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I calculated the Compton amplitude of three diagrams but how can I verify it under gauge invariance structure?
$$
{\cal A} = 2 e^2 \left[ \frac{ p_3 \cdot \epsilon_1 p_2 \cdot \epsilon_4^* }{ p_2 \cdot p_4 } - \frac{ p_2 \cdot \epsilon_1 p_3 \cdot \epsilon_4^*}{ p_2 \cdot p_1 } + \epsilon_1 \cdot \epsilon_4^* \right]
$... |
In solution of this problem the acceleration of all the blocks is taken same as $a$ . But won't the acceleration of Block $A$ and $B$ be different and the acceleration of Block $C$ would be the sum of acceleration of $A$ and $B$. Please explain.
|
I am struggling with the logic for completing the following problem.
The problem is part b of 3.19 in Goldstein's Classical Mechanics book.
A particle moves in a force field described by the Yukowa potential $$ V(r) = \frac{k}{r} exp (-\frac{r}{a}),
$$ where k and a are positive.
Show that if the orbit is nearly circu... |
In real space, the Fermi-Hubbard model can be written as:
$$ H = -t \sum_{\langle i,j \rangle\sigma} (c^\dagger_{i\sigma} c_{j\sigma} + c.c.) + U \sum_in_{i\uparrow}n_{i\downarrow}$$
The only difference between having periodic boundary conditions and not having them is that the nearest-neighbor pair, $\langle i, j \ran... |
If oxygen is removed from water by boiling the water, what is the result when the water reaches room temperature? Is it still free of oxygen?
|
We have two objects moving opposite to each other on the x-axis. They started to collide on the location $x = 0$ on x-axis.
We know that if object one $m_1 = 10 kg$, and $v_1 = 10 m/s$, and object two $m_2 = 10 kg, v_2 = -10 m/s$, then during the entire collision process (time of impact) the point of impact will remai... |
I'm currently reading this book on flight dynamics but I'm having some trouble getting my head around the way the author derives some equations of motion. He starts by showing the body in the first image as follows:
"Consider the motion referred to an orthogonal axis set (oxyz) with the origin o coincident with the cg ... |
I got some interest in String Theory when I was listening to lectures of David Tong and Brian Greene. I remember them stating that the spacetime manifold is compactified to resemble our usual 3+1 dimensions, using Calabi Yau Manifolds. But String Theory offers a lot of different possibilities of Calabi - Yau Manifolds ... |
Can someone please explain to me why is it $N\sin(\theta) = W$ instead of $-N\sin(\theta) = W$? Isn't $N\sin(\theta)$ in the opposite direction of $W$?
|
What exactly is tension force and how does it act?
When I saw a video on Khan Academy it said that tension force is just a force by which a force is transmitted across a rope, but when I was solving related problems, it was that the tension force is acting upwards on the body which is attached to a rope.
Also, how can ... |
Recently I have been reading Quantum Mechanics The Theoretical Minimum by Leonard Susskind. In the book he mentions the law of conservation of distinctions, i.e. the conservation of information.
He mentions that if two isolated systems start at different states, they will continue to stay in different states. So say I... |
From Joule's laws, we get this:
$$H\propto I^{2}Rt$$
$$\implies H = KI^{2}Rt ...(i)$$
Now, we have to find/define the value of K. According to my book, when $1A$ of current passes through a conductor of $1\Omega$ for $1s$, $1J$ heat is produced. If that's the case, then from $(i)$ we get this:
$$1=K\times1\times1\time... |
I saw this question which asks for the condition for flow of electricity through the conductor i know that electricity will flow only when there is a potential difference achieved between the conductor and the ground is at 0 potential .
My approach
I feel that when there is fluctuation of current through the wire ther... |
Can you show me a pure 1D or 2D object? A line and a plane have a thickness. A pure 1 D line is one with no width. But if its width is zero, it doesn't exist. Similarly, a 2D plane is perfectly 2D only if its thickness is 0 which makes the plane vanish.
So are all objects in the universe 3D? What's so special a... |
For the project of nondestructive testing of metal parts I have to calculate a coil with radius $R=0.4m$ that should produce $H=300 A/cm$ with supplied 50 Hz AC. I have to decide on number of turns and anything else that would make the coil feasible for real life application.
My thinking goes as follows:
for a solenoid... |
Compare this to the eigen functions $e^{-pi x} $ of linear momentum, where we could argue that $p$ had to be real to keep wavefunction bounded as $x$ tends to infinity.
I found this argument in Shankar's QM book. Real eigenvalues of $P$ operator follows from the hermiticity of the operator. Is there any connection be... |
Consider a general problem of a rigid sphere having only rotational motion placed on a rough surface where it starts rolling after some time. And final velocity is asked. Friction is just enough to provide rolling motion. All the books and class notes I've referred to say that to conserve angular momentum, external tor... |
I'd like to know what a piezoelectric sorption detector is. I can hardly find information about, only a small number of research papers which are mostly not accessable for me.
Only given from the term I cannot really imagine its functionality.
|
I want to model different 2D nano-structures, layered materials in 3D (animated version). Is there any open source where I can build these structures?
|
Recently, I had a good start with H.W. Wyld on mathematical methods for Physics and now looking forward to ask whether is there any solutions available for the problems given at the end of each chapters?
|
I'm trying to understand electromagnets and the relationship between magnetic field and current. Just thinking about a loosely wound coil, with an air core. Something on the wiki page "Electromagnet" has stumped me:
The leakage field lines between each turn of the coil exert a repulsive force between adjacent turns, t... |
I am looking for the correct Nusselt Equation to calculate the heat transfer coefficient for a rectangular fin acted upon by air with a certain speed
|
On the page of quantum fluctuation, we have a gif representing some kind of fluctuation and according to AFT answer here $H$ which is $P^{0}$ and $P^{0}|vac\rangle=0$ which would imply
$\langle vac|H^2|vac\rangle=0$
therefore $\sigma_H=0$
So how come there is even any fluctuation? And why are arguments there heavily de... |
We know that voltage/potential difference is the amount of work done or energy released by the battery/cell for transferring a unit charge for higher potential to lower potential.
Now, when we connect two point with potential difference by a superconductive wire, there remains no resistance. So when electrons traverse ... |
This particular thought crossed my mind while deriving the expression for energy density of electric field in parallel plate capacitor.
Energy density= $\frac12 \epsilon E^2$
It appears to me that initially when the plates were touching, the interface atoms were neutral.When we slowly pull the plates apart, electrons g... |
This post claims that there is no real photon (particle) with a plane wave solution well-defined momentum state).
It makes sense somehow to me. I can think of several arguments:
The plane wave solution doesn't have well-defined probability as it exists in infinite space with equal probability. We will never be able to... |
I am working with a complex solution of 2 proteins and salt. I have been trying to use DLVO (Derjaguin, Landau, Vervey, and Overbeek) theory to get an approximation of the Van Der Waals attractive force ($F_{wppr}$) and the electric double layer repulsive force ($F_{el}$) between the molecules in the solution. However,... |
It is commonly known that the eigenstates to the Hamiltonian of a constant potential are plane waves, aka
$$
V(r) = V_0 \Rightarrow H\psi = n \text{ with } \psi = \exp\left(\frac{ip}{\hbar}x\right)\exp\left(-i\frac{E}{\hbar}t\right)
$$
But is there another $V(r)$ for which this holds?
I suppose the question can be simp... |
Why is the friction static while driving a car (at constant speed) on a horizontal circular road? Please explain in details.
|
I studied a sciences of climate change module with the OU a while ago, I'm half remembering something that's bugging me and wonder whether any could help provide some clarification?
I remember that an increase in degrees of freedom of a molecule are related to increase internal energy / heating. Hence this was the reas... |
Einstein and others have thought about VSL theories. But I am unable to understand how VSL theories can be consistent, for the following reasons:
Don't we need some mechanism (like Einstein Synchronization) to synchronize distant clocks? For example, if speed of light varies with time or space, what do we use to synchr... |
I'm not sure whether this is the correct community to post this, so pardon me.
I was studying the Bicycle Kinematic Model and came across 3 possible reference points for analysis - the rear tire, front tire and the centre of gravity. For all these reference points, Instantaneous Centre of Rotation was applied and veloc... |
Now, The azimuthal part of the Schrödinger's equation for a hydrogen atom (after separating variables) is:
$$ \frac{d^2 \Phi}{d \phi^2} + m^2 \Phi = 0$$
Which has solution $A e^{im\phi} + B e^{-im\phi}$, but I often see people assuming $B=0$, why?
|
I just found a paper "On a common misunderstanding of the Birkhoff theorem". This means that inside a spherically symmetric thin shell there is no gravitational force, BUT there is time dilation, and so the interior solution is NOT the Minkowski metric, right?
|
I am quoting from "Equilibrium and non-Equilibrium Statistical Thermodynamics", by M. Bellac.
$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$
Where $Q$ is the grand partition function, $Z_N$ is the canonical partition function and:
$$\beta = \frac{1}{kT} \hspace{1cm}... |
As far as I can tell temperature seems to be defined as something like average kinetic energy per molecule, but not quite. It looks like it measures something proportional to this average kinetic energy, where the coefficient of this proportion depends on the number of independent degrees of freedom by the equipartitio... |
Well, elementary particles have no moment of inertia $I$. But what is the nearest possible answer to the question for a free, spinning electron?
In general, one has a relation with spin $J$ given by
$$ J = I \omega.$$
For an electron, the magnitude of spin is $J=\sqrt{3/4} \hbar$. But since $\omega$ is not defined, the... |
Consider the orbital angular momentum in QM, labeled by $L$ ($\mathbf{L}=\mathbf{r}\times\mathbf{p}$). In spherical coordinate, the operator can be expressed as:
\begin{equation*}
\left\{\begin{aligned}
L_x&=\frac{\hbar}{\mathrm{i}}\left(-\sin\phi\frac{\partial}{\partial \theta}-\cos\phi\cot\theta\frac{\partial}{\par... |
The last day and, some days before, I found myself incapable of proving an Equation, while the author said it was "easily" deducted (Chapter 6, Page 127, 3+1 Ideal Magnetohydrodynamics- Éric Gourgoulhon)
In almost every other derivation, I had no problems but currently stuck with this.
Stress-energy tensor of the elect... |
The FLRW metric, in the case of positive scalar curvature, is: $ds^2 =- c^2 dt^2+a(t)^2\left(dw^2+\sin^{2}w(d\theta^2+\sin^2\theta d\phi^2)\right)$.
The Birkhoff’s theorem states that "any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat".
The FLRW metric stated above ... |
Here, the natural length of the string is $l_o$, and pulling the string up by $x$ increases its length by $ \sqrt{ l_{o}^{2} +x^2}$; thus, the increase in length can be approximated as
$$ \delta l = \sqrt{ l_o^2 + x^2 }- l_o \approx \frac{x^2}{2l}$$
I got this result from Taylor expanding the square root using the ... |
I'm aware of the common misunderstanding about action and reaction canceling each other; they don't because they don't act on the same object. This is about a more subtle issue: exactly where is the work being done? Consider a bicycle wheel:
The bike wheel pushes the earth backwards (action force $F_A$) and the reacti... |
This is a thought experiment where I have made a "C" shaped hole inside diamond. The refractive index $(\mu)$ of diamond is 2.45. Say we shine a laser from top of the "C" as shown.
My calculations show that light reaching A can reach B in the least possible time if gone through the "C". but I'm pretty sure the perpend... |
Imagine two bodies, say a body A with an infinite heat capacity(reservoir) and the another body B with some finite heat capacity($C = \alpha \ T_{B}(t) $).
They come into direct contact with each other for a limited time, as B moves along the surface of A with a constant velocity v.
Given the thermal conductivity $\ka... |
I am trying to see whether the matrix formalism of the Hamiltonian formalism (used in Goldstein's textbook) is truly necessary to solve problem in this framework.
It appears so based on the problem I've run into. From problem 8.15 in Goldstein we have
A dynamical system has the Lagrangian $$ L= \dot{q}_1{}^2 + \frac{\... |
Equation of principal angles:
$$\tan 2\theta_p=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}$$
Equation of principal stresses:
$$\sigma_{max}, \sigma_{min} = {\sigma_{xx} + \sigma_{yy} \over 2} \pm
\sqrt{ \left( {\sigma_{xx} - \sigma_{yy} \over 2} \right)^2 + \tau_{xy}^2 }$$
Source of equations: Lectures notes on Mechanics of s... |
The propagation of light in optical fibers is governed by the equation
$i\frac{\partial A}{\partial z} = \frac{\beta_2}{2}\frac{\partial^2A}{\partial T^2} - \gamma|A|^2A$
where $A(z,T)$ represents the amplitude of the field envelope and $\beta_2$ and $\gamma$ are constants.
My textbook (Nonlinear Fiber Optics by Agarwa... |
The scattering $S$ operator which is defined to be the operator corresponding to $S$ matrix should be rotational invariance, does this imply $S$ operator is a scalar operator?
|
This refers to my other question Why is the ideal gas law only valid for hydrogen?. In the update, my teacher said that hydrogen is closer to an ideal gas because its mass is lower: $m_{\rm H} \thickapprox \displaystyle\frac {1}4 m_{\rm He}$. Since the mass of the object is not included in the ideal Gas law which is $P... |
I'm studying the book Techniques of Differential Topology in Relativity by Roger Penrose and I'm stuck in an exercise he left to the reader. We say that the spacetime $M$ is strongly causal in $p$ if and only if there exists an event $q$ such that $q \prec p$ and for all events $x,y$ with $x \ll p$ and $q \ll y$ we hav... |
A rigid body motion can be decomposed into translation and rotation. My question is, given a rigid body motion velocities of all points in the body, how to decompose this velocity field into a translation and a rotation? Is this decomposition unique? Or is it unique given an arbitrarily chosen "pivot" point, fixed to t... |
From my textbook:
General Relativity is the currently most complete theory of Gravitation,
and should be used to describe physical systems each time one of the
following assumptions does not hold:
Gravitational fields are small, $\Phi << c^2$
The scale of the system is much smaller than the curvature radius
Velocitie... |
Sorry if this question is too elementary, as is my level, but I'm wondering how close two supermassive black holes can get and should the Keplerian rotational frequency at that point equal to the frequency of the emitted gravitational wave? I guess I'm asking how the maximal frequency of classical mechanics of this bin... |
So Anderson et al proposed a model to explain the production of Sub Auroral Ion Drifts. In the paper they talk about how the decrease in ionospheric conductance results in an increase in the electric field, but why is this so?
I understand that decrease in conductance is an increase in resistivity. By Ohm's law $V = IR... |
I’m tackling physics recreationally from a pure math perspective.
Right now I’m looking at just the outline of gauge theory. The Wikipedia article explains that gauge fields correspond to generators of the Lie algebra of the Lie group the Lagrangian is invariant under. And then gauge bosons are the quanta of these fiel... |
Is there any way to calculate the following from a möbius strip?
(a) Electric Field :Given that the strip is an insulator and has localized charge uniformly distributed over its surface.
(b) Magnetic field generated :Given that the strip has a uniform current flowing on its surface.
And calculate equipotential surfaces... |
I noticed that coordinate systems $S,S'$ connected by a Lorentz transformation are depicted geometrically as having the same "origin event" $O$ in Minkowski spacetime. Is it correct then to state that the radius four-vector $\mathbf{x}$ of an event $P$ with respect to an inertial frame $S$ is equal to the radius four-v... |
I am in trouble with polarization and entanglement.
Let's consider three cases :
Case 1) : Statistical mixture of $|H\rangle$ and $|V\rangle$ polarized photons
Case 2) : Photons in a superposition state $1/\sqrt{2}(|H\rangle+|V\rangle)$
Case 3) : Photons which are entangled with twin ones in $1/\sqrt{2}(|H,H\rangle+|V,... |
Here is a paragraph with some statements about the Gauge Symmetry Breaking from Georgi's book Lie Algebras in Particle Physics 2nd ed -- From Isospin to Unified Theories (Georgi, 1999) p.285.
Georgi wrote:
His claim is too quick. Can some experts explain which symmetry breaking pattern he is thinking of? In particula... |
The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So what's the point; how can they be used?
|
Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (say, $A$) is displaced keeping the other (i.e. $B$) at rest. As time passes, all the energy of $A$ is transferred to $B$ t... |
Thermionic Conversion follows the classic Richardson-Dushmann Equation for thermionic current as a function of temperature squared:
$$J_{RD} = A_0 T^2 \exp\left(-\frac{\phi}{k_B T}\right)$$
where
$J_{RD}$ is the emission current density.
$T$ is the emission temperature.
$A_0$ is a material specific correction factor
$... |
With respect to this question, the power on a accelerated body, that moves in the same direction of the acceleration, can be calculated by $W = Fv$, where $F$ is the external force and $v$ the velocity.
In the case of a bicycle (or any wheeled car), some power is also necessary to turn the wheels. The power of a rotati... |
Why does $N=0$ when w=w critical?
What does "Mass m falls away from the drum if N ≤ 0, when ω ≤ ωcritical" mean?
I don't understand the relationship between N and W here.
|
If I take a charged conductor and pass a current through it and stop. Will the charge remain on that conductor or would it be flown away by the current?
|
Suppose a paper cone is made with height equal to its radius, only the two straight sides just touch each other and are not glued together. It is kept on a frictionless table and a vertical force is applied at its apex.
What force do I need to apply to the base of the cone at the point where the paper meets on straight... |
In quantum mechanics, you usually hear the phrase "the act of observing the state modifies it", but they never really define what they mean by "observing".
For example, suppose we have Stern-Gerlach analyzers aligned in the $z$-axis and we shoot atomic beams into the analyzer thus we don't know if the state is spin up ... |
I am reading arXiv:2006.03606 where through Eq. (1.1) they say that the transition amplitude for collapse of matter from initial state $\Psi_{i}$ into a black hole and eventually evaporation of black hole into final state $\Psi_{f}$ is given as :-
$$
\mathcal{A}_{fi} = \langle \Psi_{f} | \mathcal{\hat S} | \Psi_{i} \ra... |
The Bloch Sphere is regarded as the most "intuitive" way of explaining a 2-level quantum system in computation and rotations of states described on Bloch sphere provides a really easy picture. Despite that, I've been having some problems with understanding this representation of quantum states. I read quite a few artic... |
Recently during a discussion with a colleague we got into an argument. The discussion involved imagining a heated solid body at some temperature $T$ which is immersed in a large fluid medium maintained at a temperature $t$. After a long enough time has passed the solid will ultimately come in thermal equilibrium with t... |
This was first proposed in a scientific study from 2019. Essentially, the idea is that the solar cell generates power from the heat it radiates at night. That study claimed a theoretical maximum efficiency of 4 watts/m2. A study released a few months ago claimed that it could instead generate up to 50 watts/m^2. The ba... |
In the double-slit-experiment, one particle at a time (for example, the double-slit-experiment performed by Dr. Tonomura showing the build-up of an interference pattern of single electrons) can be observed in a detector or photographic plate by attenuating the source. At such a low rate of detection, I read that backgr... |
I know how the center of mass is defined, mathematically. It is the mass weighted average position of all the particles of a system. But calculating centers of mass and solving kinematic and dynamics problems related to them has only been plugging and chugging formulas so far, with no physical insight on what im actual... |
I was just reading this article on the quasicrystalline approximation (QCA). The article abstract says the following:
The quasicrystalline approximation (QCA) was first introduced by Lax to break the infinite heirarchy of equations that results in studies of the coherent field in discrete random media. It simply state... |
I believe that a gravitational field has energy, as Weinburg wrote in his textbook Gravitation and Cosmology, on page 171: "... ... the gravitational field does carry energy and momentum." As long as two points in space have energies, they attract each other. Now consider two particles in the gravitational field of the... |
My textbook states the following: " If a charge's velocity is constant, the rate-of-change of the $E$-field is steady, and the resulting $B$-field is constant.". To my understanding, this is clearly just an application of the Ampere-Maxwell equation/Law.
Now my problem in understanding is this: Suppose we have a charge... |
In the Space Exploration SE question Is there any possible reason to direct the electron gun specifically towards the ion trail behind an ion thruster? there is somewhat of a consensus that there isn't a strong compelling reason to intentionally inject the electrons directly into the ion plume.
Question: What would hap... |
There are very famous Coleman–Mandula theorem and Haag–Łopuszański–Sohnius theorem , see also this and this.
It states that "space-time and internal symmetries cannot be combined in any but a trivial way".
But this theorem didn't give any restrictions on internal symmetry group. Which symmetries can be realised in QFT?... |
What does the dynamical mass of a galaxy represent? Is it the mass of the gas in the galaxy or the total mass of the galaxy?
What can we infer from the rotation curves, is it dynamical mass or mass distribution?
|
In Wikipedia article Coleman–Mandula theorem there's statement:
Quantum group symmetry, present in some two-dimensional integrable quantum field theories like the sine-Gordon model, exploits a similar loophole.
Are some examples of quantum group symmetry in $d≥3$? Or there are arguments, why this symmetry can be real... |
Electromagnetic waves experience dispersion and these result in a "chirp" in frequency after traversing some distance. This chirp can be heard when waves from a lightning strike in one magnetic hemisphere of the Earth propagate along magnetic Earth's magnetic field lines through charged particles trapped in them and ar... |
My question is, can we diagonalize a general Hamiltonian ,
$$H=-t\sum_i^N (c_i^{\dagger}c_{i+1}+h.c.)+\sum_i \mu_i c_i^{\dagger}c_i$$ where,
$$\mu_i=\begin{cases}
\mu_0, &\text{if mod}(i,p)=0 \\
0, &\text{otherwise}.
\end{cases}$$
Obviously, $p$ is the periodicity of the lattice and $c$ is Fermionic annihilation operat... |
The Stern-Gerlach experiment is often cited as evidence of quantum superposition and there are some very simple explanations like this one https://www.youtube.com/watch?v=hkmoZ8e5Qn0 in which spin on one axis is compared to colour and spin on a perpendicular axis is compared to hardness.
The Stern Gerlach experiment r... |
I am a bit confused with the information that is provided by the Casimir operator.
First, with my understanding, a Casimir operator is defined as,
$$\Omega_\rho := \sum_{i-1}^{dim L} \rho(X_i) \circ \rho(X^i),$$
where $\rho: L \to End(V)$ is a (faithful) representation of a Lie algebra $L$ with basis ${X_i}$ and $V$ is... |
If I take a ball from the ground and take it to the top of 3m tower ,if I drop it, is it due to the fact that potential energy is converted to kinetic energy and it starts to fall or it falls under the influence of gravity?
|
I am looking at the following derivation of the potential energy of a dipole in a uniform electric field, paraphrased from phys.libretexts.org:
Consider an electric dipole $p$ placed in a uniform electric field
$E$. There is a torque on the dipole of magnitude $p E \sinθ$ . In
order to increase $θ$ by $δθ$ you wou... |
Consider a current ($I$) carrying circular coil of radius$ R$ of $N$ turns.Consider a rectangular loop $ABCD$,where length $AB=CD=\infty$
Performing the integral for axial points,
$$\int_ {-\infty}^{\infty}\vec{B}\cdot \vec{dx}=\int_ {-\infty}^{\infty} \frac{\mu_0INR^2dx}{2(R^2+x^2)^{3/2}}=\mu_0IN=\int_ {C}^{D}\vec{B... |
What are Gaussian spherical waves? and Is it necessary for a Gaussian spherical wave to be a laser beam?
I found the term in the paper Opt. Eng. 54, 035105 (2015) (eprint).
|
I am currently studying radiative transfer. In researching this subject, I found that there is stationary radiative transfer and non-stationary radiative transfer. However, it is not clear what the difference is between these two. I would greatly appreciate it if people would please take the time to explain the differe... |
I don't really know where to approach this problem from,Though I think solving might be easier in centre of mass frame.
What are your thoughts?
Thank you.
|
If we put a cube of metal on ice (ice with a certain thickness), under which conditions the cube will penetrate the ice? and how can we calculate the velocity of penetration?
|
when we draw a free body diagram of an object(at rest) hanging to a string we say that the normal force = gravitational force does this mean that the gravitational and normal force are equal?
|
The Wikipedia article for radiative transfer gives the following definition:
In terms of the spectral radiance, $I_{\nu }$, the energy flowing across an area element of area $da$, located at $\mathbf{r}$ in time $dt$, in the solid angle $d\Omega$ about the direction ${\hat {\mathbf {n} }}$ in the frequency interval $\... |
According to the equivalence principle the path of an object should not depend on it's composition.
But on the other hand a spinning object (e.g. an electron) moving past a rotating Kerr black hole will experience an additional attractive/repulsive force according to the relative spin of the two objects. This is the sp... |
I am currently studying radiative transfer. I have seen the stationary equation of radiative transfer written in two different ways:
1.$$\dfrac{\partial{I}(\mathbf{r}, \mathbf{s})}{\partial{s}} = - \mu_t I(\mathbf{r}, \mathbf{s}) + \dfrac{\mu_s}{4 \pi} \int_{4 \pi} I(\mathbf{r}, \mathbf{s}^\prime) p(\mathbf{s}, \mathbf... |
Aren't both perpendicular to $R$?
Also, doing $\nabla \times \vec{F}$ using $\hat{r}$, $\hat{t}$, $\hat{k}$ as versors (with $t$ tangent to $r$ and $k$ perpendicular to the surface) i get $0$ with both. Those informations are colliding.
|
For a system in equilibrium, the partition function is standard.
But if the system is in local thermal equilibrium but stationary (i.e. zero or negligible time variation), but the temperature varies spatially, how can one calculate the partition function?
To clarify the question, let us take a sample system. Let there ... |
In Continuum Mechanic Cauchy's Fundamental Lemma states that:
The stress vectors acting on opposite sides of the same surface are equal in magnitude and opposite in direction. Cauchy's fundamental lemma is equivalent to Newton's third law of motion of action and reaction.
See this wikipedia page if context is needed.... |
So we've performed an experiment about the resonance angular frequency and RLC circuits in the lab.
I understand that the phase of voltage on the inductor and the voltage on the capacitor are equal in magnitude but opposite in signs.
But this graph below also shows that the output voltage and the voltage on the resisto... |
Consider this form of Euler's Equation:
$$\rho \vec{a}=\nabla \cdot T+\rho \vec{f}$$
Where: $\rho$ is the density, $\vec{a}$ is the acceleration, $T$ is Cauchy's Stress Tensor and $\vec{f}$ is the force density (or if you prefer we can say that $\vec{f}$ is the acceleration per unit mass).
(This equation in practice is... |
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