Recent content by UAR

Hi Tiny Tim, Thanks for your help and for your honesty. Anyone else care to help physically and mathematically elucidate \textbf{q} in the quadrupole potential equation above. I read somewhere that it is called (or is related to ?) the "quadrupole moment tensor" (what exactly is that by the...

Aaah! Thanks! I was hesitant to do that due to a (poor notation)-induced irrational fear that p_{x'} was a function of x. But now I see it is not, since \nabla is w.r.t field point \textbf{r}, while \textbf{p} depends only on source pts \textbf{r'}. One more question: What is \textbf{q} ...

Thanks Tiny-tim! However, while you are still online, excuse my slowness: why is: (\textbf{q}\cdot\nabla)(\textbf{p}\cdot\textbf{r})=\textbf{p}\cdot\textbf{q} ?

(\textbf{q}\bullet\nabla)(\textbf{p}\bullet\nabla)\frac{1}{r} = -(\textbf{p}\bullet\textbf{q})\frac{1}{r^{3}} + 3(\textbf{p}\bullet\textbf{r})(\textbf{q}\bullet\textbf{r})\frac{1}{r^{5}} r is distance between field point and dipole source, \textbf{p} is dipole moment, and I believe \textbf{q}...

I'm now convinced it must be false. Consider the counter-example: f(x) =x for x\in\Re, then: \nabla^{2}f(x)=0

Please how would one derive the Poisson Equation model, \nabla^{2}\psi(x) = \frac{F(x)}{T}, for Transverse displacement \psi(x) of a stretched string under constant non-zero tension T and an externally applied transverse force F(x) . Assuming small angle with the horizontal (i.e...

Thanks HallsofIvy: I saw it in a book, but I agree with you that it doesn't seem to be true. However, I think 1/r may be the Green's function of the Laplacian in unbounded 3D domains. Again, I agree with you that it seems strange, perhaps even untrue that Laplace equation would apply only...

Why does laplace's equation only apply in limited regions, while Poisson's equation can apply in unbounded domains ?