Recent content by mhsd91

Hi everyone, I've encountered a curious problem I just can't figure out, and any input would be much appriciated!This is a personal project I'm working on, and as far as I know, there is no one else working on exactly the same. However, the computational study of critical phenomena is quite...

Well, I must disagree with you on this one. It is by no means trivial to solve the equations of motion for a 3D-system of masses connected with springs. I have a background in computational physics and mathematical modeling. Without having looked to much into the details, I would guess there...

So, essentially, all I wonder is: What is the The Matrix Exponent of the Identity Matrix, I? Silly question perhaps, but here follows my problem. Per definition, the Matrix Exponent of the matrix A is, e^{A} = I + A + \frac{A^2}{2} + \ldots = I + \sum_{k=1}^{\infty} \frac{A^k}{k!} =...

I have another approach, which almost solved it. I think something is wrong with problem itself, or perhaps som eother information is missing. However, will give my seconds try, and perhaps you'll find, some mistake I made and solve it... Anyways, S_n(\theta) = \sum \limits _{k=-n}^n...

Are you absolutely sure you printed the problem correctly? I ask since I get the following, S_n (\theta) = \sum \limits _{k=-n}^{n} e^{ik\theta} = 1 + \sum \limits _{k=1}^{n} \left( e^{ik\theta} + e^{-ik\theta} \right) = 1 + 2 \sum \limits _{k=1}^{n} \cos (k \theta ) Where I see no...

What you suggest is of course interesting. I fear however, I've already tried this: The Fourier (and Laplace) integral transform are indeed popular approaches for the non-stationary cases. Since I have stationarity, what you write there is equal to zero. Thus, 0 = D (\mu^2 + \nu^2) P(\mu,\nu)...

Indeed, you're absolutley right. My problem is that I'm working on a project where we're supposed to solve this eq. numerically, but by looking at it, I was really certain I could solve it analytically. It would be really nice to have such an analytical solution to compare with the numerical.

PROBLEM FORMULATION: Considering the region \Omega bounded as a square box within x \in [0,1], y \in [0,1] . We wish to solve the 2D, stationary, advection-diffusion equation, 0 = D\nabla^2 \rho(x,y) + \vec{V} \cdot \nabla \rho(x,y) where D is a scalar constant, and \vec{V} =...

I would personally recommend visiting different universities' websites for exams. For instance, here is a list of some exams at the Norwegian University of Science and Technology (NTNU): http://home.phys.ntnu.no/instdef/arkiv/eksamen/tfy4220/ for an introductory course on solid state physics...

I divided my answer in two for multiple reasons, I hope is is okay, and here follows the second part, regarding Wiens Displacement law. I'm not entirely sure if I understand your question, as a temperature does not have a wavelength. What Wien's Disp. law states, is that a black object (as...

I divided my answer into two. This is the first part considering: Well, it depends on multiple factors (and I welcome all to correct or improve my answer). I suggest you take a look at Einstein's theory of Photoelectricity. Light (photons) are absorbed by an atom if the photon's energy...

Hi again! How are you doing, figured it out yet? Reading my own answers made me realize I could have formulated myself much better. Besides, I have made a rather crucial mistake which you actually point out! Creds to you!:) You write that we can se from the condition to find the minimun...

Hi and thanks for the replay! I forgot to update this as I figured it out. I hope that it may be of help to anyone who's also struggling with this. I did just as you say to prove the Markovian and stationary property. Concerning stationarity, I applied the Wiener–Khinchin theorem, found the...

Hi again! I'm sorry I haven't been able to answer before now as I've been struggling with a project of my own. Anyways, let's see.. First, this MIT-paper answers all your questions in a really good way. I highly recommend you just read from the start of chapter 14.4 (it is not very long!)...

Having giving the problem another look, I'm now able to specify the problem a little: A OU process is characterized by beein the only non-trivial process having all of the three properties, Gaussian Stationary (in time) Markovian Then showing and confirming these for my numerical...