Boundary Definition and 900 Threads

Homework Statement Find the general solution to the boundary value problem. Homework Equations (xy')' + \lambda x^{-1}y = 0 y(1) = 0 y(e) = 0 use x = e^t The Attempt at a Solution x = e^t so \frac{dx}{dt} = e^t using chain rule: y' = e^{-t}\frac{dy}{dt} Substituting...

Homework Statement d^2T/dx^2 + S^2*T+B=0 Boundary Conditions: dT/dx=0 @ x=0 T=T_2 @ x=L Homework Equations The Attempt at a Solution I think you either have to make some type of substitution or find the roots and do it that way. P.S. This is assignment is a review of diff...

Homework Statement d^2T/dx^2+S/K=0 Boundary Conditions T=Tsub1 @ x=0 and T=Tsub2 @ x=L Homework Equations The Attempt at a Solution d^2T/dx^2 = -(S/K) <--- intergrate to get dT=-(S/K)dx+ C1 <--- intergrate to get T=(-S/K)x+c1+c2 apply both boundary conditions to get...

hi all, I am trying to solve this PDE by separation of variables, it goes like this: \frac{\partial u}{\partial t} = \alpha\frac{\partial ^2 u}{\partial z^2} for 0\leq z\leq infty the initial condition I have is: t=0; u = uo. the boundary condtions: z=0; \frac{\partial...

How to derive boundary conditions for interfaces between ferromagnetic material and air? Please see the attached figure. Any hints will be greatly appreciated!

Hi, these days I have been trying to understand the essentials of the so-called topological insulators (TBI), such as Bi2Te3, which seem very hot in current research. As i understand, these materials should possesses at the same time gapped bulk bands but gapless surface bands, and spin-orbit...

can anyone provide a Numerical algorithm to solve -y'' (x) +f(x)y(x) = \lambda _{n} y(x) with the boundary condition y(0)=y(a)=0 here 'a' is a parameter introduced at hand inside the program and f(x) is also introduced by hand in the program i am more interested in getting...

Hi folks, I was wondering how to code a Maxwell solver for a problem with time-dependent boundary conditions. This is not my homework, but I love programming and would like to implement what I learned in my physics undergrad course to get a better understanding. More precisely, if I have an...

Boundary Value Problem + Green's Function Consider the BVP y''+4y=e^x y(0)=0 y'(1)=0 Find the Green's function for this problem. I am completely lost can someone help me out?

Homework Statement I need to prove that the int(U union Bdy(U))=Int(U) when U is open. Homework Equations Bdy(U)=closure(U) intersect closure(X-U) a point is in the interior if there is an open neighborhood of the point that is contained in the set. The Attempt at a Solution...

let be the two boundary value problem -D^{2}y(x)+f(x)y(x)= \lambda _{n} y(x) with y(0)=0=y(\infty) and the same problem -D^{2}y(x)+f(x)y(x)= \beta _{n} y(x) with y(-\infty)=0=y(\infty) i assume that in both cases the problem is SOLVABLE , so my question is , are the eigenvalues in...

Let me see if I can line out my question a little better to hopefully get some sort of input. I am trying to understand where a type of boundary condition approx. called stiff spring BCs. I have, among a couple of other examples, an example comsol "dialysis" model that uses it. I have been...

Are there general boundary conditions for the wave equation PDE at infinity? If there is, could someone suggest a book/monograph that deals with these boundary conditions? More specifically, if we have the following wave equation: \[ \nabla ^2 p = A\frac{{\partial ^2 p}}{{\partial t^2...

I have dealt quite a lot with the boundary value electrostatics problem with a plane or spherical conducting surface in an electric field due to a single electric charge or dipole. This can be conveniently done using the method of images. Method of images simplifies a lot of things. Jackson's...

I am trying to write a solver for a 1D wave equation in MATLAB, and I have run into interesting problem that I just can't find a way out of. I start with the wave equation, and then discretize it, to arrive at the following, U{n+1}(j)=a*(U{n}(j+1)-2*U{n}(j)+U{n}(j-1))+2*U{n}(j)-U{n-1}(j)...

This is a topic in multi-variable calculus, extrema of functions. Our professor wrote: Boundary points: points on the edges of the domain if only such points stationary: points in the interior of the domain such that f is differentiable at x,y and gradient x,y is a zero vector...

1. Hi i need help with this question, Show, using maxwell's equations as a starting point, that the discontinuity in the component of the electric displacement normal to a boundary between different media is equal to the free surface charge density on a boundary. i have tried by using the...

Homework Statement I'm getting through a paper and have a few things I can't wrap my head around. 1. In defining the boundary conditions for a membrane (a function of vector 'r'), the author claims that for a small displacement (u) and a boundary movement (f), the boundary condition can be...

It's obvious that if Maxwell equations are fulfilled by some E(x,y,z,t) and B(x,y,z,t), they are also fullfiled by E(x,y,z,t)+ E_0 and B(x,y,z,t)+B_0, where E_0 and B_0 are constants. This freedom has physical significance as it changes the Lorentz force which act on a charge. It...

Consider the BVP y''+4y=f(x) (0\leqx\leq1) y(0)=0 y'(1)=0 Find the Green's function (two-sided) for this problem. Working: So firstly, I let y(x)=Asin2x+Bcos2x Then using the boundary conditions, Asin(2.0)+Bcos(2.0)=0 => B=0 y'(x)=2Acos(2x)-2Asin(2x) y'(0)=2A=0...

I have this, probably quite simple, problem. In the RNS superstring, when varying the action, we obtain in general a term \int d\tau [X'_{\mu}\delta X^{\mu}|_{\sigma=\pi}-X'_{\mu}\delta X^{\mu}|_{\sigma=0} + (\psi_+ \delta \psi_+ - \psi_- \delta \psi_-)|_{\sigma=\pi}-(\psi_+ \delta \psi_+ -...

Hi, I just can't understand the basics with BZ. How do I find the shortest distance to the BZ boundary, how do I compare the electron energy between the last electron in the 1st BZ with the first electron in the 2nd BZ? I think I need a visual how to calculate these things, does anyone...

Hello all,Suppose C\subseteq \mathbb{R}^{n}, if x \in \text{bd}\;C where \text{bd} denotes the boundary, a sequence \{x_{k}\} can be found such that x_{k} \notin \text{cl}\;C and \lim_{k\rightarrow \infty}x_{k} = x. The existence of such sequence is guaranteed by the definition of boundary...

Hallo Every one, Homework Statement y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct) Boundary Condition: y(0,t)=y(2pi,t)=(1/c)sin(ct) fot t>0 Initial Condition : y(x,0)=sin(x),( partial y / Partial t ) (x,0) = cos(x) for 0<x<2pi show that y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct)...

Homework Statement y''+\lambday=0 y'(0)=0 y'(pi)=0 Homework Equations The Attempt at a Solution What's puzzling me is the case when we check if the eigenvalue is zero. y''=0 y'=C1 y=C1x+C2 Now when I check the first boundary value I get C1=0 now How do I check the second one ? with the...

Homework Statement y'' + ßy = 0, y'(0)=0, y'(L)=0 Homework Equations Meh The Attempt at a Solution I so already did the ß>1 and ß<1; I'm stuck on the ß=0. It seems easy enough. y'' = 0 -----> y' = A -----> 0=A, 0=A (from the two initial conditions) ------> No...

Let's consider two media with magnetic permeability \mu_1, \mu_2 . What's the condition for magnetostatic vector potential \vec{A} on the boundary. Is it true that its tangent component should be continuous. Thanks for replay.

Is it true that there always exists Green's function for Dirichlet boundary problem. I mean a function G(r,r') which fullfils the following conditions: div (\epsilon grad G(r,r')) =- \delta(r,r') inside volume V and G(r,r') is 0 on boundary of V. If V is whole space there exists obvious...

Homework Statement So using the D'Alembert solution, I know the solution of the wave equation is of the form: y(x,t) = f(x-ct) + g(x+ct) I'm told that at t=0 the displacement of an infinitely long string is defined as y(x,t) = sin (pi x/a) in the range -a<= x <= a and y =0...

show for two positive numbers x,y>0 that limit for n->infinity : \sqrt[n]{x^n+y^n} = max {x,y} i don't know how to make a upper boundary(lower boundary is >0 i suppose) something like assume for instance x bigger than y and than make a boundary with it, but how?

Hello everybody, I've been puzzling over something (quite simple I assume). Take S^1. Now consider the action of a Z_2 which takes x to -x, where x is a natural coordinate on the cylinder ( -1< x <1). Now we mod out by this action. The new space is an orbifold: smooth except at x=0. It...

1. I have a rod of length 4,cross section 1 and thermal conductivity 1.Nothing is mentioned about the end at the origin x=0, but at the opposite end x=4, the rod is radiating heat energy at twice the difference between the temperature of that end and the air temperature of 23 celcius. Find the...

If space is expanding then at at some point we must reach the point where it's expansion is faster than C. Do we know where that is? Is the expansion uniform or is it dependent on something like Dark Matter clusters? Is the expansion accelerating or decelerating at two fixed points? In...

Apparently Fluent has this thing called an "overflow" boundary condition. I tried searching the help files and found absolutely nothing about it. Does anyone know what this is and why someone would want to use it?

Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...

Homework Statement A string is attached to a ring of mass m which is free to move up and down a frictionless pole. The string is subject to tension T and its mass per unit length is \rho. The displacement of the string from its equilibrium position along the x -axis is y(x,t). The boundary...

Homework Statement Find the solution to the two-point boundary value problem u'' + 4u' + exu = sin(8x) with u(-1) = u(1) = 0. Homework Equations The Attempt at a Solution I haven't taken an ODE course in years but I need to verify that my numerical solution to the ODE is accurate to the...

So here's the problem: I'm asked to find the solutions to the 1-D Wave equation u_{tt} = u_{xx} subject to u(x,0) = g(x), u_t(x,0) = h(x) but also u_t(0,t) = A*u_x(0,t) and discuss why A = -1 does not allow valid solutions. I can't figure it out at all. The solutions to...

I want to solve: y(x)''-(\frac{m\pi}{a})^2y(x)=0 With boundary condition y(0)=y(a)=0. First part is very easy using constant coef. which give: y(x)=c_1 cosh(\frac{m\pi}{a}x) + c_2 sinh(\frac{m\pi}{a}x) y(0)=0 \;\Rightarrow\; c_1=0 \;\Rightarrow\; y(x) = c_2 \; sinh(\frac{m\pi}{a}...

Homework Statement Consider the Heat Equation： du/dt=k(d2u/dx2), where d is a partial and d2 is the second partial. The B.C.'s are u_x(0,t)=u(0,t) and u_x(L,t)=u(L,t), where u_x is the partial of u with respect to x. The I.C is u(x,0)=f(x) Now, consider the Boundary Value Problem...

Homework Statement The problem is write this d\Psi/dy(d^2\Psi/dxdy)-d\Psi/dx(d^2\Psi/dy^2=-\nu(d^3\Psi/dy^3) in the form of -ff''=f''' where \Psi(x,y)=-sqrt(V*\nu*x)f(\eta) f(\eta)=integral(from 0 to \eta)(\Pi')*(\overline{\eta})*d(\overline{\eta}) where \overline{\eta} is a dummy...

Hello, I am looking for a reference which has solutions for the laminar flow boundary layer for the following scenario: circular cylinder, L>>d, length in direction of flow, with flat circular cap uniform laminar flow inviscid, incompressible fluid In other words, I would like the...

I was reading a website that said the boundary of a set's boundary is equal to the first boundary. Visually, this makes sense for subsets of R1 and R2 because the first boundary will not have an interior (no ball about the points will fall into the boundary). However, the reading went on to...

For a string with one endpoint attached to a wall and the other to an oscillator (so that it is under boundary conditions), what is the character of waves that are not at a harmonic frequency?

Homework Statement A high temperature, gas cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (Ka=57 W/m*K) is encased in graphite (Kb= 3 W/m*K) and gaseous helium flows through an annular coolant channel. Consider conditions for which the helium...

Hi there, I recently read that the equations of motion for an classical open string naturally give rise to two boundary conditions, namely Dirichlet and Neumann boundary conditions. (i) Could someone explain to me what do these boundary conditions physically mean, in particular for open...

Hello all, This is to do with forced longitudinal vibration of a rod (bar). It's basically a problem to do with the linearised plane wave equation (1d). The rod is fixed firmly at one end, and excited at the other by a harmonic force. The wave equation (with constant rho/E instead of...

Homework Statement Find the potential outside of a long grounded conducting cylindrical rod of radius R placed perpendicular to a uniform electric field E0. Homework Equations V(s,\phi) = a_{0}+b_0{}ln(s) + \sum(A_n{}cos(n\phi)+B_n{}sin(n\phi))*(C_n{}s^n{}+D_n{}s^{-n}) The sum being...

Hey all, I am try to model a problem in which one fluid (of known properties) sits on top of another fluid (with different properties) and there is an imposed slip boundary condition at the interface. I'm wondering if COMSOL has a Slip boundary condition that can be readily used or if...

Hi, I am in Purcell's E&M book at the section explaining why the field is zero inside a hollow conductor of any shape. The proof given is that the potential function inside the conductor must obey Laplace's equation, and that the boundary of the region (in this case a rectangular metal box) is...