Group valued flows: A possible example

@IMSc, Chennai

Am here as an attendee for the NBHM nurture programme. Today, we had a talk by one of the participants, ADG on flows in graphs (ref. Diestel’s Graph Theory). In his talk, he defined the concept of group valued flows. Let there be a function , where is the edge set of the multigraph and is an abelian group. Hence, assigns to each edge of the edgeset , an element in . This concept is an extension of the concept of integral flow in graphs, with in the latter. I won’t go much into the theory itself, but I have some different objectives here.

After the lecture, one of the attendees complained that this notion of group valued flow is too abstract. So, a possible non-trivial example happened to occur to me in which the abelian group doesn’t equal . Consider, a hypothetical mode of communication (I don’t know if one such already exists), in which information happen to travel in the form of nuclei spin in the medium carrying it. So, the source or the transmitter orients the nuclei of the medium those are just adjacent to it, in a particular direction and the fraction of nuclei in that cross section which are oriented in that particular direction determine the magnitude of the spin vector. These nuclei then transfer this spin to their neighbours and reorient themselves randomly in all the directions such that their net spin vector again becomes zero. In this fashion, the information about the nuclei spin can flow through the medium. This flow can hence be thought of as a vector valued flow in which flow in each edge of the graph is given by a vector . Hence, the group happens to be the vector space having the usual addition operation of the vector space as its abelian operation.

P.S. 1) I’ve written this post primarily so that I can refer back to this idea whenever I might need it at some future point of time.

2) This is the first post belonging to the category math on my blog .

3) To write equations and other stuff in in your WordPress blog posts, type $latex yourcodehere $. Though I feel that WordPress doesn’t adjust the sentences involving LaTeX that good, but I have no other option .

Some firsts

As neone amongst you who keep(s) track of this blog might have noticed, I have been making many dx-dx changes to my blog over past few days. I have included a site traffic monitor from tracemyip.org and also one from Clustrmaps. I liked the TraceMyIP widget more obviously because it provides greater detail about the visitors including their IP, exact location, browser, OS, time of visit, pages visited and whether they are online or not. And also u can block ur own IP from being counted. But it is free only for a period of one year I was wishing to do it for a while now, but could figure out today only how to go about it.

The web log from the first day surprises me in addition to the info that the WordPress Blog Stat widget has been givin over last month or so, Today, I had visitors from as far as Copenhagen, Saint George and LA. That simply amazes me. And on the top of it all, somebody amongst them had searched for my name itself. Now, this is something too flattering OK … enuf of gloating. But on a side note, people please do tell me who you are when you have searched for my name and do leave some comments

Also, I have included links to some blogs that I myself read and admire too!

In addition, I am posting today my first photograph, actually a computer generated painting that seems beautiful to me atleast. This is another of the firsts. The painting is a result of some computation carried out in connection with something in asteroseismology. I feel that this is why nature seems to be so beautiful. Such beautiful do these strokes of lines arising from some equations of physics seem. The image was generated from the numerical datae using GNUPLOT version 4.2 and then subsequently edited using GIMP 2.4.5

Signing off

General chit-chat

Ya, finally got sumwht free 2day … was trying to comprehend and modify a FORTRAN code written in French to suit my needs … took me 8 days to do so … I think I took too much time for it … it shud have been done in 1 day … newyz I think, in all probability, its settled as of now

well, I gave this title so as to allow myself the freedom to write many random unrelated things within a single post …

so lemme start by indulging in bashing my current host i.e. HBCSE, Mumbai … v have been given accomodatn in a flat which is at a 25 min walk from the workplace … the toilet thr is 2 ft x 3 feet, no light in d bathroom, no mirror in d house … I giv this elaborate description just to point out the indifferent attitude of the powers tht may b towards such undergraduate research programs … how do u xpect ppl to work in such conditions … is sumthing beyond my level of understandin … Also, in my experience, this seems to be the case wd most of the undergraduate research programs. Altho I must admit tht I m annoyed wd the administrative part of it only … rest everything is very good.

Nextly, it seems tht the most visited and the most useful (perhaps) post on my site is on LaTeX … and also the number of visits seems to have increased tremendously after I switched to the new display theme tht I am usin on my blog page i.e. Chaos Theory. Incidentally, I realised this after making my last post tht my theme is indeed Chaos Theory … now tht I m at it … I think tht d current theme is much better thn the Quentin theme I was using b4 … I had chosen tht to give d blog a royal look

I think I took too much time to write down all d ideas … hence will close it 4 now