ICTS Graduate Courses for Jan-April 2016 

1) Advanced Physics Lab (Core): 

Instructor: Abhishek Dhar, Vijay Kumar, Amit Apte and T.G. Ramesh

Course description:

  1. Brownian Motion: MSD of tagged particles and determination of Avogadro’s number Number fluctuations.
  2. Vibrational modes in a box: Observation of normal mode frequencies and wavefunctions in a box excited by sound waves.
  3. Physics of a radiometer: a set of experiments designed to measure the dependence of radiometer vane speed on various parameters such as intensity and colour of radiation.

 

2) Numerical Methods for Physics & Astrophysics (Core): 

  • Floating-Point Representation and Errors
  • Roots of Equations
  • Optimization
  • Interpolation and Numerical Differentiation
  • Systems of Linear Equations
  • Ordinary Differential Equations
  • Monte Carlo Methods and Simulation

Main textbooks:

  • Numerical analysis: mathematics of scientific computing by David Kincaid and Ward Cheney
  • Introduction to numerical analysis by J. Stoer and R. Bulirsch

 

3) Data Assimilation and Dynamical Systems (Elective): 

  • quick intro (or recap) for nonlinear dynamics: bifurcations, unstable manifolds and attractors, Lyapunov exponents, sensitivity to initial conditions and concept of predictability
  • Markov chains, evolution of probabilities (Fokker-Planck equation), state estimation problems
  • an introduction to the problem of data assimilation (with examples)
  • Bayesian viewpoint, discrete and continuous time cases
  • kalman filter (linear estimation theory)
  • least squares formulation (possibly PDE examples)
  • particle filtering and MCMC sampling methods
  • advanced topics (if time permits): parameter estimation, relations to control theory, relations to synchronization, etc.