Thank you John. It is a pity that my country is not investing in Science, or R+D, a national tragedy! I will see if I can find something out there, somehow. My job as acting High-School teacher is so boring in spite the passion I put on it. Hahaha. Anyway, things are not very different out there excepting the fact truly developed countries invest where future IS.

]]>The Dirac structures are the standard framework for port-Hamiltonian (open Hamiltonian not necessarily holonomic) systems. It seems to be well understood by the practitioners. Courant algebroids also show up, but mostly as trivial bundles over manifolds with Dirac structures. I have a student who tried to sort through this last summer.

We eventually discovered that it’s hard to think of port-Hamiltonian systems without having a background in standard (closed, holonomic) Hamiltonian systems. So we are trying to remedy this now.

I wrote to you about my visit by email.

]]>I don’t have much help to offer, but you can get an idea who is working on Nambu mechanics (or any other topic in math or physics) by doing an arXiv search.

]]>By ‘this subject’ I meant open Hamiltonian systems, as studied by engineers under the name of ‘port-Hamiltonian systems’. It’s possible that Dirac manifolds and even Courant algebroids are relevant, but I haven’t seem people doing the things I have in mind using those. And I don’t want to publicly say what I have in mind until I write a paper about it, or at least some blog articles!

By the way, we should plan our your visit here. I’ve been meaning to email you about this! My summer calendar is gradually getting filled up: for example, I’ll be in Barcelona at a conference on the mathematics of biodiversity from June 18 to July 6, and today I discovered I may be spending a couple of weeks in Europe before that as well—it’s my big annual journey to the west. Before this interval, and after this interval until mid-September, I should be in Singapore most of the time… though I’ll probably nip down to Java for a bit. John Huerta and Jamie Vicary will be visiting me at points, but that shouldn’t be a problem.

]]>John wrote:

I’m going to try to make these into subjects that ordinary ‘unapplied’ math grad students can work on, too.

This subject mostly exists under such names as “Courant algebroids” and “Dirac manifolds.” I wonder if I am misunderstanding / misinterpreting what you just said and you mean something else?

]]>Yesterday, I applied to an offer in plasma physics and other in “extra solar planets” detection. LOL. But, I love Mathematics (Indeed I love algebraic stuff too like division algebras, n-ary algebras, Nambu mechanics or clifford algebras) and Physics mainly.

Do you know some places where I could see specific offers? I use to watch brightrecruit, find a phD, tiptop , etc.

Do you know people working on Nambu mechanics?I recommend you to see the last news related to the rôle of the enstrophy functional. I think to remember Terence Tao has submitted a temptative proof of the Navier-Stokes Clay problem in which he uses “enstrophy” (not confuse with entropy) stuff. 92 pages and very technical, too long for me with that topic but your math-inclined readers could be interested. http://arxiv.org/abs/1108.1165

Cheers.

]]>That’s a great talk! Everyone interested in analogies between different physical theories should look at it. Among other things, it describes a mechanical analogue of a memristor on page 11, and a mechanical analogue of a meminductor on page 20. It also discusses these gadgets using the theory of ‘port-Hamiltonian systems’, meaning Hamiltonian mechanics for open systems.

It should be possible for qualified people to PhD’s on this subject in department of engineering or applied mathematics. For example, Jeltsema is in a department of applied mathematics, and Jan Willems, another good researcher in this area, is in a department of electrical engineering.

I’m going to try to make these into subjects that ordinary ‘unapplied’ math grad students can work on, too.

]]>• Arnau Dòria-Cerezo and Dimitri Jeltsema, Port-Hamiltonian modeling of the memristor and the higher order elements.

your readers can be very interested as I am! It is so cool. Unfortunately, I can not find a Ph.D position on that topic. I would be interested. My search continues… :(

]]>Amarashiki wrote:

Yes, I was meaning turning on! A typos, I am sorry, could you edit it John?

It’s too late to edit it: a whole interesting conversation has grown up around that comment. Don’t worry, we all know what you meant.

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