Boundary Definition and 900 Threads

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...

Homework Statement Solve \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) for x>0 and t>0 if w(x,0) = f(x) w(0,t) = h(t) Homework Equations The Attempt at a Solution I know how to solve for the conditions separately and that would give...

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)...

Considering the classic problem in Electrodynamics "Conducting sphere with Hemispheres at different potentials" How does one think in order to attack this problem? I didn't get it. What potential was considered in solving this problem? Was it the +V or the -V? Or both? Why is θ' considered...

Homework Statement If utt - uxx= 1-x for 0<x<1, t>0 u(x,0) = x2(1-x) for 0≤x≤1 ut(x,)=0 for 0≤x≤1 ux(x,)=0 u(1,t)=0 find u(1/4,2) Homework Equations The Attempt at a Solution I was thinking to make a judicious change of variables that not only converts the PDE to a homogenous PDE, but also...

Dear all, I am stuck with the problem which is given below; In this problem the equilibrium equations of the given functional must be derived in u, v, and w directions from which the boundary terms must be found. I think that i have derived the equilibrium equations( 5 equations), but i...

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...

Hey! Speaking electrodynamics, I can't seem to get mathematically or even physically convinced that the solution with Dirichlet or Neumann boundary conditions is UNIQUE. Can someone explain it? Thanks.

Homework Statement A rectangular plate extends to infinity along the y-axis and has a width of 20 cm. At all faces except y=0, T= 0°C. Solve the semi-infinite plate problem if the bottom edge is held at T = {0°C when, 0 < x < 10, T = {100°C when, 10 < x < 20. Homework Equations ∇2T=0...

This is a quantum mechanics problem, but the problem itself is reduced (naturally) to a differential equations problem. I have to solve the following equation: \frac{\partial}{\partial t}\psi (x,t) = i\sigma \psi (x,t) where \sigma > 0 The initial condition is: \psi (x,0) =...

Hi all, Say I am solving a PDE as \frac{\partial y^2}{\partial^2 x}+\frac{\partial y}{\partial x}=f, with the boundary condition y(\pm L)=A. I can understand for the second order differential term, there two boundary conditions are well suited. But what about the first order differential term...

Robert Oeckl proposed this new formulation of QT in December of last year. http://arxiv.org/abs/1212.5571 I think it's important and worth learning about. It could replace Dirac form of QT for some (especially general covariant) quantizations. Historically it derives from 1980s work by Witten...

Hi All, I would like to know why in the infinite well problem, after having solved the time independent SE, we are not supposed to equal to zero the x derivative of the spatial part of the wave function at -L and L (2L being the total width). We only have to make it zero at the boundary...

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...

Can someone please explain to me the nature of the boundary layer and its effects on fluid flow over an aerofoil? Thanks,

From time to time the Magic Grandmother of Philosophy flies down from the sky and touches physics with her magic wand and it the field becomes slightly different. Philosophy is the careful examination of the concepts we use to think with. It can spark revolutions in thought. I've noticed it's...

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

As learning laser fundumentals, I've just reviewed the boundary conditions for electromagnetic waves. However, I came back to a point that confused me in the past and want to get it clear now :) One of the boundary conditions, regarding the magnetic fields parallel to the medium-interface...

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)?

Homework Statement Electromagnetics, Kraus, 4th edition problem 4.7.3 The y-z plane is the boundary between 2 dielectrics of relative permittivities εr = 2 and εr = 5. For negative values of x, E = (3,0,2) V/m. Find D (magnitude and direction) for positive values of x. Homework Equations...

i have an almost square region. By 'almost' i mean the edges are curvy, not completely straight. i now need to solve the Helmholtz equation with Dirichlet boundary condition what is the best numerical method? how is Finite element, though i do not know what Finite element is

I don't have access to Comsol 4.x. I imported a 3D mesh generated from point cloud data and generated a geometry. (A hollow almost-ellipsoid.) I solve my system on the surface/boundary alone; there is no volumetric data. I need to extract 1D data from the surface/boundary at points other...

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...

Homework Statement Let C be the boundary of the domain enclosed between y = x^2 and y = x. Assuming C is oriented counterclockwise. Evaluate the integral ∫c (6xy+e^(-x^2))dx Homework Equations I was thinking of using Green's Theorem. Would be the approach be correct? The Attempt at a...

Homework Statement I'm trying to find the boundary conditions for the beam shown in the figure. Homework Equations Notation: V= Shear force M= Bending momentThe Attempt at a Solution at x=0 V=R1, M=0 at x=9 V=R3, M=0 In the solution provided at x=9 V=-R2. I don't understand why it's...

I have started studying fluid mechanics recently and seems to be a very basic conceptual question that is bugging me and unfortunately I am unable to find a reasonable explanation for it. Your help would be more than appreciated. The mathematical definition for incompressiblility in fluid...

Homework Statement I am solving an inclined flow problem, and am stuck. The problem is to find the volumetric flow rate of inclined flow in a square channel. Once I have the velocity profile, I can just integrate over that to get the flow rate. 2. The attempt at a solution Letting the...

I'm having a little difficulty in the topic 'Boundary layer Equations' in Fluid Mechanics due to my weak math skills. With reference to the figure in attachment, if we say that "we neglect \frac{∂^{2}u}{∂x^{2}}", does it mean that we will only consider the portion where \delta(x) is almost...

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 I have two questions. 1) generally speaking, when we are given two equations both describing surface in R3: f1(x,y,z)=k and f2(x,y,z)=C, The intersection of the two will be a curve that's by solving both equations. My question is, by solving f1 and f2 to get anther...

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...

Homework Statement Homework Equations {3.9b} A[2\mu -m\omega ^2 ]=2\mu Bcos(\frac{ka}{2}) B[2\mu -M\omega ^2 ]=2\mu Acos(\frac{ka}{2}) The Attempt at a Solution All I can think of is setting k =\frac{\pi}{a} so that B[2\mu -M\omega ^2 ]=A[2\mu -m\omega ^2 ] solve for omega...

Hi everyone, I'm attempting to create a computer program to solve the transient 3d heat equation using the Crank Nicolson method. I would like to model the boundaries of my domain as losing heat via convection and radiation due to the temperature difference between the boundary and the air in...

The universe is expanding as described by Hubble's law, which means that at a certain distance from an observer, expansion exceeds the speed of light, so all waves become infinitely red-shifted. In other words, if an goes beyond this point, no information about it can ever come back to the...

Boundary of a Mobius band - I think S1 V S1, everyone else says S1?? Hey I am having a huge problem! There are a few problems where I'm using Van Kampen's theorem and for one part of the problem I need to compute the fundamental group of the boundary of the Mobius band. Everyone keeps telling...

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...

I'm not sure if my answer is correct. Did I make a mistake somewhere? I'm not sure the ± needs to be there.

I get a different answer from my classmates. Where did I go wrong?

I have kind of a simple point set topology question. If I am in ℝ2 and I have a connected open set, call it O, then is it true that all points on the boundary ∂O are limit points of O? I guess I'm stuck envisioning as O as, at least homeomorphic, to an open disk of radius epsilon. So it seems...

Hi, I'm doing 'Heat and Mass transfer' at college and we're covering the topic on the hydrodynamic and thermal boundary layers. I have a couple of questions, the answers to which are not given explicitly in any of my textbooks. 1. During open flow, why does laminar flow eventually have...

Hello all, I've been wondering how water reacts in a closed, rigid system with one moving boundary. Assuming the system is perfectly filled with water, and one side of the boundary moves (increasing the volume), how does this affect the pressure in the system? Since water is...

I've been trying to get my head arround this problem for several days now, and while I deemed it relatively simple at first it turns out that I can't figure out the BCs on a conductor, to which we apply a potential U. In the simplified version of the problem, there is a rectangular conductor...

Hi, I shall show (using Fourier transform) that the solution to \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial^2 u(x,t)}{\partial x^2}\\ u(x,0) = f(x) \\ u_t(x,0) = 0 is u(x,t) = (f(x+t) + f(x-t))/2 I got it almost: Taking the Fourier transform in the variable x...

Speed of light "boundary" ? I have a simple question : When everyone is talking about the "speed of light boundary" what is it relative to ? Speed is ALWAYS relative to "something" else, otherwise it doesn't even make any sense. Which brings a second point : if there is indeed a speed...

Suppose we have the following IBVP: PDE: u_{t}=α^{2}u_{xx} 0<x<1 0<t<∞ BCs: u(0,t)=0, u_{x}(1,t)=1 0<t<∞ IC: u(x,0)=sin(πx) 0≤x≤1 It appears as though the BCs and the IC do not match. The derivative of temperature with respect to x at position x=1 is a constant 1...

I need some help!My problem is a problem of moving boundary with loss of mass... I started to use COMSOL and I need to simulate one plate with a hole on the center. And this hole is increasing with the time according to one equation (like a velocity, in m/s) which depend of the stress. Someone...