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consider a Hamiltonian, after mean-field approximation, can be written as
$$\hat{H}=\sum_{p}(\epsilon_{p}+gn_{0})a_{p}^{\dagger}a_{p}+\frac{1}{2}gn_{0}(a_{k+p}a_{k-p}+\hat{a}^{\dagger}_{k+p}\hat{a}^{\dagger}_{k-p})$$
where $g$ is the coupling strength between particles and $n_{0}$ is the particle density.
Denote $\hat{... |
Denote by $\vert n\rangle$ the eigenstates of the harmonic oscillator in $1D$.
I am wondering if there is an explicit expression for
$$\langle m \vert x^6 \vert n\rangle=?$$
It is obvious from symmetry considerations that this expectation value vanishes unless
$m $ and $n$ are both either even or odd (symmetry) and $\v... |
I have some problems about basic concepts of quantum field theory.
First let's look at Klein-Gordon field.
Klein-Gordon equation has two branches of solutions, one of which is positive frequency and the other is
negative frequency. The solution can be written as
$$\psi(x)=\int \frac{d^{3}p}{(2\pi)^{3}}\frac{1}{\sqrt{2E... |
This question is a sequel of
Some basic concepts in quantum field theory part 1
In Peskin's book, the part How Not to Quantize the Dirac Field, the writer says,"...in analogy with Klein-Gordon field...impose the canonical comutation relations $[\psi_{a}(x),\psi^{+}_{b}(y)]=\delta_{x-y}\delta_{ab}$, where $a$ and $b$ de... |
Is current a tensor or a scalar quantity? The internet seems to be divided on this one. Tensors are too complicated. So I am unable to find an answer. Can someone please clearly state whether it is a scalar or a vector?
|
I'm trying to understand the logic underneath the concept of action and lagrangian. I know this kind of questions have been asked many times, but I was unable to find an answer to this one.
I've ever read that the action should be minimized, or at least put in an extremum, in the actual physical trajectory of the syste... |
I know this is kind of a philosophical question in the risk to be opinion-based, but I would like to know what the people that know a lot more than me, think about this.
I'm asking myself about this since a lot of time now. I think everything started noticing that the maximum velocity for the propagation of an "informa... |
We see that our calculations always gives a loss of Kinetic energy in inelastic collisions while the net momentum of the system remains the same. Where does the lost energy go while there is no trace of friction or air drag in our calculation?
|
I am used to using the formula $ R_H (\frac{1}{n^2_{final}}-\frac{1}{n^2_{initial}}) $ to calculate the transition wavenumbers when an electron in a Hydrogen atom emits a photon. Can you use the same formula to calculate the wavenumber when a electron absorbs a photon?
|
If I have metal bar fixed to a support at one end while I apply a tensile force at the other end, the bar elongates while its cross sectional area decreases. I want to know How strain is developed at molecular or atomic level such that cross sectional area of the bar decreases and why is it perpendicular to the directi... |
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter J. Larkin. Section 1.1 Dispersive Systems of chapter 3 says the following:
A monochromator consists of an entrance slit, followed by a mirror to insure the light is parallel, a diffraction grating, and a focusing mirror, which ... |
Is there a certain ratio between cooper pairs and normal electrons above which the sample can be said to be in a superconducting state? According to the Ginzburg-Landau theory the sample is in a superconducting state when the order parameter is above zero, but this is hard to realize in practise. Is there more develope... |
Does Big Bang Theory imply the creation of matter before that of radiation? Thus an original mass of a giant atom decays to produce radiation leading to the creation of matter in an expanding universe rather than its origin being a primary burst of radiation.
|
In my current understanding, a space group $G_\infty$ is a combination of a crystallographic point group $G_0$ and translations in the following way: $(R_1,\vec{t_1})(R_2,\vec{t_2}):=(R_1R_2,\vec{t_1}+R_1\vec{t_2})\in G_\infty$. Now I have heard that there are space groups, which do not contain $G_0$ as a subgroup i.e.... |
Consider a siphon tube... Now consider the opening of the tube at the lower end. Isn't the pressure at the mouth of the tube, at this lower end, something intermediate between $P_a$ and $P_a + \rho gh$? ($h$ represents the difference in the height of the water surfaces in the two containers used). To ensure the flow of... |
The DGLAP equations read
$$\frac{\partial f_i(x,\mu^2)}{\partial\ln\mu^2}=\sum_j\int^1_x\frac{dz}{z}P_{ij}(z,\alpha_s(\mu^2))f_j\left(\frac{x}{z},\mu^2\right),$$
where the $f_i$ are the parton distribution functions (PDFs), $P_{ij}$ are the so-called splitting kernels and $x,z$ are longitudinal momentum fractions.
But ... |
De Broglie and David Bohm found a method (1952) that explains the double-slit experiment and its variations, which are so central to QM, in an intuitive way without appeal to probability, wave-function collapse, the "measurement problem", or invoking the consciousness of the experimenter. Although recognition of Bohm's... |
I want to calculate the flow rate of a liquid (very high viscosity, but we can assume laminar flow, for now, so I get an idea of how to go about this problem) I understand that I have to use Poiseuille's equation to calculate the flow rate along a tube length, L.
A good example is already in this answer: link
However, ... |
now I know "R=ρl⁄a"
and my doubt is would the area be a=l×l or a=l×t??
|
I' m looking at books that take the historical aproach (like "A Radical Approach to Real Analysis" by
David M. Bressoud does for calculus) but with all of the formalism.
i.e most of the math should be there but also the history (the failures and the experiments) and the philosophy (justifications) of the great thinke... |
Let us have a 2D lattice model with three sites in one unit-cell (basically 2D Kagome lattice). In Fourier space, the Hamiltonian is written as
$$
H = \sum_{k_x,k_y}
\begin{bmatrix}
a^\dagger & b^\dagger & c^\dagger
\end{bmatrix}
\begin{bmatrix}
h_{11}&h_{12}&h_{13}\\
h_{21}&h_{22}&h_{23}\\
h_{31}&h_{32}&h_{33}
\end{bm... |
This question is based on Carroll's book Spacetime and Geometry, specifically from page 33 to page 36.
In the upper mentioned section we define the Stress-Energy Tensor as:
The flux of the four momentum $p^\mu$ across a surface of constant $x^\nu$
Here lies the first problem: canonically the flux of a vector across a... |
As I understand it (feel free to correct me if I'm wrong here), the core tenet of Einstein's theory of special relativity is the idea that if you were on a sealed train moving at any constant velocity from $0$ to $c$, there would be no way to tell from within the train what velocity that is, without interacting with th... |
In this paper online, the author models the deformation of a medium as a diffeomorphism $ \mathbb{R}^3 \rightarrow \mathbb{R}^3$ as given by:
$$ y^i \mapsto x^i(y)=y^i + u^i(x) $$
as given by equation (1). The diffeomorphism induces a transformation of the metric
$$ g_{ij}(x) = \frac{\partial y^k}{\partial x^i} \frac{\... |
Q)Point A moves uniformly with velocity $v$ so that the vector $v$ is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity $u<v$. At the initial moment of time $v⊥u$ and the points are separated by a distance $l$.The time at which the points converge is given as?
Let at ti... |
In books, it is not explained exactly how the battery creates an electric field inside the wire. Also, is that the electric field inside the wire only or is it present outside the wire as well?
|
This question is motivated by Problem 3.4 in Griffiths' book on Electrodynamics.
This problem asks to calculate the average electric field on a sphere, due to charges inside the sphere and outside the sphere. For simplicity, let's just considering a point charge $q$ with field $$\mathbf{E}=\frac{1}{4\pi\epsilon_0}\le... |
In Cheng&Li's book "Gauge theory of elementary particle physics" section 16.3, the $U(1)$ problem is presented. Here is the story:
Suppose we have a theoy which contains only two quarks $q_1=u$ and $q_2=d$. The symmetry group is given by $SU(2)_L\times SU(2)_R\times U(1)_V\times U(1)_A$.
$U(1)_A$ is axial symmery, i.e.... |
Texts, such as Drela, Flight Vehicle Aerodynamics, indicate that the Kutta-Joukowski Theorem holds in compressible flow. Indeed, the KJT seems hold in linearized supersonic flow around a 2D flat plate. However, the proof that I find on Wikipedia relies on assuming that the flow is incompressible and that the total pres... |
I am currently studying the textbook The Quantum Theory of Light, third edition, by R. Loudon. In the introduction, the author says the following:
In the customary photon description of quantum-optical interference experiments, it is never the photons themselves that interfere, one with another, but rather the probabi... |
I know that in BCS theory an energy gap $\Delta(\mathbf{k})$ with s-wave symmetry would lead, in the limit for very low temperature, to a term in the free energy proportional to:
$$
F \simeq e^{-\beta \Delta_0}
$$
where $\Delta_0$ is zero-temperature value of the s-wave energy gap, and $\beta = k_B T $. By derivation, ... |
If I know the velocity of something and the angular velocity of something, how could I figure out the distance between the object and the center it is rotating at?
I just need an equation for the range or diameter of the objects path with X and Y as used as above and, if possible, an example.
|
Given a uniformly charged hemispherical shell of radius $R$, I want to calculate the potential at the center of the shell.
I can use the equation $V=k\int\frac{\sigma}{r}da$, where $\sigma$ is the surface charge density, $r$ is the distance between the center and the surface element $da$
But can i calculate $\vec E$ at... |
I understand that electrons do not orbit the nucleus, instead they have a higher probability to be found at some specific regions.
But what makes they appear more frequently in the orbital regions? There are equations (like Schrödinger) that are able to describe this wave function, but what causes it?
|
This is a rather mathematical question regarding a derivation of the harmonic lattice energy $\Phi^{ham}$ in a book about the quantum theory of solids. Specifically, I found the third equivalence in Eqn. (1) below is quite bizarre:
$$\begin{aligned}
\Phi^{\mathrm{harm}} &=\Phi_{0}+\frac{1}{4} \sum_{i \kappa, j \nu} \su... |
I know that there is more than one way to go about quantization, but operationally, I find it useful to have a go-to set of steps that can convert a classical system to its quantum analog. Is there any step in this four-step recipe that isn't valid?
Formulate the classical Hamiltonian which shall represent the mode to... |
Modeling fluid flow in a coil seems very complicated, especially for turbulent flow. Having Navier-Stokes equations seems to be the right way to go, but I was wondering... can one use the convection-diffusion equation?
$$
\rho C_p \frac{\partial T}{\partial t}+\rho C_p \vec{u} \nabla T - \nabla \cdot (-k \nabla T) = 0
... |
I'm having trouble understanding what the current voltage characteristic of a Josephson Junction looks like.
When we first looked at the voltage state of a Josephson Junction we got the following graph:
After that we analysed the RCSJ model and we got this graph:
Where a) corresponds to an overdamped Junction and b) ... |
According to Bell's spaceship paradox, a string between two uniformly accelerating spaceships will break. According to the equivalence principle, a string between two spaceships freely falling in a uniform gravitational field won't break.
The difference has already been explained with math. Can you also explain the mer... |
I know there have been a lot of threads about this topic, but I haven't found one that answers my specific question. So if we have a case of two objects that stick together after colliding, with no external force present, then the momentum of the system is conserved. From that one can calculate the velocity of the comb... |
I cannot get my head around as to which force makes the ring go up at all. I have checked the solution manual where the tension is made zero in the bead and ring equations of motion and solved along with applying energy conservation. I had further read somewhere that the normal force changes when the bead reaches the a... |
That ratio keeps popping up, yet I have nowhere read an estimated value...
Are scientists at least certain that high-energy neutrinos oscillate less often?
|
Consider two person one is travelling in a space ship and one is on the moon, now in the space ship there is a device where a light beam or photon is bouncing between two mirrors now when the space ship moves shouldnt the light beam or photon stay where it is relative to the observer on the moon meaning that space shou... |
For the purposes of this question we can assume these objects are in identical electric fields and have the same charge, but let their momentum 4-vectors be $p_1$ and $p_2$. I've seen force defined as the coordinate time derivative of the 3-momentum. If $\frac{dp_1}{dt}$ and $\frac{dp_2}{dt}$ have the same space compon... |
What is the relationship between an eigenvalue and an amplitude?
Suppose that $\hat{B}|\psi\rangle = \frac{1}{\sqrt{2}}|\psi_{1}\rangle + \frac{1}{\sqrt{2}}|\psi_{2}\rangle$ for some observable $\hat{B}$. I understand that $\frac{1}{\sqrt{2}}$ is the amplitude for each of $|\psi_{1}\rangle$ and $|\psi_{2}\rangle$. Can... |
Although I've seen the typical no-bias, reverse-bias and forward-bias band diagrams associated with the PN junction and seen the overlapping valence and conduction bands of a typical metallic conductor, I can't find any example that include all four sandwiched together (conductor-Ntype-Ptype-conductor). I'm curious ab... |
I have been thinking about the moon becoming a black hole. I was thinking about how much it would eat a day. How much mass would it suck in in 24 hours on average?
I am writing a story where the moon becomes a black hole.
|
I will first explain how I interpret the vector addition of velocities.
Let's assume that a particle moves with a velocity of $x$ horizontally and simultaneously also moves with a velocity of $y$ vertically.
Now, the resultant velocity will be the vector sum of these individual velocities, i.e. $\vec {v_1} + \vec {v_2}... |
Is it possible that all moving particle release gravitational wave?
I was trying to study gravitational wave and a question stuck in my mind. If any mass can bend space time and is moving it will also create ripple in space time. And as every thing in space is moving, why do we detect only a few gravitational waves.
|
Suppose we have a blackbody object, maybe a star or a metal (although I understand neither of these are actually blackbody objects, to some extent my understanding is they can approximate one). According to Wien's Law, as temperature increases, peak wavelength will decrease, so the color we observe will "blueshift." De... |
I'm now trying to integrate the Maxwell equation and the Ginzburg-Landau Theory in the geometric form because it can be suitable for FEM based simulation.
Wikipedia tells me the form of the equation but there is no information about its derivation.
https://en.wikipedia.org/wiki/Ginzburg%E2%80%93Landau_theory#Geometric_... |
This question is mostly about a strange seeming similarity that I've noticed between the nature of the weak force and the nature of black holes, which seems to imply that even some astrophysical black holes might be able to interact significantly with the weak force:
Only left-chiral fermions and right-chiral antifermi... |
What is the value of critical temperature in the 2D classical Ising model?
My Understanding
Suppose one can write the partition function for the 2D classical Ising model in high-temperature expansion and low-temperature expansion.
In High-temperature expansion, the partition function has form:
\begin{align*}
{\cal Z}_... |
In quantum mechanics, observable properties correspond to expectation- or eigenvalues of (hermitian) operators.
After measurement (of an eigenvalue) the system is in an eigenstate that corresponds to an eigenfunction of the operator. Sometimes, however an eigenvalue ($\lambda$) can not only arise from one certain well-... |
The energy lost on charging a capacitor can be easily found from the change in energy of the components of the circuit and the energy supplied by the battery.
On charging a capacitor I know that the energy loss appears as heat in the internal resistance of the battery and the wires.
But what if I take (Purely theoretic... |
Inflation is thought to be an extraordinarily brief period during the very early universe when the scale factor increased a remarkable $e^{60}$-fold, however this also comes with a corresponding increase in the expansion rate $\dot{a}=\mathrm{d}a/\mathrm{d}t$. When inflation ends, the exponential acceleration ceases an... |
I must convert some dimension-6 operators I've obtained to the SILH base (ref: this, "Review of the SILH basis", CERN presentation by R. Contino).
In this conversion I've got operators such as $D_{\mu}D_{\nu}H^{\dagger} D^{\nu}D^{\mu}H = \frac{1}{4}(G'_{\mu\nu}H^{\dagger} G^{\prime\nu\mu}H + \{D_{\mu},D_{\nu}\} H^{\da... |
I want to simply eliminate the effect of acceleration, which is the cornerstone in resolving the traditional twin paradox, through the following thought experiment:
Assume twins $A$ & $B$ are located in the same orbital height, far away from the surface of a massive planet, on a long concrete column at rest WRT the pla... |
I was thinking about the sun. What if it shrunk in diameter to the size of the Earth? It wouldn't change the gravity much. But would it change the heat? If so, would the earth become uninhabitable?
My hypothesis is no because it just gets smaller and has the same mass. But the sun would become invisible.
|
Nuclear reactor has to convert its heat into mechanical energy and to electric energy with its turbine heat engine. I learned the heat engine of a common PWR nuclear reactor is around 33%. The efficiency of a best heat engine is near 50%. So is it possible to fuse the best heat engine with a giant nuclear reactor to ha... |
I wanted to investigate the doppler effect on pendulums and set up an experiment where:
The bob of a pendulum is a speaker which emits a specific sound frequency.
Directly underneath the lowest point of the pendulum sits a microphone that observes the frequency being emitted by the pendulum.
In the experiment, I woul... |
How can we derive the formula for excess pressure inside a non spherical drop which is $T(1/a_1 + 1/a_2)$ as given here .I was unable to find any derivation on the internet. Also what is $a_1$ and $a_2$ in the formula is unclear to me. It says that $a_1$ and $a_2$ are radius of curvatures of the intersection of perpend... |
The beam energy is sometimes in AGeV in collider papers. I'm stuck on how to convert AGeV to GeV.
|
I am doing some experiments with spheres impacting a body of water and would like to change the wettability of the sphere. Is there some relatively easy way to do this? A procedure in one paper is extremely involved and in another they mention spraying it with something called SY-Supercoat-SHFC3150 and leaving it in ... |
We all know that if we have potential difference between two points in space, then there is an electric field between them but what if I had a region of space which is equipotential initially but has changing voltage due to some reason. So, there is an aspect of potential difference across time, would this suggest a t... |
We know that electric field inside a spherical shell is 0 . But electric potential 'V' inside a spherical shell is kQ/R (Q = charge on the spherical shell and R = radius of the shell)
We also know that V=Ed for D = distance of the point where we want to find the electric field or the potential .
My doubt is that for th... |
I wanted to calculate the impact force of some falling object
Let's assume this object has:
$85kg$ mass
the cross-section area: $0.75m^2$ (if that's necessary)
Speed of $42.64m/s$ when it reaches the impact point
With this, what would be the impact force when it falls to a concrete road
My first approach:
I've calc... |
Continuous media belongs to the continuum and could have an elaborate structure. So I guess there is a fractal solution. But at present, I do not know a specific example, so I would like to ask my friends who know about this: is there a fractal solution in continuum mechanics?
The details are as follows, I've read some... |
I have the following formula:
$$\dfrac{dE}{dx} = \dfrac{4 \pi e^4 z^2}{mV^2}NB,$$
where, for example, in the case of relativistic velocity of a particle, we have
$$B = Z\left[ \ln \dfrac{2mV^2}{I} - \ln(1 - \beta^2) - \beta^2 \right].$$
$E$ is the particle energy;
$ze$ and $V$ are its charge and velocity, respectively;... |
I am trying to find a model, or construct my own to describe the diffusion of a particle between layers of immiscible fluids with different densities.
The particle size is much larger than the sizes of molecules of both liquids, so Brownian motion assumption holds for the entire system. The particle is uncharged as wel... |
I've tried to remember everything I could thats related to physics I've learned in school and college, but I'm failing. I'm currently trying to develop the physics of my own game (I could instead use some premade tools, but this wouldnt be any fun). For any sake, this is going to be top-down viewed in 2D, kinda like th... |
I am reading through Elvang and Huang's treatment of polarization vectors for all outgoing spin-1 massless particles (metric signature $(-,+,+,+)$).
It is given in Eq. (2.50) in the PDF (but Eq. (2.51) in the textbook version) that the polarization for a particle of momentum $p$, reference spinor $q \neq p$, can be wri... |
When air or any fluid is forced out of a nozzle, why does the flow take a conical shape just outside the opening? And is there any way we can calculate the vertex angle of this cone?
|
In my fluid mechanics course we encounter a lot of vector calculus problems, one of which I have been struggling with for a while now. We must prove that
$$ \vec{V} \cdot \left(\vec{\nabla}\vec{V}\right) = \left(\vec{\nabla}\cdot\vec{V}\right)\vec{V} $$
solely using summation/index notation. $\vec{\nabla}\vec{V}$ is a ... |
$\DeclareMathOperator\Spin{Spin}\DeclareMathOperator\SL{SL}\DeclareMathOperator\SU{SU}$
We know that
$$
\Spin(1,3)=\SL(2,\mathbb C)
$$
and
$$
\Spin(4)=\SU(2) \times \SU(2).
$$
It is also said $\Spin(1,3)$ is the complexification of $\SU(2)$.
My question is that why there is a Majorana spinor (4 component Real spinor ... |
If I rotate something along some axis which has direction $\vec \Omega$, at an small angle $\epsilon$ and if the position of the body is $\vec R$ then according to my book the displacement will be $$\delta R=\epsilon\vec\Omega\times\vec R$$
I am unable to understand how this happened. I will be helpful if someone illus... |
Although I looked into similar questions regarding this subject, I could not make the link to my situation so correct me if the answer is already on StackExchange...
My starting point is a global xyz-frame and a local FLU-frame (airplane) which is aligned with the xyz-frame (F/x, L/y, U/z). The local FLU-frame does rol... |
Consider the simple case of electromagnetic irradiation of a homogeneous isotropic dielectric, neglecting the dispersion of the refractive index. Assuming a transparent medium, the spatial density of forces acting on the dielectric in a static external electromagnetic field can be given as
$$\mathbf{f} = - \nabla p - \... |
I am a high school student trying to wrap my head around the second law of thermodynamics for the past few days to no avail. Having only a cursory knowledge of calculus, and chemistry and physics in general doesn't help either.
The second law of thermodynamics says that entropy of the universe always increases. For co... |
Some say that the battery supplies charge, some say that it only maintains potential difference, I've also heard that it maintains an electric field in the wire. I'm confused. What does battery actually do? Please tell me the reality. What happens when we connect anything with battery through the wire? Do the electrons... |
The universe expanded insanely fast during inflation.
But even after it ended (maybe around 10^-32 seconds) the universe still expanded extremely quickly, far faster than it does today. It went from the size of a grapefruit (or even larger, say a football stadium) to 10-40(???) light years in size after one second. ... |
How is a starting vortex formed when an airfoil (i.e cross-section of wings of a plane) starts to move?
|
There are a lot of questions about a small BH and the Earth, none of these answer my question specifically. And there are contradictory answers. Some of them state that the effects would be negligible, since the small BH could only eat very little. Others state that the effects would destroy Earth. My question is about... |
This is a sum in a reference book( H.C. Verma, concepts of phycics). A dielectric slab is being inserted in a parallel plate capacitor as shown in the diagram. The width of the plates is given to be $b$. We need to find the force exerted by the capacitor on the slab. The solution given in the book is as follows:
As vo... |
In asymptotically flat initial data sets, one can define the ADM mass, energy, linear and angular momenta via spatial limits of integrals over 2-spheres.
My questions are: is asymptotical flatness enough to ensure that the ADM mass, energy and linear momentum converge? (I know that for the angular momentum, that is not... |
I will try my best to explain.
When I think about waves, I generally tend to first visualize a stable and flat two-dimensional surface, in position 0. When a normal sine wave travel through it, it moves the surface up and down, bouncing it to, say, +1 and -1. This is true for waves in water, sound waves and even waves ... |
Consider the simple case of electromagnetic irradiation of a homogeneous isotropic dielectric, neglecting the dispersion of the refractive index. Assuming a transparent medium, the spatial density of forces acting on the dielectric in a static external electromagnetic field can be given as
$$\mathbf{f} = - \nabla p - \... |
Inspired by this recent question.
If, sometime shortly before writing was invented, some passing alien turned the moon into a tiny black hole (xkcd) when/how/would we have figured out it was there, and what it was?
Given it's tiny cross section it is not likely to be eating much and thus would not be very bright.
I'm s... |
From basic physics any object experiencing a uniform circular motion, experiences a centripetal force. However in electric machines at high speed the rotor would be deformed outward as if a centrifugal force acting on its outer surface. How mathematicaly we can convince ourselves the force is centrifugal although we le... |
Some physics literature says Horizontal Symmetry of gauge theory, such as this paper, available also at arXiv.
What does this Horizontal Symmetry of gauge theory or Horizontal gauge group mean? Does that mean the symmetry group in the same energy scale (horizontal, not go up or down of an energy scale)?
People speak ab... |
Vortex beams are characterized by an azimuthal angle phase dependence, basically $e^{i l\phi}$. Why is this azimuthal angle phase dependence crucial and will I get a helix if I were to plot the surface of constant phase for Laguerre Gaussian beams?
NB: I have edited the question because of a confusion.
|
I have checked online and the Kerr metric never seems to be given in Cartesian coordinates (although there is a conversion factor from Cartesian to Boyer-Lindquist coordinates). Is there some reason for this, or would the metric become prohibitively complicated if one tried to switch to Cartesian coordinates?
|
So I am doing a lot of research on evaporative coolers and I have come to a question I can't find much info on.
I am currently a mechatronics engineering student that has yet to take thermodynamics so my understanding is anything but perfect; however, thermo is my favorite subject.
That being said I am wondering about ... |
I want to simulate triatomic reactions without going to spherical/hyperspherical system. I need some resources such as books or papers where the theory of triatomic reactions is given in rectangular coordinates exclusively. So far I haven't found anything exclusively for triatomic reactions in rectangular coordinates. ... |
Given a streamline, is it possible that the velocity at some point on it is non-zero but then at some other point(for example, stagnation point) it is zero? I mean does that make sense?
My existing knowledge tells me that a streamline is basically defined by the path traced by a fluid particle(maybe kind of a really ve... |
Initially, I saw Wick rotation as a useful trick to apply dimensional regularization, but then I learned about instantons and how they only exist in Euclidean Yang-Mills.
Also, I heard that path integrals are "more well-defined" in Euclidean spacetime.
What are the other advantages?
|
In this video https://youtu.be/2o3-GTk72x8, Professor Michel Biezen derives the following equation :
$$mx’’+m\ell \left(\theta’’ \cos(\theta)-\sin(\theta)(\theta’)^2\right) = -kx. $$
However, the terms inside the bracket are not dimensionally equal (the coefficient of $\sin(\theta)$ is not dimensionally equal to Force)... |
This question is motivated by Section 3.2.3 in Griffiths' book on Electrodynamics.
I am trying to calculate the force of attraction exerted on a point charge by an induced charge, from an infinite grounded plane. Using the method of images, we can calculate the potential to be $$V(x,y,z)=\frac{1}{4\pi\epsilon_0}\left[... |
I was recently doing a question on a spring block system and I was just suddenly weirded out by the fact that regardless of how much momentum or energy the block starts with (indirectly how much the spring is compressed), the time period is independent of it. Why does this happen intuitively?
Reason why I think that ti... |
As in, why is newton's second law(for constant mass systems),
$$ F= m \frac{d^2 x }{dt^2}$$
and not something of the sort like
$$ F= m \frac{d^3 x }{dt^3}$$
Why is it that sum of all force can be equated to mass times second derivative of position? Like in all cases the right side of the $F=ma$ equation is same.
My att... |
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