Boundary Definition and 900 Threads

What are the general boundary conditions for nonviscous, incompressible fluid flow? I am trying to find the velocity of fluid at the surface of a sphere with the incident fluid having uniform velocity. I am surprised to find in the solution that the radial velocity at the surface does not...

i've some problem to solve this kind of differential equation, i 've put the link where is the file of my equation, i search a methods that solve it iterativly. the file is there diablo221 .altervista.org / risultato. nb

I can't understand this conditions, and in general every boundary conditions for problems like this. they states "the choice of boundary conditions can be determined by mathematical convenience (!?) ... for if the metal is sufficiently large, we should expect its bulk properties not to be...

Hello friends, Thanks in advance for your answers, I am using genreal form of PDE to solve system of PDEs. I am dealing with cyllindrical co-ordinates under axisymmetric case. I am not able to understand how to implement boundary conditions such as, DEL. Gamma=F is system of PDEs where...

Hi I'm trying to solve a magnetostatic problem and I'm not sure which boundary conditions must be applied to the magnetic vector potential (A) on magnetostatic problems? Thanks in advance.

Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...

Hello hello, I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing...

Hey guys, The streamlines just outside a boundary layer are pushed away from the wall by the displacement thickness \delta* and I understand that; \delta*=\int^{\infty}_{0}(1-\frac{u}{U})dy Now this is for flow over a plate with length x=4m. At x=0 is the leading edge and at x=4...

Hey guys, just need some hints with this doosey Homework Statement We have (x^2 y')' + ax^2y = 0 where a the eigenvalue (a sturm-lioville problem) (sp?) with y'(0)=y(1) = 0 and we get the hint to substitute f = y/x. The Attempt at a Solution Ok so i get the general solution being a sum of...

Although the intuition makes sense, I am having trouble determining why the following proposition is correct. The document leaves this as an exercise for the reader... great. Proposition: Suppose A is a set in a topological space, and dA is the boundary of A. If x is in dA, then x is either an...

The question : Consider a thin spherical shell of radius R with a uniform charge density sigma. If a very small piece of this surface were removed, leaving a small hole, what would the electric field be at a point just above/below the hole? Relevent info : the field due to the patch of...

Homework Statement Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that: D(1)-D(2)=free surface charge density=s where D(1) is the component of the first medium normal to the surface. But suppose that there's nothing else apart from two...

Homework Statement Calculate the reflection coefficient of copper for radio waves at frequency 50Ghz and yellow light (wavelength = 0.6 micrometers) Homework Equations Reflection coefficient: R = E(r)^2/E(I)^2 = (1-n/1+n)^2 Where E(r) is the electric intensity of the reflected wave...

Hi, I would like to calculate the following integration: \oint_{\Sigma}f(x,y)g(x,y)\mathbf{n}\cdot d\mathbf{s} where g(x,y)=0 on \Sigma, and \mathbf{n} is the outward pointing unit normal field of the boundary \Sigma. In this case does the integral equals to 0? Thanks!

If I have a finite boundary, say of length L. Is it possible to demonstrate that if I were to allow all possible CONTINUOUS values of a wave to exist (with unit amplitude) then deconstrutive interference destroys all waves except those with wavelength: k=\frac{n\pi}{L} Where n =0,1...

One thing that's always bothered me about Bloch's theorem is the periodic boundary conditions which are imposed on the system. Clearly, when dealing with an actual solid, the more natural choice would be to impose zero at the boundaries. I know that periodic conditions make the math easier, but...

If not, then what are the conditions for us to construct a periodic boundary condition(PBC)? If so, then please help me construct a PBC for the lattice shape in the attachments. I want to ask that what lattice site m's left neighbor is and what lattice site i's down neighbor is.From the...

I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me. I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which...

I am confused on the definition of the "no-slip" boundary condition because of two seemingly contradicting definitions. Definition 1: The no-slip condition for viscous fluid states that at a solid boundary, the fluid will have zero velocity relative to the boundary. Definition 2: The fluid...

Hello to all! Homework Statement for testing my program i need a heat equation with numerical initial and boundary conditions: Derivative[2, 0][f][x, t] == Derivative[0, 1][f][x, t] f[x, 0] == numerical f[0, t] == numerical, f[numerical, t] == numerical PS. to moders: please, if...

solve the next differential equation: y´´- a*y= \delta (x-d) with the boundary conditions: \left.\frac{\partial y}{\partial x} \right|_ {x=0} = 0 lim _{x\rightarrow\infty} y = 0 I get the homogeneous solution: y_H = C_1 exp (\sqrt{a}x) + C_2 exp (-\sqrt{a}x) and then to...

Homework Statement We are given a word problem and asked find maxima/minima (ie a simple example would be to find the least amount surface area required to build a box of a given volume). Is it necessary to explicitly show that the relative interior max/min, calculated by setting the gradient...

finally in my search to understand why the boundary layer separates from the surface of a baseball I have come to understand that the reasons for the separation of the boundary layer from a baseball is incredibly similar to the separation of the boundary layer from a wing of an airplane after...

a question on boundary layers viscosity and air seperating from a ball I have a few questions that have to do with a viscosity on the surface of an object, the boundary layer and the boundary layer separating from the surface of a baseball! 1) my first question is if we had a stationary...

Hi, I'm trying to find an analytical solution of Laplace's equation: \phi_{xx} + \phi_{tt} = 0 with the tricky boundary conditions: 1. \phi(x=0,|t|>\tau)= 0 2. \phi(x\neq0, |t|>>\tau)=0 3. \phi_{x}(x=0, |t|<\tau)=-1 4. \phi_{t}(x, |t|>>\tau)=0 I have the following ansatz(I...

Hi, I've had trouble finding an answer to this question and was wondering if anyone could help. What happens to the envelope of a wavepacket of light when it crosses the interface between two media? I know that the field of the wavepacket will be continuous across the boundary, but does...

Homework Statement What is the boundary of a torus? What is the boundary of a sphere? The Attempt at a Solution Both 0?

what do mean the author by the red underline line? http://img164.imageshack.us/img164/7404/contfv6.jpg Why would 33.22abe false? Thanks.

So, I know that R and null are clopen, but now to prove they are the only clopen subsets of R... without the idea of boundary points? I know how to do it with boundary points, but can it be done without?

If a space is of n dimension, then the boundary of this space is n-1 dimension or not?

Finding the vibrational motion of a rod. A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 \epsilon). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod. What are the...

a. 1/n + 1/m : m and n are both in N b. x in irrational #s : x ≤ root 2 ∪ N c. the straight line L through 2points a and b in R^n. for part c. i got: intA= empty ; bdA=clA=accA=L Is this correct? how about part a and part b...i am so confused...

Homework Statement A solid sphere is placed in an otherwise uniform electric field. Its upper half is made up from a material with dielectric constant e_1; the other half has dielectric constant e_2. The plane at which the parts of the sphere intersect is parallel to the uniform field at...

So I have an equilateral triangle an I want to divide it in 4 parts, all having the same area. This can be done in a multitude of ways of course. But assuming it's a garden and the division is about putting up a fence, which division uses the least fencing? Now I have two alternatives so...

Does anybody know how to put BC at the center of a circle.

A boundary value problem "discussion" So, let's say we are given a function f : [0, 1] --> R and constants a, b, and we want to find u : [0, 1] --> R such that u''(x) + f = 0 on <0, 1> with u(1) = a and u'(0) = -b. One can easily obtain the exact solution to this problem merely by using...

Homework Statement Let Q be the set of all rational numbers Prove bd(Q)=R Homework Equations The Attempt at a Solution Let x be a real number, then since the interval |x-r| contains both rationals and irrationals for arbitrary small r, so R is the boundary of Q. Is that right?

Subject: Does the Universe have a Boundary ? Since nothing can exist outside of the Universe, how then can the Universe have a boundary in any conventional sense? Surely, if time before time is considered potentially unfathomable; in similar vein to speak of a boundary to the...

Homework Statement I have a two part question, the first part involves solving Laplace's equation u_{xx} + u_{yy} = 0 for the boundary conditions u_x(0,y) = u_x(2,y) = 0 u(x,0) = 0 u(x,1) = \sin(\pi x) for 0 < x < 2, 0 < y < 1. The second part now states a new boundary problem...

Homework Statement What is the stationary (steady state) solution to the following reaction diffusion equation: \frac{\partial C}{\partial t}= \nabla^2C - kC Subject to the boundary conditions C(x, y=0) = 1, C(x = 0, y) = C(x = L, y) (IE, periodic boundary conditions along the...

Hi to all community of Physic's help from Florence, looking at born-von karman BC I'm a bit confused. I put this condition when i assume periodicity of wave function where the period is the spatial dimension of my system. I found that BC first in solid state physic, then I've noticed that...

Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...

Hi I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?

I am not sure if the universe ever expanded at speed inferior to that of light, but if it did, I am curious to know what would have happened (if it didn't happen) if a light ray (or any electromagnetic wave that is) had hit the boundary of the universe?

I need help figuring out the solution to this diff.eq. y(x) = x + (1/2)*∫(from u=-1 to 1)[ ( 1-| x – u | ) y(u) du] , x є [ -1, 1] I have to show that: y``(x) + y(x) = 0 , x є [ -1, 1] subject to: y(1) + y(-1) = 0 y`(1) + y`(-1) = 2 Thanks for any help you can give.

I am really confused. Would you please tell me what the turbulent boundary layer thickness is on a flat plate? There is a well-known Schlichting formula in the previous editions of his book “boundary layer theory”, which is: \delta = 0.37 X Re^{-0.2} But actually I could not find this...

Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...

what are the properties of this alloy about grain boundary?and what is the process to have magnetic property to this alloy?

how do you prove/show that there really is a vector space defined by certain boundary conditions? unfortunatly this part of pde's was glossed over in my professor's lecture notes and I don't recall him talking about it in class.

What is the boundary of a surface? A surface is a two dimensional manifold. I would like to know what constitute the boundary of a surface. (wiki is nor clear enough for me)