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...

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...

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}...

Hi, When I solve the diffusion equation for a spherically symmetric geometry in spherical coordinates I obtain the following general solution (after application of the boundary conditions). T(r,t) = \sum_{n=1}^{\infty}\, \frac{A_n}{r}\sin(\lambda_nr)\exp(-\alpha\lambda_n^2t) So to...

Hello thanks for the reply. I've found out that my spatial equation is in the form of the spherical Bessel function equation, where the Bessel functions of the first and second kinds are given by J_0(\lambda{r}) = \frac{\sin(\lambda{r})}{\lambda{r}} Y_0(\lambda{r}) =...