Transport Definition and 265 Threads

In Dirac's GTR. Sec. 12 (p. 22), he wants to show the equivalence of: (a) Vanishing of the curvature tensor ##R^\beta_{\sigma\nu\rho}=0##; or equivalently, the equality of mixed second covariant derivatives ##A_{\nu:\sigma:\rho}=A_{\nu:\rho:\sigma}##. (b) Path independence of parallel transport...

I'm using a ``downwind'' approximation for the spatial derivative: \frac{\partial v}{\partial x}\approx -\frac{3}{2h}v_{j}+\frac{2}{h}v_{j-1}-\frac{1}{2h}v_{j-2} I'm using the usual approximation for the time derivative, I get the following for a stencil...

I feel quite confused for a few days, when I apply the bipolar transport equation into a voltage-applied semicondutor material (e.g. p-type c-Si bar, or a resistor) which just have some light-generated electron-hole pairs by a pulse of photon at somewhere on the bar. In terms of bipolar...

Hallo, I would like to display the RTE (Radiation Transport Equation) dimensionless. In the picture, the RTE is shown. I would like to have the Planck number (or N) inside at the end. Additionally, the Prandtl number and the Rayleigh number can be inside. I have already many attempts behind me...

This privately held company developed a technology to extract H from methanol stored onboard marine craft, then the H can be used in a fuel cell for power. I assume the reason for a H fuel cell vs a direct methanol fuel cell (DMFC) in a marine vessel is that direct methanol cannot deliver large...

Hi, i would like to write my own MC code in order to simulate the transport of Neutrons in Nuclear reactors. I know the basics of MC and i have already written a code for homogeneus reactors, my problem is the generalization to more complex geometries made of different materials, such as fuel...

This is another open ended question, exploring a space of design concepts, in similar spirit to this. I want to explore monopods with regard to travel in densely populated cities(even possibly intercity travel). The main idea is to use small personalized pods to travel in tubes(or tracks). The...

According to my book, the equation that should meet a vector ##\mathbf{v}=v^i\mathbf{e}_i## in order to be parallel-transported in a manifold is: ##v_{, j}^{i}+v^{k} \Gamma_{k j}^{i}=0## Where ##v_{, j}^i## stands for ##\partial{v^i}{\partial y^j}##, that is, the partial derivative of the...

I am able to find and understand T from kinetic theory, but I do not understand how to use pressure gradient per unit of area and per unit pressure gradient.

Suppose you have a tensor quantity called "B" referenced in a certain locally inertial frame (with four Minkowski components for instance). As far as I know, a parallel transportation of this quantity from a certain point "p" to another point "q" consists in expressing it in terms of the...

I am having too much trouble to solve this exercise, see: Using (R,phi,z) ub is the path derivative U is the path V is the vector $$V^{a};_{b}u^{b} = (\partial_{b}V^{a} + \Gamma^{a}_{\mu b} V^{\mu})u^{b}$$ $$U = (0,\theta,Z)$$ I am not sure what line element to use, i mean, a circle around a...

Hi all, I Fix $$(t,x) ∈ (0,\infty) \times R^n$$and consider auxillary function $$w(s)=u(t+s,x+sb)$$ Then, $$\partial_s w(s)=(\partial_tu)(t+s,x+sb)\frac{d}{ds}(t+s)+<Du(t+s,x+sb)\frac{d}{ds}(x+sb)>$$ $$=(\partial_tu)(t+s,x+sb)+<b,Du(t+s,x+sb)>$$ $$=-cu(t+s,x+sb)$$...

I am considering the magnitude of the gravitational redshift and I look at the process of a photon leaving an atom from the Sun. I am asking whether the processes in the atom, viewed as a clock, would lead us to conclude that the emitted photon, at the time of emission, would itself be...

When parallel transporting a vector along a straight line on flat space, does the connection (when calculating the covariant derivative) always equal zero? Do things change at all when using an arbitrary connection, rather than Christoffel symbols?

In the solid state physics by Ashcroft & Mermin, in chapter 9 there is a paragraph that I would be grateful if anyone could explain it more for me. The paragraph is: As it said in chapter 12 it will be seen. I read chapter 12 but unfortunately I can't understand what exactly it want to say...

Sorry if the question is not rigorously stated.Statement: Let ##(q,p)## be a set of local coordinates in 2-dimensional symplectic space. Let ##\lambda=(\lambda_{1},\lambda_{2},...,\lambda_{n})## be a set of local coordinates of certain open set of a differentiable manifold ##\mathcal{M}.## For...

I'm reading 'Core Principles of Special and General Relativity' by Luscombe - the part on parallel transport. I guess ##U^{\beta}## and ##v## are vector fields instead of vectors as claimed in the quote. Till here I can understand, but then it's written: I want to clarify my understanding of...

If we consider a system of fixed mass as well as a control volume which is free to move and deform, then Reynolds transport theorem says that for any extensive property ##B_{S}## of that system (e.g. momentum, angular momentum, energy, etc.) then$$\frac{dB_{S}}{dt} = \frac{d}{dt} \int_{CV} \beta...

Hi, I would like to ask for a clarification about the difference between parallel transport vs Lie dragging in the following scenario. Take a vector field ##V## defined on spacetime manifold and a curve ##C## on it. The manifold is endowed with the metric connection (I'm aware of it does exist...

a) I found this part to be quite straight forward. From the Parallel transport equation we obtain the differential equations for the different components of ##X^\mu##: $$ \begin{align*} \frac{\partial X^{\theta}}{\partial \varphi} &=X^{\varphi} \sin \theta_{0} \cos \theta_{0}, \\ \frac{\partial...

Hello everyone, I would like to obtain the equation for mass transfer of contaminant in a river. Here the fluid flow is laminar and I don't have reaction. I solved it and obtained this equation, but I think this equation is wrong because when I solved it numerically I got wrong answers. Would...

Let ##S_t## be a uniformly expanding hemisphere described by ##x^2+y^2+z^2=(vt)^2, (z\ge0)## I assume by verify they just want me to calculate this for the surface. I guess that ##\textbf{v}=(x/t,y/t,z/t)## because ##v=\frac{\sqrt{x^2+y^2+z^2}}{t}##. The three terms in the parentheses evaluate...

I am currently reading Foster and Nightingale and when it comes to the concept of parallel transport, the authors don't go very deep in explaining it except just stating that if a vector is subject to parallel transport along a parameterized curve, there is no change in its length or direction...

I need to find the properties such as specific heat capacity, thermal conductivity, density and others.

Good day all. Since the gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. Then If we form the Gradient vector field...

question1 : if you draw a small circle around the north pole (it should be the same at every points because of the symmetry of the sphere),then it is approximately a flat space ,then we can translate the vector on sphere just like what we have done in flat space(which translate the vector...

If a vector moves along a particular curve ##l## from point ##x_0## to point ##x## on a manifold whose connection is ##\Gamma^i_{jk}(x)##, then the vector field we get obviously satisfy the pareallel transport equations: $$\partial_kv^i(x)+\Gamma^i_{jk}(x)v^j(x)=0$$ Because ##[\Gamma^i_{jk}(x)...

What is the usefulness of parallel transporting a vector? Of course, you can use it to determine whether a curve is a geodesic, but aside from that, what can it be used for?

Molecular Transport equations for Liquids are harder to compute than that for gases, because intermolecular interactions are far more important in liquids. A System of equations for particle Distribution function and the correlation functions (BBGKY-Hierarchy) is used in General. For gases, it...

What's really the difference between pressure and normal stress? Also I know pressure acts normal to a surface from the outside Do normal stress acts from inside? I'm reading bird transport phenomena and this is confusing

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Schwarzschild Spacetime Continue reading the Original Blog Post.

Is it difficult to show that a Fermi-Walker "rotation" happens only in the plane formed by a particle four-acceleration and four-velocity?

Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.damtp.cam.ac.uk/user/hsr1000/part3_gr_lectures_2017.pdf&ved=2ahUKEwi468HjtNbgAhWEeisKHRj9DNEQFjAEegQIARAB&usg=AOvVaw3UvOQyTwkcG7c7yKkYbjSp&cshid=1551081845109 Here in page 55 it is written that geodesic is a curve whose tangent...

I was trying to understand the momentum transport between gas molecules in 2d.In the image below, it is stated that half of the molecules move up(positive velocity in y direction) and half negative.But the author didnt explain why he assumed it.

With a new fuel cell to make ammonia from nitrogen and water (producing oxygen as a side product), Australian researchers are hoping to develop an efficient carbon-free way to store and transport energy from sources like solar panels and wind generators. Ammonia's: Longish Science mag news...

My book states that when a flow around object is considered, Non dimensional momentum flux is defined as the drag coefficient In case of flow through tubes it states The non dimensional momentum flux is defined as the friction factor What do these statements mean? What do they practically...

Hi, I'm working on a C++ library for second-quantized models called TBTK (https://github.com/dafer45/TBTK). To make it easy for people to get started using the library, I have recently begun implementing solutions to the exercises in the book "Quantum transport: Atom to Transistor, S. Datta...

I'm trying to understand why convection is an efficient mode of energy transport in the outer layers of the solar interior. Could anyone give me a little bit of knowledge? Thank you!

I am an undergrad physics major in my final semester currently taking Intro to Thermodynamics. As a final project, each student must choose a topic related to thermodynamics that is more advanced than what is covered in the curriculum and write a paper and present our findings to the class on...

I'm trying to understand length contraction from wikipedia, and they mention clock synchronization: The observer installs a row of clocks that either are synchronized a) by exchanging light signals according to the Poincaré-Einstein synchronization, or b) by "slow clock transport", that is, one...

Hello. In the following(p.2): https://michaelberryphysics.files.wordpress.com/2013/07/berry187.pdf Berry uses parallel transport on a sphere to showcase the (an)holonomy angle of a vector when it is parallel transported over a closed loop on the sphere. A clearer illustration of this can be...

Hello and thanks for looking at this question. I have a semi-conducting sample which has been run on a PPMS system - measuring it's resistivity as a function of temperature. I switched to AC transport mode in order to measure the resistivity again while applying frequencies between 1Hz -...

Hi. I have written a code to solve the one dimensional one group (a fixed velocity is considered for the particles) time independent transport equation. The code uses the ##S_N## discrete ordinates method, a Gauss-Legendre quadrature in the angular directions, and a Diamond Difference formula...

In general relativity, a vector parallel along a curve on a manifold M with a connection field Γ can be expressed: ∂v+Γv=0 We know that if the curvature corresponding to Γ is non-zero, which means if we parallel transport a vector along different paths between two points, we will get different...

Hello! In my GR class we were introduced to the parallel transport as the way in which 2 tensors can be compared with each other at different points (and how one reaches the curvature tensor from here). I was wondering why can't one use Lie derivatives, instead of parallel transport. As far as I...

In the biological cell, is the bulk transport the same as the vesicular transport? I read about them separately and found that they happen in the same way, so I guessed that they are the same thing, or am I wrong?

Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...