Wolfram Computation Meets Knowledge

Wolfram Summer School


Arnab Kar

Summer School

Class of 2013


My journey on this planet started in a small town in the eastern part of India. After finishing my undergraduate studies in Physics at Chennai Mathematical Institute, I joined the PhD program in Physics at the University of Rochester. Of the many things that I am interested in, I mostly work on ideas related to renormalization in field theory. This got me interested in several mathematical topics like measure theory and metrics. The notion of distance (metrics) forms an important component in complex network systems. While I was awestruck by its varied applications (social networking being one of them), I started coding in Mathematica to visualize and analyze different properties of a network for problems related to physics.

All these aside, what interests me most is playing sports like soccer, cricket, volleyball, badminton, and a few more. After having stayed in a place where bright sunshine is rare to come by, my interests in movies and music for the weary winters have escalated on one hand, while outdoor activities like biking, hiking, and kayaking keep me me exhausted during the short summer.

Project: Complexity in Nonlinear n+1 Fields

In the early days of relativistic quantum mechanics, when attempts were made to describe various particles in nature, an equation was proposed by Oskar Klein and Walter Gordon to describe the electrons. However, their proposal turned out to be wrong, though it could, on the other hand, describe spinless particles like pion. We study a nonlinear version of that differential equation for certain boundary conditions in various dimensions.

Surprisingly, a connection between those solutions and the Duffing oscillator was found. Duffing oscillator is an example of a forced and damped harmonic oscillator. The trajectories on the phase space for the two entirely different dynamical systems were plotted and striking resemblance was found. It goes without saying that the nonlinearity in the systems makes them chaotic in nature and worth investigating.

Favorite Four-Color, Four State Turing Machine

Rule 963557619986781740299