Boundary condition Definition and 136 Threads

I have a simple question about Lewkowycz and Maldacena's paper http://arxiv.org/abs/1304.4926v2'][/PLAIN] http://arxiv.org/abs/1304.4926v2 In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field, $\phi \sim e^{i\tau}$ . This...

I have created a matrix with a class called Lattice. The lattice is filled with objects of type 'Dipole' which is created with another class. The problem I am having is with boundary conditions when I look for a neighbour. e.g If i pick a dipole on the top row, I want its 'above' neighbour to be...

given the generalized SL conditions Let's say psi_m and psi_n are eigenfunctions of the given y. Its Wronskian is 0 because otherwise the boundary condition doesn't make sense much. However, I wonder if it is possible to have, S={ x | W[psi_m(x) , psi_n(x)] =/= 0 } otherwise...

As required by the Green's identity, the integrated function has to be smooth and continuous in the integration region Ω. How about if the function is just discontinuous at the boundary? Actually, this function is an electric field. So its tangential component is naturally continuous, but the...

http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdf (Page 4.4 )I am having a trouble with understanding why closed loop line integration is 0 at dielectric boundary. As far as I know, closed loop line integration is 0 because electric field is...

I have come across the paper attached in which a 1D fluid piston is modeled. I have question on the boundary conditions (BCs) of the system. Essentially, the problem consists of a fluid chamber in contact with a spring (a mass -spring system). ALE is used to move the mesh. I am not certain...

Homework Statement Consider the boundary value problem \begin{equation} u''(t)=-4u+3sin(t),u(0)=1,u(2)=2sin(4)+sin(2)+cos(4) \end{equation} Homework Equations Derive the linear system that arise when discretizating this problem using \begin{equation} u''(t)=\frac{u(t-h)-2u(t)+u(t+h)}{h^2}...

Beginning with the Schrodinger equation for N particles in one dimension interacting via a δ-function potential ##(-\sum_{1}^{N}\frac{\partial^2}{\partial x_i^2}+2c\sum_{<i,j>}\delta(x_i-x_j))\psi=E\psi## The boundary condition equivalent to the ##\delta## function potential is...

Hello! I need to understand one seemingly simple thing in wave mechanics, so any help is much appreciated! When a pulse travels to the right toward an open end(like a massless ring that is free to oscillate only in the vertical direction), then when the wave reaches the end it gets reflected and...

Homework Statement Two elastic bars are joined. A step wave is coming in from left. Derive the shape and magnitude of the reflected wave if the right bar is approximated by a rigid body (point- mass) that is free to move in the axial direction. The Attempt at a Solution I have problem with...

Hello all, I am solving a heat transfer problem for cooling of laminate plate in a cooling press and I intend to use a Robin boundary condition on one of the sides to evaporate heat away from the plate. The Robin boundary equation is specified thus: k∂T(t)/∂n + hT(t) = g(t) where k is the...

By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides: ##E_{\parallel} = 0## -- (1)...

In solving the Navier Stokes equation, the typical boundary condition imposed on the tangential velocity at a solid surface is that of no-slip. However, it is known that for gaseous flow there always exists a non-zero velocity near the wall, especially at relatively big Knudsen number. Is there...

Hello I'm getting confused when I want to use magnetic boundary equation could you tell me how we define the unit vector(an) in this equation? for example you assume that we have two different region (A in red and B in yellow) which vector (1,2,3,4) is right for equation and which is right...

I have a PDE of the following form: f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\ \lim_{t\to s^+} f(t,x,y) = \delta (x-y) Here k and c are real numbers and g, h are (infinitely) smooth real-valued functions. I have been trying to learn how to do this...

For an imperfect conductor, when there is current, an electric field is set up inside the wire along the direction of the current flow, and is parallel to the wire. If this is true, then what I don't understand is boundary condition tells me the tangential E-field is always continuous, if...

Hi all, Generally boundary condition (Dirichlet and Neumann) are applied on the Load Vector, in FEM formulation. The equation i solved, is Generalized eigenvalue equation for Scalar Helmholtz equation in homogeneous wave guide with perfectly conducting wall ( Kψ =λMψ ), and found, doesn't...

Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...

Homework Statement Find the deflection at x=L/4 and x=L/2 for the beam Homework Equations See attached pic. The Attempt at a Solution So I have the solution derived in class. Only 0<x<L/2 is derived because since the load on the beam is at L/2, the equation is valid for the...

Homework Statement now I have a PDE $$u_{xx}+u_{yy}=0,for 0<x,y<1$$ $$u(x,0)=x,u(0,y)=y^2,u(x,1)=0,u(1,y)=y$$ Then I want to know whether there are some method to make the PDE become homogeneous boundary condition. $$i.e. u|_{\partialΩ}=0$$

Hello, According to Stephen Hawking no boundary condition universe does not have any boundary in space time.If it is so then it is like earth.You can not go north to north pole.Earth does not have any edge or boundary.So universe is like closed structure like earth.Means after some times it...

when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors

Hi all, I'm asking a question about the number of the boundary conditions in high-order PDE. Say, we are solving the nonlinear Burger's equation \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\nu \frac{\partial^2 u}{\partial x^2} subject to the initial condition u(x,0)=g(x)...

Hi all, It may be a trivial question. But, if I have a PDE of variable u(x,t) -------------------------------- \dot{u} = f(u,\partial_x{u},..) with boundary condition : u(0,t) = u(L,t) =0. -------------------------------- Now I need to calculate \partial_x{u} for that can I define the...

Hi, I am working on a quite difficult, though seemingly simple, non-homogeneous differential equation in cylindrical coordinates. The main equation is the non homogeneous modified Helmholtz Equation \nabla^{2}\psi - k^{2}\psi =...

The book states that ##P(x|y,t)## represents the probability density that the potential has a value x at time t, knowing that it had the value y at t=0. I understand this, the words are very clear. However I'd find much more intuitive the notation ##P(x,t|y,0)##, but I guess that's just me...

suppose function f is define on the interval [0,1] it satisfies the eigenvalue equation f'' + E f=0, and it satisfies the boundary conditions f'(0)+ f(0)=0, f(1)=0. How to solve this eigenvalue problem numerically? the mixed boundary condition at x=0 really makes it difficult

A rope is tied at one end then rotated in a vertical circle. Why do we take the tension at the free end of the rope as 0(Boundary Condition)?

Hi, I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this. Suppose we have a dielectric in space subjected to some external static electric field. I have read (without explanation)...

Homework Statement A wave function is given by: \Psi (x) = a cos(2\pi x) + b sin (2\pi x) for\: x<0 \\ and\\ \Psi (x) = Ce^{-kx} for\: x>0 \\ Determine the constant k in terms of a, b and c using the boundary conditions and discuss the case a >> b. Homework Equations...

Hello! Let a plane wave propagate towards the -y direction. It is normally incident upon the plane (x,z) (whose normal unit vector is the y-direction unit vector, \mathbf{\hat{u}}_y): the plane represents the interface between the free space (in y > 0) and a general lossy medium (in y < 0). We...

Homework Statement hey, i have a heat equation question which asks to solve for u(x,t) given that u(0,t)=Q_0 + ΔQsin(ωt).Homework Equations d_xx u = k d_t u u(0,t)=Q_0 + ΔQsin(ωt) The Attempt at a Solution so you can solve the equation pretty easily with separation of variables, i.e...

Hi, I am trying to solve a Poisson equation \nabla^2 \phi = f in \Omega, with Dirichlet boundary condition \phi = 0 on \partial \Omega. My problem is that I am trying to understand the condition under which a solution exists. All the text I consulted says that the problem is solvable. However...

We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.

Homework Statement I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise? Homework Equations (∂^2 T)/(∂x^2...

I'm having trouble finding out how to set up Neumann (or, rather, "Robin") boundary conditions for a diffusion-type PDE. More specifically, I have a scalar function f(\boldsymbol{x}, t) where \boldsymbol{x} is n-dimensional vector space with some boundary region defined by A(\boldsymbol{x})=0...

One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. What does this mean physically?

BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length...

Homework Statement BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is...

Hi, I am looking at a problem where I have two electrically conducting fluids where charge accrues on the interface, I know that one of the equations that I have to use comes straight from the usual boundary conditions for the normal component of the electric field, the other one apparent comes...

Homework Statement A one-dimensional wave function associated with a localized particle can be written as \varphi (x) = \begin{cases} 1- \frac{x^2}{8}, & \text{if } 0<x<4, \\ C_1 - \frac{C_2}{x^2}, & \text{if} \,x \geq 4. \end{cases} Determine C_1 and C_2 for which this wave...

in electromagnetics , considering boundary conditions of dielectric and perfect conductor , inside conductor E = 0. So, there should not be any time varying magnetic field. But in many books i have seen that inside conductor normal component of B is 0 because there is no time varying magnetic...

Good afternoon, I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that: ∇2\phi=0 \phix=1 when x=-A and x=A \phiy=0 when y=-B and y=B \phiz=0 when z=Ztop and z=Zbot I have tried...

hi can anyone teach me how to put Mur's ABC in my fortran code for 1d fdtd maxwell's equation as below !1d fdtd Simulation in free space subroutine fd1d01(f0,miu,delta,S,E0) implicit none double precision :: f0 !frequency double precision...

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?

I am trying to understand Ritz method, but i have troubles wtih determining the boundary conditions. After weak formulation of a differential equation how do we determine natural and essential b.c.? What are boundary terms, secondary variables, primary variables, natural and essential...

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...

Hi guys, I'm solving a Poisson Equation with Mixed Boundary condition. But I have trouBle with that mixed BC in MATLAB. Anyone can help to fix? Thanks a lot! dT^2/dx^2+dT/dy^2=-Q(x,y)/k Rectangular domain (HxL), BC: Top: T(x,H)=Th, Left: dT/dx=0, Bottom: dT/dy=q, Right: dT/dx+B(T-Tinf)=0...

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...

I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the...