Weeks 3 and 4 at TIFR

Ahh, a month has passed without me achieving the progress that I wanted to achieve in a month. I hope I will use the other half of the month very efficiently and effectively. All it takes is a little discipline, that I don’t have, but this might be a good chance to cultivate that.

Week 3 was when I learnt about the Langevin Equation, Markov Processes, the Fokker-Planck equation, the Master Equation and the Boltzmann Transport Equation. I referred Balescu’s Equilibrium and Non-Equilibrium Statistical Mechanics for the earlier three topics, and some random article I found on the internet for the Master Equation. As for the Boltzmann Transport Equation, I just looked at Wikipedia without going through much detail. So I learnt some non-equillibrium statistical mechanics, but this stuff is yet to sink in. I’m going to make some notes about it very soon (started this today) and that should get things in place.

Loganayagam (Dr. Shiraz’s doctoral student) helped me solve the “stirring of a colloid” problem, as I’d like to call it – the problem of Brownian Motion of a colloidal particle with an external force that has a curl. The idea is that there’s no detailed balance in the non-equillibrium system. Of course, we could solve only toy problems in 2 and 3 dimensions, while we’d have ideally wanted to solve it in an uncountably infinite number of dimensions! In the 2-D toy problem of Brownian diffusion under a force with a constant curl, we encountered an equation whose solutions were Bessel functions and that’s when I learnt about the Hankel transform. I thought it was pretty amazing. Loganayagam converted it into a Fourier transform in no time. Incidentally, the very next day, my co-VSRP Kaushik encountered the same equation and the same situation in a problem related to a wave propogating in AdS space. (He’s working on AdS/CFT correspondance)

I also read a bit of Katepalli Srinivasan’s Physics Today article on Turbulence, which gave me more physical insight. I still need to complete reading it.

I went home last weekend because I was feeling rather home-sick. I spent a wonderful time at home, two complete days with my family for a change (it’s usually astronomy sessions, visiting the planetarium, BAS meetings, meetings with old friends or something of that sort on a conventional weekend, where I see family for ~3 hours!). On the flight down to Bangalore, I tried working out the Correlation-generating functional of a free Quantum particle after Prof. Wadia gave me the path integral representation. The path integral was hard to evaluate, but waiting at the airport being the time when I’m most productive, I came to a point where it looked like I hadn’t got anything. However, that exercise made me comfortable with evaluating path integrals by first principles.

Week 4 started with me playing further with the toy problem. I became a little more comfortable with that form of the Fokker-Planck equation. I worked with the Burgers’ equation (which is the same form as the Navier-Stokes equation in 1-D). We had to find the determinant of an infinite-dimensional operator, in the context of which I proved that det A = exp( Tr ln A ). I also learnt about the WKB approximation in the context of path integrals from Prof. Spenta and made some notes on it, but am yet to use it. I also tried to evaluate the determinant of the operator we had at hand, and there are still some minor glitches. I also verified that the Cole-Hopf transformation, which is mentioned in the Wikipedia page on Burgers’ Equation linearizes the viscous Burgers’ Equation – and this had some sort of “guage symmetry” which kept us confused for a while. I’m glad I could find that out!

On Thursday, I joined the string theory group for lunch. While string lunch doesn’t make much difference to me (except I don’t pay the already highly subsidised amount for lunch), it was nice to many of the string theorists together. Everyone in the department, except Prof. Sandeep Trivedi, were present. To “make up” for his absence, Prof. Gopakumar from HRI was present, and so was Prof. Atish Dhabolkar. Once in a way, when I heard things like “the spectrum of a closed string with the left moving and right moving stuff”, I used to think ‘Hey, I know what that means’. (Thanks to Dr. Suresh’s boltzmann talk). I’m now so used to hearing the word ‘Gauge Theory’ (I usually get the spelling wrong), that I feel as comfortable with it as I would if I knew what it actually meant. (Well, I know it’s a “Quantum Field Theory” with some sort of Gauge Invariant action, but it takes more than words to know something in Physics.)

This week, I attended three talks – one by artist and TIFR employee Sukant Saran on art-science interaction and a popular talk on the “Ubiquity of Symmetry” by Prof. Ramanan, a former professor at the TIFR Math department with well known contributions to mathematics. I also “half-attended” a talk by Dr. Atish Dhabolkar on Mock Modular Forms – obviously, I didn’t understand much, but I learnt at least something.

I felt that Week 4 was not upto my full working potential. I feel I should’ve worked more. Will try and make sure that Week 5 is going to change that. It’s just that there’s a point in-between reading something where you get “frustrated”, and I end up breaking for long hours at that point. I also found out I take a really long time to see and reply to mail – that needs to be optimized a bit, which means more procmail filters to cut out mail that I amn’t interested in.

On a side note, I’m trying to read some Quantum Field Theory, so that I can at least get an idea of what the subject is like. Dr. Suresh recommended the book by Srednicki, in which I’m slowly finishing the 1st chapter.

On other aspects of life, I made some contributions to KStars this week – particularly those pending from GSoC 2008 and there’s a little more stuff to do. Prakash (whom I’m mentoring under GSoC this summer) is pretty much taking care of himself and needs my support only once in a way – and it has been very enjoyable working with him. As I know from earlier experience with him, he learns things really fast – so I had to explain things to him initially, but I no longer need to. He seems to be enjoying his summer work and is rather passionate about it. I realised I needn’t push him to do stuff, which I thought will be the hardest part of the game when I told Lydia that I’d chosen Prakash; now he needs to push me to do stuff!

While I’ve realised that I’m more productive at work when I’m back in my flat, I took a break from that yesterday and played the flute for a whole 75 minutes! I put on the shruti looping on my laptop, and it started off with Behag, followed by a bit of Revati, followed by a pseudo-”RTP” in Kalyani, ending with my favourite – kApi. Of course, my flautistry is still very n00bish, but I can at least manage to entertain myself with it! I’m pretty sure my neighbours will be cursing my existance, that too now that the flute is pitched at G#.

Yet again, I’m going to Bangalore for the weekend – not to visit home – but to attend a workshop by (to be Dr.) Vishnu Reddy on “Asteroids, Comets and Meteorites”. Vishnu has promised to teacch us some professional astronomers’ techniques, so I thought I’d learn something by attending it. Pavan, Vivek and Naveen Nanjundappa are doing a great job at organizing it – and for a change, I’ve been at the “customers’ end” rather than at the organizers’ end. I’ll be returning to Bombay on Monday evening (considering that my weekend will be rather intense) and I hope to finish notemaking from Frisch’s turbulence and get to the place where he constrains correlation functions using symmetries by the time I’m back at TIFR.

Metric Tensor

After a discussion with Henry de Valence (hdevalence) on IRC, who wanted to know something about the metric tensor, I thought I should put down some stuff that I explained to him. This is like a “Why a metric tensor” article.

A quadratic form, is a homogeneous polynomial of degree 2, like

We can always represent such a polynomial of degree 2 by a symmetric matrix:

[x y][1 1][x]
     [1 1][y]

[I'm sorry, I still don't know how to type matrices in LaTeX, and I want to put-off learning that for a later time]

So, let’s try to represent the distance between two points, which is a quadratic form, as a matrix. Let’s consider very small distances – between two closely separated points: (x, y, z) and (x + dx, y + dy, z + dz) where dx, dy and dz are “very small” distances.

Ordinary 3-D “Euclidian” Space, Pythagoras theorem reads:


[dx  dy  dz][1 0 0][ dx ]
            [0 1 0][ dy ]
            [0 0 1][ dz ]


Special relativity tells us that time is just like a “coordinate” and we shouldn’t treat it separately. Space and time are now put together and called “space-time” and there are 4 coordinates. The “distance” (Space-Time interval) between two points (t, x, y, z) and (t + dt, x + dx, y + dy, z + dz) is defined like this:


[dt dx dy dz][ -c^2           ][ dt ]
             [       1        ][ dx ]
             [           1    ][ dy ]
             [              1 ][ dz ]


Just like distances don’t change under rotations, space-time intervals don’t change under “Lorentz Transformations” in Special Relativity, which is why it is useful to have the notion of such a weird distance. Ordinary 3-D distances do change under “Lorentz Transformations” – as is demonstrated by the effect of “Length Contraction”.

The matrix that we’ve written in the above is (a representation of what is) called a “metric tensor”.

We can write the metric tensor for the surface of a “two-sphere”. That refers to the surface of the ordinary sphere in three dimensions, that we are accustomed to. It’s called a two-sphere because we are talking about the surface of a sphere in 3-D – which is 2-dimensional. Note that this metric varies from point to point (it’s a function of r and \theta) and hence, is a tensor field:


[dr d \theta d \phi][ 1                          ][ dr       ]
                    [    r^2                     ][ d \theta ]
                    [          r^2 sin^2(\theta) ][ d \phi   ]


Finally, any ”Riemannian Manifold” (curved spacetime) can be described by the metric tensor and its derivatives. So the metric tensor plays a central role in General Relativity. Formally, space-time intervals are written in the following manner:

The above follows a notation called “Einstein Summation Convention”, which my 17-year-old friend already knew, which can be read from other sources.

I knew KStars code was bad, but I never knew it was _this_ bad!

SVN commit 977470 by khudyakov:

Replace strange and loopy way of accesing array index with
common one.

 M  +5 -7      altvstime.cpp

--- trunk/KDE/kdeedu/kstars/kstars/tools/altvstime.cpp #977469:977470
@@ -306,13 +306,11 @@

     avtUI->View->update();

-    for ( int i=0; i raBox->showInHours( p->ra() );
-            avtUI->decBox->showInDegrees( p->dec() );
-            avtUI->nameBox->setText(
-        avtUI->PlotList->currentItem()->text() );
-        }
+    if( row >= 0 && row raBox->showInHours( p->ra() );
+        avtUI->decBox->showInDegrees( p->dec() );
+        avtUI->nameBox->setText(
-        avtUI->PlotList->currentItem()->text() );
     }
 }

Week 2 at TIFR

Yesterday marked the end of my second week at TIFR. I’m slowly getting acclamatized to life here and the rather hard routine of going to bed at 10:30 PM and waking up at 6 AM. I now understand why Dr. Suresh told me that being bused in is, in some ways, a good thing. Maybe my body will learn to go into deep sleep real fast, at last.

That apart, the food here is slowly getting boring, my project is slowly progressing with a lot of back-tracking (like those progress bars on most applications – the KStars conjunction tool for instance – that seem to make time travel in the past a reality), and I’m learning stuff.

This week started off with some more reading of Frisch’s book on ‘Turbulence’. I finally managed to start Chapter 6, on Kolmogorov theory. Early this week, I had a long discussion with Prof. Spenta Wadia, which eventually gave me an understanding of Functional Integrals, the Feynman Path Integral formulation… He loaned me his copy of Feynman and Hibbs (Quantum Mechanics and Path Integrals) from which I learnt the basics of the path integral formulation of QM. I think it’s a nice idea. He said he’d also teach me the Dirac equation sometime for fun.

We were trying to write part of the Navier-Stokes equation as a potential energy. I even came up with a solution, that I realised was incorrect because of an extremely stupid mistake I had made – I had written the convective derivative which is $v^i \partial_i v^j$ as $\partial_i v^i v^j$ which is zero for an incompressible fluid! For a whole day, I thought I was right and we tried to put in Lagrangian multipliers into the potential to fix the $\partial_i v^i$ appearing in it. When I realised my mistake yesterday, I was looking for other possibilities and realised that no “local” potential is possible. In the evening, my guide told me that it was not possible because the field was not curl-free in the first place to get a potential term! We’re now left to deal with more complicated stuff, and in the meanwhile I’m going to continue my reading of Frisch’s book and Srinivasan’s articles on turbulent flow. But the point of this exercise for me, was that I learnt something – and I got a feel for what research might look like.

Recently, there were two interesting colloquia here. I attended a talk on the LHC and the Dark Universe by Dr. Rolf Heuer, Director General of CERN. He had pitched it at a low level, so I could understand a fairly large part of it. There was yet another colloquium by Dr. Atsuto Suzuki, Director of KEK which I attended, in which Dr. Suzuki talked about Neutrino Telescopes, the Solar Neutrino problem, and the Super-Kamiokande and KamLAND neutrino detectors. Again, the talk was at a popular level, so I could understand most of it. The departmental introduction talks for VSRP students ended this week, with the last one being the Theoretical Physics department. I learnt quite some stuff there as well.

I also went to Dr. Umesh’s labs, where he did his research to earn his PhD, and built quality instrumentation. He also showed plots of electron scattering by Hydrogen molecules that showed the Young’s double-slit interference due to the two hydrogen atoms, which he had talked about in our class. I also saw parts of the Pelletron from outside. I hope to visit the Petawatt LASER lab and the Pelletron some time.

I’m now trying to find ways to spend the weekend.

My first week at TIFR

Today marks the end of my first week at TIFR. So far, this place has been amazing. Let’s make a quick summary of plus points and minus points:

Work environment:
I’ve currently settled on a desk in the students’ room with my laptop and just enough space to keep my books. Air conditioned, Wireless net access. I’m surrounded by a lot of PhD students. They work a lot and that’s good because it motivates me to work as well. It’s so nice to see the next generation of scientists pacing up and down thinking, occasionally writing a few equations (that interestingly seem at least remotely familiar!) on the board. I like the work environment, although sometimes I wish it were cleaner – but after all, I’m used to dirty desks!

Lectures and other stuff:
We’re currently hearing from various departments about their work. So far, we’ve heard from 6 departments. Some of the speakers were very impressive, while some were talking to their colleagues and not to students – making their talks drab. Today, we heard from the condensed matter physics group, and we also had a nice discussion after the talk. I’ve been learning something new, something totally different everyday!
It was interesting to see a non-scientist at TIFR saying “You should always try to do science with enthusiasm.” or something carrying a similar message, as he fiddled around with an interesting experiment saying, “The scientists at TIFR have done this to me!”. I enjoyed the fact that learning about the world around is so enjoyable – to everyone.

My project:
My project’s about hydrodynamics. My guide et al found new symmetries in the non-relativistic Navier-Stokes equation for incompressible flow. The symmetry group is the conformal group. Given the generators of the conformal group, I verified today that the Navier-Stokes equation is indeed invariant under the action of the infinitesimal generators conformal group. My summer project will be related to these symmetries.
Today, when I went to meet Prof. Spenta, the discussion drifted to Green’s functions. He explained to me what a Green’s function was in brief (I still need to think), and eventually pulled out a functional integral and said “This is what’s called a Feynman Path Integral”. I said, I don’t know this stuff. And the reply was approximately, ‘Yes! That’s the point! You don’t know this stuff – so try to think about it and reconstruct it – don’t read about it’. He’s always put in the point that the best way to learn things is to think about them and reconstruct them, and not by reading them up in the past few times I’ve met him. I liked that! I’m now left to figure out all by myself what a special conformal transform does, and how a certain Feynman path integral gives me a two-point correlation function!
In the last one week, I also learnt a lot from Frisch’s book on Turbulence.

Food:
Well, I have the choice of 4 canteens! That’s much better than IITM. I don’t complain. Food here is good. The only stuff I don’t like about it is the garlic. It feels great to have nearly authentic Mysore Masala Dosa in Mumbai! We don’t have a choice for dinner, though, and I nevertheless manage to eat roughly the same stuff every evening.

Peers:
My co-VSRPs in the Theoretical Physics Dept are pretty good too. I’m yet to interact with most of the PhD students. I have knowledgeable peers to discuss stuff with.

Accomodation:
We’re accomodated in a furnished apartment at a place called Wadala, which is an hour’s journey by road from TIFR. That’s a little pain, but the accomodation isn’t as bad as we thought it was initially. I feel it’s better than hostel back at IITM, but I do miss internet connection. It doesn’t matter that much because I get just enough time to sleep at the accomodation and spend the rest of the time at TIFR.

I did feel a bit homesick initially, but that’s the case with me everytime I face change. It’s something that happens when you don’t give your brain enough work – but I now have enough to pack my day already!

Overall, I rate the first-week experience as good

I’m going home this weekend and returning on Sunday evening. Our department will introduce its research activities on Tuesday, and I’m looking forward for that!

Summer Project Decided!

Yes!

This summer, as I stated in an earlier blogpost, I’m going to be working under Prof. Spenta Wadia and Prof. Avinash Dhar at TIFR as a part of VSRP 2009.

I met Prof. Wadia today and decided the details of my project. I will be doing a “pure” fluid dynamics project, at least on the outset. Prof. Wadia’s group has discovered a new symmetry in the Navier-Stokes equations that was unknown earlier, and my summer project will be closely connected to that.

So far, my initial task is to read the book on “Turbulence” by U. Frisch. It’s quite amazing that concepts from the Dynamical Systems course that I did under Prof. V Balakrishnan last semester are used in this book’s description of turbulence, and I’m glad I did that course. Somehow, it turns out that I can understand that book, although I feel that it is of a pretty advanced level (it’s meant for graduate first years, but we’ve done those required courses now anyway). Frisch also discusses the symmetries in the Navier Stokes equations pretty neatly. I’m still going through the second chapter and will need an understanding of 6th chapter for my work – so there’s some good lot of reading coming up. But the book is really interesting. He presents intuition and phenomenology when required.

Overall, I’m happy with the project.

Heading for Two months at TIFR

I’ll be heading for Mumbai tomorrow to join the Visiting Students’ Research Programme [VSRP 2009] at TIFR.

I will be studying Theoretical Physics under Dr. Avinash Dhar and Dr. Spenta Wadia. My summer project is going to be on ‘Fluid Mechanics from Gravity’, which will eventually merge with my BTech project.

Arun Chaganty – one year ahead of his batch

Time for some random musings.

Just noticed something interesting about a friend of mine: Arun Chaganty a.k.a. vimzard (on IRC). Of course, he’s not the guy who’ll blog about himself, so I’m taking the opportunity to blog about him.

Doing a GSoC:

The average IITM-ian does a GSoC in their 2nd Year Summer. Take Kashyap, Prakash, Kirtika and me for instance – we constitute 4/7 of the institute’s GSoC-ers; another 2/7 of them being from higher years (4th / MTech).
Arun Chaganty did it in his first year.

Becoming a Coordinator for Saarang / Shaastra

A typical IITM guy ends up as a coordinator (”coord”) for Shaastra or Saarang in his second year. People think it is a crime to give the looked-down-upon “freshies” a “coord-ship” in their first year.
Arun Chaganty, of course was an exception. He was given a Saarang 2008 Coordship for “Web Operations”, as a freshie.

Becoming a Core for Saarang / Shaastra

A typical IITM guy climbs up to the “Core” post for Shaastra / Saarang only in his 4th year.
As expected, Arun is now “Web Operations Core, Shaastra 2009″ in his third year.

Doing a shtudd* internship
*shtudd = IIT(M?) lingo for “great”, “awesome”, …

Most IITians do their internships in their 3rd year summers. People usually get relatively “paltry” internships at local / Indian companies or JEE coaching institutes.
Our man is going abroad in his 2nd year summer to a highly covetable intern (not the official BTech internship thanks to a rule that stresses on Indian internships), along with a 3rd year. Once again ahead of his batch.

In summary: Arun has many-a-time been one year ahead of his batchmates. Isn’t that rather inspiring?

I wonder what Arun will do in his fourth and fifth years. I wonder if there’ll be something left for him to do. Maybe he could comment on his future plans.

KDE GSoC students from India

The KDE India community is slowly expanding, and much of this is because of Pradeepto’s remarkable efforts. GSoC adds to the developer strength of the community every year, and even this ’small’ increase in number is rather significant by percentage.

Following the same trend as the last two years, we’ve got three GSoC students from India working on KDE this summer – Kashyap Puranik, will be working on Kalzium with Carsten Niehaus, Prakash Mohan will be working on KStars with me and Kaushik Saurabh will be working on Akonadi with George Goldberg.

In addition, we may see some Season of KDE students as well, and I’m going to blog about them sometime soon

Welcoming KStars GSoC 2009 student, Prakash Mohan!

Prakash Mohan, who’s been a contributor to KStars for some time now, joins us this summer as a GSoC student. He’ll be working for a better ‘Observation Planner in KStars’.

Prakash has contributed several bugfixes to KStars. He recently added a feature for finding Oppositions to the conjunction tool. (This makes the prediction of Lunar Eclipses possible, amongst many other things.)

His project has a lot of potential and will be of immense use to amateur astronomers. The aim of the project is to integrate a lot of the tools that KStars already has into a usable interface for planning observations, and at the same time, add further useful features.

I wish Prakash the very best this summer.