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1. A tricky inverse Laplace transform

Homework Statement I want to invert a function from Laplace transform space to normal space. Homework Equations In Laplace transform space, the function takes the form $$\bar f (s) = \frac{\exp\left[ x (-a +\sqrt{a^2+ b +c s} )\right]}{-a +\sqrt{a^2+ b +c s}}.$$ Here, ##s## is the Laplace...
2. A scalar on a semi-infinite domain with source and sink

Hi everyone, I've been looking at a problem that seems simple at first, but appears to be deceptively difficult (unless I'm missing something). 1. Homework Statement I've been looking at a problem that involves the diffusion of a scalar quantity, ##q(x)##, on the semi-infinite domain, ##\leq...
3. Looking for a modified Poisson distribution

I'm looking to model a system in which events are nearly perfectly randomly distributed but with a slight tendency for events to avoid each other. As you know, if the system were perfectly random, I could use a Poisson distribution. The probability distribution for the number of events would...
4. Approximating unsolvable recursion relations

I have a complicated recursion replation, which I'm sure is unsolvable. (By "unsolvable" I mean that there is no closed form solution expressing \xi_1, \xi_2, \xi_3, etc. in terms of \xi_0.) It goes \frac{(k+4)!}{k!}\xi_{k+4} +K_1 (k+2)(k+1)\xi_{k+2}+ [ K_2 k(k-1) +K_3] \xi_{k} +K_4...
5. Why doesn't this method work? (Re: Simultaneous ODEs)

I have been working on a derivation in which the following simultateous ordinary differential equations have appeared: f^{(4)}(x)-2 a^2 f''(x)+a^4 f(x)+b(g''(x)-a^2 g(x))=0, g^{(4)}(x)-2 a^2 g''(x)+a^4 g(x)-b(f''(x)-a^2 f(x))=0, where a and b are constants. I figured that I could solve...
6. Issue with Green's function for Poisson's equation

Say we have a 3D function, p(x,y,z) and we define it in terms of another function f(x,y,z) via, \nabla ^2 p = f. I know that if we are working in R^3 space (with no boundaries) we can say that, p= \frac{-1}{4\pi}\iiint \limits_R \frac{f(x',y',z')}{\sqrt{(x-x')^2 +(y-y')^2+(z-z')^2}} dx'...
7. Fourier sine transform of 1

Homework Statement I'm looking to determine the Fourier sine transfom of 1. Homework Equations One this site http://mechse.illinois.edu/research/dstn/teaching_files2/fouriertransforms.pdf [Broken] (page 2) it gives the sine transform as \frac{2}{\pi \omega} The Attempt at a...
8. What is a lifting function ?

What is a "lifting function"? Hi, I was reading a journal article and they mentioned something called a "lifting function". It was apparently used with the Navier-Stokes equation to translate the boundary conditions (which were complicated, and NOT non-slip), into a body force. It looks...
9. MATLAB MATLAB: Average a large number of matricies from .mat files

I have a series of large 2x2 matricies, each of which is stored inside a .mat file. These files have the names data1.mat, data2.mat, data3.mat,..., data60.mat. I have sucessfully loaded each of these .mat files. I want to create a 1x60 array whose entires are the average values of the...
10. Notation issue: Grad with a vector subscript

I'm reading a journal article at the moment which uses a piece of notation which they dont actually define. It looks like this: \nabla_{\vec Q} (As it happens, \vec Q is an ordinary vector indicating the orientation of a polymer.) I've never seen vector subscript on the gradient symbol...
11. A Difficult Method of Characteristics Problem

I'm trying to find characteristic curves for the following ordinary differential equations: \frac{d\kappa }{dt} = \mu \kappa \xi (1-\chi ), \qquad && \frac{d\chi }{dt} = \mu \chi \xi (\chi -1), \qquad \frac{d\zeta }{dt} = \lambda \zeta (1-\zeta ) + \mu \zeta ( 1-\xi ), \qquad && \frac{d\xi...
12. Evaporation of the tube-side coefficient in a heat exchanger

I've got a problem. I'm trying to design a reactor with internal cooling provided by water flowing through tubes directly within the reactor. Basically, it's like a shell and tube heat exchanger with an internal heat source. The problem is that the cooling water is to be evaporated within...
13. Estimate for the liquid flow-rate into a gas scrubber

I need a method for estimating the liquid flow rate required by a gas scrubber (I know the amount of gas that needs to be scrubbed and the amount of particulates with it, but I don't know about the nature of the particles, except that they are organic). It doesn't need to be particularly...
14. Manipulation of Cartesian Tensors

I have a question relating to a particle rotating around a point with velocity u = \Omega \times r, where \Omega is the angular velocity and r is the position relative to the pivot point. I need to prove that the acceleration is given by, a = -\frac{1}{2} \nabla [(\Omega \times r)^2] I...
15. Laplace Transform problem

I have the problem, ty(t)= \int_{0}^{t}\tau^{\alpha-1}y(t-\tau)d\tau subject to the constraint that \int_{0}^{\infty}y(t)dt=1. In need to get the answer in the form of, Y(p)=something (where Y(p) is the Laplace transform of y(t)). I can see that the right hand side is...
16. The inverse Mellin Transform

To invert the Mellin transformed function F(s), the equation is, f(x) = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty} x^{-s}F(s)ds What is the rule the value of c? I know that in inverse Laplace Transforms, c is any real number large enough that all the residues of F(s) lie to the left of the...
17. Using the method of steepest descent

I have the question, \int_{-\pi/2}^{\frac{\pi}{2}} e^{-ilk}cos^n kdk It says, "Set t=ik". So, -i\int_{-i\pi/2}^{i\pi/2}e^{-lt} cosh^n tdt But then it says, "Use the method of steepest descent to show that as n \rightarrow \infty with r = l/n." I'm supposed to get: \sim...
18. LaTeX LaTexing not working at the moment

Is the LaTexing not working at the moment, or am I just not doing it correctly? x^2 EDIT: I see now that it works, but not when I preview the post.
19. Steam tables

I've been looking for steam tables on the internet, but all that I can find are those steam table computer programs. So... Does anyone know a site which has the old fashioned steam tables? And which of those steam table computer programs would be worth getting?
20. When can the limit be brought inside the integral?

When is it alright to bring the limit within the integral? In other words, when is it true to say... lim∫f(x)dx = ∫limf(x)dx ?
21. Need help figuring out what this Maths question means

Hi everybody, this is my first post here. I got this question, but I don't know what it means: Fix n ≥ 1. If the nth roots of 1 are w0, w1, w2, . . . , wn−1, show that they satisfy: (z − w0)(z − w1)(z - w2) · · · (z − wn−1) = z^n − 1 (z and wn are all complex numbers) What I don't...