Boundary Definition and 900 Threads

I want to model the diffusion-controlled combustion of a small carbon particle. The system I want to model is similar to this one However, I'm not going to use the stagnant gas film model as shown in the figure, since I lack data for the film thickness, and I want to evaluate the problem...

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? For example, I intend to make a volume integration of a product of electric fields, the field function is...

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}...

Hello, Can anyone help me find the boundary conditions of the below given beam please. Its a clamped-free beam but the overhanging sectiona and the mass makes it confusing. Actually I am puzzled about finding the initial conditions.

Hi, so I have this question: A wave pulse on a string has the dimensions shown in the figure (Figure 1) at t = 0. The wave speed is 40 cm/s. a) Draw the total wave on the string at t=15ms, 20ms 25ms, 30ms, 35ms, 40ms and 45ms. b) repeat part (a) for the case in which the end of the string is...

Hello, I am simulating an experiment I did in the lab where we had air flow over a tray of water to determine the mass transfer coefficient scaling with velocity, as well as boundary layer thickness scaling with velocity. Now I am using COMSOL to simulate the experiment, and here is the...

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'm doing an experiment where I will be blowing warm air parallel to a stagnant water surface, and I will investigate the scaling of air velocity with mass transfer coefficient. I am trying to find some kind of scaling of the concentration boundary layer thickness with air velocity, and...

Hello! (Wave)Consider the boundary value problem $\left\{\begin{matrix} - \epsilon u''+u'=1 &, x \in [0,1] \\ u(0)=u(1)=0 & \end{matrix}\right.$ where $\epsilon$ is a positive given constant. I have to express a finite difference method for its numerical solution. How can we know whether it...

Hello, PF! Recently, while reading chapter 10 (microscopic energy balances) of the second edition of BSL, I found a minor discrepancy which is confusing me, especially when considering the mathematical analogies of heat and mass transfer. In section 10.1, the authors introduce Newton's law of...

How to find value of integration constant?I know with the help of boundary conditions,but How boundary conditions help in finding integration constant?

Homework Statement Under what condition on the constant ##c## and ##c'## are the boundary conditions ##f(b) = cf(a)## and ##f'(b)=c'f'(a)## self-adjoint for the operator ##L(f) = (rf')'+pf## on ##[a,b]##? (Assume that ##r,p## are real.) Homework Equations The boundary conditions are...

I am reading Jackson Electrodynamics (section 1.10 in 3rd edition) and he is discussing the Poisson eqn $$\nabla^2 \Phi = -\rho / \epsilon_0$$ defined on some finite volume V, the solution using Greens theorem is $$\Phi (x) = \frac{1}{4 \pi \epsilon_0} \int_V G(x,x') \rho(x')d^3x' +\frac{1}{4...

I've forgotten a lot of field theory so I've been rereading it in a couple of electric field theory textbooks. What seems like a simple problem falls between the cracks. I hope some readers can help - it will be appreciated. My application seems simple (solution will require numerical FEA but...

I am working with a fixed fixed bar with a distributed axial load to the right as w(x)=CX/L. I am having a hard time determining the force boundary conditions. I know that U(0)=0 and U(L)=0. However, I need to come up with something in regards to U'(Value). Any help would be appreciated.

There is a general topic of boundary constructions, which means how to adjoin idealized points in a sensible way to a given spacetime. There is a menagerie of these methods, including the g-boundary (Geroch), b-boundary (Schmidt), c-boundary (Geroch, Kronheimer, and Penrose) and a-boundary...

Hi, I have two coupled differential equations d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2) d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda) where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions...

I'm upgrading a non-PFC (power factor corrected) offline power supply design to include PFC for European deployment. The total output power is less than 25W, and the two output windings are around 20V. I'm familiar with boost-flyback topologies for isolated PFC supplies, but that seems to...

Consider the heat equation dT/dt - aΔT + v⋅∇T = S where S is a source term dependent of the radiation intensity I and the temperature T. The fluid velocity v is prescribed. We also consider the radiative transfer equation describing the radiative intensity I(x,ω,t) where ω is the ray direction...

Somehow I can't relate two things and confused over this. What I understand when someone say that some spacetime has conformal boundary it means that I can write the metric conformally to some other metric where the coordinates are finite ..So it has boundary. Now I just read something on Ads...

Hey this isn't so much a homework problem but one I have just had an exam over. I have absolutely no idea how to calculate it and in all past papers/tutorial questions and the notes, makes no mention of the sort of problem. I'm not bothered over the exact answer, just how you go about it...

Lumley, turbulence textbook on boundary layers, introduction pages: "The turbulent eddies transfer momentum deficit away from the surface". Can anyone explain what this means, specifically what is momentum deficit? In my mind, the word "deficit" means a shortage of something, so how can one...

Hi PF! I'm using a finite differencing scheme to solve the following $$h_t = h h_{zz} + 2h_z^2$$ where the subscripts denote partial derivatives. The difficulty I'm facing is the boundary conditions are dynamic, and move with time ##t##. This makes choosing a ##\Delta z## very difficult and...

I'm trying to work up some examples to help me understand this concept. Would the periodic flow on a solid torus be transverse to it's boundary?

Hey! :o Prove using Green's theorem that the boundary value problem $$\frac{\partial}{\partial{x}}\left ( (1+x^2)\frac{\partial{u}}{\partial{x}}\right )+\frac{\partial}{\partial{y}}\left ( (1+x^2+y^2)\frac{\partial{u}}{\partial{y}}\right ) -(1+x^2+y^4)u=f(x,y), x^2+y^2<1 \\ u(x, y)=g(x,y)...

Solve the boundary value problem: $\left\{ \begin{array}{lcl} y''&=&0,\hspace{1.0mm} 1<x<2\\ y(1)&=&0\\ y(3)+y'(3)&=&0 \end{array} \right. $ For the problem, I first calculate the eigenvalues and after check the roots and finally find the eigenvectors. Is correct this? Help me please :).

I am trying to set up the mass matrix for a 1D system which I want to solve using finite elements. So the mass matrix is defined as M = \int{NN^T}dL, where N is the finite element linear basis functions. I use hat functions. Say I have 10 elements, corresponding to 11 nodes running from -5...

Hi! When we model bloch-waves in a solid we assume that there exist some kind of periodic boundary conditions such that the wave function is periodic. In 1D, ##\psi(x)## repeats itself for every ##L##, ##\psi(x) = \psi(x+L)##, such as here: OK, fine, we get pretty wave solutions if we assume...

we have that Ht1 (x,y,z) - Ht2 (x,y,z) = Js and for the special case Ht1 (x,y,z) - Ht2 (x,y,z) = 0 where there is no surface current. At a boundary with Js =0, which for simplicity let's asume is at at x = a, then knowing that Ht1 and Ht2 are the magnetic fields to the left and right of the...

Hi all, I have the next dude: To utilize the Huygens principle at the boundary of a volume, do we need to know precisely material properties inside the volume? Thanks!

Consider the radial differential equation ##\bigg( - \frac{d^2}{dr^2} + \frac{(l+\frac{d-3}{2})(l+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_l (r) = \lambda\ \phi_l (r)##, which I've obtained by solving the Schrodinger equation in ##d## dimensions using the method of separation of...

Hello Guys, Could someone explain to me the meaning of greater thermal boundary layer over hydrodynamic boundary layer over a flat plate surface? I know how to calculate both streams, but I don't understand the meaning of smaller thermal boundary vs. hydrodynamic boundary and vice-versa. What...

Suppose that we want to solve the eigenvalue equation with Dirichlet boundary conditions ## \bigg(-\frac{d^2}{dx^2}+V(x)\bigg) \phi_n = \lambda_n \phi_n,\ \ \ \ \ \ \ \ \ \ \ \ \ \phi_n(0)=0,\ \phi_n(1)=0, ## where ##0 < \lambda_1 < \lambda_2 < ...## are discrete, non-degenerate eigenvalues...

I have a question I'm a little embarrassed to be asking: what is meant in condensed matter when someone describes a system with "open boundary conditions," say in one-dimension for simplicity? I am comfortable with the statement of fixed (Dirichlet) or free (von Neumann) boundary conditions, as...

I read in wikipedia that the boundary of a spinfoam is a spin network. Is it true? How can we define what is the boundary of a finite connected spinfoam? I have the same question for a spin network. As in LQG boundaries are of paramount importance, I think that we have to define them. Thanks

Hi all! I am trying to solve a system of partial differential equations in Matlab, with both derivatives in time and space domains. I am using the pdepe function for that. The system is, to be simple, a sort of solar thermal panel, made of three layers: an absorber plate, a fluid layer of...

I have created such vibrating feeder model on SW but on ANSYS I'm only analyzing the frame. 1)How do I set up boundary conditions, I think I need elastic supports? 2)In modal analysis I have elastic, fixed supports, remote displacement - which should I use and in what directions? 3)Do I perform...

I'm reading griffiths electrodynamics and I am confused about a concept. Mainly because I might be interpreting it in different ways. Why does the equation contain an E with a negative in front? Namely, E_below. Isn't the Electric field pointing away from the surface with the surface charge...

Edit: Sorry about the vague title, it was intended to be complex beam system boundary conditions but somehow it turned out like this. Hello, I am trying to learn complex beam system designs and I sometimes struggle to assign boundary conditions. For example I am trying to design the lifting...

In the derivation of the boundary conditions we apply the integral form of maxwell's equations, but once we take a very small volume we find that some terms disappear like the displacement current as well as the time derivative of the magnetic field. Why do these terms disappear? For reference...

Does anyone here have a copy of Griffith's E&M? On page 128, condition III V=V_0 (y) when x = 0. Do you know why then value V_0(y) does not appear in in equation 3.28, V(x,y) = Ce^(-ky)sin(ky)? The author does not explain this.

Taken from my textbook: My understanding is that: One valence electron, 2 spin states -> Half-filled Brillouin zone Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries States nearer to zone boundaries get pushed down in energy further Since a fermi...

I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential. From what I...

Hi, My final goal is to solve numerically Schrodinger's equation in 3D with some potential for the unbounded states, meaning that far away from the potential (at infinity) we may find a free wave and not something that goes to zero. The basic idea is that I have a particle in (0,0,0) that...

Homework Statement See the figure below. A thin pipe, open at both ends, with length 0.400 m and 1.0 cm diameter is placed vertically in a cylindrical bucket so that it nearly touches the flat bottom of the bucket, which has an area of 0.100 m2 . The air temperature is 22o C. Water is slowly...

Hello, I have some trouble to solve this exercise Homework Statement E={ (-1)n (8n+7)/(4n-1) : n ∈ℕ} Show that 2∈[PLAIN]http://www.ilemaths.net/img/smb-bleu/derivepartielle.gifE Homework EquationsThe Attempt at a Solution We have to show that (2-r,2+r)∩ E ≠∅ and (2-r,2+r)∩ ℝ/E ≠∅ If I take...

It is said that the metric tensor in GR is generally covariant and obey diffeomorphism invariance.. but the signature, boundary conditions and topology are not. What would be GR like if these 3 obey GC and DI too? Is it possible?

Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...

Please help! I read a statement by Lee Smolin (Time Reborn) that an "open" infinite universe necessarily has a "boundary", through which information would be received, which he used as an argument that cosmological models should prefer a "closed" universe approach. In fairness, he said that this...

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)...