Sakuntala Chatterjee

Shock probes in a one-dimensional Katz-Lebowitz-Spohn model.

We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Dynamics of shock probes in driven diffusive systems

We study the dynamics of shock-tracking probe particles in driven diffusive systems and also in equilibrium systems. In a driven system, they induce a diverging timescale that marks the crossover between a passive scalar regime at early times and a diffusive regime at late times; a scaling form characterizes this crossover. Introduction of probes into an equilibrium system gives rise to a system-wide density gradient, and the presence of even a single probe can be felt across the entire system.

Diffusion of a hydrocarbon mixture in a one-dimensional zeolite channel: An exclusion model approach

Zeolite channels can be used as effective hydrocarbon traps. Earlier experiments (Czaplewski {\sl et al.}, 2002) show that the presence of large aromatic molecules (toluene) block the diffusion of light hydrocarbon molecules (propane) inside the narrow pore of a zeolite sample. As a result, the desorption temperature of propane is significantly higher in the binary mixture than in the single component case. In order to obtain further insight into these results, we use a simple lattice gas model of diffusion of hard-core particles to describe the diffusive transport of two species of molecules in a one-dimensional zeolite channel. Our dynamical Monte Carlo simulations show that taking into account an Arrhenius dependence of the single molecule diffusion coefficient on temperature, one can explain many significant features of the temperature programmed desorption profile observed in experiments. However, on a closer comparison of the experimental curve and our simulation data, we find that it is not possible to reproduce the higher propane current than toluene current near the desorption peak seen in experiment. We argue that this is caused by a violation of strict single-file behavior.

Strong molecular traffic control effect in TNU-9 zeolite channel topology.

Reactivity enhancement in a catalytic zeolite grain through molecular traffic control (MTC) rests on the basic notion that the reactant and product molecules prefer to diffuse along different channels inside the grain and therefore do not mutually hinder their transport in and out of the grain. We investigate the conditions of reactivity enhancement in the presence of MTC for a realistic channel topology that describes the pore structure of a TNU-9 zeolite. We compare the output current of an MTC system with a reference system, which does not show any channel selectivity. For a wide range of reaction rates and for different grain sizes, we find that there is a very significant enhancement of reactivity for the MTC system. This effect remains strong as the grain size increases. The mechanism behind reactivity enhancement is argued to be generic rather than being confined to the particular structure of TNU-9.

Actin filaments growing against a barrier with fluctuating shape.

We study force generation by a set of parallel actin filaments growing against a nonrigid obstacle, in the presence of an external load. The filaments polymerize by either moving the whole obstacle, with a large energy cost, or by causing local distortion in its shape which costs much less energy. The nonrigid obstacle also has local thermal fluctuations due to which its shape can change with time and we describe this using fluctuations in the height profile of a one-dimensional interface with Kardar-Parisi-Zhang dynamics. We find the shape fluctuations of the barrier strongly affect the force generation mechanism. The qualitative nature of the force-velocity curve is crucially determined by the relative time scale of filament and barrier dynamics. The height profile of the barrier also shows interesting variation with the external load. Our analytical calculations within mean-field theory show reasonable agreement with our simulation results.

Large compact clusters and fast dynamics in coupled nonequilibrium systems.

We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle densities and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains.

Optimal search in E.coli chemotaxis

We study chemotaxis of a single E. coli bacterium in a medium where the nutrient chemical is also undergoing diffusion and its concentration has the form of a Gaussian whose width increases with time. We measure the average first passage time of the bacterium at a region of high nutrient concentration. In the limit of very slow nutrient diffusion, the bacterium effectively experiences a Gaussian concentration profile with a fixed width. In this case we find that there exists an optimum width of the Gaussian when the average first passage time is minimum, i.e., the search process is most efficient. We verify the existence of the optimum width for the deterministic initial position of the bacterium and also for the stochastic initial position, drawn from uniform and steady state distributions. Our numerical simulation in a model of a non-Markovian random walker agrees well with our analytical calculations in a related coarse-grained model. We also present our simulation results for the case when the nutrient diffusion and bacterial motion occur over comparable time scales and the bacterium senses a time-varying concentration field.

The importance of boundary effects in diffusion of hydrocarbon molecules in a one-dimensional zeolite channel

Single-file diffusion of propane and toluene molecules inside a narrow, effectively one-dimensional zeolite pore was experimentally studied by Czaplewski et al. Using a stochastic lattice gas approach, we obtain an analytical description of this process for the case of single-component loading. We show that a good quantitative agreement with the experimental data for the desorption temperature of the hydrocarbon molecules can be obtained if the process of desorption from the boundary is associated with a higher activation energy than the diffusion process in the bulk. We also present dynamical Monte Carlo simulation results for two-component loading which demonstrate in agreement with the experimental findings the effects of mutual blockage of the molecules due to single-file diffusion.

Interacting particles in a periodically moving potential: traveling wave and transport.

We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.

Ordered phases in coupled nonequilibrium systems: Dynamic properties

We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in different ways. As a result of this two-way coupling between the landscape and the particles, the system shows interesting new phases, characterized by different sorts of long-ranged order in the particles and in the landscape. In all these ordered phases, the two particle species phase separate completely from each other, but the underlying landscape may either show complete ordering, with macroscopic regions with distinct average slopes, or may show coexistence of ordered and disordered regions, depending on the differential nature of effect produced by the particle species on the landscape. We discuss several aspects of static properties of these phases in this paper, and we discuss the dynamics of these phases in the sequel.