Projects

I'm very interested in a wide range of areas, right from Engineering to Linguistics, and a daily dose of Wikipedia keeps increasing it
:-) More specifically, I love to model, simulate and visualize equations and see them come alive.In my stay at IITM, I've tried my hand out at a few things, and here is some info about them.

Biological structures viewed as optimization problems

In my project in Prof. Ganesh Subbarayan's lab at Purdue University during Summer 2007, I worked on analysing biostructures by posing them as optimization problems. Biostructures like Nacre (found in sea-shells) show remarkable mechanical properties that are of immense significance in bio-mimetic engineering. For example, Nacre has such amazingly high fracture resistance that many materials used in artificial bones are starting to be based on it. A sea-sponge called Euplectella is made, literally, of glass ! Imagine a sponge made of glass!! It turns out that this organism's structure has an extremely complicated, seven-level hierarchy that gives it this amazing property. ( More here ) My work involved applying ideas from optimization theory and geometric modelling to efficiently analyse simplified models of these structures under a large number of loading conditions and geometric constraints

Ultrasonic Ray tracing

Ultrasonic testing is a wonderful way of checking for cracks inside a component. Typically, an ultrasonic transducer is used to send waves into a component in a specfic direction, and the resulting echoes are received and studied. However, unless the geometry of the component involved is very simple, the echo "signature" obtained cannot easily be interpreted. Further, even if we do know where a crack or a defect approximately lies, it is a dauntingly difficult task to set the intial direction and intensity of the transducer so that we receive a clean echo.
To solve these problems, Ultrasonic simulations are run on computers. There are several flavors of Ultrasonic Simulations possible, right from solving the wave equation explicitly using FDM or FEM, to Multi-beam methods to Ray-tracing. The advantage of Ray-tracing is that it is very fast compared to all other methods ( ~ 15s vs 4 hrs for FDM ). At my lab here at IITM, the Center for Non Destructive Evaluation, I worked on extending ray based simulation models to include complicated geometries, and incorporating features such as cracks, voids, unconventional scan methods, etc. You can read more about the simulation software and its application in this PDF File (400 KB)

Numerical Solutions to the Wave Equation

Solving the Wave Equation exactly in a computational domain of need is the dream of anybody working in ultrasonic testing: we're getting there, but so far we've only managed to approximately solve it. One of the most direct methods of solving it is the Finite Difference Method, wherein the differentials in the wave equation are approximated by finite differences. I was part of the team which used this method to solve the QNDE 2006 Benchmark problem. The problem required Simulating the intensity of reflection from a corner echo in a steel block.The catch was, there were 5 steel blocks with varying angles of the backwall. It turns out that modeling the corner with an angled wall is rather difficult, and that complications like Staircasing, errors in Courant numbers, Applying free-surface boundary conditions, etc come up. We discovered quite a few practical insights when solving these problems, and I'll write about them here soon. Meanwhile, you could read this PDF (400 KB) for more info on our results.

Using Phased arrays to examine complex geometries

Phased Array sector scans are a convenient way of gauging cracks in a specimen. Phased arrays work on the principle of having an array of transmitters, each pulsing with a small time lag. Adjusting this time lag will let us control how the generated pulses interfere, and using a clever "delay law", we can make a near-plane beam travel at any angle! This is miles ahead of conventional ultrasonics, where a plexiglas shoe must be specially manufactured and used to send in the wave at a desired angle. However, the application of phased arrays to complex geometries like elbows has been limited because of a lack of accurate simulation models for verification and experiment design. In this work, I was part of the team which developed such a model, and validated it with experiments. (Aug – Dec 2006)

The DUIBot!

As part of the Course, Design Synthesis, I was part of a 4 member team that built an autonomous real time library cataloguing robot (functional prototype) that could scan 400 books in one minute (Named after Melvil Dui, the inventor of the near-universal Dewey Decimal Classification and advocate of spelling reform :-) ). The robot worked on both RFID and custom optical barcodes. The robot is capable of indexing books by scanning rows in succession. The software that controlled it could take in the call number as the input and search the latest database to give the user the precise last known location of the book in the library. You can download the report of the project here (PDF, 3M). Our presentation is here.

The Meru Project

I am part of the team which is in the process of engineering an open distributed computing architecture to utilize the free computing power of the 5000+ computers on the Institute network. Our aim is to make an easily accessible grid supercomputer, the first of its kind and scale in India. We are using the BOINC architecture as our base.

Vehicle Routing Problems

I am working on using evolutionary algorithms to solve Vehicle Routing Problems. VRPs, though ubiquitous in distribution systems, tend to be extremely computationally intensive, and are out of the reach of the capabilities of most small industries. My work aims at providing near-optimum solutions within affordable computing times.