Recent content by praban

Hello, I am trying to find Fourier Bessel Transform (i.e. Hankel transform of order zero) for Yukuwa potential of the form f(r) = - e1*e2*exp(-kappa*r)/(r) (e1, e2 and kappa are constants). I am using the discrete sine transform routine from FFTW ( with dst routine). For this potential...

Dear All, Can someone suggest me an appropriate routine (in Fortran) or command (in mathematica) to perform numerical integration of a function, which is specified numerically on a one dimensional grid with equal spacing (and we cannot generate additional data on other grid points)? There are...

I am giving the details below (equation numbers are from my original posts, except the equation I have written below). The sigma1 and sigma2 of eq. (5) and (6) are taken as 2.0 and 2.5 I am using 128 points in my discrete FT (values -63 to +64). Inverse FT of the FT of these gaussians give...

Hello, I am trying to numerically evaluate a convolution integral of two functions (f*g) using Fourier transform (FT) i.e using FT(f*g) = FT(f) multiplied by FT(g) (1) I am testing for a known case first. I have taken the gaussian functions (eq. 5, 6 and 7) as given in...

Hello, It may be trivial to many of you, but I am struggling with the following integral involving two spheres i and j separated by a distance mod |rij| ∫ ui (ρ).[Tj (ρ+rij) . nj] d2ρ The integration is over sphere j. ui is a vector (actually velocity of the fluid around i th...

I would like to take divergence of the following expression ∇.((xi × xj × xk)/r^3), which is a triadic. here × denote a dyadic product and r=mod(r vector) and xi, xj and xk are the components of r vector. So, the above eq. can also be written as ∇.((xixjxk ei×ej×ek)/r^3), where ei...

Yes, Fredrik, Dextercioby is right. Praban

Dextercioby, Thanks. Now I think I have understood. So, in my notation it would be . ∇.(T.v0) = (∇.T).(v0) + T.(∇v0) where dot in the 2nd term in the rhs is double contraction of tensors and ∇v0 is the gradient of the vector v0 (which is a tensor). Fredrik, the dot product...

Sorry for the late reply. Let me be more specific I have ∇.v (1) i.e. divergence of a vector v. then v is expressed as v=T.v0 (T is a tensor and v0 is another vector. The book I am using - Happel and Brenner - Hydrodynamics does say that the T and v0 can have dot product and...

Yes, Dextercioby - it is the contraction. Is the formula given by Fredrik valid in that case? thanks

Thanks, Fredrik. The first dot i.e. the one after ∇ is for the divergence and the second dot is dot product. Is your formula still valid? Praban

Sorry, there was a mistake in my post. The 1st term in the rhs is a scalar (because div T is a vector and vector. vector =scalar).

I am new to tensor algebra. I have an expression involving a 2nd rank tensor (actually a dyadic) and a vector. I want to take divergence of the product i.e. ∇. (T.V) However, I am not sure if the simple product rule would work here. If I use that ∇. (T.V)= (∇.T).V + T. (∇.V)...