Talks

We investigate the dynamics of subsystem particle number fluctuations in a long-range system with power-law decaying hopping strength and subjected to a local dephasing at every site. We introduce an efficient bond length representation for the four-point correlator, enabling the large-scale simulation of the dynamics of particle number fluctuations from translationally invariant initial states. Our results show that the particle number fluctuation dynamics exhibit one-parameter Family-Vicsek scaling, with superdiffusive scaling exponents for long-range hopping exponent values less than 3/2 and diffusive scaling exponents for values greater or equal to 3/2. Finally, exploiting the bond-length representation, we provide an exact analytical expression for the particle number fluctuations and their scaling exponents in the short-range limit.

We explore the phenomena of prethermalization in a many-body classical system of rotors under aperiodic drives characterised by waiting time distribution (WTD), where the waiting time is defined as the time between two consecutive kicks. We consider here two types of aperiodic drives: random and quasi-periodic. We observe a short-lived pseudo-thermal regime with algebraic suppression of heating for the random drive where WTD has an infinite tail, as observed for Poisson and binomial kick sequences. On the other hand, quasi-periodic drive characterised by a WTD with a sharp cut-off, as observed for Thue-Morse sequence of kick, leads to prethermal region where heating is exponentially suppressed. The kinetic energy growth is analyzed using an average surprise associated with WTD quantifying the randomness of drive. In all of the aperiodic drives we obtain the chaotic heating regime for late time, however, the diffusion constant gets renormalized by the average surprise of WTD in comparison to the periodic case.

Cilia and flagella are micron-sized slender filaments that actively beat in a viscous medium with remarkable accuracy despite thermal fluctuations and other uncertainties. Such precise beating is essential for swift locomotion for microorganisms and for generating an efficient flow in a carpet of cilia in fluid media. To understand the role of the interplay between dissipation and cilia activity in achieving such a precise oscillation, we study a minimal model of cilia known as the rower model. Here, the complex beating of a filament is simplified by a one-dimensional periodic motion of a micron-sized bead between two positions (the amplitude) immersed in a viscous fluid. The bead performs Brownian motion in one of the two harmonic potentials and switches to the other once it reaches two specific positions with a pump of energy which is a measure of cilia activity. We quantify the precision using the quality factor and find a scaling law for the precision with activity and dissipation. Interestingly, for an optimal amplitude where the precision becomes maximum. The scaling and optimal behavior in the quality factor can be explained by studying the noise in the first passage time. Finally, we discuss the energy budget in achieving precision.

The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. In this talk I will present a simple, analytically tractable model which fills the gap between mathematical formulations of multifractional Brownian motion and empirical studies. In the model, called telegraphic multifractional Brownian motion (TeMBM), the Hurst exponent is modelled by a smoothed telegraph process which results in a stationary beta distribution of exponents as observed in biological experiments. I will also discuss a methodology to identify TeMBM in experimental data and present concrete examples from biology, climate and finance to demonstrate the efficacy of the presented approach.

Mathlib is a vast and constantly growing library of formalized mathematics. As its size increases, it becomes increasingly easy to spend a significant amount of time formalizing a theorem, only to later discover that it was already present in the library. This can be both frustrating and discouraging. In this talk, we will introduce and demonstrate a variety of tools and techniques that can help users efficiently navigate Mathlib, search for existing results, and better understand the structure of the library.

Proteins are biopolymers, composed of repeating sequence of amino acids (AA). In a typical sequence, the constituting AAs have different charges, hydrophobicity, and capacities to form directional and non-directional interactions. Such heterogeneity can results in sequences lacking a stable three dimensional structure. This class of proteins are intrinsically disordered protein (IDPs). A deeper understanding of IDPs require appropriate characterization of the conformations. To this end, scattering and single molecular spectroscopic measurements often assign a single Flory exponent (equivalently fractal dimension) to the IDPs. In this talk, I highlight limitation of this method by enhanced sampling of atomistic resolution conformations of disordered \beta-casein. I will show that the underlying energy landscape of the IDP contains a global minimum along with two shallow funnels. Employing static polymeric scaling laws separately for individual funnels, we find that they cannot be described by the same polymeric scaling exponent. Around the global minimum, the conformations are globular, whereas in the vicinity of local minima, we recover coil-like scaling. To elucidate the implications of structural diversity on equilibrium dynamics, we initiated standard MD simulations in the NVT ensemble with representative conformations from each funnel. Global and internal motions for different classes of trajectories show heterogeneous dynamics with globule to coil-like signatures. Thus, IDPs can behave as entirely different polymers in different regions of the conformational space.