Boundary Definition and 900 Threads

I am currently reading up on some algebraic topology\differential geometry and have reached the section on de Rham theory. This is my first encounter with such notions and I am a little confused by what is meant when one applies a boundary operator to a simplex. Conceptually, I know that it...

I recently solved a differential equation with the solution: f(x) = Aexp(ikx) + Bexp(-ikx) with the periodic boundary condition f(x+L)=f(x). This condition leads to: Aexp(ikx)exp(ikL) + Bexp(-ikx)exp(-ikL) = Aexp(ikx) + Bexp(-ikx) (1) Now the way I figured out the constants A and B was that...

I wrote a wave equation simulation in C# a while ago, and while everything works fine, I am running into the expected problem that my simulation boundaries (ie the edges of the grid) reflect the waves coming to them. Obviously I want to keep the grid of reasonable size, so I looked into what...

If I am trying to derive the energy eigenvalues and quantum numbers for the hydrogen atom (basic hydrogen-1), I obviously need to solve the hydrogen Schrodinger equation and account for some boundary conditions. However, no website ever gives me the boundary conditions. What would be the...

Hi, I'm studying multivariable analysis using Spivak's book "calculus on manifolds" When I see this book, one strange problem arouse. Thank you for seeing this. Here is the problem. c0 , c1 : [0,1] → ℝ2 - {0} c : [0,1]2 → ℝ2 - {0} given by c0(s) = (cos2πs,sin2πs) : a circle of radius 1 c1(s) =...

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...

Homework Statement The question is Ytt- c^2Yxx =0 on the doman 0<x< +infinity where initia conditions are y(x,0) = e^-x^2 = f(x) , Yt(x,0) =x*e^-x^2 = g(n) and boundary condition is y(0,t) = 0 and c = 2 Homework Equations D'Almbert solution 1/2(f(x+ct)+f(x-ct))+1/2c∫ g(n) dn over the...

I am trying to understand in more detail the answer to: http://math.stackexchange.com/questions/673187/universal-cover-of-a-surface-with-boundary It is mentioned that the universal cover of a hyperbolic surface ##S## with geodesic boundary is a closed disk ##D^2## with a Cantor set removed from...

Homework Statement I'm trying to plot the steady state concentration of yA vs. x, yB vs x and yu vs x using centered finite difference method. Homework Equations The Attempt at a Solution τ represents the dimensionless time variable, so steady state would mean that the left hand side of...

Homework Statement Example Question: an electron with mass m is confined in a thin wire, with periodic boundary conditions applied in the x direction and harmonic potentials in the y and z direction. Write an expression for the wave functions in the ground state. Write down all the energy eigen...

For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related. Also found some 1-d examples, but I need d>3 dimensional objects since my calculations...

As i understand, the purpose of laplaces/poissons equation is to recast the question from a geometrical one to a differential equation. im trying to figure out what are the appropriate boundary conditions for poissons equation: http://www.sciweavers.org/upload/Tex2Img_1418842096/render.png...

Homework Statement Let a slab 0 \le x \le c be subject to surface heat transfer, according to Newtons's law of cooling, at its faces x = 0 and x = c , the furface conductance H being the same on each face. Show that if the medium x\le0 has temperature zero and medium x=c has the...

I am currently reading Zwiebach and intend on reading Becker and Polchonski afterwoods. In chapter 4 he slves a partial differential equation with the Dirichlet and Neumann BC. My question is what the difference is between the two BC.(BC=Boundary conditions). Thanks for any help.

Hi All, This is my first post on these forums. I am not looking for a solution to this problem but more interested in seeing if someone can point me to a resource that can explain the following. Thanks in advance for any help. I'm trying to solve a pde which gives a temperature profile. We...

Hi All, I am trying to figure out the details on giving a surface S a hyperbolic metric with geodesic boundary, i.e., a metric of constant sectional curvature -1 so that the (manifold) boundary components, i.e., a collection of disjoint simple-closed curves are geodesics under this metric. So...

I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions...

Hello, I have two different discrepancies to this system: a) How and when is possible to have more solution of differential eq. or their system for same initial problem? For example this is happening in following system. It is written about this system: "Different value of constant \dot{M}=4\pi...

My question is the same as the title 'Is there a boundary present for our universe?'

Hi, could you tell the physical meaning of the displacement and momentum thickness of a boundary layer.And why the stream line diverges away from the body in the boundary layer to conserve mass?

this is a rather stupid question regarding preliminaries for the definition of boundaries the question is whether every closed n-1 dim. closed submanifold C of an arbitrary n-dim. manifold defines a volume V; i.e. whether \partial V = C can be turned around such that V is defined as the...

Homework Statement I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0). Homework Equations...

Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...

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...

Hello! When considering the boundary conditions for the electromagnetic field \mathbf{E}, \mathbf{H} on the surface of a Perfect Eletric Conductor we have: \mathbf{E} \times \mathbf{\hat{n}} = 0 \mathbf{J}_S = \mathbf{\hat{n}} \times \mathbf{H} the tangential electric field should vahish...

Hello! In http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf, pages 19-20, the Love's Theorem in Electromagnetism is declared. In presence of some electric sources \mathbf{J} and magnetic sources \mathbf{M} enclosed by an arbitrary geometrical surface S, which produce outside S a...

All, I recently completed a project where transient thermal boundary conditions are rotated around a cylinder for a general number of revolutions. In reality, the cylinder rotated but it was much easier to rotate the thermal conditions around the model in the ANSYS environment. I used 360...

Homework Statement An #a*b*c box is given in x,y,z (so it's length #a along the x axis, etc.). Every face is kept at #V=0 except for the face at #x=a , which is kept at #V(a,y,z)=V_o*sin(pi*y/b)*sin(pi*z/c). We are to, "solve for all possible configurations of the box's potential" Homework...

Let f(x,y) be defined by f(x,y) = [x2y2]/[x2y2 + (x-y)2] a) Find the domain of the function f. b) show that (0,0) is a boundary point of the domain of f c) Compute the following limit if it exists: lim (x,y) ---> (0,0) f(x,y) The Attempt at a Solution a) I first change the value (x-y)2 to...

Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?

Homework Statement I have a hollow, grounded, conducting sphere of radius R, inside of which is a point charge q lying distance a from the center, such that a<R. The problem claims, "There are no other charges besides q and what is needed on the sphere to satisfy the boundary condition". I...

Does anybody know papers in which the asymptotic safety approach has been applied to the "no boundary" proposal?

Suppose we have this rectangle that is stretched equally on both sides with some force, F. Neglect shear force or moments and assuming transverse waves, is the solution still ε = Ae^(i(wt-kx))+Be^(i(wt+kx)) With boundary conditions: X = +L/2, ∂ε/∂x = 0 and X = -L/2, ∂ε/∂x =...

Homework Statement Determine the boundary of the following set. As usual, z=(x,y). 0<\left| z-z_0 \right|<2 2. The attempt at a solution The book's solution says "The circle \left| z-z_0 \right|=2 together with the point (0,0)" Why should the answer not be "... together with the...

Homework Statement I have an infinite plate of which two electrodes are attached at a distance ##2a## and the electric potential between them is ##U##. Now I have to find a function ##\phi (x,y)## that satisfies Laplace's equation ##\nabla ^2 \phi =0## and is equal to ##0## at all possible...

Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

To prevent grain boundary sliding so that creep is less likely to occur, usually engineers would design components of larger grains or have columnar grain structure to prevent grain-boundary sliding. Why this two method can prevent grain-boundary sliding? For columnar grains, would they be more...

Homework Statement . Let ##X## be a nonempty set and let ##x_0 \in X##. (a) ##\{U \in \mathcal P(X) : x_0 \in U\} \cup \{\emptyset\}## is a topology on ##X##. (b) ##\{U \in \mathcal P(X) : x_0 \not \in U\} \cup \{X\}## is a topology on ##X##. Describe the interior, the closure and the...

Hi there Can anyone tell what is the meaning of boundary conditions for temperature distribution in a flowing viscous fluid in a pipe ? for example I need some one explane for me this: T = T1 at r = R, x<0 T = T0 at x = 0, r<R where T1 is a temperature of well and T0 is a temperature...

Homework Statement ##\mathscr{C}: x=1,x=3,y=2,y=3## ##\int_\mathscr{C} (xy^2-y^3)dx+(-5x^2+y^3)dy## Homework Equations The Attempt at a Solution ##\frac{\partial Q}{\partial x} = -10x^2 \,\,; \frac{\partial P}{\partial y} = 2xy-3y^2## ##\int\int_\mathscr{C} \frac{\partial...

Calculate the thickness of the boundary Layer δ at a location x= 0.3m along the chord length of an aircraft wing at each of the following velocities. (u = 20, 40,60,80,100 knots) Assume ISA P=101325 R=287 T=288.5 μ =18 x 10-6 (1)Re transition=5 x 10^5 (2)δ Laminar = x 4.91 Rex^-0.5 (3)δ...

4m3 rigid tank contains saturated H2O vapour at 3.5 bar. When this tank is left for a long time in a laboratory at 25.4oC, its temperatures reduces to this temperature. The thermodynamic properties of H2O is attached. Questions What would the boundary of the system be and what would the...

Hi, Can anybody help me withg the following problem: A rectangular plate with points starting from top left corner and going clockwise:: A B C D. Sides CD and DA are simply supported, and a point force F is applied anywhere on the surface. I am looking for the bending stress distribution...

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...

Hi, I am studying fluid mechanics and I am trying to get to grips with slip and no-slip boundaries. I know that: Slip ---> Occurs when fluid is inviscid so no viscous stress at boundary. No-slip ---> Viscous effects mean the the tangential velocity must be zero, relative to the boundary...

Hey! :o I have to solve the following initial and boundary value problem: $$u_t=u_{xx}, 0<x<L, t>0 (1)$$ $$u_x(0,t)=u_x(L,t)=0, t>0$$ $$u(x,0)=H(x - \frac{L}{2} ), 0<x<L, \text{ where } H(x)=1 \text{ for } x>0 \text{ and } H(x)=0 \text{ for } x<0$$ I have done the following: Using the method...

hi pf! i was reading a sample problem in a text on ode's and came across a boundary condition that didnt really make sense to me. the physical scenario is: a liquid ##L## measured in moles/cubic meter (##mol / m^3##) is injected into a stream of water. ##L## is being injected at a rate...

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that is not grounded, then there will be (as long as I am dealing with static problems) no electric...

Homework Statement Part (a): List the boundary conditions Part (b): Show the relation for potential is: Part (c): Find Potential everywhere. Part (d): With a surface charge, where does the Electric field disappear? Homework Equations The Attempt at a Solution Part (a) Boundary conditions...