Raphael J.F. Berger

Thank you @ACuriousMind!

Yes that works now! I have to solve now another poisson equation to determine g but that makes sense for the no-free lunch theorem!

Now was thew question since these seem so asimilar if I can obtain the TP directly from B^{ind} without solving Poisson eqs.

I am investigating the topology of J^B but its nasty stuff in part, and I stubmlede across what is called toroidal-poloidal ddecomposition of solenoidal vector fields. Which seems as exactly what I need. Now it turned out that this TP decomposition is numerically not as nice as what I require. Then it occured to me that I can achieve almost the same if I split B^ind into its z-component and the x- and y.

not sure about that though :D

If you are interested I try to eaplain it.

Actually I am doing something very different, which is quite difficult and very lengthy to explain, and now these W fell into my hands and I need to understand how they might be related to B^ind and if and how one can determine the one from the other. Actually I have good access to B^ind but I can use the W for another purpose, which is the actual problem.

I basically solve some poisson equations.

Long story ...

@ACuriousMind would you agree?

So I take J^B determine my strange W vector potential then I add the gradient of a scalaf function g with div(grad(g))=-div(W) then W+grad(g) = B^{ind}?

Yes

Could it be that div(W+grad g) = \Delta g= 0 is what I am searching? That at least would give ma antother constraint.

Or what I want to know, if I can avoid it.

I mean one could do the Biot-Savart integral, but this is what I want to avoid.

Oh, you are saying div(W) must be zero, right?

Oh, I see. So if I give you W could you determine $B^\text{ind}$ from it?

But $\nabla \times (W + grad g) = J$ then as well, for any scalar g

But I think/hope that is not important for my question

Yeah!

in Quantum mechanics it induces non zero but "static" currents.

Obviously the two vector potentials B^ind and the other one lets call it W are related via a gradient of a scalar function f. Like W + grad(f) = B^ind. What I would like to know now is if B^ind is special among all W+grad(g) potentials of this form for all possible g. And if B^ind for example fullfills some variational property ?

Via some considerations I have obtained a method for computing a "vector potential" for the currents that is obviously in general different from B^ind but from which J^B also can be obtained by taking the curl (and dividing by \mu_0).

I investigate current density functions. the currents are induced into an electron cloud, the underlying mechanisms are QM, but the quantituies I obtain can be treated classically. So I have an external homogeneous time independent mag field B^ext that induces currents J^B into the electron cloud, lets say. These currents correspond to some induced magnetic field B^ind from which they can be obtained for example ma the Ampere law from the curl.

Hi people. I have a possibly stupid question in electromagnetism, anyone interesetd?

Hi guys,

In particular I would be happy on some hints on how to perform such a decomposition numerucally. i.e. if you have "only" numercial access to the field.

Hi there, I posted a Q on MSE but obtained no resonance. As it's strongly physically motivated maybe someone of you can help me here a bit? math.stackexchange.com/questions/4477140/…

Yes, also what I thought! thanks. ChatGPT claims the contrary ...

What is the most acidic proton in butanone? The one at C1 or the one at C3, and why?

Hi all, any ideas on this: mathematica.stackexchange.com/questions/277059/… ?

@LukasLang Exactly this! Thank you very much, again!

Thank you very much!!! I have one more (sorry) Now I want to "convert" this List/Array into real valued step function. where the list element positions encode the x-intervals say 1st entry is from 1<x=<2 and the value of the entry is the y-value

Wow thank you very much!!

The second parameter "4" should just give the total number/length of the output list.

and the output list gives just the values at the position of the entry number

Thank you for your interest!

In a sense you interpret the input list as x/y coordinates: {{x,y}, ...

there is the list of two element-lists {{1,2},{3,1}} and I want to "convert" that into a list where the 1st entry is 2 and the third entry is 1

F[{{1,2},{3,1}},4] = {2,0,1,0}

Hi all! I have an inputlist of two-element lists like i={{1,2},{3,1}} and I want to construct a function F[] that produces a one-element list using the first element of the input list-elements as the list index and the second-element as the new element of the list, the second argument shall be the total number of elements of the resulting list: like F[i,4]={2,0,1,0}. What is the syntactically simplest/shortest way to do that?

Hi there, I need the Biot-Savart law for a current in an infinitely thin cyclic loop but not as common over the centre of the loop but shifted by some distance. Can someone help me?

Hi there, I posted the Q math.stackexchange.com/questions/4477140/… 2 days ago but haven't got any resonance as yet. Has someone some idea what I could improve with the question or on the topic itself?

@MehdiSlimani Thank you very much and I have meanwhile discovered that its also the kernel of the Matrix!

I mean the $rank$ of $M$ is 2.

Hi all, regard a 3x3 matrix $M$ with $dim=2$ of the column/row vector space. Hence $det(M)=0$. This 2-dim vecor space spanned by the columns/rows corresponds to a plane with a well defined normal. My question is has this direction/norm vector a name and is there any "text book construction" (such as a wedge product of ...) that generates it?

It confuses me since the Schur-Weyl duality deals with the tensor spaces, rather than elements of it.

Hi all, I have group/representation theory thing that I want to understand, but its a bit hard to formulate.I try it: Lets consider a finite group with a 2-dim irreducible representation over $\mathbb{C}$ lets call it $\rho_E$. Now say the tensor square of the representation $\rho_e\otimes\rho_E$ can be decomposed into $Sym^2(\rho_E)\oplus Alt^2(\rho_E)$. My question is, has this anything to do with the Schur-Weyl duality. In particular is it an instance of it?

Hi all, I have a surface $A$ which is delimited by a curve $S$, how to most neatly call that? Would $\partial A = S$ be cool?

But it always confuses me what is the factor and what the remainder.