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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 27th 2011

• CommentRowNumber2.
• CommentAuthordomenico_fiorenza
• CommentTimeAug 31st 2011
• (edited Aug 31st 2011)

created stubs for curl and divergence

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 31st 2011

Thanks!

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeAug 31st 2011

I added redirect rotation of a vector field to the more cryptic anglosaxon alternative curl (and which I could prefer to be a title in fact, wikipedia givee 2.1 mil hits, for curl of a vactor field 320 thousand hits).

1. added a link to and created a stub for symplectic gradient. By trhe way, I notice now that moment map is still very stubby; i hope to be able to expand that soon.

• CommentRowNumber6.
• CommentAuthorTobyBartels
• CommentTimeAug 31st 2011

People are forgetting that you need an orientation, not just a metric, to do Hodge duals (and thus, for example, to define the curl of a vector field as a vector field on a Riemannian $3$-fold).

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeAug 31st 2011

go on, jump in, I seem not to have time these days to reconcentrate on this topic, which I started

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeSep 1st 2011

Anyway, I did expand moment map following Joel Robbin’s notes (well, I think I have learned the first steps into the subject from my advisor, so I follow his notes). Still not much there but at least the basic reasoning leading to the definition is produced (and the literature).

• CommentRowNumber9.
• CommentAuthorTobyBartels
• CommentTimeSep 2nd 2011

Unhappy that we had the curl only in the classical $3$ dimensions, I discussed its relation to the cross product and described nonclassical cross products. The latter page is now massively general!

• CommentRowNumber10.
• CommentAuthorzskoda
• CommentTimeSep 2nd 2011

Well, a further justification should go from the Stokes theorem. I mean, there is a limit of an integral formula for the rotation of the vector field, similar to the one for the divergence.

• CommentRowNumber11.
• CommentAuthorzskoda
• CommentTimeSep 2nd 2011
• (edited Sep 2nd 2011)

I mean

$rot \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\times \vec\mathcal{A} d S$ $div \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\cdot \vec\mathcal{A} d S$

where $D$ runs over the domains with smooth boundary containing point $x$ at which the rotation or the divergence of the vector field is calculated. These formulas are invariant.

• CommentRowNumber12.
• CommentAuthorzskoda
• CommentTimeSep 2nd 2011

I added the above remarks in the case of divergence (in which case this works in any dimension).

• CommentRowNumber13.
• CommentAuthorzskoda
• CommentTimeSep 2nd 2011

New entry nabla and additions to rotation of a vector field.

• CommentRowNumber14.
• CommentAuthorTobyBartels
• CommentTimeSep 5th 2011

I’ve generalised nabla to discuss all applications of the operator, defined using the integral formula in a very general way, and moved the formula originally there (for the gradient only) to gradient.

• CommentRowNumber15.
• CommentAuthorzskoda
• CommentTimeSep 5th 2011

Right, I have left it in a rudimentary form, planning something similar and I am happy with your way of finishing the job!

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeSep 5th 2011

There is something funny going on with the rendering: at least on my system that

  \nabla \odot T


in the entry sometimes (such as in the big displayed formula) comes out as “$\nabla box T$”.

• CommentRowNumber17.
• CommentAuthorTobyBartels
• CommentTimeSep 5th 2011

You probably caught this while I was in the midst of editing for itex’s capabilities. Reload the page and check again.

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeSep 5th 2011

Ah, right, now it dsiplays correctly.