Transport Definition and 265 Threads

I have been reading section 3.1 of Wald's GR book in which he introduces the notion of a covariant derivative. As I understand, this is introduced as the (partial) derivative operators \partial_{a} are dependent on the coordinate system one chooses and thus not naturally associated with the...

Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:(a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z; 4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd. 4π The integrals are over 4π. This is part of the derivation of the diffusion equation...

I am studying parallel transport in order to understand Berry curvature, but I know this topic is most commonly used in GR so I'm posting my question here. I do not know differential geometry. I am looking for a general explanation of what it means to parallel transport a vector. Mostly I am...

Clock transport can be used to compare one clock with another in an absolute sense. All we have to do is to transport a clock between two A-frame clocks that have been synchronized per Einstein's definition. Let's call the transported clock "T" and the left-hand and right-hand E-synch'd clocks...

1. Homework Statement Calculate the torque on the dam about the origin (Picture attached) due to the pressure force of the fluid. Homework Equations Pressure force is correct (dF) The Attempt at a Solution [/B] I have solve it; however, I am not sure if I calculated over the origin asked...

In several fiber-optic-based probes in medical imaging fields, the light travels towards an object through an optical fiber (or even free space), interacts with the object and then travels back through the same fiber (or the same path in free space) and is captured by a camera or photodetector...

Hi guys, I want to calculate an explicit example of a vector parallel transported along a cardioid to see what happens. Maybe someone could help me with that since no author of any book or pdf on the topic is capable of showing a single numerical example. So we need a vector field on a manifold...

In my recent studies of curvature, I worked with the Riemann tensor and the equation: (\deltaV)a= A\muB\nuRab\mu\nuVb Now previously, I worked in 2D with the 2 sphere. While doing so, I learned that if I set my x1 coordinate to be θ and my x2 coordinate to be ø, then the vectors that serve...

I recently derived the Riemann tensor (Rabmv) for the 2 sphere. I then did RabmvUbVmWv to calculate dva (the change in the vector va as you parallel transport it around the loop of the sphere). The result I got for dv1 was 0. I got 0 for dv2 as well. I am just making this thread to...

I am little bit confused about derivation for Boltzmann equation for electron look at this link http://relativity.livingreviews.org/Articles/lrr-2008-10/articlesu25.html which is final boltazmann equation ?

Hi all, I want to learn Quantum Transport materials . I would like to know some good material to start with and also I want to learn NEGF formalism. please suggest me some good books that teach from fundamentals in these areas.. Thank you ...!

I have this equation ux(x,t) + c(x)ux(x,t) = 0 x>0 I want to obtain information on how the initial input uo(x)=u(x,o) would deform when the sound speed is not constant. c(x) is the sound speedi wanted to start this by finding a DE for the level curves x=X(t) so that i can solve in terms the...

am given a scaled transport equation ut(x,t) + ux(x,t)=0 x>0; t>0 u(x,0)=0 x>0 u(0,t)= sint t>0 how can I begin to find a solution in the quadrant {x.0,t>0} to this problem, am really struglling:(

ut(x,t) + c(x) ux(x,t) = 0 I was given the equation above and c is said to be the propagation velocity and not constant what do they mean when they say i must use a method of characteristics to show that the above equation will be an ordinary diff equa

Published values for the room temperature thermal conductivity of graphene vary from ~2000 W/m*k to 5600 W/m*k, for freely suspended samples. The large discrepancy shows the sensitivity of graphene to lattice defects (contact with substrate, edge defects, etc.) Thermal conductivity increases...

Hi everyone, I am currently undertaking my honours year in physics focusing on atmospheric physics. I am wondering if anyone knows where I can get a model to determine how much energy is moved to the top of the troposphere by deep convective "hot towers". I wish it was as simple as...

From the Wikipedia article on the Riemann curvature tensor: The last sentence assumes that ##\tau_{sX}^{-1}\tau_{tY}^{-1}\tau_{sX}\tau_{tY}## returns Z back to x0. It isn't obvious to me that this should be true. My guess is that this is true because X and Y commute, but I can't think of a...

This is an expression I came across in a paper I am going through. It involves an expression for the parallel transport of a tangent vector taking into consideration the sectional curvature of simply connected space-forms in \mathbb R^4 . I have not been able to derive it.The equation simply...

I am starting to work with the high temperature superconductor BSCCO (Bi–Sr–Ca–Cu–O). I have read that the carriers of superconducting current is hole pairs. (As opposed to electron-pairs in normal superconductors) I am trying to understand how the transport would work. If I contact it with...

Say we have an electron traveleing in a crystalline conductor. It can scatter off of defects such as vacancies, interstitial atoms, grain boundaries, etc. Is there a way to quantify the relationship between conductance and defect density? I.e., if I want to build a 2D crystalline...

I have this question on the calculation of the geometric phase (Berry phase) of a parallel transporting vector over the surface of a sphere, illustrated by Prof. Berry for example in the attached file starting on page 2. The vector performing parallel transport is defined as ψ=(e+ie')/√2...

Given a curve c(τ) with tangent vector V, a vector field X is parallel transported along c if \nabla_V X=0 at each point along c. Let x^\mu(\tau) denote the coordinates of the curve c. In components the parallel transport condition is \frac{dx^\mu}{d\tau}\left(\partial_\mu X^\alpha +...

Would it be possible? -- A fifth mode of transport... There has been a lot of talk about developing a fifth mode of transport, and most of these involve some sort of tube such as the hyperloop idea from Elon Musk. Now I don't know why but I have the idea stuck in my head that the fifth mode of...

Hi, The transmission of nano devices are generally done without cosidering the spin polarization. However, as I saw in some papers, the effect of spin is sometimes included. How can I decide to use spin or not when simulationg transmission of nanoscale devices? Thanks in advance...

In GR, the geodesic equation for a test particle can be seen in 2 ways. (1) It is a fundamental postulate consistent with the EP that is experimentally verified. (2) It is derived from more fundamental postulates such as the Hilbert action with minimally coupled matter as an approximation...

One of these days on the TV I have seen news which has shaken me: Elon Musk has decided to intrigue the world - has declared that will soon open the project of essentially new personal transport. Which will move with speed of a sound, but will be cheaper than the plane . The construction cost...

Homework Statement Hi guys, I'm having trouble with a homework problem: I will have to solve for the IVP of a transport equation on R: the equations are: Ut-4Ux=t^2 for t>0, XER u=cosx for t=0, XER Homework Equations transport equation The Attempt at a Solution...

Hi guys, I'm having trouble with a homework problem: I will have to solve for the IVP of a transport equation on R: the equations are: Ut-4Ux=t^2 for t>0, XER u=cosx for t=0, XER I've actually never seen a transportation problem like this and any help would be...

I have a book on nuclear reactions which details the mean free paths for thermal neutron scattering as: 0.37cm for water and 2.2cm for heavy water The transport cross sections are listed as 0.45cm for water and 2.6cm for heavy water. Does anyone know how to calculate these from the thermal...

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for v-space (Velocity) or E-axis (Energy), since that will get me the wrong dimensions in the end. I...

Discussion

Homework Statement I will honestly be so grateful if someone can explain this to me. I am studying the Reynolds transport theorem, particularly mass conservation. I have read over my notes and I really do not understand how to calculate the mass flow rate through the control surface if it...

You've heard of "Snakes on a Plane", right? How about roaches on a bus?

Homework Statement An engineer is designing a system that requires transporting .01 m^3/s of helium at 15°C and 120 kPa. The velocity of the pipe is limited to 40 m/s. What size (diameter) of pipe is needed? My question is what equation do i need to solve this problem? Homework...

In neurons during re-polarization ATP is used to "actively transport" Na ions out of the cell and K ions into the cell. Does this mean that the ions are flowing against their concentration gradient or the word "actively transported" is just used because ATP is used in this process?

Before I ask the question, let me explain a little bit about myself. I graduated just over a year ago with a bachelors in Physics, and am now starting my first semester of grad school in Energy Engineering. I have been out of practice, and am facing major struggles getting back into my...

Author: R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot Title: Transport Phenomena, Revised 2nd Edition [Hardcover] Amazon Link: https://www.amazon.com/dp/0470115394/?tag=pfamazon01-20 Prerequisities: Advanced Calculus, Differential Equations (ODE, PDE), Introductory Heat Transfer...

I am a graduate student in physics. Can someone recommend a book that explores transport phenomena or diffusion from a physical sciences (instead of engineering) point of view? I would like that because I'm not dealing with industrial equipment and don't want to spend chapters wading through...

Hi everyone, I'm trying to design a simple model by using Comsol Multiphysics. I set an inlet concentration of a species "cp" that will be adsorbed to a circular surface located at the center of the microfluidic cell (I named the concentration of adsorbed protein "cpl" ). I used laminar flow...

Torsion has propped up in a couple of recent threads, but none of my texts really cover it well. Does torsion make parallel transport direction dependent? I.e. if we parallel transport some vector v "forwards" along a curve, and then "backwards" along the very same curve to its starting...

Hello, everyone! I'm studying Nakahara's book, Geometry, Topology and Physics and now studying the connection theory. I come across a problem. Please look at the two attachments. In the attachment , Nakahara said we could use the similar method in the attachment to get \tilde X, but why...

Hi! My friends and I have been working on a project which encapsulates the use of semi porous transparent membranes that can selectively pass glucose molecules through them in one direction. Does such a membrane already exist? Where can I get literature on the construction and/or existence of...

Hello! I have two questions for knowledge. Q) Explain under what conditions Maxwell Boltzmann and Fermi Dirac statistics are applied on free electrons. Q) Explain each parameter of Boltzmann Transport's equation. Thank you in advance. :-)

I'm listening to Prof. Leonard Susskind's lectures on GR on youtube.com at http://www.youtube.com/watch?v=hbmf0bB38h0&feature=relmfu He's trying to explain how to visualize parallel transport of a vector. But I'm having a hard time of it. I think I understand it. Let me know if I got it...

I am a physicist trying to understand the notion of holonomy in principal bundles. I am reading about the horizontal lift of a curve in the base manifold of a principal bundle (or just fiber bundle) to the total space and would like to relate it to the "classic" parallel transport one comes...

I've heard that gravitational fields carry energy themselves, and are therefore a source for their own existence. I take this as a "pre-requisite" of a sort for gravitational waves. If I were to shoot a high energy laser in space and cause a rippling effect of space-time. Could somebody...

The future of the automotive industry and transport in the us? Why will Americans never fully take to rail? Because we are adventurers by nature. The people that came to this Country had adventure in their blood. We like our cars, and we like em big and fast. So then I tell you Rail is the...

So Reynold's transport theorem states that \frac{\mathrm d}{\mathrm d t} \int_{V(t)} f \; \mathrm d V = \int_{V(t)} \partial_t f \; \mathrm d V + \int_{V(t)} \nabla \cdot \left( f \mathbf v \right) \; \mathrm d V. Now I would expect (on basis of conceptual reasoning) that if I were to apply...

So from what I understand if you pass a vector (using parallel transport) through a closed curve where there is curvature in the interior, the vector will come back not to it's original vector but with a changed sense. However if the vector is on a geodesic it will not change its sense after it...

Homework Statement Please show that the defining equation for the parallel transport of a contravariant vector along a curve \dot{\lambda}^a+\Gamma^a_{bc}\lambda^b\dot{x}^c=0 is coordinate-independent, given that the transformation formula for the christoffel symbol being...