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seen Aug 20 at 21:27

Jul
2
awarded  Curious
Apr
8
awarded  Popular Question
Mar
25
comment Solution to the “cubic” Helmholtz equation
This is a cross-post from MSE. The question has had sufficient time with no comments or answers so I thought I'd try the physics side for some different insight. If this cross-post behavior is not allowed, please let me know and I'll delete.
Mar
25
asked Solution to the “cubic” Helmholtz equation
Feb
21
accepted Objective measure of anisotropy
Feb
19
comment Objective measure of anisotropy
Thanks for the input. My biggest concern with using multipoles is the choice of origin - if you are comparing higher moments it seems that the choice can invalidate comparisons (not an issue with the CMB, but by its nature that problem is different). Where did you place the origin for your simulation - or did it not matter since there was a well-defined point for differing systems?
Feb
18
asked Objective measure of anisotropy
Jan
9
comment Geodesics in a point mass universe
Thank you for the reference and the great answer. I admit I hadn't considered the fact that the masses themselves wouldn't have static positions relative to each other. Is it possible though to consider something like an instantaneous geodesic, i.e. the geodesic made by connecting the series geodesics over a small differential of space between two points? I envision something like a calculus of variations problem, the path that would connect the two points over the shortest spacetime.
Jan
9
accepted Geodesics in a point mass universe
Jan
8
comment Geodesics in a point mass universe
Thanks @joshphysics, I figured the solution would be extremely difficult but I'm completely out of my element here. I'd be happy for a numerical solution, I think I'd learn a lot reading over the algorithm.
Jan
8
awarded  Yearling
Jan
8
asked Geodesics in a point mass universe
Jan
8
awarded  Informed
May
28
comment Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments
The observations are nice and indeed useful when $N=2^\ell$, but my original idea was to approximate the potential with some value of $N$ such that $N < 2^\ell$. In this case I'd like to approximate the basis vectors as "best" as possible using only a limited subset.
Jan
19
accepted Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments
Dec
4
awarded  Caucus
Dec
4
awarded  Constituent
Nov
2
revised Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments
Added a new observation
Nov
2
comment Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments
@LuboŇ°Motl I agree, but the problem is motivated by a practical concern, making (pseudo) accurate "toy models" of electrostatics for protein solutions. As such any thoughts on the matter, canonical or not, would suffice as solutions in this case. I would expect that the symmetry of the problem should suggest something better than brute force optimization.
Nov
2
asked Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments