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  1. H

    A tricky inverse Laplace transform

    Oh yeah, I didn't look closely enough at that function. That inverse Laplace transform I posted does work too though, which is odd. I guess it's probably just a rearranged form of the other inverse Laplace transform though.
  2. H

    A tricky inverse Laplace transform

    I think the difference relates to the process of rearranging the function. If we first make the substitution $$ A=\pm \alpha, \qquad \alpha > 0.$$ Then the left-hand-side becomes $$ \frac{\sqrt{B+s}\pm \alpha}{B+s-\alpha^2} =\frac{\sqrt{B+s}\pm \alpha}{(\sqrt{B+s}+ \alpha)(\sqrt{B+s}- \alpha)}...
  3. H

    A tricky inverse Laplace transform

    I tried that, and it gives a function that can only be rearranged into the function I'm looking for if ##A<0##. However, this did lead me to find a solution. First rearrange into $$ \frac{1}{-A+\sqrt{B+s}} = \sum_{n=0}^\infty \frac{A^n}{(B+s)^{(n+1)/2 }}.$$ Then take the inverse Laplace...
  4. H

    A tricky inverse Laplace transform

    Hi Ray. Thanks for your response. However, if I rearrange the function as you've suggested, and then ask Mathematica to find the inverse Laplace transform, it also gives the function you've written there, but only as a conditional expression for the case where ##A<0##. The problem is that my...
  5. H

    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...
  6. H

    A scalar on a semi-infinite domain with source and sink

    Because if we integrate both sides over ##a-\epsilon <t< a+\epsilon## (then taking ##\epsilon \rightarrow 0##), the left-hand-side will appear to be zero (because ##f(t)## is incorrectly assumed to continuous with no singularities), while the right-hand-side equals 1. I say appears to be zero...
  7. H

    A scalar on a semi-infinite domain with source and sink

    I see what you mean about the integration method for equations with delta functions, Orodruin. It works in this instance because there's a double derivative in the equation. However, if we were to try to use it to solve, for example $$f'(t) = \delta (t-s),$$ it wouldn't work. So it's not a very...
  8. H

    A scalar on a semi-infinite domain with source and sink

    Hi Orodruin, thanks for your response. Yes, it's not the heat equation. I just mentioned heat as an example of a possible scalar quantity. I can see no reason why the time derivative couldn't be removed from the heat equation if the system is assumed to be steady state though. As for sink...
  9. H

    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...
  10. H

    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...
  11. H

    Approximating unsolvable recursion relations

    That's correct. In fact my equation is S''''+(a+bx^2)S''+(c+dx^2)S=0, with some inhomogenious boundary conditions.
  12. H

    Approximating unsolvable recursion relations

    Oops, sorry. I had the wrong equation for S. I've fixed it now.
  13. H

    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...
  14. H

    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...
  15. H

    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'...
  16. H

    Fourier sine transform of 1

    That's a good trick. I'll have to remember that one. Cheers.
  17. H

    Fourier sine transform of 1

    Excellent. Thanks, LCKrutz.
  18. H

    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...
  19. H

    What is a lifting function ?

    Thanks, HoI. The divergence theorem could well be what they meant.
  20. H

    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...
  21. H

    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...
  22. H

    Notation issue: Grad with a vector subscript

    Thanks, the derivative in the direction of the vector makes sense in context.
  23. H

    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...
  24. H

    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...
  25. H

    Evaporation of the tube-side coefficient in a heat exchanger

    Thanks for your help, guys. It's actually the final design project for my degree, so it has to be designed in detail, but without the information we'd have available in industry.
  26. H

    Evaporation of the tube-side coefficient in a heat exchanger

    I just realised I used the word "coefficient" in the title instead of coolant for some reason. Well, if the mass of water entering the tubes is equal to the mass exiting, then the flow speed should be inversely proportional to the density. Of course, it not so possible to pump steam at that...
  27. H

    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...
  28. H

    Estimate for the liquid flow-rate into a gas scrubber

    You would think so. But no particle masses were given. Fortunately, I found out that scrubbers are often rated by their liquid flowrate/gas flowrate ratio, and so I just used that.
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