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    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...
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    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...
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    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...
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    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...
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    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...
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    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'...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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.
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    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?
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    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 ?
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    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...
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