**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.

**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

**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