1.  Advanced Classical Mechanics

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.

Course webpage

2. Physics of Living Matter

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

Dynamical systems
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

Soft matter
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 matter
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

 Course webpage

3. General Physics Lab

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

Course outline:

1. Young’s modulus by flexural vibrations of a bar. This involves a partial differential equation of fourth order in space and second order in time. The boundary conditions lead to an overtone which is 6.22 times the fundamental.

2. Thermal diffusivity of brass. In this experiment we have a damped thermal wave and we find the decay of the amplitude and the phase constant determining the phase difference of the wave between two points. Since the heating is not by a sine wave, one has to Fourier analyze the temperature as a function of time at two points to measure the constants.

3. Dielectric constant of a polar liquid and the dipole moment of Acetone. This introduces the concept of local electric field and uses the Clausius Mosotti relation.

4. Verification of Curie-Weiss law by studying the temperature variation of the capacitance of a ceramic capacitor.

5. Thermal relaxation of a serial light bulb to verify Debye Relaxation formula.

6. B-H curve of a hard magnetic material using an integrator.

7. Calibration of a lock in amplifier and measuring the mutual inductance of a coil.

8. Experiments in Non-linear dynamics – Feigenbaum and Chua circuits

9. Measurement of electron charge by Shot Noise.

10. Seebeck coefficient setup for Semiconductors

11. Van der Paw Arrangement for Resistivity