Boundary Definition and 1000 Threads

For a parallel polarization EM hitting the conductor boundary in an oblique angle. z axis is perpendicular to the boundary and point into the conductor. y-axis it out of the page which give x pointing up. Let the boundary surface by xy plane. With this: The direction of the incident is...

Standard electrostatics problem (in spherical polar coords): spherical cavity of radius R in an infinite dielectric of permittivity ε centred at origin of the coord system. Surface charge stuck on to the cavity: \sigma(\theta) = \sigma_0 \cos (\theta) Problem is to find the potential in...

Homework Statement "Solve for t > 0 the one-dimensional wave equation \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2} with x > 0, with the use of Fourier transformation. The boundary condition in x = 0 is u(0,t) = 0. Assume that the initial values u(x,0) and...

If a PDE has no boundary conditions specified, how does one go about providing a solution--even if this is a general solution? I'm stuck looking at the separation of variables and other methods which all seem to heavily rely on those boundary conditions and initial conditions. If anyone...

Homework Statement A cantilever beam has uniform load w over a length of L as described by the eq. EI y'''' = -w y(0) = y'(0) = 0 y''(L) = y'''(L) = 0 EI are constants find y(x) Homework Equations L[y^4] = S^4*Y(s) - S^3*Y(0) - S^2*Y'(0) - s*Y''(0) - Y'''(0) The...

I'm playing with the PDE toolbox in Matlab and solving Laplace's equation, ∇2V = 0, for various electrostatic geometries. I say 'playing' because I started in the wrong end (or right end, depending on how you look at it) by simple trial and error until the solutions looked like something...

Klein–Gordon equation with time dependent boundary conditions. Suppose we look for solutions to the Klein–Gordon equation with the following time dependent boundary conditions, psi(r,theta,phi,t) = 0 zero at infinity psi(on surface of small ball, B_1,t) = C*exp[i*omega*t] psi(on...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Homework Statement Find the area of the surface that is the boundary of the region enclosed by the surfaces x^{2}+y^{2}=9 and y+z=5 and z=0 Homework Equations A(S)=\int\int_{D}\left|r_{u}\times r_{v}\right| \; dA The Attempt at a Solution I am really confused as to what he...

Homework Statement Find the closure, interior, boundary and limit points of the set [0,1) Homework Equations The Attempt at a Solution I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be...

No, the boundary operator is not relative--sorry, Einstein . I mean, the boundary operator in relative homology. I have seen it defined in two different ways , which I do not believe are equivalent to each other: Given a pair (X,A), A<X, and Del is the Bdry. operator on...

Alternative boundary conditions -- Thomas-algorithm Hello, I have to solve a diffusion equation: MatrixL * Csim(:,i+1) = MatrixR * Csim(:,i) + BoundaryConditions where Csim = concentration, j = location, i = time. Boundary conditions are of type Dirichlet (Csim = 5 at j = 1, Csim = 0...

The greatest problem of thermoelectrics is the need to maintain very low thermal conductivity. How is it possible that pyroelectrics do not have this limitation and do not need temperature differences to produce electricity from heat?If we will heat all pyroelectric body uniformly it will still...

Homework Statement So we have a string of N particles connected by springs like so: *...*...*...*...* A corresponding Hamiltonian that looks like: H= 1/2* \Sigma P_j^2 + (x_j - x_(j+1) )^2 Where x is transverse position of the particle as measured from the equilibrium position, and...

Homework Statement I am trying to solve the Laplacian Equation with mixed boundary conditions on a rectangular square that is 1m x 1m. Homework Equations \nabla2T=0 .....T=500K ....________ ....|@@@@| T=500K...|@@@@|...T=500K ....|@@@@| ....|______.| ....Convection ....dT...

I understand \vec J_{free} only exist on boundary surface of perfect conductors. Copper is close enough and have surface current. Also copper is paramagnetic material which implies \mu_{cu} = \mu_0 or very very close. In order to find the exact angle of the of the magnetic field inside the...

Homework Statement I have to study the limit of a sequence which is defined as follows. I'm not looking for an answer, just a method of how to do it, or even what this notation means. An = { (\frac{n^{2}}{3n^{3}+1}, \frac{4n^{2}}{n^{2}+1} ] n even An = { (\frac{n^{2}}{6n^{2}-4}...

Why does the grain boundary cut directly through a particle, instead of looping around the particle's surface?

boundary conditions for pressurized cylinder in fem?

My understanding of: \int_S \nabla X \vec{H} \cdot d\vec{S} = \int_C \vec{H} \cdot d \vec{l} = I Means the current I creates the magnetic field in the form of \nabla X \vec{H} instead of magnetic field creates the current I. But in the boundary condition, it claims the tangential...

Thant helped. thank you!

Suppose I want to integrate f(z)(z-a)^{-1} where |a|=1 over the circle |a|=1, why is it that: f(a)=\frac{1}{\pi i}\int_{|z|=1}\frac{f(z)}{z-a}dz instead of: f(a)=\frac{1}{2\pi i}\int_{|z|=1}\frac{f(z)}{z-a}dz

Homework Statement Use a Green's function to solve: u" + 2u' + u = e-x with u(0) = 0 and u(1) = 1 on 0\leqx\leq1 Homework Equations This from the lecture notes in my course: The Attempt at a Solution Solving for the homogeneous equation first: u" + 2u' + u = 0...

Hi All, I am trying to convert a file that has three arrays of 528 samples into three arrays of 301. The first is log spaced frequency points the second is the impedance values at each frequency and the last is phase values. I have the routines spline and splint. My problem is the the second...

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

Homework Statement A point charge Q is at the boundary plane of two infinite, homogeneous dielectrics with dielectric constants \epsilon_1 and \epsilon_2. Calculate the electric potential, the electric field and the displacement vector at any point in space. Homework Equations...

Determine the boundary of A. A= (-1,1) U {2} with the lower limit topology on R What I know is that the topology defines open sets as those of the form [a,b). In this case, if they want an interval in the form of [a,b) for the interior, then it comes to mind that [0,1) would be the...

Homework Statement S = Set of rational numbers Boundary(interior(S)) = ? The Attempt at a Solution I have no Idea how to do this, I don't know what interior of the rational numbers are. Maybe you guys could give an example of like the interior of the natural numbers or the boundary of the...

Let E be a subset of R2 that is non-empty, compact, and connected. Suppose furthermore that E is the union of a countably infinite number of almost disjoint closed cubes {Ri} with non-zero volume. Is there anything interesting about this set, particularly its boundary? Can it have infinite...

Homework Statement http://img843.imageshack.us/img843/3515/11193469.png Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img801.imageshack.us/img801/4829/scan0001i.jpg An upload of my attempt to solve the problem. Not sure to interpret the results. A = B...

Homework Statement http://img685.imageshack.us/img685/5585/63862334.png Homework Equations -The Attempt at a Solution y_1(0,t)=y_2(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} = \frac{C}{A} y_1_x(0,t)=y_2_x(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} =\frac{k_2}{k_1}...

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

what is the real boundary(or difference) between discrete&continous(as the title)? my major is physics and i find that scientists are dealing with the different treatment to these two kinds of phenomenons, but what is the real boundary? by this i mean what they actually are and how they ARE...

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...