1. Advanced Classical Mechanics (Aug 2015)
Instructor : Pallab Basu (ICTS)
Course outline :
Basics of modern classical mechanics
We discuss Lagrangian, Principle of least action, Symmetry and Noether charge, Poission bracket, Hammilton-Jacobi equations etc. Includes a review of various regular topics like spherically symmetric potential, rigid and non-rigid body, reference frame etc in a language of Lagrangian and Hamiltonian. We also discuss friction, dissipative systems and hydro-statics.
Chaos and Fractals
We discuss various topics in Chaos theory including non-linear dynamics, discrete maps, bifurcation, Hamiltonian and driven-dissipative chaotic systems, Lyapunov exponent, fractals, strange attractors etc.
* Special Relativity
We discuss Lorent'z transformation and some introductory special relativity.
* Classical Field theory
We would discuss some introductory classical field theory and fluid-dynamics.
Topics marked * are special topics and may be skipped partially (or altogether) depending on circumstances.
The course will often use numerical techniques. If needed, there will be few lectures introducing aspects of various software like Mathematica, Python, C++ etc.
2. Physics of Living Matter (Aug 2015)
Instructor(s) : K Vijay Kumar (ICTS) and Madan Rao (NCBS)
Course outline :
Basic phenomenology of living systems
Scales, order-of-magnitudes, structures in cells and tissues, genetics, cellular processes, information processing, morphogenesis, population genetics and evolution
Chemical dynamics, signalling, networks, stochastic chemical kinetics
Basic concepts in condensed matter
Stochastic dynamics of particles and fields - Langevin/Fokker-Planck equations, linear response, correlation functions, fluctuation-dissipation theorems, Onsager relations, Kramers rates, active processes
Generalised hydrodynamics - Passive solids and fluids, Generalised elasticity, Navier-Stokes equations, Reynolds numbers, Stokesian flows, Viscoelasticity
Polymers - Freely jointed chain, bead-spring models, semiflexible polymers, persistence length
Liquid crystals - Phenemenology, bend-splay-twist, Frank free energies, nematodynamics
Membranes - Differential geometry of surfaces, bending energy, Monge representation
Active particles - Molecular motors, ratchet models, swimming microorganisms, contractile-extensile active particles
Active fluids - Conservation laws, broken symmetries, Vicsek model, Toner-Tu theory, active anisotropic media
Pattern formation - Chemical systems, bifurcations, linear-stability analysis, reaction-diffusion theory, French-flag and
Turing models, pattern formation in active fluids