Transport Definition and 265 Threads

I am really not all that intelligent and fairly new to the whole mathematical equation solving thing. So please bare with me, I came to the conclusion instead of reading the daily paper I will read daily articles, as I am reading I am unfamiliar of course with the symbols being undefined in the...

Homework Statement Show that \frac{d}{dt}\int \rho r^{2}\phi dr = \int \rho r^{2}\frac{d\phi}{dr} dr Homework Equations Fundamental theorem of calculus The Attempt at a Solution So I follow the derivation from the textbook and I think I get the rather sneaky rearrangement of...

Assuming that we are working with an infinitessimally small region of a manifold so that we can consider only first order effects, does parallel transport in the absence of torsion necessarily "close the quadrilateral"? What I mean is, if I have two vectors (very small vectors) V and U, and I...

Homework Statement See attached picture of the problem. Homework Equations See attached picture of the pair of diff equations. The Attempt at a Solution I was able to solve the problem up to the point the picture gets to. However, the author says he obtained this by integrating...

Hi All, I am an idiot but I don't understand the parallel transport: Parallel transport should be in surface right? How to keep parallel and still be in surface?

I have some questions about heat and moisture transport. 1. It is known that The water vapor permeability (μ) is a function of relative humidity (φ ) within the cavity of the porous materials: μ = B1 + B2 *exp(B3*φ ) where B1, B2 and B3 are coefficients of the water vapor permeability...

Hello, First of all, please excuse me if I posted in the inappropriate place.. While a student few years ago, I used to work a lot with advanced differential geometry concepts, but never got an intuitive view of HOW humanity got to think about parallel transport, why it contained two words...

I am facing a problem on transport phenomena. Can anyone help me to solve this problem. I would really appreciate it. Its little urgent. I know that i have to use shell mass balance to start the problem but how to proceed further is what making me confused. In a beaker, a solid sphere of...

how do you use the change of variable: \xi = x - ct on the PDE ut + c ux = 0 where u(t,x) = v(t,x-ct) = v(t,\xi) to get vt = 0 I am trying to follow the steps of Peter J. Olver in this document http://www.math.umn.edu/~olver/pd_/lnw.pdf starting on pg 4 but get stuck here...i...

Hi, I've begun learning about General Relativity, though I've already had some exposure to differential geometry. In particular, I understand that Lie Differentiation is a more "primitive" process than Covariant Differentiation (in that the latter requires some sort of connection). My...

Hi all, Can anybody explain the Transport Theorem (http://en.wikipedia.org/wiki/Rotating_reference_frame#Relating_rotating_frames_to_stationary_frames) in more non-physicist terms? I simply can't wrap my head around the visual of this theorem, which has the gist of: d/dt f = df/dt +...

Can anyone explain to me reynolds transport theorem in the simplest way possible? for eg, under what circumstances is it used...etc

As an aero, I'm rather interested on what PFers would feel about flying on an UAV airliner... I'm kind of mixed; on one hand I would have no problems, but on the other hand I know some of the people who would be designing the control laws! I don't think the general public would want to fly...

Hello everyone! I have been on this website for quite a while, and found some interesting answers to many questions, and I decided to create an account to seek you help with a particular issue I encountered in my assignment. Please have a read, and thank you for any input! Homework...

Any one have online documents showing the complete derivation of the both with the numerical solution ?

I'm looking at a coordinate system where \vec{s} is tangential to the ideal beam path \vec{S}(s) , and x and y are the horizontal and vertical displacement of the beam from this path s. I'm not understanding why a linear approximation of the momentum in the x direction would be p_x \approx...

i got this from my notws and i just can't seem to figure out how the second step is obtained? can someone explain to me where the where r's in the numerator came from on the second line when dividing by the volume of the shell?

On My Knees Need Help! to transport a load of 1kg up a ramp. Homework Statement Your group are required to design a transporter, A, which will be required to transport a load of 1kg up a ramp. The dimension of the ramp is shown in the figure below. The requirement of the transporter are: 1...

Hey guys, there is this superhard question (atleast for me). I've been trying at it for days but I seem to get nowhere. The Trans-Alaska Pipeline System (TAPS) carries around 100,000m3 of oil per day from the Northern Alaskan oil fields to the nearest ice-free port of Valdez, around 1300km...

Hi, I'm struggling to understand one step in the derivation of the Reynold's Transport Theorem. I get as far as: \begin{equation} \frac{d}{dt} \int_{V(t)} f(\mathbf x, t) \, dV = \frac {d} {dt} \int_{V_0} f(\mathbf X,t) J(\mathbf X,t) \, dV = \int_{V_0} J \frac {\partial f} {\partial t}...

Can anyone break down "quantum interference" in the tunneling transport through aromatic organic molecules? The Math is a little fuzzy, but with a few seminal reference or a conceptual description i might be able to wrap my mind lips around this knowledge pop! haha. any help would be appreciated.

Hi Folks, In the quantum transport, specially in calculating nano transistors' characteristics, we use a set of equations to find electron's density and specteral function. I want to know where they came from. The equations are : [G]: Green's function matrix [A(E)]: Spectral function f1...

If you walk at constant latitude with your arm always sticking towards the North pole, is that parallel transport of your arm? The equations don't seem to say it is. The vector field would be \vec{V}=V(\theta)e_\theta . The component of the vector only depends on theta, but at constant...

Can anybody explain in a few words these two modes of spin transport and what are the difference between them. Thanks.

I am having trouble understanding the concept of parallel transport of a vector along a closed curve. It is said that if the space where the curve resides has a curvature the orientation of the vector will change when it comes back to its original position. Can you help me in visualizing this...

Hi guys, here's my question: An accelerated observer (both in curved or non-curved space) who Fermi Walker transports his own basis vectors set along his world line will have the metric in the minkowsky form \eta_{\mu\nu} at each point of the world line? AND if the observer follows a...

Boltzmann transport equation & drift-diffusion equation ~ Plz help me! 1. From the Boltzmann transport equation, derive the energy conservation equation for mass conserving particles. Use the momentum equation to subtract the mechanical energy component, and then derive the equation for...

Hello. Do you know any textbook about Statistical Mechanics that discusses Boltzmann Transport Equation? It is not discussed in the textbooks that I know. Thank you.

Homework Statement If I have a two curves \gamma_{1}, \gamma_{2} with the same start and end points, lying on a smooth manifold M. For a vector v at the "start" point, if I parallelly transport down both curves to the "end" point, will the two vectors at the "end" be different or the same...

A large truck is to transport 30,000 Kg of orange pre-cooled to 4oC under average temperature of 27oC. The structure of the walls of the truck is such that the rate of heat transportation is UA=80W per oC temperature difference between the ambient and the oranges. From past experience, ambient...

If I know the metric everywhere, and I specify a closed path, how can I calculate whether a vector parallel transported around the path will return to being the same vector or not? I assume there is some simple integral to describe this, but I'm not sure how to write it down. Unfortunately...

Hello all: I'm a thermodynamicist wanting to get into transport modeling. In my reading, I have come across "operator splitting." I'm confused about exactly what this means in the context of transport modeling. This is probably a silly question, but does it refer to an advective term...

can anyone please explain me following errors of gyroscopes used in inertial navigation systems of aircraft : a) what is transport wander , how actually it happens ? b) what is apparent drift in gyroscope ? c) what is coriolis effect and how it causes errors in gyroscopes ?

I'm trying to understand parallel transport and I'm stuck. The example given is if you have a unit sphere and you take one of the latitudes (not the equator), take at a point on the latitude the tangent vector to the curve, and parallel transport it around the curve. I don't understand why the...

hi, i've never posted on here before but would appreciate any help given for this question. The scattering term (4th term) in the Boltzmann transport equation contains a double integral. What are you integrating over in each case and why is this? this may be a simple question but...

Homework Statement Attached image please, sorry I tried LaTeXing and i failed super hard. Homework Equations Fundamental Theorem of Calculus Multivariate chain ruleThe Attempt at a Solution I'm basically at a loss of words on this question. I might be thinking of this incorrectly but what my...

Hello all, I have a sort of fundamental question regarding charge transport problems. In general, the transport problems treated semi-classically using the Boltzmann Transport Equation and coupled with Maxwell's equations. Specifically, I am contemplating a traveling wave problem. where...

A vector field Y is parallely propagated (with respect to the Levi-Civita connection) along an affinely parameterized geodesic with tangent vector X in a Riemannian manifold. Show that the magnitudes of the vectors X, Y and the angle between them are constant along the geodesic.

I have to identify whether the following are primary active transport, secondary active transport, or passive transport. Then I have to decide what is the energy source: a chemical reaction, concentration gradient of cotransported ion, or conc gradient of transported solute. Below are my...

Many groups have created Boltzmann solvers for photon/neutron transport simulations of reactors over the years - but has anyone released their code? I am specifically interested in Boltzmann solvers, not Monte Carlo based calculations. If you know of any open source projects, please let me know...

I want to combine the advective transport equation for two solutes such that dC1(z)/dt=D(d2C1(z)/dz2)-v dC1(z)/dz + J1 and dC2(z)/dt=D(d2C1(z)/dz2)-v dC2(z)/dz + J2 where C is the concentration in the fluid, t = time, z = distance, v = velcity, D = dispersion coefficient, and J is a...

Homework Statement Use a shell balance method to derive the equation governing the two dimensional temperature distribution,u, in a circular disk in polar coordinate system(r,theta). allow for the possibility of differing thermal conductivities in the r and theta directions. Homework...

A boat is jet-propelled by a pump that develops a volume flow rate Q and ejects water out the stern at velocity v'. If the boat drag force is F=kv^2 where k is a constant, develop a formula for the steady forward speed v of the boat.

Hello i just joined this forum because i had an idea that i think, if it hasnt already been thought of would be a unique mode of transport over short distances, its based on the maple seed, basically it would be a single seat mono blade helicopter, the actual blade would be above the...

Hi! I've finally decided to tackle a diff geom book, but I'm having trouble with this Problem 4/Chapter 2 from Do Carmo's Riemannian Geometry: Let M^2\subset R^3 be a surface in R^3 with induced Riemannian metric. Let c:I\rightarrow M be a differentiable curve on M and let V be a vector...

This is what I currently understand by parallel transport. The definitions I've read don't talk about it in quite this way, as a vector field, but I think this is equivalent to them: Given a tangent vector V0 at some point P0, construct a vector field along an oriented curve P(?), where ...

Could anyone give me a descriptive picture on WHY geodetic precession occurs? I understand the equations from which it follows, so I can derive it algebraically, but I would like to get an intuitive feeling of why it occurs too. My problem is the following: parallel transport of vectors along...

Homework Statement in Intrinsic GaAs,electron and hole mobility are 0.85 and 0.04 meter square/volt-sec and corresponding effective mass are 0.068m and 0.5m, where m=9.11*10^(-31)kg. band gap energy is 1.43 eV at 300K. ---calculate intrinsic carrier concentration(!) and Conductivity. Homework...

I'm trying to show that \frac{d}{dt}\; g_{\mu \nu} u^{\mu} v^{\nu} = 0 in the context of parallel transport (or maybe not zero), and I'm rather insecure about the procedure. This is akin to problem 3.14 in Hobson's et al. book (General Relativity an introduction for physicists). As a guess, I...

Homework Statement The latex document for these equations wasnt updating correctly, so I've included them as an attachment wherever there is a ... in the text Ok, I am trying to understand the Reynolds transport theorem, but i don't understand part of it. Homework Equations This is the...