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Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…
We present results for collective diffusion of adatoms on a stepped substrate with a submonolayer coverage. We study the combined effect of the additional binding at step edge, the Schwoebel barrier, the enhanced diffusion along step edges,…
Active matter such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. Among these properties, the enhanced diffusion of tracer particles is generally deemed as a hallmark…
Several recent experiments suggest that rather generally the diffusion of enzymes may be augmented through their activity. We demonstrate that such swimming motility can emerge from the interplay between the enzyme energy landscape and the…
Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice gas model we study how the interplay between active and…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
The rate-limiting step of some enzymatic reactions is a physical step, i.e. diffusion. The efficiency of such reactions can be improved through an increase in the arrival rate of the substrate molecules, e.g. by a directed passage of…
We study transport of a weakly diffusive pollutant (a passive scalar) by thermoconvective flow in a fluid-saturated horizontal porous layer heated from below under frozen parametric disorder. In the presence of disorder (random frozen…
Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These…
We study the effect of the crowded nature of the cellular cytoplasm on the translocation of a polymer through a pore in a membrane. By systematically treating the entropic penalty due to crowding, we show that the translocation dynamics are…
The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field.…
Intracellular transport of vesicular cargos, organelles, and other macromolecules is an essential process to move large items through a crowded, and inhomogeneous cellular environment. In an effort to dissect the fundamental effects of…
Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and…
We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the…
Chemically active colloids or enzymes cluster into dense droplets driven by their phoretic response to collectively generated chemical gradients. Employing Brownian dynamics simulation techniques, our study of the dynamics of such a…
To study the impact of active systems on their surroundings, we introduce a model that couples an active nematic fluid to an isotropic substrate fluid via friction. We numerically show that as the active layer develops turbulence, the…
We analytically study the time-averaged electromagnetic energy stored inside scatterers containing inclusions of arbitrary shapes. Assuming the low density of inclusions, we derive the expression for the energy-transport velocity through…
The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…
Fluctuations in the energy gap and coupling constants in and between chromophores can play important role in the absorption and energy transfer across a collection of two level systems. In a noisy environment, fluctuations can control…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…