Boundary Definition and 900 Threads

Homework Statement At the boundary between water (n=1.33) and flint glass (n=1.66), incoming light at ~49 degrees from the normal is refracted. Of course, I can use Snell's law to calculate the angle of refraction. However, my question is whether any of the light at this boundary is also...

Not really a specific problem, but just a general question: Does anyone have any good references (preferably online) for solving E&M problems with this method? I'm using Griffith's Electrodynamics book for my class and I'm trying to get ready for a final. This is the only part I'm having...

This problem arises in a paper on population genetics (Kimura 1962). 1. The problem statement Let f(p) = \int_0^p ((1 - x)/x)^k dx. For a small value of p, we have approximately f(p) = (p ^ (1-k)) / (1-k) How is this obtained? 2. My attempt at a solution I tried to expand the f(p) around p =...

Hey all, First off, I'd like to mention that I am completely unfamiliar with this ANSYS and have been fighting with this program for last 2 and half weeks. Any feedback and help is greatly appreciated! Please refer to the photos attached for referral. My project currently involves analyzing...

I have a problem how to select the boundary condition when i answer this deflection of beam. for example: the boundary condition is [x=o,y=0],[x=l,y=0],[x=o,dy/dx=o] and [x=L,dy/dx=0] given that EIdy/dx= Ax+wx^2/2 EIy= Ax^2/2+wx^3/6 anybody can tell me how to select this?

\begin{align} \varphi''+\lambda\varphi &= 0, & \quad 0< x < L\\ \varphi'(0) &= 0 &\\ \varphi'(L)+h\varphi(L) &=0, & \quad h\in\mathbb{R} \end{align} $$ \varphi = A\cos x\sqrt{\lambda} + B\frac{\sin x\sqrt{\lambda}}{\sqrt{\lambda}} $$ Since $\varphi'(0) = 0$, $\varphi = A\cos x\sqrt{\lambda}$...

Hi, I'm not sure if this is on the right thread but here goes. It's a perturbation type problem. Consider the boundry value problem $$\epsilon y'' + y' + y = 0$$ Show that if $$\epsilon = 0$$ the first order constant coefficient equation has the solution $$y_{outer} (x) = e^{1-x} $$...

Hi, I'm not sure if this is on the right thread but here goes. It's a perturbation type problem. Consider the boundry value problem $$\epsilon y'' + y' + y = 0$$ Show that if $$\epsilon = 0$$ the first order constant coefficient equation has the solution $$y_{outer} (x) = e^{1-x} $$ I have...

The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces. So, for example, in a shearing flow where there is a moving surface, the fluid velocity at the fluid/surface interface has to...

The Hubble radius R is defined by: R(t) = c / H(t) where H(t) is the Hubble parameter which is a function of time. Objects beyond the Hubble radius are receeding from us faster than the velocity of light. At first glance one would think that light from those objects can never reach us...

Homework Statement Find the eigenvalues and eigenfunction for the BVP: y'''+\lambda^2y'=0 y(0)=0, y'(0)=0, y'(L)=0 Homework Equations m^3+\lambdam=0, auxiliary equation The Attempt at a Solution 3 cases \lambda=0, \lambda<0, \lambda>0 this first 2 give y=0 always, as the only...

Hi, I'm currently working on a thesis in Economics. I have stumbled upon a system of differential equations that needs to be solved. I am stuck, and have trouble getting the right help from my advisor who is also not very acquainted with numerical methods. For the past couple of days I have...

Homework Statement Let X be a metric space, and A its nonempty proper subset. Then is \partial A not open? If it is, how do I prove it? Could you give me just some hints, not the whole solution? Homework Equations The Attempt at a Solution I cannot even start..

Homework Statement y"+xy'=cos(2x), y(0)=1, y'(5)+2y(5)=10 Homework Equations The Attempt at a Solution I am trying to solve this using matlab. I split the 2nd order d.e. into 2 first order d.e.'s. I set y1=y, and y2= dy/dx. Thus dy1/dx=y2 and dy2/dx= cos(2x)-x*y2. Then dy/dt=...

Hello, I was wondering if anyone can help me with my FEA approach. I want to check that my boundary conditions for a simple quarter torus (representing a section of a helical spring) are correct. I'm neglecting the helical angle at this stage. I have fixed one end in all axes, and applied...

Hello, I am trying to solve a vibration problem analytically but I don't understand how to implement the non-homogeneous boundary conditions. The problem is defined as below: y_{t}_{t}(x,t) = a^{2}y_{x}_{x}(x,t) With Boundary conditions: y(0,t) = 0 [ fixed...

I came across this statement from James Hartle on Stephen Hawking's website, http://www.hawking.org.uk/ and wondered where you see this proposal currrently [Hartle sure seems to think it explains an awful lot] : James Hartle: Wikipedia has a brief discussion here...

This is the problem I'm working on: http://i.imgur.com/PBMFG.png I'm very behind with normal modes and waves, and I need to figure out how to do this sort of question in time for my exams, so I'm hoping that you guys will be able to help me see how this can be answered. I've answered the...

Hi all, I am looking to learn more about boundary layer control devices that can delay boundary layer transition (Laminar to Turbulent) and also BL devices that can delay flow separation. I have already found loads of info on Vortex Generators but i am having trouble finding info on things...

Homework Statement Solve: y'' - λy = 0 where y(0)=y(1)=0, y=y(t) Homework Equations The Attempt at a Solution Hi everyone, This is part of a PDE question, I just need to solve this particular ODE. I know how to do it in the case for y'' + λy = 0, where you get the...

This is the problem I'm working on: http://i.imgur.com/PBMFG.png I'm very behind with normal modes and waves, and I need to figure out how to do this sort of question in time for my exams, so I'm hoping that you guys will be able to help me see how this can be answered. I've answered the...

I am working on an assignment here; A linear chain with a two-atom primitive basis, both atoms of the same mass but different nearest neighbor separation and thus different force constants. I have made a rigorous calculation in order to find the dispersion relation ω(k), with extensive...

Hi there: I am trying to solve a two points boundary value problem. Consider a function f:[x1,x2]->[x2,x3] x1 and x3 are knowns x2 is an unknown parameter f'(x) = exp( -a*x + b*f(x) ) where b>a>0 Two boundaries conditions: f(x1) = x2 f(x2) = x3 Does anyone know how to...

Homework Statement Here's the question: Use laplace transforms to find X(t), Y(t) and Z(t) given that: X'+Y'=Y+Z Y'+Z'=X+Z X'+Z'=X+Y subject to the boundary conditions X(0)=2, Y(0)=-3,Z(0)=1. Now I have learned the basics of laplace transforms, but have not seen a question in...

If we place an infinite conducting sheet in free space, and fix its potential to \varphi_0, how do we solve solve for the potential on either side of the sheet? Since the potential blows up at infinity, it seems impossible to define boundary conditions.

Homework Statement Suppose that T(x, y) satisfies Laplace’s equation in a bounded region D and that ∂T/∂n+ λT = σ(x, y) on ∂D, where ∂D is the boundary of D, ∂T/∂n is the outward normal deriva- tive of T, σ is a given function, and λ is a constant. Prove that there is at most one solution...

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...

The radius of convergence of \sum\limits_{k=1}^\infty\displaystyle\frac{z^n}{n} is 1. It converges on all of the boundary \partial B(0,1) except at z=1. One way of looking at this is to analyse \sum\limits_{k=1}^\infty\displaystyle\frac{\cos n\theta}{n}+\frac{\sin n\theta}{n}. You can see the...

First off, I've never taken a differential equations class. This is for my Math Methods for Physicists class, and we are on the topic of DE. Unfortunately, we didn't cover this much, so most of what I am about to show you comes from the professor giving me tips and my own common sense. I'd...

Hi All, I was reading this paper the other day and I've been trying to find the numerical techniques its mentions but have been thus far unsuccessful. The authors simply state that is well know and straightforward, and they believe this so much that they don't even include a reference. Ok...

Is it true, that if A and B are oriented manifolds with boundary, having dimensions n and m respectivelly, then the boundary of A\times B is \partial(A\times B)=\partial A\times B + (-1)^n A\times \partial B? If not, then what can we say about the boundary of product manifolds? Could someone...

In solving a flux integral over a flat surface, inclined above the xy-plane, does the boundary of the surface influence the flux only through the integral limits? (and not through its normal vector) Let's say that there is an elliptic surface inclined above the xy-plane. The orientation is...

I need to apply D'Lembert's method but in this case I don't know how. How to proceed? Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions: $\begin{aligned} & u(x,0)=\left\{ \begin{align}...

Homework Statement Solve Laplace's equation u_{xx} + u_{yy} = 0 on the semi-infinite domain -∞ < x < ∞, y > 0, subject to the boundary condition that u_y = (1/2)x u on y=0, with u(0,0) = 1. Note that separation of variables will not work, but a suitable transform can be applied...

http://img821.imageshack.us/img821/7901/heatp.png Uploaded with ImageShack.us I'm having difficulty with the boundary conditions on this problem. I don't need a solution or a step by step. I've just never solved a boundary condition like this. Its the u(pi,t) = cos(t) that is giving me...

Hi all, I was wondering if anyone knows of any literature that explains why larger grains "absorb" smaller grains during cross-boundary diffusion in solid state diffusion. I read a book that explains it analogously in terms of pressure differences and boundary tension but I'm not quite happy...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0 \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1, \\ & {{u}_{x}}(0,t)=0=u(1,t),\text{ }t>0. \end{aligned} $ Here's something new for me, the boundary...

Hello, whenever I come to the derivation of the Fresnel equations I get stuck on the boundary condition for the component of the E-Field that is parallel to the surface. I know for the parallel components Maxwell dictates that: E_{1t} = E_{2t}. For the parallel incoming light field...

user meopemuk mentioned this: In the case of a crystal model with periodic boundary conditions, basis translation vectors e1 and e2 are very large (presumably infinite), which means that basis vectors of the reciprocal lattice k1 and k2 are very small, so the distribution of k-points is very...

Well as the topics says I need a clarification why do we need the so called boundary conditions? I have seen it in electostatics, magnetostatics etc. I tried in many ways to get that stuff into my head, but its just only banging my head not getting into.. I really wana know what is that and...

Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed Dirichlet-Neumann boundary conditions. Maybe someone here can help me and point to a book or article where I...

ansys -- Boundary conditions for 2 cylinders and fluid i want to do a analysis in ansys in which a cylinder will rotate about a axis which is out side of the cylinder and this cylinder is also rotating about its own axis. cylinder is half filled with liduid. i want to do the stress analysis or...

I'm having a ton of trouble understanding how to solve diff eqs by using Fourier or laplace transforms to solve for the green's function, with boundary conditions included. I can understand the basics of green's function solutions, especially if transforms are not needed, but my textbook seems...

1) Transform the problem so that boundary conditions turn to homogeneous ones assuming that $g_0$ and $g_1$ are differentiable. $\begin{align} &{{u}_{t}}=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ &{{u}_{x}}(0,t)={{g}_{0}}(t),\text{ }{{u}_{x}}(L,t)={{g}_{1}}(t),\text{ for }t>0, \\...

1) Solve $\begin{aligned} {{u}_{t}}&=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ {{u}_{x}}(0,t)&=0,\text{ }{{u}_{x}}(L,t)=0,\text{ for }t>0, \\ u(x,0)&=6+\sin \frac{3\pi x}{L} \end{aligned}$ 2) Transform the problem so that the boundary conditions get homogeneous: $\begin{aligned}...

I like to know if electromagnetic waves pass through a medium (Glass) and if this medium were in contact with two other mediums in its boundary which the first one with same optical dense (Glass) and the second with less optical dense (air). Is there any tendency or priority for wave to pass...

Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am...

http://imageupload.org/getfile.php?id=171120&a=a955b8cf905480ad89ee96abfea140da&t=4f27421f&o=36BBD6199C49C981F6CC7562A37DC69B664D4F14FBA06DFCF24E9B24875233233B2BA7CB1980&n=%E6%9C%AA%E5%91%BD%E5%90%8D.png&i=1 I have just been given the question without much support so I can't even get a...

Homework Statement From a previous exercise (https://www.physicsforums.com/showthread.php?t=564520), I obtained u(r,\phi) = \frac{1}{2}A_{0} + \sum_{k = 1}^{\infty} r^{k}(A_{k}cos(k\phi) + B_{k}sin(k\phi)) which is the general form of the solution to Laplace equation in a disk of radius a. I...

So I'm reading through Jackson's Electrodynamics book (page 39, 3rd edition), and they're covering the part about Green's theorem, where you have both \Phi and \frac{\delta \Phi}{\delta n} in the surface integral, so we often use either Dirichlet or Neumann BC's to eliminate one of them. So for...