Recent content by lostidentity

Hi, I have a set of experimental data given in terms of speed u versus distance x. But I want to obtain a plot of distance x versus time t. The problem is I don't have the end time of the experiment. In this experiment velocity is a function of distance, u=u(x) and distance is in turn of...

I'm wondering if there is another way to solve the ODE I gave in the previous post, i.e. \left(1+2\frac{\Psi}{r}\right)\frac{dr}{dt} = \Phi

I'm trying integrate the following equation and make r the subject \frac{dr}{dt} = \Phi - \Psi \frac{2}{r}\frac{dr}{dt} I first collect the derivative terms together and integrate the equation with respect to r and t to obtain r + 2\Psi\ln{r} = \Phi{t} + r_0 where r0 is the constant...

I've been trying to find the exact solution to the advection equation in spherical coordinates given below \frac{\partial{\phi}}{\partial{t}} + \frac{u}{r^2}\frac{\partial{}}{\partial{r}}r^2\phi = 0 Where the velocity u is a constant. First I tried to expand the second term using product...

Thanks for the reply. Actually I'm working with a transport equation for a scalar variable N that has the following form (I've ignored a number of terms and constant coefficients as I don't think they are relevant). {u_j}\frac{\partial{N}}{\partial{x_j}} =...

Hello, About the second order spatial derivative \partial^2 f(\mathbf x)/\partial x_i \partial x_j which DH wrote above, in tensor notation can it be written as \nabla(\nabla{f}(\mathbf x))?

Could \frac{\partial^2{c}}{\partial{x_k}\partial{x_i}} be a second order tensor? Since \frac{\partial{c}}{\partial{x_i}} is the gradient of c (i.e. a vector), therefore \frac{\partial}{\partial{x_k}}\left(\frac{\partial{c}}{\partial{x_i}}\right) would be the gradient of a vector field, i.e. a...

Hi, Sorry I don't think I defined the problem correctly. c is a scalar field and \vec{u} is a vector field. I checked with a paper and it seems that what I've got for the vector notation is correct. However, I'm having difficulty with the following term...

Hi, I have the following term in tensor notation \frac{\partial{c}}{\partial{x_i}}\frac{\partial{u_i}}{\partial{x_j}}\frac{\partial{c}}{\partial{x_j}} I'm not sure how to write this in vector notation. Would it be? \nabla{c}\cdot\nabla\boldsymbol{u}\cdot{c} The problem I have...

Hi, I'm trying to find analytical solution to an advection equation written in Spherical coordinates. It's spherically symmetric so I'm only interested in radial variances. The equation is: \frac{\partial{c}}{\partial{t}} + \frac{1}{r^2}\frac{\partial}{\partial{r}}(r^2uc) = 0 I've seen...

I'm trying to find the volume and surface area of a 1-D dimensional sphere, i.e. retaining only the radial dependence. I know that the volume element for a 3-D sphere would be dV = r^2\sin\theta{d}\theta{d}\phi{d}r If it's one-dimensional would it just be dV = r^2{d}r? Or would it...

I'm trying to analytically solve a simple diffusion problem (written in non-conservative form) with that of numerical simulation that essentially solves the equations in conservative form. The transport equation which I'm solving numerically is \frac{\partial\rho{c}}{\partial{t}} +...

Thanks very much for that, I was trying to find out more about Hilbert spaces and how it's used for PDEs. I've yet to figure out what you've explained but I do like mathematical rigour.

Sorry to sound daft here but can't I take g(r) = rf(r) and then A_n = \frac{2}{b}\int_{0}^{b}\, g(r)\sin(\lambda{r})\, dr

Thanks for the replies. So does this mean that now the Fourier coefficient has to be written as A_n = \frac{2}{b}\int_0^b\, rf_0(r)\sin(\lambda{r}) \, dr And when I substitute it back into the original equation I have to divide by r i.e. f(r) = \sum_{n=1}^{\infty}\left[ \frac{1}{r}...