, the geometric distribution is the maximum entropy probability distribution of all discrete probability distributions. The corresponding continuous distribution is the exponential distribution.
The geometric distribution defined on is infinitely divisible, that is, for any positive integer , there exist independent identically distributed random variables whose sum is also geometrically distributed. This is because the negative binomial distribution can be derived from a Poisson-stopped sum of logarithmic random variables.
The decimal digits of the geometrically distributed random variable Y are a sequence of independent (and not identically distributed) random variables. For example, the hundreds digit D has this probability distribution:
where q = 1 − p, and similarly for the other digits, and, more generally, similarly for numeral systems with other bases than 10. When the base is 2, this shows that a geometrically distributed random variable can be written as a sum of independent random variables whose probability distributions are indecomposable.
Golomb coding is the optimal prefix code for the geometric discrete distribution.
Related distributions
The sum of independent geometric random variables with parameter is a negative binomial random variable with parameters and . The geometric distribution is a special case of the negative binomial distribution, with .
The geometric distribution is a special case of discrete compound Poisson distribution.
The minimum of geometric random variables with parameters is also geometrically distributed with parameter .
Suppose 0 < r < 1, and for k = 1, 2, 3, ... the random variable Xk has a Poisson distribution with expected value rk/k. Then
has a geometric distribution taking values in , with expected value r/(1 − r).
The exponential distribution is the continuous analogue of the geometric distribution. Applying the floor function to the exponential distribution with parameter creates a geometric distribution with parameter defined over . This can be used to generate geometrically distributed random numbers as detailed in § Random variate generation. | Geometric distribution | Wikipedia | 418 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
If p = 1/n and X is geometrically distributed with parameter p, then the distribution of X/n approaches an exponential distribution with expected value 1 as n → ∞, sinceMore generally, if p = λ/n, where λ is a parameter, then as n→ ∞ the distribution of X/n approaches an exponential distribution with rate λ: therefore the distribution function of X/n converges to , which is that of an exponential random variable.
The index of dispersion of the geometric distribution is and its coefficient of variation is . The distribution is overdispersed.
Statistical inference
The true parameter of an unknown geometric distribution can be inferred through estimators and conjugate distributions.
Method of moments
Provided they exist, the first moments of a probability distribution can be estimated from a sample using the formulawhere is the th sample moment and . Estimating with gives the sample mean, denoted . Substituting this estimate in the formula for the expected value of a geometric distribution and solving for gives the estimators and when supported on and respectively. These estimators are biased since as a result of Jensen's inequality.
Maximum likelihood estimation
The maximum likelihood estimator of is the value that maximizes the likelihood function given a sample. By finding the zero of the derivative of the log-likelihood function when the distribution is defined over , the maximum likelihood estimator can be found to be , where is the sample mean. If the domain is , then the estimator shifts to . As previously discussed in § Method of moments, these estimators are biased.
Regardless of the domain, the bias is equal to
which yields the bias-corrected maximum likelihood estimator,
Bayesian inference
In Bayesian inference, the parameter is a random variable from a prior distribution with a posterior distribution calculated using Bayes' theorem after observing samples. If a beta distribution is chosen as the prior distribution, then the posterior will also be a beta distribution and it is called the conjugate distribution. In particular, if a prior is selected, then the posterior, after observing samples , isAlternatively, if the samples are in , the posterior distribution isSince the expected value of a distribution is , as and approach zero, the posterior mean approaches its maximum likelihood estimate.
Random variate generation | Geometric distribution | Wikipedia | 467 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
The geometric distribution can be generated experimentally from i.i.d. standard uniform random variables by finding the first such random variable to be less than or equal to . However, the number of random variables needed is also geometrically distributed and the algorithm slows as decreases.
Random generation can be done in constant time by truncating exponential random numbers. An exponential random variable can become geometrically distributed with parameter through . In turn, can be generated from a standard uniform random variable altering the formula into .
Applications
The geometric distribution is used in many disciplines. In queueing theory, the M/M/1 queue has a steady state following a geometric distribution. In stochastic processes, the Yule Furry process is geometrically distributed. The distribution also arises when modeling the lifetime of a device in discrete contexts. It has also been used to fit data including modeling patients spreading COVID-19. | Geometric distribution | Wikipedia | 180 | 45922 | https://en.wikipedia.org/wiki/Geometric%20distribution | Mathematics | Probability | null |
Index fossils (also known as guide fossils or indicator fossils) are fossils used to define and identify geologic periods (or faunal stages). Index fossils must have a short vertical range, wide geographic distribution and rapid evolutionary trends. Another term, "zone fossil", is used when the fossil has all the characters stated above except wide geographical distribution; thus, they correlate the surrounding rock to a biozone rather than a specific time period. | List of index fossils | Wikipedia | 89 | 45930 | https://en.wikipedia.org/wiki/List%20of%20index%20fossils | Physical sciences | Stratigraphy | Earth science |
A set of primary colors (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a broad range of colors in, e.g., electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors can be predicted by an appropriate mixing model (e.g., additive, subtractive) that reflects the physics of how light interacts with physical media, and ultimately the retina. The most common color mixing models are the additive primary colors (red, green, blue) and the subtractive primary colors (cyan, magenta, yellow). Red, yellow and blue are also commonly taught as primary colors (usually in the context of subtractive color mixing as opposed to additive color mixing), despite some criticism due to its lack of scientific basis.
Primary colors can also be conceptual (not necessarily real), either as additive mathematical elements of a color space or as irreducible phenomenological categories in domains such as psychology and philosophy. Color space primaries are precisely defined and empirically rooted in psychophysical colorimetry experiments which are foundational for understanding color vision. Primaries of some color spaces are complete (that is, all visible colors are described in terms of their primaries weighted by nonnegative primary intensity coefficients) but necessarily imaginary (that is, there is no plausible way that those primary colors could be represented physically, or perceived). Phenomenological accounts of primary colors, such as the psychological primaries, have been used as the conceptual basis for practical color applications even though they are not a quantitative description in and of themselves.
Sets of color space primaries are generally arbitrary, in the sense that there is no one set of primaries that can be considered the canonical set. Primary pigments or light sources are selected for a given application on the basis of subjective preferences as well as practical factors such as cost, stability, availability etc.
The concept of primary colors has a long, complex history. The choice of primary colors has changed over time in different domains that study color. Descriptions of primary colors come from areas including philosophy, art history, color order systems, and scientific work involving the physics of light and perception of color. | Primary color | Wikipedia | 466 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Art education materials commonly use red, yellow, and blue as primary colors, sometimes suggesting that they can mix all colors. No set of real colorants or lights can mix all possible colors, however. In other domains, the three primary colors are typically red, green and blue, which are more closely aligned to the sensitivities of the photoreceptor pigments in the cone cells.
Color model primaries
A color model is an abstract model intended to describe the ways that colors behave, especially in color mixing. Most color models are defined by the interaction of multiple primary colors. Since most humans are trichromatic, color models that want to reproduce a meaningful portion of a human's perceptual gamut must use at least three primaries. More than three primaries are allowed, for example, to increase the size of the gamut of the color space, but the entire human perceptual gamut can be reproduced with just three primaries (albeit imaginary ones as in the CIE XYZ color space).
Some humans (and most mammals) are dichromats, corresponding to specific forms of color blindness in which color vision is mediated by only two of the types of color receptors. Dichromats require only two primaries to reproduce their entire gamut and their participation in color matching experiments was essential in the determination of cone fundamentals leading to all modern color spaces. Despite most vertebrates being tetrachromatic, and therefore requiring four primaries to reproduce their entire gamut, there is only one scholarly report of a functional human tetrachromat, for which trichromatic color models are insufficient.
Additive models | Primary color | Wikipedia | 333 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
The perception elicited by multiple light sources co-stimulating the same area of the retina is additive, i.e., predicted via summing the spectral power distributions (the intensity of each wavelength) of the individual light sources assuming a color matching context. For example, a purple spotlight on a dark background could be matched with coincident blue and red spotlights that are both dimmer than the purple spotlight. If the intensity of the purple spotlight was doubled it could be matched by doubling the intensities of both the red and blue spotlights that matched the original purple. The principles of additive color mixing are embodied in Grassmann's laws. Additive mixing is sometimes described as "additive color matching" to emphasize the fact the predictions based on additivity only apply assuming the color matching context. Additivity relies on assumptions of the color matching context such as the match being in the foveal field of view, under appropriate luminance, etc.
Additive mixing of coincident spot lights was applied in the experiments used to derive the CIE 1931 colorspace (see color space primaries section). The original monochromatic primaries of the wavelengths of 435.8 nm (violet), 546.1 nm (green), and 700 nm (red) were used in this application due to the convenience they afforded to the experimental work.
Small red, green, and blue elements (with controllable brightness) in electronic displays mix additively from an appropriate viewing distance to synthesize compelling colored images. This specific type of additive mixing is described as partitive mixing. Red, green, and blue light are popular primaries for partitive mixing since primary lights with those hues provide a large color triangle (gamut).
The exact colors chosen for additive primaries are a compromise between the available technology (including considerations such as cost and power usage) and the need for large chromaticity gamut. For example, in 1953 the NTSC specified primaries that were representative of the phosphors available in that era for color CRTs. Over decades, market pressures for brighter colors resulted in CRTs using primaries that deviated significantly from the original standard. Currently, ITU-R BT.709-5 primaries are typical for high-definition television.
Subtractive models | Primary color | Wikipedia | 462 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
The subtractive color mixing model predicts the resultant spectral power distribution of light filtered through overlaid partially absorbing materials, usually in the context of an underlying reflective surface such as white paper. Each layer partially absorbs some wavelengths of light from the illumination while letting others pass through, resulting in a colored appearance. The resultant spectral power distribution is predicted by the wavelength-by-wavelength product of the spectral reflectance of the illumination and the product of the spectral reflectances of all of the layers. Overlapping layers of ink in printing mix subtractively over reflecting white paper, while the reflected light mixes in a partitive way to generate color images. Importantly, unlike additive mixture, the color of the mixture is not well predicted by the colors of the individual dyes or inks. The typical number of inks in such a printing process is 3 (CMY) or 4 (CMYK), but can commonly range to 6 (e.g., Pantone hexachrome). In general, using fewer inks as primaries results in more economical printing but using more may result in better color reproduction.
Cyan (C), magenta (M), and yellow (Y) are good chromatic subtractive primaries in that filters with those colors can be overlaid to yield a surprisingly large chromaticity gamut. A black (K) ink (from the older "key plate") is also used in CMYK systems to augment C, M and Y inks or dyes: this is more efficient in terms of time and expense and less likely to introduce visible defects. Before the color names cyan and magenta were in common use, these primaries were often known as blue and red, respectively, and their exact color has changed over time with access to new pigments and technologies. Organizations such as Fogra, European Color Initiative and SWOP publish colorimetric CMYK standards for the printing industry.
Traditional red, yellow, and blue primary colors as a subtractive system
Color theorists since the seventeenth century, and many artists and designers since that time, have taken red, yellow, and blue to be the primary colors (see history below). This RYB system, in "traditional color theory", is often used to order and compare colors, and sometimes proposed as a system of mixing pigments to get a wide range of, or "all", colors.
O'Connor describes the role of RYB primaries in traditional color theory: | Primary color | Wikipedia | 501 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Traditional color theory is based on experience with pigments, more than on the science of light. In 1920, Snow and Froehlich explained:
The widespread adoption of teaching of RYB as primary colors in post-secondary art schools in the twentieth century has been attributed to the influence of the Bauhaus, where Johannes Itten developed his ideas on color during his time there in the 1920s, and of his book on color published in 1961.
In discussing color design for the web, Jason Beaird writes:
As with any system of real primaries, not all colors can be mixed from RYB primaries.
For example, if the blue pigment is a deep Prussian blue, then a muddy desaturated green may be the best that can be had by mixing with yellow. To achieve a larger gamut of colors via mixing, the blue and red pigments used in illustrative materials such as the Color Mixing Guide in the image are often closer to peacock blue (a blue-green or cyan) and carmine (or crimson or magenta) respectively.
Printers traditionally used inks of such colors, known as "process blue" and "process red", before modern color science and the printing industry converged on the process colors (and names) cyan and magenta RYB is not the same as CMY, nor exactly subtractive, but that there is a range of ways to conceptualize traditional RYB as a subtractive system in the framework of modern color science.
Faber-Castell identifies the following three colors: "Cadmium yellow" (number 107) for yellow, "Phthalo blue" (number 110) for blue and "Deep scarlet red" (number 219) for red, as the closest to primary colors for its Art & Graphic color pencils range. "Cadmium yellow" (number 107) for yellow, "Phthalo blue" (number 110) for blue and "Pale geranium lake" (number 121) for red, are provided as primary colors in its basic 5 color "Albrecht Dürer" watercolor marker set.
Mixing pigments in limited palettes
The first known use of red, yellow, and blue as "simple" or "primary" colors, by Chalcidius, ca. AD 300, was possibly based on the art of paint mixing. | Primary color | Wikipedia | 474 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Mixing pigments for the purpose of creating realistic paintings with diverse color gamuts is known to have been practiced at least since Ancient Greece (see history section). The identity of a/the set of minimal pigments to mix diverse gamuts has long been the subject of speculation by theorists whose claims have changed over time, for example, Pliny's white, black, one or another red, and "sil", which might have been yellow or blue; Robert Boyle's white, black, red, yellow, and blue; and variations with more or fewer "primary" color or pigments. Some writers and artists have found these schemes difficult to reconcile with the actual practice of painting. Nonetheless, it has long been known that limited palettes consisting of a small set of pigments are sufficient to mix a diverse gamut of colors.
The set of pigments available to mix diverse gamuts of color (in various media such as oil, watercolor, acrylic, gouache, and pastel) is large and has changed throughout history. There is no consensus on a specific set of pigments that are considered primary colors the choice of pigments depends entirely on the artist's subjective preference of subject and style of art, as well as material considerations like lightfastness and mixing behavior. A variety of limited palettes have been employed by artists for their work.
The color of light (i.e., the spectral power distribution) reflected from illuminated surfaces coated in paint mixes is not well approximated by a subtractive or additive mixing model. Color predictions that incorporate light scattering effects of pigment particles and paint layer thickness require approaches based on the Kubelka–Munk equations, but even such approaches are not expected to predict the color of paint mixtures precisely due to inherent limitations. Artists typically rely on mixing experience and "recipes" to mix desired colors from a small initial set of primaries and do not use mathematical modeling.
MacEvoy explains why artists often chose a palette closer to RYB than to CMY:
Color space primaries | Primary color | Wikipedia | 419 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
A color space is a subset of a color model, where the primaries have been defined, either directly as photometric spectra, or indirectly as a function of other color spaces. For example, sRGB and Adobe RGB are both color spaces based on the RGB color model. However, the green primary of Adobe RGB is more saturated than the equivalent in sRGB, and therefore yields a larger gamut. Otherwise, choice of color space is largely arbitrary and depends on the utility to a specific application.
Imaginary primaries
Color space primaries are derived from canonical colorimetric experiments that represent a standardized model of an observer (i.e., a set of color matching functions) adopted by Commission Internationale de l'Eclairage (CIE) standards. The abbreviated account of color space primaries in this section is based on descriptions in Colorimetry - Understanding The CIE System.
The CIE 1931 standard observer is derived from experiments in which participants observe a foveal secondary bipartite field with a dark surround. Half of the field is illuminated with a monochromatic test stimulus (ranging from 380 nm to 780 nm) and the other half is the matching stimulus illuminated with three coincident monochromatic primary lights: 700 nm for red (R), 546.1 nm for green (G), and 435.8 nm for blue (B). These primaries correspond to CIE RGB color space. The intensities of the primary lights could be adjusted by the participant observer until the matching stimulus matched the test stimulus, as predicted by Grassman's laws of additive mixing. Different standard observers from other color matching experiments have been derived since 1931. The variations in experiments include choices of primary lights, field of view, number of participants etc. but the presentation below is representative of those results.
Matching was performed across many participants in incremental steps along the range of test stimulus wavelengths (380 nm to 780 nm) to ultimately yield the color matching functions: , and that represent the relative intensities of red, green, and blue light to match each wavelength (). These functions imply that units of the test stimulus with any spectral power distribution, , can be matched by , , and units of each primary where: | Primary color | Wikipedia | 452 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Each integral term in the above equation is known as a tristimulus value and measures amounts in the adopted units. No set of real primary lights can match another monochromatic light under additive mixing so at least one of the color matching functions is negative for each wavelength. A negative tristimulus value corresponds to that primary being added to the test stimulus instead of the matching stimulus to achieve a match.
The negative tristimulus values made certain types of calculations difficult, so the CIE put forth new color matching functions , , and defined by the following linear transformation:
These new color matching functions correspond to imaginary primary lights X, Y, and Z (CIE XYZ color space). All colors can be matched by finding the amounts , , and analogously to , , and as defined in . The functions , , and based on the specifications that they should be nonnegative for all wavelengths, be equal to photometric luminance, and that for an equienergy (i.e., a uniform spectral power distribution) test stimulus.
Derivations use the color matching functions, along with data from other experiments, to ultimately yield the cone fundamentals: , and . These functions correspond to the response curves for the three types of color photoreceptors found in the human retina: long-wavelength (L), medium-wavelength (M), and short-wavelength (S) cones. The three cone fundamentals are related to the original color matching functions by the following linear transformation (specific to a 10° field):
LMS color space comprises three primary lights (L, M, and S) that stimulate only the L-, M-, and S-cones respectively. A real primary that stimulates only the M-cone is impossible, and therefore these primaries are imaginary. The LMS color space has significant physiological relevance as these three photoreceptors mediate trichromatic color vision in humans.
Both XYZ and LMS color spaces are complete since all colors in the gamut of the standard observer are contained within their color spaces. Complete color spaces must have imaginary primaries, but color spaces with imaginary primaries are not necessarily complete (e.g. ProPhoto RGB color space).
Real primaries | Primary color | Wikipedia | 460 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Color spaces used in color reproduction must use real primaries that can be reproduced by practical sources, either lights in additive models, or pigments in subtractive models. Most RGB color spaces have real primaries, though some maintain imaginary primaries. For example, all the sRGB primaries fall within the gamut of human perception, and so can be easily represented by practical light sources, including CRT and LED displays, hence why sRGB is still the color space of choice for digital displays.
A color in a color space is defined as a combination of its primaries, where each primary must give a non-negative contribution. Any color space based on a finite number of real primaries is incomplete in that it cannot reproduce every color within the gamut of the standard observer.
Practical color spaces such as sRGB and scRGB are typically (at least partially) defined in terms of linear transformations from CIE XYZ, and color management often uses CIE XYZ as a middle point for transformations between two other color spaces.
Most color spaces in the color-matching context (those defined by their relationship to CIE XYZ) inherit its three-dimensionality. However, more complex color appearance models like CIECAM02 require extra dimensions to describe colors appear under different viewing conditions.
Psychological primaries
The opponent process was proposed by Ewald Hering in which he described the four unique hues (later called psychological primaries in some contexts): red, green, yellow and blue. To Hering, the unique hues appeared as pure colors, while all others were "psychological mixes" of two of them. Furthermore, these colors were organized in "opponent" pairs, red vs. green and yellow vs. blue so that mixing could occur across pairs (e.g., a yellowish green or a yellowish red) but not within a pair (i.e., reddish green cannot be imagined). An achromatic opponent process along black and white is also part of Hering's explanation of color perception. Hering asserted that we did not know why these color relationships were true but knew that they were. Although there is a great deal of evidence for the opponent process in the form of neural mechanisms, there is currently no clear mapping of the psychological primaries to neural correlates.
The psychological primaries were applied by Richard S. Hunter as the primaries for Hunter L,a,b colorspace that led to the creation of CIELAB. The Natural Color System is also directly inspired by the psychological primaries.
History
Philosophy | Primary color | Wikipedia | 511 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Philosophical writing from ancient Greece has described notions of primary colors, but they can be difficult to interpret in terms of modern color science. Theophrastus (c. 371–287 BCE) described Democritus' position that the primary colors were white, black, red, and green. In Classical Greece, Empedocles identified white, black, red, and, (depending on the interpretation) either yellow or green as primary colors. Aristotle described a notion in which white and black could be mixed in different ratios to yield chromatic colors; this idea had considerable influence in Western thinking about color. François d'Aguilon's notion of the five primary colors (white, yellow, red, blue, black) was influenced by Aristotle's idea of the chromatic colors being made of black and white.The 20th century philosopher Ludwig Wittgenstein explored color-related ideas using red, green, blue, and yellow as primary colors.
Light and color vision
Isaac Newton used the term "primary color" to describe the colored spectral components of sunlight. A number of color theorists did not agree with Newton's work. David Brewster advocated that red, yellow, and blue light could be combined into any spectral hue late into the 1840s. Thomas Young proposed red, green, and violet as the three primary colors, while James Clerk Maxwell favored changing violet to blue. Hermann von Helmholtz proposed "a slightly purplish red, a vegetation-green, slightly yellowish, and an ultramarine-blue" as a trio. Newton, Young, Maxwell, and Helmholtz were all prominent contributors to "modern color science" that ultimately described the perception of color in terms of the three types of retinal photoreceptors.
Colorants | Primary color | Wikipedia | 356 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
John Gage's The Fortunes Of Apelles provides a summary of the history of primary colors as pigments in painting and describes the evolution of the idea as complex. Gage begins by describing Pliny the Elder's account of notable Greek painters who used four primaries. Pliny distinguished the pigments (i.e., substances) from their apparent colors: white from Milos (ex albis), red from Sinope (ex rubris), Attic yellow (sil) and atramentum (ex nigris). Sil was historically confused as a blue pigment between the 16th and 17th centuries, leading to claims about white, black, red, and blue being the fewest colors required for painting. Thomas Bardwell, an 18th century Norwich portrait painter, was skeptical of the practical relevance of Pliny's account.
Robert Boyle, the Irish chemist, introduced the term primary color in English in 1664 and claimed that there were five primary colors (white, black, red, yellow, and blue). The German painter Joachim von Sandrart eventually proposed removing white and black from the primaries and that one only needed red, yellow, blue, and green to paint "the whole creation".
Red, yellow, and blue as primaries became a popular notion in the 18th and 19th centuries. Jacob Christoph Le Blon, an engraver, was the first to use separate plates for each color in mezzotint printmaking: yellow, red, and blue, plus black to add shades and contrast. Le Blon used primitive in 1725 to describe red, yellow, and blue in a very similar sense as Boyle used primary. Moses Harris, an entomologist and engraver, also describes red, yellow, and blue as "primitive" colors in 1766. Léonor Mérimée described red, yellow, and blue in his book on painting (originally published in French in 1830) as the three simple/primitive colors that can make a "great variety" of tones and colors found in nature. George Field, a chemist, used the word primary to describe red, yellow, and blue in 1835. Michel Eugène Chevreul, also a chemist, discussed red, yellow, and blue as "primary" colors in 1839.
Color order systems | Primary color | Wikipedia | 453 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Historical perspectives on color order systems ("catalogs" of color) that were proposed in the 18th and 19th centuries describe them as using red, yellow, and blue pigments as chromatic primaries. Tobias Mayer (a German mathematician, physicist, and astronomer) described a triangular bipyramid with red, yellow and blue at the 3 vertices in the same plane, white at the top vertex, and black and the bottom vertex in a public lecture in 1758. There are 11 planes of colors between the white and black vertices inside the triangular bipyramid. Mayer did not seem to distinguish between colored light and colorant though he used vermilion, orpiment (King’s yellow), and Bergblau (azurite) in partially complete colorings of planes in his solid. Johann Heinrich Lambert (a Swiss mathematician, physicist, and astronomer) proposed a triangular pyramid with gamboge, carmine, and Prussian blue as primaries and only white at the top vertex (since Lambert could produce a mixture that was sufficiently black with those pigments). Lambert's work on this system was published in 1772. Philipp Otto Runge (the Romantic German painter) firmly believed in the theory of red, yellow and blue as the primary colors (again without distinguishing light color and colorant). His color sphere was ultimately described in an essay titled Farben-Kugel (color ball) published by Goethe in 1810. His spherical model of colors equally spaced red, yellow, and blue longitudinally with orange, green, and violet between them, and white and black at opposite poles.
Red, yellow, and blue as primary colors
Numerous authors have taught that red, yellow, and blue (RYB) are the primary colors in art education materials since at least the 19th century, following the ideas tabulated above from earlier centuries.
A wide variety of contemporary educational sources also describe the RYB primaries. These sources range from children's books and art material manufacturers to painting and color guides. Art education materials often suggest that RYB primaries can be mixed to create all other colors.
Criticism
Albert Munsell, an American painter (and creator of the Munsell color system), referred to the notion of RYB primaries as "mischief", "a widely accepted error", and underspecified in his book A Color Notation, first published in 1905. | Primary color | Wikipedia | 478 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
Itten's ideas about RYB primaries have been criticized as ignoring modern color science with demonstrations that some of Itten's claims about mixing RYB primaries are impossible. | Primary color | Wikipedia | 35 | 45939 | https://en.wikipedia.org/wiki/Primary%20color | Physical sciences | Basics_7 | null |
A building or edifice is an enclosed structure with a roof and walls, usually standing permanently in one place, such as a house or factory. Buildings come in a variety of sizes, shapes, and functions, and have been adapted throughout history for numerous factors, from building materials available, to weather conditions, land prices, ground conditions, specific uses, prestige, and aesthetic reasons. To better understand the concept, see Nonbuilding structure for contrast.
Buildings serve several societal needs – occupancy, primarily as shelter from weather, security, living space, privacy, to store belongings, and to comfortably live and work. A building as a shelter represents a physical separation of the human habitat (a place of comfort and safety) from the outside (a place that may be harsh and harmful at times).
Ever since the first cave paintings, buildings have been objects or canvasses of much artistic expression. In recent years, interest in sustainable planning and building practices has become an intentional part of the design process of many new buildings and other structures, usually green buildings.
Definition
A building is 'a structure that has a roof and walls and stands more or less permanently in one place'; "there was a three-storey building on the corner"; "it was an imposing edifice". In the broadest interpretation a fence or wall is a building. However, the word structure is used more broadly than building, to include natural and human-made formations and ones that do not have walls; structure is more often used for a fence. Sturgis' Dictionary included that differs from architecture in excluding all idea of artistic treatment; and it differs from construction in the idea of excluding scientific or highly skilful treatment."
Structural height in technical usage is the height to the highest architectural detail on the building from street level. Spires and masts may or may not be included in this height, depending on how they are classified. Spires and masts used as antennas are not generally included. The distinction between a low-rise and high-rise building is a matter of debate, but generally three stories or less is considered low-rise.
History
There is clear evidence of homebuilding from around 18,000 BC. Buildings became common during the Neolithic period.
Types
Residential | Building | Wikipedia | 455 | 45995 | https://en.wikipedia.org/wiki/Building | Technology | Structures | null |
Single-family residential buildings are most often called houses or homes. Multi-family residential buildings containing more than one dwelling unit are called duplexes or apartment buildings. Condominiums are apartments that occupants own rather than rent. Houses may be built in pairs (semi-detached) or in terraces, where all but two of the houses have others on either side. Apartments may be built round courtyards or as rectangular blocks surrounded by plots of ground. Houses built as single dwellings may later be divided into apartments or bedsitters, or converted to other uses (e.g., offices or shops). Hotels, especially of the extended-stay variety (apartels), can be classed as residential.
Building types may range from huts to multimillion-dollar high-rise apartment blocks able to house thousands of people. Increasing settlement density in buildings (and smaller distances between buildings) is usually a response to high ground prices resulting from the desire of many people to live close to their places of employment or similar attractors.
Terms for residential buildings reflect such characteristics as function (e.g., holiday cottage (vacation home) or timeshare if occupied seasonally); size (cottage or great house); value (shack or mansion); manner of construction (log home or mobile home); architectural style (castle or Victorian); and proximity to geographical features (earth shelter, stilt house, houseboat, or floating home). For residents in need of special care, or those society considers dangerous enough to deprive of liberty, there are institutions (nursing homes, orphanages, psychiatric hospitals, and prisons) and group housing (barracks and dormitories).
Historically, many people lived in communal buildings called longhouses, smaller dwellings called pit-houses, and houses combined with barns, sometimes called housebarns.
Common building materials include brick, concrete, stone, and combinations thereof. Buildings are defined to be substantial, permanent structures. Such forms as yurts and motorhomes are therefore considered dwellings but not buildings.
Commercial
A commercial building is one in which at least one business is based and people do not live. Examples include stores, restaurant, and hotels.
Industrial
Industrial buildings are those in which heavy industry is done, such as manufacturing. These edifices include warehouses and factories.
Agricultural
Agricultural buildings are the outbuildings, such as barns located on farms.
Mixed use
Some buildings incorporate several or multiple different uses, most commonly commercial and residential.
Complex | Building | Wikipedia | 500 | 45995 | https://en.wikipedia.org/wiki/Building | Technology | Structures | null |
Sometimes a group of inter-related (and possibly inter-connected) builds are referred to as a complex – for example a housing complex, educational complex, hospital complex, etc.
Creation
The practice of designing, constructing, and operating buildings is most usually a collective effort of different groups of professionals and trades. Depending on the size, complexity, and purpose of a particular building project, the project team may include:
A real estate developer who secures funding for the project;
One or more financial institutions or other investors that provide the funding
Local planning and code authorities
A surveyor who performs an ALTA/ACSM and construction surveys throughout the project;
Construction managers who coordinate the effort of different groups of project participants;
Licensed architects and engineers who provide building design and prepare construction documents;
The principal design Engineering disciplines which would normally include the following professionals: Civil, Structural, Mechanical building services or HVAC (heating Ventilation and Air Conditioning) Electrical Building Services, Plumbing and drainage. Also other possible design Engineer specialists may be involved such as Fire (prevention), Acoustic, façade engineers, building physics, Telecoms, AV (Audio Visual), BMS (Building Management Systems) Automatic controls etc. These design Engineers also prepare construction documents which are issued to specialist contractors to obtain a price for the works and to follow for the installations.
Landscape architects;
Interior designers;
Other consultants;
Contractors who provide construction services and install building systems such as climate control, electrical, plumbing, decoration, fire protection, security and telecommunications;
Marketing or leasing agents;
Facility managers who are responsible for operating the building.
Regardless of their size or intended use, all buildings in the US must comply with zoning ordinances, building codes and other regulations such as fire codes, life safety codes and related standards.
Vehicles—such as trailers, caravans, ships and passenger aircraft—are treated as "buildings" for life safety purposes.
Ownership and funding
Mortgage loan
Real estate developer
Environmental impacts
Building services
Physical plant
Any building requires a certain general amount of internal infrastructure to function, which includes such elements like heating / cooling, power and telecommunications, water and wastewater etc. Especially in commercial buildings (such as offices or factories), these can be extremely intricate systems taking up large amounts of space (sometimes located in separate areas or double floors / false ceilings) and constitute a big part of the regular maintenance required.
Conveying systems
Systems for transport of people within buildings:
Elevator
Escalator
Moving sidewalk (horizontal and inclined)
Systems for transport of people between interconnected buildings:
Skyway
Underground city
Building damage | Building | Wikipedia | 506 | 45995 | https://en.wikipedia.org/wiki/Building | Technology | Structures | null |
Buildings may be damaged during construction or during maintenance. They may be damaged by accidents involving storms, explosions, subsidence caused by mining, water withdrawal or poor foundations and landslides. Buildings may suffer fire damage and flooding. They may become dilapidated through lack of proper maintenance, or alteration work improperly carried out. | Building | Wikipedia | 63 | 45995 | https://en.wikipedia.org/wiki/Building | Technology | Structures | null |
Porpoises () are small dolphin-like cetaceans classified under the family Phocoenidae. Although similar in appearance to dolphins, they are more closely related to narwhals and belugas than to the true dolphins. There are eight extant species of porpoise, all among the smallest of the toothed whales. Porpoises are distinguished from dolphins by their flattened, spade-shaped teeth distinct from the conical teeth of dolphins, and lack of a pronounced beak, although some dolphins (e.g. Hector's dolphin) also lack a pronounced beak. Porpoises, and other cetaceans, belong to the clade Cetartiodactyla with even-toed ungulates.
Porpoises range in size from the vaquita, at in length and in weight, to the Dall's porpoise, at and . Several species exhibit sexual dimorphism in that the females are larger than males. They have streamlined bodies and two limbs that are modified into flippers. Porpoises use echolocation as their primary sensory system. Some species are well adapted for diving to great depths. As all cetaceans, they have a layer of fat, or blubber, under the skin to keep them warm in cold water.
Porpoises are abundant and found in a multitude of environments, including rivers (finless porpoise), coastal and shelf waters (harbour porpoise, vaquita) and open ocean (Dall's porpoise and spectacled porpoise), covering all water temperatures from tropical (Sea of Cortez, vaquita) to polar (Greenland, harbour porpoise). Porpoises feed largely on fish and squid, much like the rest of the odontocetes. Little is known about reproductive behaviour. Females may have one calf every year under favourable conditions. Calves are typically born in the spring and summer months and remain dependent on the female until the following spring. Porpoises produce ultrasonic clicks, which are used for both navigation (echolocation) and social communication. In contrast to many dolphin species, porpoises do not form large social groups. | Porpoise | Wikipedia | 451 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Porpoises were, and still are, hunted by some countries by means of drive hunting. Larger threats to porpoises include extensive bycatch in gill nets, competition for food from fisheries, and marine pollution, in particular heavy metals and organochlorides. The vaquita is nearly extinct due to bycatch in gill nets, with a predicted population of fewer than a dozen individuals. Since the extinction of the baiji, the vaquita is considered the most endangered cetacean. Some species of porpoises have been and are kept in captivity and trained for research, education and public display.
Taxonomy and evolution
Porpoises, along with whales and dolphins, are descendants of land-living ungulates (hoofed animals) that first entered the oceans around 50 million years ago (Mya). During the Miocene (23 to 5 Mya), mammals were fairly modern, meaning they seldom changed physiologically from the time. The cetaceans diversified, and fossil evidence suggests porpoises and dolphins diverged from their last common ancestor around 15 Mya. The oldest fossils are known from the shallow seas around the North Pacific, with animals spreading to the European coasts and Southern Hemisphere only much later, during the Pliocene. | Porpoise | Wikipedia | 257 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
ORDER Artiodactyla
Infraorder Cetacea
Parvorder Odontoceti toothed whales
Superfamily Delphinoidea
Family Phocoenidae – porpoises
Genus †Haborophocoena
H. toyoshimai
Genus Neophocaena
N. phocaeniodes – Indo-Pacific finless porpoise
N. sunameri – East Asian finless porpoise
N. asiaeorientalis – Yangtze finless porpoise
Genus †Numataphocoena
N. yamashitai
Genus Phocoena
P. phocoena – harbour porpoise
P. sinus – vaquita
P. dioptrica – spectacled porpoise
P. spinipinnis – Burmeister's porpoise
Genus Phocoenoides
P. dalli – Dall's porpoise
Genus †Semirostrum
S.ceruttii
Genus †Septemtriocetus
S. bosselaersii
Genus †Piscolithax
P. aenigmaticus
P. longirostris
P. boreios
P. tedfordi
Recently discovered hybrids between male harbour porpoises and female Dall's porpoises indicate the two species may actually be members of the same genus.
Biology
Anatomy
Porpoises have a bulbous head, no external ear flaps, a non-flexible neck, a torpedo shaped body, limbs modified into flippers, and a tail fin. Their skull has small eye orbits, small, blunt snouts, and eyes placed on the sides of the head. Porpoises range in size from the and vaquita to the and Dall's porpoise. Overall, they tend to be dwarfed by other cetaceans. Almost all species have female-biased sexual dimorphism, with the females being larger than the males, although those physical differences are generally small; one exception is Dall's porpoise. | Porpoise | Wikipedia | 404 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Odontocetes possess teeth with cementum cells overlying dentine cells. Unlike human teeth, which are composed mostly of enamel on the portion of the tooth outside of the gum, whale teeth have cementum outside the gum. Porpoises have a three-chambered stomach, including a fore-stomach and fundic and pyloric chambers. Porpoises, like other odontocetes, possess only one blowhole. Breathing involves expelling stale air from the blowhole, forming an upward, steamy spout, followed by inhaling fresh air into the lungs. All porpoises have a thick layer of blubber. This blubber can help with insulation from the harsh underwater climate, protection to some extent as predators would have a hard time getting through a thick layer of fat, and energy for leaner times. Calves are born with only a thin layer of blubber, but rapidly gain a thick layer from the milk, which has a very high fat content.
Locomotion
Porpoises have two flippers on the front and a tail fin. Their flippers contain four digits. Although porpoises do not possess fully developed hind limbs, they possess discrete rudimentary appendages, which may contain feet and digits. Porpoises are fast swimmers in comparison to seals, which typically cruise at . The fusing of the neck vertebrae, while increasing stability when swimming at high speeds, decreases flexibility, making it impossible for them to turn their head. When swimming, they move their tail fin and lower body up and down, propelling themselves through vertical movement, while their flippers are mainly used for steering. Flipper movement is continuous. Some species log out of the water, which may allow them to travel faster, and sometimes they porpoise out of the water, meaning jump out of the water. Their skeletal anatomy allows them to be fast swimmers. They have a very well defined and triangular dorsal fin, allowing them to steer better in the water. Unlike their dolphin counterparts, they are adapted for coastal shores, bays, and estuaries.
Senses | Porpoise | Wikipedia | 423 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
The porpoise ear has specific adaptations to the marine environment. In humans, the middle ear works as an impedance equaliser between the outside air's low impedance and the cochlear fluid's high impedance. In whales, and other marine mammals, there is no great difference between the outer and inner environments. Instead of sound passing through the outer ear to the middle ear, porpoises receive sound through the throat, from which it passes through a low-impedance fat-filled cavity to the inner ear. The porpoise ear is acoustically isolated from the skull by air-filled sinus pockets, which allow for greater directional hearing underwater. Odontocetes send out high frequency clicks from an organ known as a melon. This melon consists of fat, and the skull of any such creature containing a melon will have a large depression. The large bulge on top of the porpoises head is caused by the melon.
The porpoise eye is relatively small for its size, yet they do retain a good degree of eyesight. As well as this, the eyes of a porpoise are placed on the sides of its head, so their vision consists of two fields, rather than a binocular view like humans have. When porpoises surface, their lens and cornea correct the nearsightedness that results from the refraction of light; their eyes contain both rod and cone cells, meaning they can see in both dim and bright light. Porpoises do, however, lack short wavelength sensitive visual pigments in their cone cells indicating a more limited capacity for colour vision than most mammals. Most porpoises have slightly flattened eyeballs, enlarged pupils (which shrink as they surface to prevent damage), slightly flattened corneas and a tapetum lucidum; these adaptations allow for large amounts of light to pass through the eye and, therefore, they are able to form a very clear image of the surrounding area.
The olfactory lobes are absent in porpoises, suggesting that they have no sense of smell.
Porpoises are not thought to have a good sense of taste, as their taste buds are atrophied or missing altogether. However, some have preferences between different kinds of fish, indicating some sort of attachment to taste.
Sleep | Porpoise | Wikipedia | 471 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Unlike most animals, porpoises are conscious breathers. All mammals sleep, but porpoises cannot afford to become unconscious for long because they may drown. While knowledge of sleep in wild cetaceans is limited, porpoises in captivity have been recorded to sleep with one side of their brain at a time, so that they may swim, breathe consciously, and avoid both predators and social contact during their period of rest.
Behaviour
Life cycle
Porpoises are fully aquatic creatures. Females deliver a single calf after a gestation period lasting about a year. Calving takes place entirely under water, with the foetus positioned for tail-first delivery to help prevent drowning. Females have mammary glands, but the shape of a newborn calf's mouth does not allow it to obtain a seal around the nipple—instead of the calf sucking milk, the mother squirts milk into the calf's mouth. This milk contains high amounts of fat, which aids in the development of blubber; it contains so much fat that it has the consistency of toothpaste. The calves are weaned at about 11 months of age. Males play no part in rearing calves. The calf is dependent for one to two years, and maturity occurs after seven to ten years, all varying between species. This mode of reproduction produces few offspring, but increases the probability of each one surviving.
Diet
Porpoises eat a wide variety of creatures. The stomach contents of harbour porpoises suggests that they mainly feed on benthic fish, and sometimes pelagic fish. They may also eat benthic invertebrates. In rare cases, algae, such as Ulva lactuca, is consumed. Atlantic porpoises are thought to follow the seasonal migration of bait fish, like herring, and their diet varies between seasons. The stomach contents of Dall's porpoises reveal that they mainly feed on cephalopods and bait fish, like capelin and sardines. Their stomachs also contained some deep-sea benthic organisms.
The finless porpoise is known to also follow seasonal migrations. It is known that populations in the mouth of the Indus River migrate to the sea from April through October to feed on the annual spawning of prawns. In Japan, sightings of small pods of them herding sand lance onto shore are common year-round. | Porpoise | Wikipedia | 480 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Little is known about the diets of other species of porpoises. A dissection of three Burmeister's porpoises shows that they consume shrimp and euphausiids (krill). A dissection of a beached Vaquita showed remains of squid and grunts. Nothing is known about the diet of the spectacled porpoise.
Interactions with humans
Research history
In Aristotle's time, the 4th century BCE, porpoises were regarded as fish due to their superficial similarity. Aristotle, however, could already see many physiological and anatomical similarities with the terrestrial vertebrates, such as blood (circulation), lungs, uterus and fin anatomy. His detailed descriptions were assimilated by the Romans, but mixed with a more accurate knowledge of the dolphins, as mentioned by Pliny the Elder in his "Natural history". In the art of this and subsequent periods, porpoises are portrayed with a long snout (typical of dolphins) and a high-arched head. The harbour porpoise was one of the most accessible species for early cetologists, because it could be seen very close to land, inhabiting shallow coastal areas of Europe. Much of the findings that apply to all cetaceans were first discovered in porpoises. One of the first anatomical descriptions of the airways of the whales on the basis of a harbor porpoise dates from 1671 by John Ray. It nevertheless referred to the porpoise as a fish, most likely not in the modern-day sense, where it refers to a zoological group, but the older reference as simply a creature of the sea (cf. for example star-fish, cuttle-fish, jelly-fish and whale-fish).
In captivity | Porpoise | Wikipedia | 359 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Harbour porpoises have historically been kept in captivity, under the assumption that they would fare better than their dolphin counterparts due to their smaller size and shallow-water habitats. Up until the 1980s, they were consistently short-lived. Harbour porpoises have a very long captive history, with poorly documented attempts as early as the 15th century, and better documented starting in the 1860s and 1870s in London Zoo, the now-closed Brighton Aquarium & Dolphinarium, and a zoo in Germany. At least 150 harbour porpoises have been kept worldwide, but only about 20 were actively caught for captivity. The captive history is best documented from Denmark where about 100 harbour porpoises have been kept, most in the 1960s and 1970s. All but two were incidental catches in fishing nets or strandings. Nearly half of these died within a month of diseases caught before they were captured or from damage sustained during capture. Up until 1984, none lived for more than 14 months. Attempts to rehabilitate seven rescued individuals in 1986 only resulted in three that could be released 6 months later. Very few have been brought into captivity later, but they have lived considerably longer. In recent decades, the only place keeping the species in Denmark is the Fjord & Bælt Centre, where three rescues have been kept, along with their offspring. Among the three rescues, one (father of world's first harbour porpoise born in captivity) lived for 20 years in captivity, another for 15 years, while the third (mother of first born in captivity) is the world's oldest known harbour porpoise, being 28 years old in 2023. The typical age reached in the wild is 14 years or less. Very few harbour porpoises have been born in captivity. Historically, harbour porpoises were often kept singly and those who were together often were not mature or of the same sex. Disregarding one born more than 100 years ago that was the result of a pregnant female being brought into captivity, the world's first full captive breeding was in 2007 in the Fjord & Bælt Centre, followed by another in 2009 in the Dolfinarium Harderwijk, the Netherlands. In addition to the few kept in Europe, harbour porpoise were displayed at the Vancouver Aquarium (Canada) until recently. This was a female that had beached herself onto Horseshoe Bay in 2008 and a male that had done the same in 2011. They died in 2017 and 2016 respectively. | Porpoise | Wikipedia | 497 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Finless porpoises have commonly been kept in Japan, as well as China and Indonesia. As of 1984, ninety-four in total had been in captivity in Japan, eleven in China, and at least two in Indonesia. As of 1986, three establishments in Japan had bred them, and there had been five recorded births. Three calves died moments after their birth, but two survived for several years. This breeding success, combined with the results with harbour porpoise in Denmark and the Netherlands, proved that porpoises can be successfully bred in captivity, and this could open up new conservation options. The reopened Miyajima Public Aquarium (Japan) houses three finless porpoises. As part of an attempt of saving the narrow-ridged (or Yangtze) finless porpoise, several are kept in the Baiji Dolphinarium in China. After having been kept in captivity for 9 years, the first breeding happened in 2005.
Small numbers of Dall's porpoises have been kept in captivity in both the United States and Japan, with the most recent being in the 1980s. The first recorded instance of a Dall's taken for an aquarium was in 1956 captured off Catalina Island in southern California. Dall's porpoises consistently failed to thrive in captivity. These animals often repeatedly ran into the walls of their enclosures, refused food, and exhibited skin sloughing. Almost all Dall's porpoises introduced to aquaria died shortly after, typically within days. Only two have lived for more than 60 days: a male reached 15 months at Marineland of the Pacific and another 21 months at a United States Navy facility.
As part of last-ditch effort of saving the extremely rare vaquita (the tiny remaining population is rapidly declining because of bycatch in gillnets), there have been attempts of transferring some to captivity. The first and only caught for captivity were two females in 2017. Both became distressed and were rapidly released, but one of them died in the process. Soon after the project was abandoned.
Only a single Burmeister's porpoise and a single spectacled porpoise have been kept in captivity. Both were stranded individuals that only survived a few days after their rescue.
Threats
Hunting | Porpoise | Wikipedia | 460 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Porpoises and other smaller cetaceans have traditionally been hunted in many areas, at least in Asia, Europe and North America, for their meat and blubber. A dominant hunting technique is drive hunting, where a pod of animals is driven together with boats and usually into a bay or onto a beach. Their escape is prevented by closing off the route to the ocean with other boats or nets. This type of fishery for harbour porpoises is best documented from the Danish straits, where it occurred until the end of the 19th century (it was banned in 1899), and again during the shortages in World War I and World War II. The Inuit in the Arctic hunt harbour porpoises by shooting and drive hunt for Dall's porpoise still takes place in Japan. The number of individuals taken each year is in the thousands, although a quota of around 17,000 per year is in effect today making it the largest direct hunt of any cetacean species in the world and the sustainability of the hunt has been questioned.
Fishing
Porpoises are highly affected by bycatch. Many porpoises, mainly the vaquita, are subject to great mortality due to gillnetting. Although it is the world's most endangered marine cetacean, the vaquita continues to be caught in small-mesh gillnet fisheries throughout much of its range. Incidental mortality caused by the fleet of El Golfo de Santa Clara was estimated to be at around 39 vaquitas per year, which is over 17% of the population size. Harbour porpoises also suffer drowning by gillnetting, but on a less threatening scale due to their high population; their mortality rate per year increases a mere 5% due to this.
The fishing market, historically has always had a porpoise bycatch. Today, the Marine Mammal Protection Act of 1972 has enforced the use of safer fishing equipment to reduce bycatch.
Environmental hazards | Porpoise | Wikipedia | 397 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Porpoises are very sensitive to anthropogenic disturbances, and are keystone species, which can indicate the overall health of the marine environment. Populations of harbor porpoises in the North and Baltic Seas are under increasing pressure from anthropogenic causes such as offshore construction, ship traffic, fishing, and military exercises. Increasing pollution is a serious problem for marine mammals. Heavy metals and plastic waste are not biodegradable, and sometimes cetaceans consume these hazardous materials, mistaking them for food items. As a result, the animals are more susceptible to diseases and have fewer offspring. Harbour porpoises from the English Channel were found to have accumulated heavy metals.
The military and geologists employ strong sonar and produce an increases in noise in the oceans. Marine mammals that make use of biosonar for orientation and communication are not only hindered by the extra noise, but may race to the surface in panic. This may lead to a bubbling out of blood gases, and the animal then dies because the blood vessels become blocked, so-called decompression sickness. This effect, of course, only occurs in porpoises that dive to great depths, such as Dall's porpoise.
Additionally, civilian vessels produce sonar waves to measure the depth of the body of water in which they are. Similar to the navy, some boats produce waves that attract porpoises, while others may repel them. The problem with the waves that attract is that the animal may be injured or even killed by being hit by the vessel or its propeller.
Conservation
The harbour porpoise, spectacled porpoise, Burmeister's porpoise, and Dall's porpoise are all listed on Appendix II of the Convention on the Conservation of Migratory Species of Wild Animals (CMS). In addition, the Harbour porpoise is covered by the Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas (ASCOBANS), the Agreement on the Conservation of Cetaceans in the Black Sea, Mediterranean Sea and Contiguous Atlantic Area (ACCOBAMS) and the Memorandum of Understanding Concerning the Conservation of the Manatee and Small Cetaceans of Western Africa and Macaronesia. Their conservation statuses are either at least concern or data deficient. | Porpoise | Wikipedia | 478 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
As of 2014, only 505 Yangtze finless porpoises remained in the main section of the Yangtze, with an alarming population density in Ezhou and Zhenjiang. While many threatened species decline rate slows after their classification, population decline rates of the porpoise are actually accelerating. While population decline tracked from 1994 to 2008 has been pegged at a rate of 6.06% annually, from 2006 to 2012, the porpoise population decreased by more than half. Finless porpoise population decrease of 69.8% in just a 22-year span from 1976 to 2000. 5.3%. A majority of factors of this population decline are being driven by the massive growth in Chinese industry since 1990 which caused increased shipping and pollution and ultimately environmental degradation. Some of these can be seen in damming of the river as well as illegal fishing activity. To protect the species, China's Ministry of Agriculture classified the species as being National First Grade Key Protected Wild Animal, the strictest classification by law, meaning it is illegal to bring harm to a porpoise. Protective measures in the Tian-e-Zhou Oxbow Nature Reserve has increased its population of porpoises from five to forty in 25 years. The Chinese Academy of Science's Wuhan Institute of Hydrobiology has been working with the World Wildlife Fund to ensure the future for this subspecies, and have placed five porpoises in another well-protected area, the He-wang-miao oxbow. Five protected natural reserves have been established in areas of the highest population density and mortality rates with measures being taken to ban patrolling and harmful fishing gear in those areas. There have also been efforts to study porpoise biology to help specialize conservation through captivation breeding. The Baiji Dolphinarium, was established in 1992 at the Institute of Hydrobiology of the Chinese Academy of Sciences in Wuhan which allowing the study of behavioral and biological factors affecting the finless porpoise, specifically breeding biology like seasonal changes in reproductive hormones and breeding behavior. | Porpoise | Wikipedia | 412 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Because vaquitas are indigenous to the Gulf of California, Mexico is leading conservation efforts with the creation of the International Committee for the Recovery of the Vaquita (CIRVA), which has tried to prevent the accidental deaths of vaquitas by outlawing the use of fishing nets within the vaquita's habitat. CIRVA has worked together with the CITES, the Endangered Species Act, and the Marine Mammal Protection Act (MMPA) to nurse the vaquita population back to a point at which they can sustain themselves. CIRVA concluded in 2000 that between 39 and 84 individuals are killed each year by such gillnets. To try to prevent extinction, the Mexican government has created a nature reserve covering the upper part of the Gulf of California and the Colorado River delta. They have also placed a temporary ban on fishing, with compensation to those affected, that may pose a threat to the vaquita. | Porpoise | Wikipedia | 184 | 46037 | https://en.wikipedia.org/wiki/Porpoise | Biology and health sciences | Cetaceans | null |
Halley's Comet is the only known short-period comet that is consistently visible to the naked eye from Earth, appearing every 72–80 years, though with the majority of recorded apparations (25 of 30) occurring after 75–77 years. It last appeared in the inner parts of the Solar System in 1986 and will next appear in mid-2061. Officially designated 1P/Halley, it is also commonly called Comet Halley, or sometimes simply Halley.
Halley's periodic returns to the inner Solar System have been observed and recorded by astronomers around the world since at least 240 BC, but it was not until 1705 that the English astronomer Edmond Halley understood that these appearances were re-appearances of the same comet. As a result of this discovery, the comet is named after Halley.
During its 1986 visit to the inner Solar System, Halley's Comet became the first comet to be observed in detail by a spacecraft, Giotto, providing the first observational data on the structure of a comet nucleus and the mechanism of coma and tail formation. These observations supported a number of longstanding hypotheses about comet construction, particularly Fred Whipple's "dirty snowball" model, which correctly predicted that Halley would be composed of a mixture of volatile ices—such as water, carbon dioxide, ammonia—and dust. The missions also provided data that substantially reformed and reconfigured these ideas; for instance, it is now understood that the surface of Halley is largely composed of dusty, non-volatile materials, and that only a small portion of it is icy.
Pronunciation
Comet Halley is usually pronounced , rhyming with valley, or sometimes , rhyming with daily. As to the surname Halley, Colin Ronan, one of Edmond Halley's biographers, preferred , rhyming with crawly. Spellings of Halley's name during his lifetime included Hailey, Haley, Hayley, Halley, Haly, Hawley, and Hawly, so its contemporary pronunciation is uncertain, but the version rhyming with valley seems to be preferred by current bearers of the surname. | Halley's Comet | Wikipedia | 441 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
Computation of orbit
Halley was the first comet to be recognised as periodic. Until the Renaissance, the philosophical consensus on the nature of comets, promoted by Aristotle, was that they were disturbances in Earth's atmosphere. This idea was disproven in 1577 by Tycho Brahe, who used parallax measurements to show that comets must lie beyond the Moon. Many were still unconvinced that comets orbited the Sun, and assumed instead that they must follow straight paths through the Solar System. In 1687, Sir Isaac Newton published his Philosophiæ Naturalis Principia Mathematica, in which he outlined his laws of gravity and motion. His work on comets was decidedly incomplete. Although he had suspected that two comets that had appeared in succession in 1680 and 1681 were the same comet before and after passing behind the Sun (he was later found to be correct; see Newton's Comet), he was initially unable to completely reconcile comets into his model.
Ultimately, it was Newton's friend, editor and publisher, Edmond Halley, who, in his 1705 Synopsis of the Astronomy of Comets, used Newton's new laws to calculate the gravitational effects of Jupiter and Saturn on cometary orbits. Having compiled a list of 24 comet observations, he calculated that the orbital elements of a second comet that had appeared in 1682 were nearly the same as those of two comets that had appeared in 1531 (observed by Petrus Apianus) and 1607 (observed by Johannes Kepler). Halley thus concluded that all three comets were, in fact, the same object returning about every 76 years, a period that has since been found to vary between 72 and 80 years. After a rough estimate of the perturbations the comet would sustain from the gravitational attraction of the planets, he predicted its return for 1758. While he had personally observed the comet around perihelion in September 1682, Halley died in 1742 before he could observe its predicted return.
Halley's prediction of the comet's return proved to be correct, although it was not seen until 25 December 1758, by Johann Georg Palitzsch, a German farmer and amateur astronomer. Other observers from throughout Europe and its colonies sent in confirmations to Paris after the comet brightened the following spring. In the Americas, John Winthrop lectured at Harvard University to explain the implications of the comet's reappearance for Newtonian mechanics and natural theology. | Halley's Comet | Wikipedia | 496 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
Another independent recognition that the comet had returned was made by the Jamaican astronomer Francis Williams, but his observations did not reach Europe. A unique portrait commissioned by Williams demonstrates the impact of the comet's return on period astronomers. Williams' hand rests on the page of Newton's Principia with procedures to predict comet sightings. The white smudge in the sky is probably a depiction of Halley's comet relative to the constellations in March 1759, and the chord hanging above the book likely represents the comet's orbit. In 2024, using X-ray imaging, the painting was shown to depict the field of stars in which the comet would have been visible in 1759. Williams likely commissioned the portrait to commemorate his observations.
The comet did not pass through its perihelion until 13 March 1759, the attraction of Jupiter and Saturn having caused a delay of 618 days. This effect was computed before its return (with a one-month error to 13 April) by a team of three French mathematicians, Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute. The confirmation of the comet's return was the first time anything other than planets had been shown to orbit the Sun. It was also one of the earliest successful tests of Newtonian physics, and a clear demonstration of its explanatory power. The comet was first named in Halley's honour by French astronomer Nicolas-Louis de Lacaille in 1759.
Some scholars have proposed that first-century Mesopotamian astronomers already had recognised Halley's Comet as periodic. This theory notes a passage in the Babylonian Talmud, tractate Horayot that refers to "a star which appears once in seventy years that makes the captains of the ships err". Others doubt this idea based on historical considerations about the exact timing of this alleged observation, and suggest it refers to the variable star Mira.
Researchers in 1981 attempting to calculate the past orbits of Halley by numerical integration starting from accurate observations in the seventeenth and eighteenth centuries could not produce accurate results further back than 837 owing to a close approach to Earth in that year. It was necessary to use ancient Chinese comet observations to constrain their calculations.
Orbit and origin | Halley's Comet | Wikipedia | 451 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
Halley's orbital period has varied between 74 and 80 years since 240 BC. Its orbit around the Sun is highly elliptical, with an orbital eccentricity of 0.967 (with 0 being a circle and 1 being a parabolic trajectory). The perihelion, the point in the comet's orbit when it is nearest the Sun, is . This is between the orbits of Mercury and Venus. Its aphelion, or farthest distance from the Sun, is , roughly the orbital distance of Pluto. Unlike the overwhelming majority of objects in the Solar System, Halley's orbit is retrograde; it orbits the Sun in the opposite direction to the planets, or, clockwise from above the Sun's north pole. The orbit is inclined by 18° to the ecliptic, with much of it lying south of the ecliptic. This is usually represented as 162°, to account for Halley's retrograde orbit. The 1910 passage was at a relative velocity of . Because its orbit comes close to Earth's in two places, Halley is associated with two meteor showers: the Eta Aquariids in early May, and the Orionids in late October.
Halley is classified as a periodic or short-period comet: one with an orbit lasting 200 years or less. This contrasts it with long-period comets, whose orbits last for thousands of years. Periodic comets have an average inclination to the ecliptic of only ten degrees, and an orbital period of just 6.5 years, so Halley's orbit is atypical. Most short-period comets (those with orbital periods shorter than 20 years and inclinations of 30 degrees or less) are called Jupiter-family comets. Those resembling Halley, with orbital periods of between 20 and 200 years and inclinations extending from zero to more than 90 degrees, are called Halley-type comets. , 105 Halley-type comets have been observed, compared with 816 identified Jupiter-family comets. | Halley's Comet | Wikipedia | 406 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
The orbits of the Halley-type comets suggest that they were originally long-period comets whose orbits were perturbed by the gravity of the giant planets and directed into the inner Solar System. If Halley was once a long-period comet, it is likely to have originated in the Oort cloud, a sphere of cometary bodies around 20,000–50,000 au from the Sun. Conversely the Jupiter-family comets are generally believed to originate in the Kuiper belt, a flat disc of icy debris between 30 au (Neptune's orbit) and 50 au from the Sun (in the scattered disc). Another point of origin for the Halley-type comets was proposed in 2008, when a trans-Neptunian object with a retrograde orbit similar to Halley's was discovered, , whose orbit takes it from just outside that of Uranus to twice the distance of Pluto. It may be a member of a new population of small Solar System bodies that serves as the source of Halley-type comets.
Halley has probably been in its current orbit for 16,000–200,000 years, although it is not possible to numerically integrate its orbit for more than a few tens of apparitions, and close approaches before 837 AD can only be verified from recorded observations. The non-gravitational effects can be crucial; as Halley approaches the Sun, it expels jets of sublimating gas from its surface, which knock it very slightly off its orbital path. These orbital changes cause delays in its perihelion passage of four days on average. | Halley's Comet | Wikipedia | 325 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
In 1989, Boris Chirikov and Vitold Vecheslavov performed an analysis of 46 apparitions of Halley's Comet taken from historical records and computer simulations, which showed that its dynamics were chaotic and unpredictable on long timescales. Halley's projected dynamical lifetime is estimated to be about 10 million years. The dynamics of its orbit can be approximately described by a two-dimensional symplectic map, known as the Kepler map, a solution to the restricted three-body problem for highly eccentric orbits. Based on records from the 1910 apparition, David Hughes calculated in 1985 that Halley's nucleus has been reduced in mass by 80 to 90% over the last 2,000 to 3,000 revolutions, and that it will most likely disappear completely after another 2,300 perihelion passages. More recent work suggests that Halley will evaporate, or split in two, within the next few tens of thousands of years, or will be ejected from the Solar System within a few hundred thousand years.
Structure and composition
The Giotto and Vega missions gave planetary scientists their first view of Halley's surface and structure. The nucleus is a conglomerate of ices and dust, often referred to as a "dirty snowball". Like all comets, as Halley nears the Sun, its volatile compounds (those with low boiling points, such as water, carbon monoxide, carbon dioxide and other ices) begin to sublimate from the surface. This causes the comet to develop a coma, or atmosphere, at distances up to from the nucleus. Sublimation of this dirty ice releases dust particles, which travel with the gas away from the nucleus. Gas molecules in the coma absorb solar light and then re-radiate it at different wavelengths, a phenomenon known as fluorescence, whereas dust particles scatter the solar light. Both processes are responsible for making the coma visible. As a fraction of the gas molecules in the coma are ionised by the solar ultraviolet radiation, pressure from the solar wind, a stream of charged particles emitted by the Sun, pulls the coma's ions out into a long tail, which may extend more than 100 million kilometres into space. Changes in the flow of the solar wind can cause disconnection events, in which the tail completely breaks off from the nucleus. | Halley's Comet | Wikipedia | 474 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
Despite the vast size of its coma, Halley's nucleus is relatively small: barely long, wide and perhaps thick. Based on a reanalysis of images taken by the Giotto and Vega spacecraft, Lamy et al. determined an effective diameter of . Its shape has been variously compared to that of a peanut, a potato, or an avocado. Its mass is roughly 2.2 kg, with an average density of about . The low density indicates that it is made of a large number of small pieces, held together very loosely, forming a structure known as a rubble pile. Ground-based observations of coma brightness suggested that Halley's rotation period was about 7.4 days. Images taken by the various spacecraft, along with observations of the jets and shell, suggested a period of 52 hours. Given the irregular shape of the nucleus, Halley's rotation is likely to be complex. The flyby images revealed an extremely varied topography, with hills, mountains, ridges, depressions, and at least one crater.
Halley's day side (the side facing the Sun) is far more active than the night side. Spacecraft observations showed that the gases ejected from the nucleus were 80% water vapour, 17% carbon monoxide and 3–4% carbon dioxide, with traces of hydrocarbons although more recent sources give a value of 10% for carbon monoxide and also include traces of methane and ammonia. The dust particles were found to be primarily a mixture of carbon–hydrogen–oxygen–nitrogen (CHON) compounds common in the outer Solar System, and silicates, such as are found in terrestrial rocks. The dust particles ranged in size down to the limits of detection (≈0.001 μm). The ratio of deuterium to hydrogen in the water released by Halley was initially thought to be similar to that found in Earth's ocean water, suggesting that Halley-type comets may have delivered water to Earth in the distant past. Subsequent observations showed Halley's deuterium ratio to be far higher than that found in Earth's oceans, making such comets unlikely sources for Earth's water. | Halley's Comet | Wikipedia | 438 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
Giotto provided the first evidence in support of Fred Whipple's "dirty snowball" hypothesis for comet construction; Whipple postulated that comets are icy objects warmed by the Sun as they approach the inner Solar System, causing ices on their surfaces to sublime (change directly from a solid to a gas), and jets of volatile material to burst outward, creating the coma. Giotto showed that this model was broadly correct, though with modifications. Halley's albedo, for instance, is about 4%, meaning that it reflects only 4% of the sunlight hitting it – about what one would expect for coal. Thus, despite astronomers predicting that Halley would have an albedo of about 0.17 (roughly equivalent to bare soil), Halley's Comet is in fact pitch black. The "dirty ices" on the surface sublime at temperatures between in sections of higher albedo to at low albedo; Vega 1 found Halley's surface temperature to be in the range . This suggested that only 10% of Halley's surface was active, and that large portions of it were coated in a layer of dark dust that retained heat. Together, these observations suggested that Halley was in fact predominantly composed of non-volatile materials, and thus more closely resembled a "snowy dirtball" than a "dirty snowball".
History
Before 1066
The first certain appearance of Halley's Comet in the historical record is a description from 240 BC, in the Chinese chronicle Records of the Grand Historian or Shiji, which describes a comet that appeared in the east and moved north. The only surviving record of the 164 BC apparition is found on two fragmentary Babylonian tablets, which were rediscovered in August 1984 in the collection of the British Museum. | Halley's Comet | Wikipedia | 360 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
The apparition of 87 BC was recorded in Babylonian tablets which state that the comet was seen "day beyond day" for a month. This appearance may be recalled in the representation of Tigranes the Great, an Armenian king who is depicted on coins with a crown that features, according to Vahe Gurzadyan and R. Vardanyan, "a star with a curved tail [that] may represent the passage of Halley's Comet in 87 BC." Gurzadyan and Vardanyan argue that "Tigranes could have seen Halley's Comet when it passed closest to the Sun on August 6 in 87 BC" as the comet would have been a "most recordable event"; for ancient Armenians it could have heralded the New Era of the brilliant King of Kings.
The apparition of 12 BC was recorded in the Book of Han by Chinese astronomers of the Han dynasty who tracked it from August through October. It passed within 0.16 au of Earth. According to the Roman historian Cassius Dio, a comet appeared suspended over Rome for several days portending the death of Marcus Vipsanius Agrippa in that year. Halley's appearance in 12 BC, only a few years distant from the conventionally assigned date of the birth of Jesus Christ, has led some theologians and astronomers to suggest that it might explain the biblical story of the Star of Bethlehem. There are other explanations for the phenomenon, such as planetary conjunctions, and there are also records of other comets that appeared closer to the date of Jesus's birth.
If Yehoshua ben Hananiah's reference to "a star which arises once in seventy years and misleads the sailors" refers to Halley's Comet, he can only have witnessed the 66 AD appearance. Another possible report comes from Jewish historian Josephus, who wrote that in 66 AD "The signs ... were so evident, and did so plainly foretell their future desolation ... there was a star resembling a sword, which stood over the city, and a comet, that continued a whole year". This portent was in reference to the city of Jerusalem and the First Jewish–Roman War.
The 141 AD apparition was recorded in Chinese chronicles, with observations of a bluish white comet on 27 March and 16, 22 and 23 April. The early Tamil bards of southern India (c. 1st - 4th century CE) also describe a certain relatable event. | Halley's Comet | Wikipedia | 508 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
The 374 AD and 607 approaches each came within 0.09 au of Earth. The 451 AD apparition was said to herald the defeat of Attila the Hun at the Battle of Chalons.
The 684 AD apparition was reported in Chinese records as the "broom star".
The 760 AD apparition was recorded in the Zuqnin Chronicle'''s entry for iyyōr 1071 SE (May 760 AD), calling it a "white sign":
In 837 AD, Halley's Comet may have passed as close as from Earth, by far its closest approach. Its tail may have stretched 60 degrees across the sky. It was recorded by astronomers in China, Japan, Germany, the Byzantine Empire, and the Middle East; Emperor Louis the Pious observed this appearance and devoted himself to prayer and penance, fearing that "by this token a change in the realm and the death of a prince are made known".
In 912 AD, Halley is recorded in the Annals of Ulster, which states "A dark and rainy year. A comet appeared."
1066
In 1066, the comet was seen in England and thought to be an omen: later that year Harold II of England died at the Battle of Hastings and William the Conqueror claimed the throne. The comet is represented on the Bayeux Tapestry and described in the tituli as a star. Surviving accounts from the period describe it as appearing to be four times the size of Venus, and shining with a light equal to a quarter of that of the Moon. Halley came within 0.10 au of Earth at that time.
This appearance of the comet is also noted in the Anglo-Saxon Chronicle. Eilmer of Malmesbury may have seen Halley in 989 and 1066, as recorded by William of Malmesbury:
Not long after, a comet, portending (they say) a change in governments, appeared, trailing its long flaming hair through the empty sky: concerning which there was a fine saying of a monk of our monastery called Æthelmær. Crouching in terror at the sight of the gleaming star, "You've come, have you?", he said. "You've come, you source of tears to many mothers. It is long since I saw you; but as I see you now you are much more terrible, for I see you brandishing the downfall of my country." | Halley's Comet | Wikipedia | 502 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
The Irish Annals of the Four Masters recorded the comet as "A star [that] appeared on the seventh of the Calends of May, on Tuesday after Little Easter, than whose light the brilliance or light of The Moon was not greater; and it was visible to all in this manner till the end of four nights afterwards." Chaco Native Americans in New Mexico may have recorded the 1066 apparition in their petroglyphs.
The Italo-Byzantine chronicle of Lupus the Protospatharios mentions that a "comet-star" appeared in the sky in the year 1067 (the chronicle is erroneous, as the event occurred in 1066, and by Robert he means William).
The Emperor Constantine Ducas died in the month of May, and his son Michael received the Empire. And in this year there appeared a comet star, and the Norman count Robert [sic] fought a battle with Harold, King of the English, and Robert was victorious and became king over the people of the English.
1145–1378
The 1145 apparition may have been recorded by the monk Eadwine.
According to legend, Genghis Khan was inspired to turn his conquests toward Europe by the westward-seeming trajectory of the 1222 apparition. In Korea, the comet was reportedly visible during the daylight on 9 September 1222.
The 1301 apparition was visually spectacular, and may be the first that resulted in convincing portraits of a particular comet. The Florentine chronicler Giovanni Villani wrote that the comet left "great trails of fumes behind", and that it remained visible from September 1301 until January 1302. It was seen by the artist Giotto di Bondone, who represented the Star of Bethlehem as a fire-coloured comet in the Nativity section of his Arena Chapel cycle, completed in 1305. Giotto's depiction includes details of the coma, a sweeping tail, and the central condensation. According to the art historian Roberta Olson, it is much more accurate than other contemporary descriptions, and was not equaled in painting until the 19th century. Olson's identification of Halley's Comet in Giotto's Adoration of the Magi is what inspired the European Space Agency to name their mission to the comet Giotto, after the artist.
Halley's 1378 appearance is recorded in the Annales Mediolanenses as well as in East Asian sources.
1456 | Halley's Comet | Wikipedia | 502 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
In 1456, the year of Halley's next apparition, the Ottoman Empire invaded the Kingdom of Hungary, culminating in the siege of Belgrade in July of that year. In a papal bull, Pope Callixtus III ordered special prayers be said for the city's protection. In 1470, the humanist scholar Bartolomeo Platina wrote in his that,
A hairy and fiery star having then made its appearance for several days, the mathematicians declared that there would follow grievous pestilence, dearth and some great calamity. Calixtus, to avert the wrath of God, ordered supplications that if evils were impending for the human race He would turn all upon the Turks, the enemies of the Christian name. He likewise ordered, to move God by continual entreaty, that notice should be given by the bells to call the faithful at midday to aid by their prayers those engaged in battle with the Turk.
Platina's account is not mentioned in official records. In the 18th century, a Frenchman further embellished the story, in anger at the Church, by claiming that the Pope had "excommunicated" the comet, though this story was most likely his own invention.
Halley's apparition of 1456 was also witnessed in Kashmir and depicted in great detail by Śrīvara, a Sanskrit poet and biographer to the Sultans of Kashmir. He read the apparition as a cometary portent of doom foreshadowing the imminent fall of Sultan Zayn al-Abidin (AD 1418/1420–1470).
After witnessing a bright light in the sky which most historians have identified as Halley's Comet, Zara Yaqob, Emperor of Ethiopia from 1434 to 1468, founded the city of Debre Berhan (tr. City of Light) and made it his capital for the remainder of his reign.
1531-1759
Petrus Apianus and Girolamo Fracastoro described the comet's visit in 1531, with the former even including graphics in his publication. Through his observations, Apianus was able to prove that a comet's tail always points away from the Sun. | Halley's Comet | Wikipedia | 456 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
In the Sikh scriptures of the Guru Granth Sahib, the founder of the faith Guru Nanak makes reference to "a long star that has risen" at Ang 1110, and it is believed by some Sikh scholars to be a reference to Halley's appearance in 1531.
Halley's periodic returns have been subject to scientific investigation since the 16th century. The three apparitions from 1531 to 1682 were noted by Edmond Halley, enabling him to predict it would return. One key breakthrough occurred when Halley talked with Newton about his ideas of the laws of motion. Newton also helped Halley get John Flamsteed's data on the 1682 apparition. By studying data on the 1531, 1607, and 1682 comets, he came to the conclusion these were the same comet, and presented his findings in 1696.
One difficulty was accounting for variations in the comet's orbital period, which was over a year longer between 1531 and 1607 than it was between 1607 and 1682. Newton had theorised that such delays were caused by the gravity of other comets, but Halley found that Jupiter and Saturn would cause the appropriate delays. In the decades that followed, more refined mathematics would be worked on, notable by Paris Observatory; the work on Halley also provided a boost to Newton and Kepler's rules for celestial motions. ( | Halley's Comet | Wikipedia | 279 | 46083 | https://en.wikipedia.org/wiki/Halley%27s%20Comet | Physical sciences | Solar System | null |
An eared seal, otariid, or otary is any member of the marine mammal family Otariidae, one of three groupings of pinnipeds. They comprise 15 extant species in seven genera (another species became extinct in the 1950s) and are commonly known either as sea lions or fur seals, distinct from true seals (phocids) and the walrus (odobenids). Otariids are adapted to a semiaquatic lifestyle, feeding and migrating in the water, but breeding and resting on land or ice. They reside in subpolar, temperate, and equatorial waters throughout the Pacific and Southern Oceans, the southern Indian, and Atlantic Oceans. They are conspicuously absent in the north Atlantic.
The words "otariid" and "otary" come from the Greek meaning "little ear", referring to the small but visible external ear flaps (pinnae), which distinguishes them from the phocids.
Evolution and taxonomy
Morphological and molecular evidence supports a monophyletic origin of pinnipeds, sharing a common ancestor with Musteloidea, though an earlier hypothesis suggested that Otаriidae are descended from a common ancestor most closely related to modern bears. Debate remains as to whether the phocids diverged from the otariids before or after the walrus.
Otariids arose in the Miocene (15–17 million years ago) in the North Pacific, diversifying rapidly into the Southern Hemisphere, where most species now live. The earliest known fossil otariid is Eotaria crypta from southern California, while the genus Callorhinus (northern fur seal) has the oldest fossil record of any living otariid, extending to the middle Pliocene. It probably arose from the extinct fur seal genus Thalassoleon. | Eared seal | Wikipedia | 368 | 46086 | https://en.wikipedia.org/wiki/Eared%20seal | Biology and health sciences | Pinnipeds | null |
Traditionally, otariids had been subdivided into the fur seal (Arctocephalinae) and sea lion (Otariinae) subfamilies, with the major distinction between them being the presence of a thick underfur layer in the former. Under this categorization, the fur seals comprised two genera: Callorhinus in the North Pacific with a single representative, the northern fur seal (C. ursinus), and eight species in the Southern Hemisphere under the genus Arctocephalus; while the sea lions comprise five species under five genera. Recent analyses of the genetic evidence suggests that Callorhinus ursinus is in fact more closely related to several sea lion species. Furthermore, many of the Otariinae appear to be more phylogenetically distinct than previously assumed; for example, the Japanese sea lion (Zalophus japonicus) is now considered a separate species, rather than a subspecies of the California sea lion (Zalophus californius).
In light of this evidence, the subfamily separation has been removed entirely and the family Otariidae has been organized into seven genera with 16 species and two subspecies.
Nonetheless, because of morphological and behavioral similarities among the "fur seals" and "sea lions", these remain useful categories when discussing differences between groups of species. Compared to sea lions, fur seals are generally smaller, exhibit greater sexual dimorphism, eat smaller prey and go on longer foraging trips; and, of course, there is the contrast between the coarse short sea lion hair and the fur seal's fur.
Anatomy and appearance
Otariids have proportionately much larger foreflippers and pectoral muscles than phocids, and have the ability to turn their hind limbs forward and walk on all fours, making them far more maneuverable on land. They are generally considered to be less adapted to an aquatic lifestyle, since they breed primarily on land and haul out more frequently than true seals. However, they can attain higher bursts of speed and have greater maneuverability in the water. Their swimming power derives from the use of flippers more so than the sinuous whole-body movements typical of phocids and walruses. | Eared seal | Wikipedia | 447 | 46086 | https://en.wikipedia.org/wiki/Eared%20seal | Biology and health sciences | Pinnipeds | null |
Otariids are further distinguished by a more dog-like head, sharp, well-developed canines, and the aforementioned visible external pinnae. Their postcanine teeth are generally simple and conical in shape. The dental formula for eared seals is: . Sea lions are covered with coarse guard hairs, while fur seals have a thick underfur, which has historically made them the objects of commercial exploitation.
Male otariids range in size from the Galápagos fur seal, smallest of all otariids, to the over 1,000-kg (2,200-lb) Steller sea lion. Mature male otariids weigh two to six times as much as females, with proportionately larger heads, necks, and chests, making them the most sexually dimorphic of all mammals.
Behavior
All otariids breed on land during well-defined breeding seasons. Except for the Australian sea lion, which has an atypical 17.5 month breeding cycle, they form strictly annual aggregations on beaches or rocky substrates, often on islands. All species are polygynous; i.e. successful males breed with several females. In most species, males arrive at breeding sites first and establish and maintain territories through vocal and visual displays and occasional fighting. Females typically arrive on shore a day or so before giving birth. While considered social animals, no permanent hierarchies or statuses are established on the colonies. The extent to which males control females or territories varies between species. Thus, the northern fur seal and the South American sea lion tend to herd specific harem-associated females, occasionally injuring them, while the Steller sea lion and the New Zealand sea lion control spatial territories, but do not generally interfere with the movement of the females. Female New Zealand sea lions are the only otrariids that move up to into forests to protect their pups during the breeding season.
Otariids are carnivorous, feeding on fish, squid and krill. Sea lions tend to feed closer to shore in upwelling zones, feeding on larger fish, while the smaller fur seals tend to take longer, offshore foraging trips and can subsist on large numbers of smaller prey items. They are visual feeders. Some females are capable of dives of up to . | Eared seal | Wikipedia | 461 | 46086 | https://en.wikipedia.org/wiki/Eared%20seal | Biology and health sciences | Pinnipeds | null |
Species
Family Otariidae
Subfamily Arctocephalinae (fur seals)
Genus Arctocephalus
Brown fur seal, A. pusillus
South African fur seal, A. pusillus pusillus
Australian fur seal, A. pusillus doriferus
Antarctic fur seal, A. gazella
Guadalupe fur seal, A. townsendi
Juan Fernández fur seal, A. philippii
Galápagos fur seal, A. galapagoensis
New Zealand fur seal (or southern fur seal), A. forsteri
Subantarctic fur seal, A. tropicalis
South American fur seal, A. australis
Genus Callorhinus
Northern fur seal, C. ursinus
Subfamily Otariinae (sea lions)
Genus Eumetopias
Steller sea lion, E. jubatus
Genus Neophoca
Australian sea lion, N. cinerea
Genus Otaria
South American sea lion, O. flavescens
Genus Phocarctos
New Zealand sea lion (or Hooker's sea lion), P. hookeri
Genus Zalophus
California sea lion, Z. californianus
†Japanese sea lion, Z. japonicus – extinct (1970s)
Galápagos sea lion, Z. wollebaeki
Although the two subfamilies of otariids, the Otariinae (sea lions) and Arctocephalinae (fur seals), are still widely used, recent molecular studies have demonstrated that they may be invalid. Instead, they suggest three clades within the family; one consisting of the northern sea lions (Eumetopias and Zalophus), one of the northern fur seal (Callorhinus) and its extinct relatives, and the third of all the remaining Southern Hemisphere species. | Eared seal | Wikipedia | 359 | 46086 | https://en.wikipedia.org/wiki/Eared%20seal | Biology and health sciences | Pinnipeds | null |
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined property, there is the set of all and only the objects that have that property. Let R be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox. In symbols:
Russell also showed that a version of the paradox could be derived in the axiomatic system constructed by the German philosopher and mathematician Gottlob Frege, hence undermining Frege's attempt to reduce mathematics to logic and calling into question the logicist programme. Two influential ways of avoiding the paradox were both proposed in 1908: Russell's own type theory and the Zermelo set theory. In particular, Zermelo's axioms restricted the unlimited comprehension principle. With the additional contributions of Abraham Fraenkel, Zermelo set theory developed into the now-standard Zermelo–Fraenkel set theory (commonly known as ZFC when including the axiom of choice). The main difference between Russell's and Zermelo's solution to the paradox is that Zermelo modified the axioms of set theory while maintaining a standard logical language, while Russell modified the logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be that of first-order logic.
The paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At the end of the 1890s, Georg Cantor – considered the founder of modern set theory – had already realized that his theory would lead to a contradiction, as he told Hilbert and Richard Dedekind by letter. | Russell's paradox | Wikipedia | 496 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Informal presentation
Most sets commonly encountered are not members of themselves. Let us call a set "normal" if it is not a member of itself, and "abnormal" if it is a member of itself. Clearly every set must be either normal or abnormal. For example, consider the set of all squares in a plane. This set is not itself a square in the plane, thus it is not a member of itself and is therefore normal. In contrast, the complementary set that contains everything which is not a square in the plane is itself not a square in the plane, and so it is one of its own members and is therefore abnormal.
Now we consider the set of all normal sets, R, and try to determine whether R is normal or abnormal. If R were normal, it would be contained in the set of all normal sets (itself), and therefore be abnormal; on the other hand if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.
Formal presentation
The term "naive set theory" is used in various ways. In one usage, naive set theory is a formal theory, that is formulated in a first-order language with a binary non-logical predicate , and that includes the axiom of extensionality:
and the axiom schema of unrestricted comprehension:
for any predicate with as a free variable inside . Substitute for to get
Then by existential instantiation (reusing the symbol ) and universal instantiation we have
a contradiction. Therefore, this naive set theory is inconsistent.
Philosophical implications
Prior to Russell's paradox (and to other similar paradoxes discovered around the time, such as the Burali-Forti paradox), a common conception of the idea of set was the "extensional concept of set", as recounted by von Neumann and Morgenstern:
In particular, there was no distinction between sets and proper classes as collections of objects. Additionally, the existence of each of the elements of a collection was seen as sufficient for the existence of the set of said elements. However, paradoxes such as Russell's and Burali-Forti's showed the impossibility of this conception of set, by examples of collections of objects that do not form sets, despite all said objects being existent. | Russell's paradox | Wikipedia | 486 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Set-theoretic responses
From the principle of explosion of classical logic, any proposition can be proved from a contradiction. Therefore, the presence of contradictions like Russell's paradox in an axiomatic set theory is disastrous; since if any formula can be proved true it destroys the conventional meaning of truth and falsity. Further, since set theory was seen as the basis for an axiomatic development of all other branches of mathematics, Russell's paradox threatened the foundations of mathematics as a whole. This motivated a great deal of research around the turn of the 20th century to develop a consistent (contradiction-free) set theory.
In 1908, Ernst Zermelo proposed an axiomatization of set theory that avoided the paradoxes of naive set theory by replacing arbitrary set comprehension with weaker existence axioms, such as his axiom of separation (Aussonderung). (Avoiding paradox was not Zermelo's original intention, but instead to document which assumptions he used in proving the well-ordering theorem.) Modifications to this axiomatic theory proposed in the 1920s by Abraham Fraenkel, Thoralf Skolem, and by Zermelo himself resulted in the axiomatic set theory called ZFC. This theory became widely accepted once Zermelo's axiom of choice ceased to be controversial, and ZFC has remained the canonical axiomatic set theory down to the present day.
ZFC does not assume that, for every property, there is a set of all things satisfying that property. Rather, it asserts that given any set X, any subset of X definable using first-order logic exists. The object R defined by Russell's paradox above cannot be constructed as a subset of any set X, and is therefore not a set in ZFC. In some extensions of ZFC, notably in von Neumann–Bernays–Gödel set theory, objects like R are called proper classes. | Russell's paradox | Wikipedia | 393 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
ZFC is silent about types, although the cumulative hierarchy has a notion of layers that resemble types. Zermelo himself never accepted Skolem's formulation of ZFC using the language of first-order logic. As José Ferreirós notes, Zermelo insisted instead that "propositional functions (conditions or predicates) used for separating off subsets, as well as the replacement functions, can be 'entirely arbitrary [ganz beliebig]"; the modern interpretation given to this statement is that Zermelo wanted to include higher-order quantification in order to avoid Skolem's paradox. Around 1930, Zermelo also introduced (apparently independently of von Neumann), the axiom of foundation, thus—as Ferreirós observes—"by forbidding 'circular' and 'ungrounded' sets, it [ZFC] incorporated one of the crucial motivations of TT [type theory]—the principle of the types of arguments". This 2nd order ZFC preferred by Zermelo, including axiom of foundation, allowed a rich cumulative hierarchy. Ferreirós writes that "Zermelo's 'layers' are essentially the same as the types in the contemporary versions of simple TT [type theory] offered by Gödel and Tarski. One can describe the cumulative hierarchy into which Zermelo developed his models as the universe of a cumulative TT in which transfinite types are allowed. (Once we have adopted an impredicative standpoint, abandoning the idea that classes are constructed, it is not unnatural to accept transfinite types.) Thus, simple TT and ZFC could now be regarded as systems that 'talk' essentially about the same intended objects. The main difference is that TT relies on a strong higher-order logic, while Zermelo employed second-order logic, and ZFC can also be given a first-order formulation. The first-order 'description' of the cumulative hierarchy is much weaker, as is shown by the existence of countable models (Skolem's paradox), but it enjoys some important advantages."
In ZFC, given a set A, it is possible to define a set B that consists of exactly the sets in A that are not members of themselves. B cannot be in A by the same reasoning in Russell's Paradox. This variation of Russell's paradox shows that no set contains everything. | Russell's paradox | Wikipedia | 495 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Through the work of Zermelo and others, especially John von Neumann, the structure of what some see as the "natural" objects described by ZFC eventually became clear: they are the elements of the von Neumann universe, V, built up from the empty set by transfinitely iterating the power set operation. It is thus now possible again to reason about sets in a non-axiomatic fashion without running afoul of Russell's paradox, namely by reasoning about the elements of V. Whether it is appropriate to think of sets in this way is a point of contention among the rival points of view on the philosophy of mathematics.
Other solutions to Russell's paradox, with an underlying strategy closer to that of type theory, include Quine's New Foundations and Scott–Potter set theory. Yet another approach is to define multiple membership relation with appropriately modified comprehension scheme, as in the Double extension set theory.
History
Russell discovered the paradox in May or June 1901. By his own account in his 1919 Introduction to Mathematical Philosophy, he "attempted to discover some flaw in Cantor's proof that there is no greatest cardinal". In a 1902 letter, he announced the discovery to Gottlob Frege of the paradox in Frege's 1879 Begriffsschrift and framed the problem in terms of both logic and set theory, and in particular in terms of Frege's definition of function:
Russell would go on to cover it at length in his 1903 The Principles of Mathematics, where he repeated his first encounter with the paradox:
Russell wrote to Frege about the paradox just as Frege was preparing the second volume of his Grundgesetze der Arithmetik. Frege responded to Russell very quickly; his letter dated 22 June 1902 appeared, with van Heijenoort's commentary in Heijenoort 1967:126–127. Frege then wrote an appendix admitting to the paradox, and proposed a solution that Russell would endorse in his Principles of Mathematics, but was later considered by some to be unsatisfactory. For his part, Russell had his work at the printers and he added an appendix on the doctrine of types. | Russell's paradox | Wikipedia | 442 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Ernst Zermelo in his (1908) A new proof of the possibility of a well-ordering (published at the same time he published "the first axiomatic set theory") laid claim to prior discovery of the antinomy in Cantor's naive set theory. He states: "And yet, even the elementary form that Russell9 gave to the set-theoretic antinomies could have persuaded them [J. König, Jourdain, F. Bernstein] that the solution of these difficulties is not to be sought in the surrender of well-ordering but only in a suitable restriction of the notion of set". Footnote 9 is where he stakes his claim:
Frege sent a copy of his Grundgesetze der Arithmetik to Hilbert; as noted above, Frege's last volume mentioned the paradox that Russell had communicated to Frege. After receiving Frege's last volume, on 7 November 1903, Hilbert wrote a letter to Frege in which he said, referring to Russell's paradox, "I believe Dr. Zermelo discovered it three or four years ago". A written account of Zermelo's actual argument was discovered in the Nachlass of Edmund Husserl.
In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows:
The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition F(F(fx)), in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(fx) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of F(Fu) we write (do) : F(Ou) . Ou = Fu. That disposes of Russell's paradox. (Tractatus Logico-Philosophicus, 3.333) | Russell's paradox | Wikipedia | 454 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Russell and Alfred North Whitehead wrote their three-volume Principia Mathematica hoping to achieve what Frege had been unable to do. They sought to banish the paradoxes of naive set theory by employing a theory of types they devised for this purpose. While they succeeded in grounding arithmetic in a fashion, it is not at all evident that they did so by purely logical means. While Principia Mathematica avoided the known paradoxes and allows the derivation of a great deal of mathematics, its system gave rise to new problems.
In any event, Kurt Gödel in 1930–31 proved that while the logic of much of Principia Mathematica, now known as first-order logic, is complete, Peano arithmetic is necessarily incomplete if it is consistent. This is very widely—though not universally—regarded as having shown the logicist program of Frege to be impossible to complete.
In 2001, A Centenary International Conference celebrating the first hundred years of Russell's paradox was held in Munich and its proceedings have been published.
Applied versions
There are some versions of this paradox that are closer to real-life situations and may be easier to understand for non-logicians. For example, the barber paradox supposes a barber who shaves all men who do not shave themselves and only men who do not shave themselves. When one thinks about whether the barber should shave himself or not, a similar paradox begins to emerge.
An easy refutation of the "layman's versions" such as the barber paradox seems to be that no such barber exists, or that the barber is not a man, and so can exist without paradox. The whole point of Russell's paradox is that the answer "such a set does not exist" means the definition of the notion of set within a given theory is unsatisfactory. Note the difference between the statements "such a set does not exist" and "it is an empty set". It is like the difference between saying "There is no bucket" and saying "The bucket is empty".
A notable exception to the above may be the Grelling–Nelson paradox, in which words and meaning are the elements of the scenario rather than people and hair-cutting. Though it is easy to refute the barber's paradox by saying that such a barber does not (and cannot) exist, it is impossible to say something similar about a meaningfully defined word. | Russell's paradox | Wikipedia | 492 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
One way that the paradox has been dramatised is as follows: Suppose that every public library has to compile a catalogue of all its books. Since the catalogue is itself one of the library's books, some librarians include it in the catalogue for completeness; while others leave it out as it being one of the library's books is self evident. Now imagine that all these catalogues are sent to the national library. Some of them include themselves in their listings, others do not. The national librarian compiles two master catalogues—one of all the catalogues that list themselves, and one of all those that do not.
The question is: should these master catalogues list themselves? The 'catalogue of all catalogues that list themselves' is no problem. If the librarian does not include it in its own listing, it remains a true catalogue of those catalogues that do include themselves. If he does include it, it remains a true catalogue of those that list themselves. However, just as the librarian cannot go wrong with the first master catalogue, he is doomed to fail with the second. When it comes to the 'catalogue of all catalogues that do not list themselves', the librarian cannot include it in its own listing, because then it would include itself, and so belong in the other catalogue, that of catalogues that do include themselves. However, if the librarian leaves it out, the catalogue is incomplete. Either way, it can never be a true master catalogue of catalogues that do not list themselves.
Applications and related topics
Russell-like paradoxes
As illustrated above for the barber paradox, Russell's paradox is not hard to extend. Take:
A transitive verb , that can be applied to its substantive form.
Form the sentence:
The er that s all (and only those) who do not themselves,
Sometimes the "all" is replaced by "all ers".
An example would be "paint":
The painter that paints all (and only those) that do not paint themselves.
or "elect"
The elector (representative), that elects all that do not elect themselves.
In the Season 8 episode of The Big Bang Theory, "The Skywalker Intrusion", Sheldon Cooper analyzes the song "Play That Funky Music", concluding that the lyrics present a musical example of Russell's Paradox. | Russell's paradox | Wikipedia | 475 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
Paradoxes that fall in this scheme include:
The barber with "shave".
The original Russell's paradox with "contain": The container (Set) that contains all (containers) that do not contain themselves.
The Grelling–Nelson paradox with "describer": The describer (word) that describes all words, that do not describe themselves.
Richard's paradox with "denote": The denoter (number) that denotes all denoters (numbers) that do not denote themselves. (In this paradox, all descriptions of numbers get an assigned number. The term "that denotes all denoters (numbers) that do not denote themselves" is here called Richardian.)
"I am lying.", namely the liar paradox and Epimenides paradox, whose origins are ancient
Russell–Myhill paradox
Related paradoxes
The Burali-Forti paradox, about the order type of all well-orderings
The Kleene–Rosser paradox, showing that the original lambda calculus is inconsistent, by means of a self-negating statement
Curry's paradox (named after Haskell Curry), which does not require negation
The smallest uninteresting integer paradox
Girard's paradox in type theory | Russell's paradox | Wikipedia | 250 | 46095 | https://en.wikipedia.org/wiki/Russell%27s%20paradox | Mathematics | Discrete mathematics | null |
GLONASS (, ; ) is a Russian satellite navigation system operating as part of a radionavigation-satellite service. It provides an alternative to Global Positioning System (GPS) and is the second navigational system in operation with global coverage and of comparable precision.
Satellite navigation devices supporting both GPS and GLONASS have more satellites available, meaning positions can be fixed more quickly and accurately, especially in built-up areas where buildings may obscure the view to some satellites. Owing to its higher orbital inclination, GLONASS supplementation of GPS systems also improves positioning in high latitudes (near the poles).
Development of GLONASS began in the Soviet Union in 1976. Beginning on 12 October 1982, numerous rocket launches added satellites to the system until the completion of the constellation in 1995. In 2001, after a decline in capacity during the late 1990s, the restoration of the system was made a government priority, and funding increased substantially. GLONASS is the most expensive program of the Roscosmos, consuming a third of its budget in 2010.
By 2010, GLONASS had achieved full coverage of Russia's territory. In October 2011, the full orbital constellation of 24 satellites was restored, enabling full global coverage. The GLONASS satellites' designs have undergone several upgrades, with the latest version, GLONASS-K2, launched in 2023.
System description
GLONASS is a global navigation satellite system, providing real time position and velocity determination for military and civilian users. The satellites are located in middle circular orbit at altitude with a 64.8° inclination and an orbital period of 11 hours and 16 minutes (every 17 revolutions, done in 8 sidereal days, a satellite passes over the same location). GLONASS's orbit makes it especially suited for usage in high latitudes (north or south), where getting a GPS signal can be problematic.
The constellation operates in three orbital planes, with eight evenly spaced satellites on each. A fully operational constellation with global coverage consists of 24 satellites, while 18 satellites are necessary for covering the territory of Russia. To get a position fix the receiver must be in the range of at least four satellites.
Signal
FDMA
GLONASS satellites transmit two types of signals: open standard-precision signal L1OF/L2OF, and obfuscated high-precision signal L1SF/L2SF. | GLONASS | Wikipedia | 481 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
The signals use similar DSSS encoding and binary phase-shift keying (BPSK) modulation as in GPS signals. All GLONASS satellites transmit the same code as their standard-precision signal; however each transmits on a different frequency using a 15-channel frequency-division multiple access (FDMA) technique spanning either side from 1602.0 MHz, known as the L1 band. The center frequency is 1602 MHz + n × 0.5625 MHz, where n is a satellite's frequency channel number (n=−6,...,0,...,6, previously n=0,...,13). Signals are transmitted in a 38° cone, using right-hand circular polarization, at an EIRP between 25 and 27 dBW (316 to 500 watts). Note that the 24-satellite constellation is accommodated with only 15 channels by using identical frequency channels to support antipodal (opposite side of planet in orbit) satellite pairs, as these satellites are never both in view of an Earth-based user at the same time.
The L2 band signals use the same FDMA as the L1 band signals, but transmit straddling 1246 MHz with the center frequency 1246 MHz + n × 0.4375 MHz, where n spans the same range as for L1. In the original GLONASS design, only obfuscated high-precision signal was broadcast in the L2 band, but starting with GLONASS-M, an additional civil reference signal L2OF is broadcast with an identical standard-precision code to the L1OF signal.
The open standard-precision signal is generated with modulo-2 addition (XOR) of 511 kbit/s pseudo-random ranging code, 50 bit/s navigation message, and an auxiliary 100 Hz meander sequence (Manchester code), all generated using a single time/frequency oscillator. The pseudo-random code is generated with a 9-stage shift register operating with a period of 1 milliseconds. | GLONASS | Wikipedia | 424 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
The navigational message is modulated at 50 bits per second. The superframe of the open signal is 7500 bits long and consists of 5 frames of 30 seconds, taking 150 seconds (2.5 minutes) to transmit the continuous message. Each frame is 1500 bits long and consists of 15 strings of 100 bits (2 seconds for each string), with 85 bits (1.7 seconds) for data and check-sum bits, and 15 bits (0.3 seconds) for time mark. Strings 1-4 provide immediate data for the transmitting satellite, and are repeated every frame; the data include ephemeris, clock and frequency offsets, and satellite status. Strings 5-15 provide non-immediate data (i.e. almanac) for each satellite in the constellation, with frames I-IV each describing five satellites, and frame V describing remaining four satellites.
The ephemerides are updated every 30 minutes using data from the Ground Control segment; they use Earth Centred Earth Fixed (ECEF) Cartesian coordinates in position and velocity, and include lunisolar acceleration parameters. The almanac uses modified orbital elements (Keplerian elements) and is updated daily.
The more accurate high-precision signal is available for authorized users, such as the Russian military, yet unlike the United States P(Y) code, which is modulated by an encrypting W code, the GLONASS restricted-use codes are broadcast in the clear using only security through obscurity. The details of the high-precision signal have not been disclosed. The modulation (and therefore the tracking strategy) of the data bits on the L2SF code has recently changed from unmodulated to 250 bit/s burst at random intervals. The L1SF code is modulated by the navigation data at 50 bit/s without a Manchester meander code.
The high-precision signal is broadcast in phase quadrature with the standard-precision signal, effectively sharing the same carrier wave, but with a ten-times-higher bandwidth than the open signal. The message format of the high-precision signal remains unpublished, although attempts at reverse-engineering indicate that the superframe is composed of 72 frames, each containing 5 strings of 100 bits and taking 10 seconds to transmit, with total length of 36 000 bits or 720 seconds (12 minutes) for the whole navigational message. The additional data are seemingly allocated to critical Lunisolar acceleration parameters and clock correction terms. | GLONASS | Wikipedia | 500 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
Accuracy
At peak efficiency, the standard-precision signal offers horizontal positioning accuracy within 5–10 metres, vertical positioning within , a velocity vector measuring within , and timing within 200 nanoseconds, all based on measurements from four first-generation satellites simultaneously; newer satellites such as GLONASS-M improve on this.
GLONASS uses a coordinate datum named "PZ-90" (Earth Parameters 1990 – Parametry Zemli 1990), in which the precise location of the North Pole is given as an average of its position from 1990 to 1995. This is in contrast to the GPS's coordinate datum, WGS 84, which uses the location of the North Pole in 1984. As of 17 September 2007, the PZ-90 datum has been updated to version PZ-90.02 which differ from WGS 84 by less than in any given direction. Since 31 December 2013, version PZ-90.11 is being broadcast, which is aligned to the International Terrestrial Reference System and Frame 2008 at epoch 2011.0 at the centimetre level, but ideally a conversion to ITRF2008 should be done.
CDMA
Since 2008, new CDMA signals are being researched for use with GLONASS.
The interface control documents for GLONASS CDMA signals was published in August 2016.
According to GLONASS developers, there will be three open and two restricted CDMA signals. The open signal L3OC is centered at 1202.025 MHz and uses BPSK(10) modulation for both data and pilot channels; the ranging code transmits at 10.23 million chips per second, modulated onto the carrier frequency using QPSK with in-phase data and quadrature pilot. The data is error-coded with 5-bit Barker code and the pilot with 10-bit Neuman-Hoffman code. | GLONASS | Wikipedia | 378 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
Open L1OC and restricted L1SC signals are centered at 1600.995 MHz, and open L2OC and restricted L2SC signals are centered at 1248.06 MHz, overlapping with GLONASS FDMA signals. Open signals L1OC and L2OC use time-division multiplexing to transmit pilot and data signals, with BPSK(1) modulation for data and BOC(1,1) modulation for pilot; wide-band restricted signals L1SC and L2SC use BOC (5, 2.5) modulation for both data and pilot, transmitted in quadrature phase to the open signals; this places peak signal strength away from the center frequency of narrow-band open signals.
Binary phase-shift keying (BPSK) is used by standard GPS and GLONASS signals. Binary offset carrier (BOC) is the modulation used by Galileo, modernized GPS, and BeiDou-2.
The navigational message of CDMA signals is transmitted as a sequence of text strings. The message has variable size - each pseudo-frame usually includes six strings and contains ephemerides for the current satellite (string types 10, 11, and 12 in a sequence) and part of the almanac for three satellites (three strings of type 20). To transmit the full almanac for all current 24 satellites, a superframe of 8 pseudo-frames is required. In the future, the superframe will be expanded to 10 pseudo-frames of data to cover full 30 satellites.
The message can also contain Earth's rotation parameters, ionosphere models, long-term orbit parameters for GLONASS satellites, and COSPAS-SARSAT messages. The system time marker is transmitted with each string; UTC leap second correction is achieved by shortening or lengthening (zero-padding) the final string of the day by one second, with abnormal strings being discarded by the receiver.
The strings have a version tag to facilitate forward compatibility: future upgrades to the message format will not break older equipment, which will continue to work by ignoring new data (as long as the constellation still transmits old string types), but up-to-date equipment will be able to use additional information from newer satellites. | GLONASS | Wikipedia | 456 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
The navigational message of the L3OC signal is transmitted at 100 bit/s, with each string of symbols taking 3 seconds (300 bits). A pseudo-frame of 6 strings takes 18 seconds (1800 bits) to transmit. A superframe of 8 pseudo-frames is 14,400 bits long and takes 144 seconds (2 minutes 24 seconds) to transmit the full almanac.
The navigational message of the L1OC signal is transmitted at 100 bit/s. The string is 250 bits long and takes 2.5 seconds to transmit. A pseudo-frame is 1500 bits (15 seconds) long, and a superframe is 12,000 bits or 120 seconds (2 minutes).
L2OC signal does not transmit any navigational message, only the pseudo-range codes:
Glonass-K1 test satellite launched in 2011 introduced L3OC signal. Glonass-M satellites produced since 2014 (s/n 755+) will also transmit L3OC signal for testing purposes.
Enhanced Glonass-K1 and Glonass-K2 satellites, to be launched from 2023, will feature a full suite of modernized CDMA signals in the existing L1 and L2 bands, which includes L1SC, L1OC, L2SC, and L2OC, as well as the L3OC signal. Glonass-K2 series should gradually replace existing satellites starting from 2023, when Glonass-M launches will cease.
Glonass-KM satellites will be launched by 2025. Additional open signals are being studied for these satellites, based on frequencies and formats used by existing GPS, Galileo, and Beidou/COMPASS signals:
open signal L1OCM using BOC(1,1) modulation centered at 1575.42 MHz, similar to modernized GPS signal L1C, Galileo signal E1, and Beidou/COMPASS signal B1C;
open signal L5OCM using BPSK(10) modulation centered at 1176.45 MHz, similar to the GPS "Safety of Life" (L5), Galileo signal E5a, and Beidou/COMPASS signal B2a;
open signal L3OCM using BPSK(10) modulation centered at 1207.14 MHz, similar to Galileo signal E5b and Beidou/COMPASS signal B2b.
Such an arrangement will allow easier and cheaper implementation of multi-standard GNSS receivers. | GLONASS | Wikipedia | 499 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
With the introduction of CDMA signals, the constellation will be expanded to 30 active satellites by 2025; this may require eventual deprecation of FDMA signals. The new satellites will be deployed into three additional planes, bringing the total to six planes from the current three—aided by System for Differential Correction and Monitoring (SDCM), which is a GNSS augmentation system based on a network of ground-based control stations and communication satellites Luch 5A and Luch 5B.
Six additional Glonass-V satellites, using Tundra orbit in three orbital planes, will be launched starting in 2025; this regional high-orbit segment will offer increased regional availability and 25% improvement in precision over Eastern Hemisphere, similar to Japanese QZSS system and Beidou-1. The new satellites will form two ground traces with inclination of 64.8°, eccentricity of 0.072, period of 23.9 hours, and ascending node longitude of 60° and 120°. Glonass-V vehicles are based on Glonass-K platform and will broadcast new CDMA signals only. Previously Molniya orbit, geosynchronous orbit, or inclined orbit were also under consideration for the regional segment.
Navigational message
L1OC
L3OC
Common properties of open CDMA signals
Satellites
The main contractor of the GLONASS program is Joint Stock Company Information Satellite Systems Reshetnev (ISS Reshetnev, formerly called NPO-PM). The company, located in Zheleznogorsk, is the designer of all GLONASS satellites, in cooperation with the Institute for Space Device Engineering (:ru:РНИИ КП) and the Russian Institute of Radio Navigation and Time. Serial production of the satellites is accomplished by the company Production Corporation Polyot in Omsk.
Over the three decades of development, the satellite designs have gone through numerous improvements, and can be divided into three generations: the original GLONASS (since 1982), GLONASS-M (since 2003) and GLONASS-K (since 2011). Each GLONASS satellite has a GRAU designation 11F654, and each of them also has the military "Cosmos-NNNN" designation.
First generation | GLONASS | Wikipedia | 462 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
The true first generation of GLONASS (also called Uragan) satellites were all three-axis stabilized vehicles, generally weighing and were equipped with a modest propulsion system to permit relocation within the constellation. Over time they were upgraded to Block IIa, IIb, and IIv vehicles, with each block containing evolutionary improvements.
Six Block IIa satellites were launched in 1985–1986 with improved time and frequency standards over the prototypes, and increased frequency stability. These spacecraft also demonstrated a 16-month average operational lifetime. Block IIb spacecraft, with a two-year design lifetimes, appeared in 1987, of which a total of 12 were launched, but half were lost in launch vehicle accidents. The six spacecraft that made it to orbit worked well, operating for an average of nearly 22 months.
Block IIv was the most prolific of the first generation. Used exclusively from 1988 to 2000, and continued to be included in launches through 2005, a total of 56 satellites were launched. The design life was three years, however numerous spacecraft exceeded this, with one late model lasting 68 months, nearly double.
Block II satellites were typically launched three at a time from the Baikonur Cosmodrome using Proton-K Blok-DM2 or Proton-K Briz-M boosters. The only exception was when, on two launches, an Etalon geodetic reflector satellite was substituted for a GLONASS satellite.
Second generation
The second generation of satellites, known as Glonass-M, were developed beginning in 1990 and first launched in 2003. These satellites possess a substantially increased lifetime of seven years and weigh slightly more at . They are approximately in diameter and high, with a solar array span of for an electrical power generation capability of 1600 watts at launch. The aft payload structure houses 12 primary antennas for L-band transmissions. Laser corner-cube reflectors are also carried to aid in precise orbit determination and geodetic research. On-board cesium clocks provide the local clock source. 52 Glonass-M have been produced and launched.
A total of 41 second generation satellites were launched through the end of 2013. As with the previous generation, the second generation spacecraft were launched three at a time using Proton-K Blok-DM2 or Proton-K Briz-M boosters. Some were launched alone with Soyuz-2-1b/Fregat. | GLONASS | Wikipedia | 484 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
In July 2015, ISS Reshetnev announced that it had completed the last GLONASS-M (No. 61) spacecraft and it was putting it in storage waiting for launch, along with eight previously built satellites.
As on 22 September 2017, GLONASS-M No.52 satellite went into operation and the orbital grouping has again increased to 24 space vehicles.
Third generation
GLONASS-K is a substantial improvement of the previous generation: it is the first unpressurised GLONASS satellite with a much reduced mass of versus the of GLONASS-M. It has an operational lifetime of 10 years, compared to the 7-year lifetime of the second generation GLONASS-M. It will transmit more navigation signals to improve the system's accuracy — including new CDMA signals in the L3 and L5 bands, which will use modulation similar to modernized GPS, Galileo, and BeiDou. Glonass-K consist of 26 satellites having satellite index 65-98 and widely used in Russian Military space.
The new satellite's advanced equipment—made solely from Russian components — will allow the doubling of GLONASS' accuracy. As with the previous satellites, these are 3-axis stabilized, nadir pointing with dual solar arrays. The first GLONASS-K satellite was successfully launched on 26 February 2011.
Due to their weight reduction, GLONASS-K spacecraft can be launched in pairs from the Plesetsk Cosmodrome launch site using the substantially lower cost Soyuz-2.1b boosters or in six-at-once from the Baikonur Cosmodrome using Proton-K Briz-M launch vehicles.
Ground control
The ground control segment of GLONASS is almost entirely located within former Soviet Union territory, except for several in Brazil and one in Nicaragua.
The GLONASS ground segment consists of:
a system control centre;
five Telemetry, Tracking and Command centers;
two Laser Ranging Stations; and
ten Monitoring and Measuring Stations.
Receivers
Companies producing GNSS receivers making use of GLONASS:
Furuno
JAVAD GNSS, Inc
Septentrio
Topcon
C-Nav
Magellan Navigation
Novatel
ComNav technology Ltd.
Leica Geosystems
Hemisphere GNSS
Trimble Inc
u-blox
NPO Progress describes a receiver called GALS-A1, which combines GPS and GLONASS reception.
SkyWave Mobile Communications manufactures an Inmarsat-based satellite communications terminal that uses both GLONASS and GPS. | GLONASS | Wikipedia | 506 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
, some of the latest receivers in the Garmin eTrex line also support GLONASS (along with GPS). Garmin also produce a standalone Bluetooth receiver, the GLO for Aviation, which combines GPS, WAAS and GLONASS.
Various smartphones from 2011 onwards have integrated GLONASS capability in addition to their pre-existing GPS receivers, with the intention of reducing signal acquisition periods by allowing the device to pick up more satellites than with a single-network receiver, including devices from:
Xiaomi
Sony Ericsson
ZTE
Huawei
Samsung
Apple (since iPhone 4S, concurrently with GPS)
HTC
LG
Motorola
Nokia
Status
Availability
, the GLONASS constellation status is:
The system requires 18 satellites for continuous navigation services covering all of Russia, and 24 satellites to provide services worldwide. The GLONASS system covers 100% of worldwide territory.
On 2 April 2014, the system experienced a technical failure that resulted in practical unavailability of the navigation signal for around 12 hours.
On 14–15 April 2014, nine GLONASS satellites experienced a technical failure due to software problems.
On 19 February 2016, three GLONASS satellites experienced a technical failure: the batteries of GLONASS-738 exploded, the batteries of GLONASS-737 were depleted, and GLONASS-736 experienced a stationkeeping failure due to human error during maneuvering. GLONASS-737 and GLONASS-736 were expected to be operational again after maintenance, and one new satellite (GLONASS-751) to replace GLONASS-738 was expected to complete commissioning in early March 2016. The full capacity of the satellite group was expected to be restored in the middle of March 2016.
After the launching of two new satellites and maintenance of two others, the full capacity of the satellite group was restored.
Accuracy
According to Russian System of Differentional Correction and Monitoring's data, , precision of GLONASS navigation definitions (for p=0.95) for latitude and longitude were with mean number of navigation space vehicles (NSV) equals 7—8 (depending on station). In comparison, the same time precision of GPS navigation definitions were with mean number of NSV equals 6—11 (depending on station). | GLONASS | Wikipedia | 459 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
Some modern receivers are able to use both GLONASS and GPS satellites together, providing greatly improved coverage in urban canyons and giving a very fast time to fix due to over 50 satellites being available. In indoor, urban canyon or mountainous areas, accuracy can be greatly improved over using GPS alone. For using both navigation systems simultaneously, precision of GLONASS/GPS navigation definitions were with mean number of NSV equals 14—19 (depends on station).
In May 2009, Anatoly Perminov, then director of the Roscosmos, stated that actions were undertaken to expand GLONASS's constellation and to improve the ground segment to increase the navigation definition of GLONASS to an accuracy of by 2011. In particular, the latest satellite design, GLONASS-K has the ability to double the system's accuracy once introduced. The system's ground segment is also to undergo improvements. As of early 2012, sixteen positioning ground stations are under construction in Russia and in the Antarctic at the Bellingshausen and Novolazarevskaya bases. New stations will be built around the southern hemisphere from Brazil to Indonesia. Together, these improvements are expected to bring GLONASS' accuracy to 0.6 m or better by 2020. The setup of a GLONASS receiving station in the Philippines is also now under negotiation.
History | GLONASS | Wikipedia | 272 | 46149 | https://en.wikipedia.org/wiki/GLONASS | Technology | Navigation | null |
Tillage is the agricultural preparation of soil by mechanical agitation of various types, such as digging, stirring, and overturning. Examples of human-powered tilling methods using hand tools include shoveling, picking, mattock work, hoeing, and raking. Examples of draft-animal-powered or mechanized work include ploughing (overturning with moldboards or chiseling with chisel shanks), rototilling, rolling with cultipackers or other rollers, harrowing, and cultivating with cultivator shanks (teeth).
Tillage that is deeper and more thorough is classified as primary, and tillage that is shallower and sometimes more selective of location is secondary. Primary tillage such as ploughing tends to produce a rough surface finish, whereas secondary tillage tends to produce a smoother surface finish, such as that required to make a good seedbed for many crops. Harrowing and rototilling often combine primary and secondary tillage into one operation.
"Tillage" can also mean the land that is tilled. The word "cultivation" has several senses that overlap substantially with those of "tillage". In a general context, both can refer to agriculture. Within agriculture, both can refer to any kind of soil agitation. Additionally, "cultivation" or "cultivating" may refer to an even narrower sense of shallow, selective secondary tillage of row crop fields that kills weeds while sparing the crop plants.
Definitions
Primary tillage loosens the soil and mixes in fertilizer or plant material, resulting in soil with a rough texture. | Tillage | Wikipedia | 330 | 46191 | https://en.wikipedia.org/wiki/Tillage | Technology | Horticultural techniques | null |
Secondary tillage produces finer soil and sometimes shapes the rows, preparing the seed bed. It also provides weed control throughout the growing season during the maturation of the crop plants, unless such weed control is instead achieved with low-till or no-till methods involving herbicides.
The seedbed preparation can be done with harrows (of which there are many types and subtypes), dibbles, hoes, shovels, rotary tillers, subsoilers, ridge- or bed-forming tillers, rollers, or cultivators.
The weed control, to the extent that it is done via tillage, is usually achieved with cultivators or hoes, which disturb the top few centimeters of soil around the crop plants but with minimal disturbance of the crop plants themselves. The tillage kills the weeds via two mechanisms: uprooting them, burying their leaves (cutting off their photosynthesis), or a combination of both. Weed control both prevents the crop plants from being outcompeted by the weeds (for water and sunlight) and prevents the weeds from reaching their seed stage, thus reducing future weed population aggressiveness.
History
Tilling was first performed via human labor, sometimes involving slaves. Hoofed animals could also be used to till soil by trampling, in addition to pigs, whose natural instincts are to root the ground regularly if allowed to. The wooden plow was then invented. (It is difficult to pinpoint the exact date of its invention. However, the earliest evidence of plow usage dates back to around 4000 BCE in Mesopotamia (modern-day Iraq) . It could be pulled with human labor, or by mule, ox, elephant, water buffalo, or a similar sturdy animal. Horses are generally unsuitable, though breeds such as the Clydesdale were bred as draft animals.
Tilling could at times be very labor-intensive. This aspect is discussed in the 16th-century French agronomic text written by Charles Estienne: | Tillage | Wikipedia | 403 | 46191 | https://en.wikipedia.org/wiki/Tillage | Technology | Horticultural techniques | null |
The popularity of tillage as an agricultural technique in early modern times had to do with theories about plant biology proposed by European thinkers. In 1731, English writer Jethro Tull published the book "Horse-Hoeing Husbandry: An Essay on the Principles of Vegetation and Tillage," which argued that soil needed to be pulverized into fine powder for plants to make use of it. Tull believed that, since water, air, and heat were clearly not the primary substance of a plant, plants were made of earth, and thus had to consume very small pieces of earth as food. Tull wrote that each subsequent tillage of the soil would increase its fertility, and that it was impossible to till the soil too much. However, scientific observation has shown that the opposite is true; tillage causes soil to lose structural qualities that allow plant roots, water, and nutrients to penetrate it, accelerates soil loss by erosion, and results in soil compaction.
The steel plow allowed farming in the American Midwest, where tough prairie grasses and rocks caused trouble. Soon after 1900, the farm tractor was introduced, which made modern large-scale agriculture possible. However, the destruction of the prairie grasses and tillage of the fertile topsoil of the American Midwest caused the Dust Bowl, in which the soil was blown away and stirred up into dust storms that blackened the sky. This prompted re-consideration of tillage techniques, but in the United States as of 2019, 3 trillion pounds of soil were estimated to be lost due to erosion while adoption of improved techniques for controlling erosion are still not widespread. In the mid-1930s Frank and Herbert Petty of Doncaster, Victoria, Australia developed the Petty Plough. This steerable plough could be pulled by either two horses or a tractor and the disc wheels could be steered in unison, or separately allowing the operator to plough the center of rows as well as between and around orchard trees.
Types
Primary and secondary tillage
Primary tillage is usually conducted after the last harvest, when the soil is wet enough to allow plowing but also allows good traction. Some soil types can be plowed dry. The objective of primary tillage is to attain a reasonable depth of soft soil, incorporate crop residues, kill weeds, and to aerate the soil. Secondary tillage is any subsequent tillage, to incorporate fertilizers, reduce the soil to a finer tilth, level the surface, or control weeds.
Reduced tillage | Tillage | Wikipedia | 500 | 46191 | https://en.wikipedia.org/wiki/Tillage | Technology | Horticultural techniques | null |
Reduced tillage leaves between 15 and 30% crop residue cover on the soil or 500 to 1000 pounds per acre (560 to 1100 kg/ha) of small grain residue during the critical erosion period. This may involve the use of a chisel plow, field cultivators, or other implements. See the general comments below to see how they can affect the amount of residue.
Intensive tillage
Intensive tillage leaves less than 15% crop residue cover or less than 500 pounds per acre (560 kg/ha) of small grain residue. This type of tillage is often referred to as conventional tillage, but as conservational tillage is now more widely used than intensive tillage (in the United States), it is often not appropriate to refer to this type of tillage as conventional. Intensive tillage often involves multiple operations with implements such as a mold board, disk, or chisel plow. After this, a finisher with a harrow, rolling basket, and cutter can be used to prepare the seed bed. There are many variations.
Conservation tillage
Conservation tillage leaves at least 30% of crop residue on the soil surface, or at least 1,000 lb/ac (1,100 kg/ha) of small grain residue on the surface during the critical soil erosion period. This slows water movement, which reduces the amount of soil erosion. Additionally, conservation tillage has been found to benefit predatory arthropods that can enhance pest control. Conservation tillage also benefits farmers by reducing fuel consumption and soil compaction. By reducing the number of times the farmer travels over the field, significant savings in fuel and labor are made.
Conservation tillage is used on over 370 million acres, mostly in South America, Oceania and North America. In most years since 1997, conservation tillage was used in US cropland more than intensive or reduced tillage.
However, conservation tillage delays warming of the soil due to the reduction of dark earth exposure to the warmth of the spring sun, thus delaying the planting of the next year's spring crop of corn. | Tillage | Wikipedia | 420 | 46191 | https://en.wikipedia.org/wiki/Tillage | Technology | Horticultural techniques | null |
No-till – plows, disks, et cetera are not used. Aims for 100% ground cover.
Strip-till – Narrow strips are tilled where seeds will be planted, leaving the soil in between the rows untilled.
Mulch-till - Soil is covered with mulch to conserve heat and moisture. 100% soil disturbance.
Rotational tillage – Tilling the soil every two years or less often (every other year, or every third year, etc.).
Ridge-till
Zone tillage
Zone tillage is a form of modified deep tillage in which only narrow strips are tilled, leaving soil in between the rows untilled. This type of tillage agitates the soil to help reduce soil compaction problems and to improve internal soil drainage. It is designed to only disrupt the soil in a narrow strip directly below the crop row. In comparison to no-till, which relies on the previous year's plant residue to protect the soil and aids in postponement of the warming of the soil and crop growth in Northern climates, zone tillage produces a strip approximately five inches wide that simultaneously breaks up plow pans, assists in warming the soil and helps to prepare a seedbed. When combined with cover crops, zone tillage helps replace lost organic matter, slows the deterioration of the soil, improves soil drainage, increases soil water and nutrient holding capacity, and allows necessary soil organisms to survive.
It has been successfully used on farms in the Midwest and West of the US for over 40 years, and is currently used on more than 36% of the U.S. farmland. Some specific states where zone tillage is currently in practice are Pennsylvania, Connecticut, Minnesota, Indiana, Wisconsin, and Illinois.
Its use in the USA's Northern Corn Belt states lacks consistent yield results; however, there is still interest in deep tillage within agriculture. In areas that are not well-drained, deep tillage may be used as an alternative to installing more expensive tile drainage.
Effects | Tillage | Wikipedia | 407 | 46191 | https://en.wikipedia.org/wiki/Tillage | Technology | Horticultural techniques | null |
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