Trapped tracer in a non-equilibrium bath: dynamics and energetics.

We study the dynamics of a tracer that is elastically coupled to active particles being kept at two different temperatures, as a prototype of tracer dynamics in a non-equilibrium bath. Employing analytical techniques, we find the exact solution of the probability density function for the effective motion of the tracer. The analytical results are supported by numerical simulations. By combining the experimentally accessible quantities such as the response function and the power spectrum, we measure the non-equilibrium fluctuations in terms of the effective temperature. In addition, we compute the energy dissipation rate to find the precise effects of activity. Our study is relevant in understanding athermal fluctuations arising in cytoskeletal networks or inside a chromosome.

Inertial particle under active fluctuations: Diffusion and work distributions.

We study the underdamped motion of a passive particle in an active environment. Using the phase space path integral method we find the probability distribution function of position and velocity for a free and a harmonically bound particle. The environment is characterized by an active noise which is described as the Ornstein-Uhlenbeck process (OUP). Taking two similar, yet slightly different OUP models, it is shown how inertia along with other relevant parameters affect the dynamics of the particle. Further we investigate the work fluctuations of a harmonically trapped particle by considering the trap center being pulled at a constant speed. Finally, the fluctuation theorem of work is validated with an effective temperature in the steady-state limit.

Motion of an active particle with dynamical disorder.

We propose a model for investigating the motion of a single active particle in a heterogeneous environment where the heterogeneity may arise due to crowding, conformational fluctuations and/or slow rearrangement of the surroundings. Describing the active particle in terms of the Ornstein-Uhlenbeck process (OUP) and incorporating heterogeneity in a thermal bath using two separate models, namely "diffusing diffusivity" and "switching diffusion", we explore the essential dynamical properties of the particle for its one-dimensional motion. In addition, we show how the dynamical behavior is controlled by dynamical variables associated with active noise such as strength and persistence time. Our model is relevant in the context of single particle dynamics in a crowded environment, driven by activity.

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise.

We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ=0 and κ=∞ correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.

Exact solution to the first-passage problem for a particle with a dichotomous diffusion coefficient.

We consider the problem of first-passage time for reaching a boundary of a particle which diffuses in one dimension and is confined to the region x∈(0,L), with a diffusion coefficient that switches randomly between two states, having diffusivities that are different. Exact analytical expressions are found for the survival probability of the particle as a function of time. The survival probability has a multiexponential decay, and to characterize it, we use the average rate constant k, as well as the instantaneous rate r(t). Our approach can easily be extended to the case where the diffusion coefficient takes n different values. The model should be of interest to biological processes, in which a reactant searches for a target in a heterogeneous environment, making the diffusion coefficient a random function of time. The best example for this is a protein searching for a target site on the DNA.

Heat fluctuation of a harmonically trapped particle in an active bath.

We study the heat fluctuation of an overdamped Brownian particle trapped in a harmonic potential and driven by active noise. Employing the phase-space path integral method we derive a general formula for the probability distribution of heat exchange in a generic model of an active bath. The work has been extended by considering two particular models of active noise and computing an exact analytical expression for distribution in Gaussian colored noise and a semianalytical result in the Poissonian bath. We corroborate the fluctuation theorem with our analytical findings by introducing the familiar concept of effective temperature and as a corollary the total entropy production is calculated.

Synthesis of optically active 2- and 3- indolylglycine derivatives and their oxygen analogues.

2-Indolylglycine derivative and its oxygen analogue have been synthesized by Sonogashira coupling followed by cyclization in one pot between 2-iodoheteroarenes and ethynyloxazolidinone where 3-indolylglycine derivative and its oxygen analogue have been synthesized from silylated internal alkyne using Larock's heteroannulation as the key reaction.

Some novel molecular frameworks involving representative elements.

Several new molecular frameworks with interesting structures, based on clusters of main group elements have been studied at different levels of theory with various basis sets. Conceptual density functional theory based reactivity descriptors and nucleus independent chemical shift provide important insights into their bonding, reactivity, stability and aromaticity.