ICTS

In my first lecture I’ll cover physical properties of membranes like self-assembly, elasticity, thermal fluctuations, and budding transitions. If time permits I’ll also discuss analogy between membrane dynamics and dynamics of semi-flexible polymers.

Quantized lattice vibrations called phonons are the primary heat carriers in semiconductors and certain metals. Mathematically, phonons are defined as the eigenmodesof an idealized crystal lattice with perfectly harmonic potential, and so, can propagate through the crystal without damping when a non-equilibrium distribution of phonons is established. Weak perturbative anharmonicities and defects/boundaries/imperfections in real crystals, however, cause damping of these phonon modes through phonon-phonon and phonon-defect scattering respectively. While first principles computational techniques have enabled accurate descriptions of some of the scattering processes that the phonon modes undergo [1-3], it has been challenging to extract any scattering-related information experimentally, due to the difficulties in exciting individual phonon modes in a non-equilibrium thermal experiment. In this talk, I will describe the theory and implementation of our recent work on the mode-resolved phonon scattering spectroscopy using the transient grating experiment, that enables the extraction of microscopic phonon scattering information, such as phonon mean free paths, directly from a thermal experiment. I will also show some results on the mode-resolved surface scattering rates of phonons in silicon nanofilms extracted using this technique [4].
References:
[1] K. Chen*, B. Song*, N. Ravichandran* et al., Science 367(6477), 2020. [*: Equal contribution]
[2] N. Ravichandran & D. Broido, Nature Communications, 10(827), 2019
[3] F. Tian, B. Song, X. Chen, N. Ravichandran et al., Science 361(6402), 2018
[4] N. Ravichandran, H. Zhang & A. Minnich, Phys. Rev. X, 8(4), 041004, 2018

We study the static and dynamic properties of the gap between two run and tumble particles (RTPs) interacting through hardcore repulsion and moving in one dimension in the presence of translational diffusion. We calculate exact gap distribution in the steady state on a ring and find that this is exponentially localised in space, in contrast to the `jammed' configuration emerging in the absence of thermal noise. We also study the relaxation which is an exponential, characterised by a time scale which undergoes a crossover from a system size independent value to a size dependent form. For large systems, the relaxation time increases as the square of the system size. Using the symmetries in the problem we analytically study the full spectrum of the time evolution operator and characterise the transient properties of the gap distribution. On infinite line the system does not have a steady state. The long time behaviour on the infinite line is exactly computed which resembles the gap distribution between interacting passive particles, except a signature of activity for small gap.

We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive forces, aggregate into several motile and dynamical clusters of comparable size. We find that the cluster size distribution of these aggregates is a scaled function of the density and activity parameters across the three models of active particles with the same scaling function. The velocity distribution function of these mobile clusters is non-Gaussian. We show that the effective dynamics of these clusters can explain the observed emergent scaling of the mean-squared displacement of tagged particles for all the three models with identical scaling exponents and functions. Concomitant with the clustering seen at high activities, we observe that the static density correlation function displays rich structures, including several peaks in the static two-point function, reminiscent of particle clustering induced by effective attractive interactions, while the dynamical variant shows non-diffusive scaling. Our study reveals a universal scaling behavior in the single-file dynamics of strongly interacting active particles.

Brief review of relevant macroscopic thermodynamics.
Introduction to and derivations of nonequilibrium work relations.
Connections to 2nd Law: probabilities of observing "violations".
Guessing the direction of Time's Arrow.
Discussion of fluctuation theorems for entropy production.

I will discuss (i) an exact mapping  between  trajectories of Active Brownian Particles (ABP) and various polymer configuration and (ii) an exact method of computing all moments, of both positional and orientational degrees of freedom of free and harmonically trapped ABPs. Some applications will be discussed.

I will talk about run and tumble dynamics in inhomogeneous medium in one dimension. The run and tumble dynamics is a simple model that mimics bacterial chemotaxis. The dynamics in  homogenous medium is known to become diffusive at large times. Question is what happens in inhomogeneous medium? Presenting a toy model, I will show that the fluctuations become non-diffusive at large time and the distribution obeys a scaling form which can be exactly computed. I will also discuss about the first-passage properties and persistent exponents for the toy model.

First I will review theoretical and experimental efforts to characterize sources of irreversibility and dissipation in living systems from measurements of few fluctuating variables. Special emphasis will be given to the case of active mechanosensory hair bundles in the ear of the bullfrog. 

The second lecture will discuss fluctuations of RNA polymerases during transcription. I will present minimal models that describe recovery from transcriptional pauses using stochastic resetting and their application to experimental data.