Understanding transport processes through membranes require the modeling of diffusion, particularly when it comes to enhancing process effectiveness. The goal of this research is to understand the relationship between membrane structures, external forces, and the characteristic features of diffusive transport. We investigate Cauchy flight diffusion with drift in heterogeneous membrane-like...

We discuss the impact of polydispersity on particle currents generated by Brownian hard spheres when they are driven through periodic potentials by a constant drag force. Considering random mixtures of two types of spheres, we explain the variation of the currents with the mixing ratio of the two components and with the hard-sphere diameters. A basic unit cell exists in the space of the two...

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in...

Investigation of non-equilibrium fermionic transport in a periodically-driven tilted lattice is currently a subject of major interest. Transport properties in this setting are influenced by the drive, tilt, and interactions, as well as the non-Markovian nature of the fermionic reservoirs. We address this setup with two complementary tools, with an ultimate aim at addressing the interplay of...

Recent developments in experimental condensed matter physics allow for realization of Abelian gauge Hamiltonians on routinely controllable systems (Josephson junction arrays, optical lattices, etc). This opened the prospect of simulation of the phenomena of compact quantum electrodynamics and quantum chromodynamics (e.g, quark confinement) in the laboratory setup.

We consider $Z_N$ symmetric...

To describe the growth of a cell colony, processes such as cell division, cell death and cell movement must be taken into account. All of these mechanisms can have multiple contributing factors, and one of them is the density of cells in the surroundings.

It is often assumed that the growth of cancer cell colonies is characterized by an exponential increase in the number of cells, and a...

Biological systems ranging from cytoskeletal networks to bacterial suspensions and epithelial monolayers exhibit complex chaotic flows known as active turbulence. Countless active molecular interactions combine to form a turbulent mix of behaviours, with fascinating non-equilibrium properties. With an eye to developing a quantitative understanding, we study turbulence and spatiotemporal chaos...

Knotted proteins can become jammed when forced through pores if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, enabling translocation. This process can be described using a simple energy landscape model with a time-periodic potential that mimics the action of a molecular motor. Such a stochastic model exhibits similar behaviour to results...

Active nematics are active fluids composed of elongated constituents in which force dipoles at the micro scale generate macroscopic flows. As in other active systems, bulk active nematics exhibit chaotic flows known as active turbulence. Unique to active nematics, however, is the existence of local orienational order, allowing the prescription of topological defects from various boundary...

In this work we study the problem of a random walk

in a finite-size randomly inhomogeneous one-dimensional medium by using a Fock space approach.

We map the master equation of the walker into a Schr\"odinger-like equation

and we describe the evolution of the random walk in a Fock space in which the

system states are assigned to the sites of a regular one-dimensional lattice.

This...

Patterns arise in nature at different scales. We can recognize animals based on their furry patterns alone, from the spots on a leopard to the stains on a cow. However, patterns are established also during embryonic development, through interactions of diffusing molecules that activate expression of target genes. As a result a striped pattern of gene expression emerges. These stripes will...

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of diffusion on all time scales in equilibrium or non-equilibrium steady states [1,2] and for transient or non-ergodic dynamics [3]. The time averaging and coarse graining hardwired in the definition of the functionals under consideration give rise to experimentally relevant...

We investigate the anomalous kinetics of two-species reaction-diffusion system $A+A \rightarrow (\emptyset, A)$, $A+B \rightarrow A$ near its upper critical dimension $d_c = 2$. In particular, we analyze an advection of reactants by random velocity field generated by the stochastically forced Navier-Stokes equation. The model is analysed by means of field-theoretic renormalization group (RG)...

Magnetohydrodynamic (MHD) turbulence driven by the stochastic Navier-Stokes equation always has been a subject of intense study. In an electrically conducting media developed turbulence has a number of specific properties associated with magnetic field fluctuations which under certain conditions can increase and lead to the formation of a non-zero average large-scale magnetic field. This...

Often the motion in complex systems is subdiffusive. Meaning, instead of a linear dependence on time, the mean square displacement (MSD) grows as $\sim t^\alpha$ where $0 < \alpha < 1$. This can be attributed to long waiting times that cause a significant slowdown from the classical description of Brownian motion. But a slow down of the MSD can also arise from repeated collisions with...

Slow compression of a hard-sphere fuid at constant temperature yields an entropy-driven first-order transition from the liquid to a crystalline phase [1, 2]. When the fuid is compressed quickly rather than slowly, however, crystallization can be avoided and the particles "jam" in a disordered configuration. The determination of the so-called *random close packing* (RCP) density, defined as the...

Classical measuring methods used in material engineering are not suited for biological tissues, especially in microscale. It is almost impossible to produce a homogenous specimen of biological material for a classical tensile test. Indentation experiments are much easier to perform on a microscopic object like a cell. However, this comes at a cost: interpretation of the results. Extracting...

Engines powered by active particles are well-known for their exceptionally high performance: their efficiency can surpass the Carnot efficiency while simultaneously achieving positive power. However, this 'super-Carnot' behavior arises from considering the apparent statistical signature of the system as a whole, without distinguishing heat and work.

Consequently, this ‘apparent’ description...

Active work quantifies the amount of energy converted into the actual motion of active particles. In the long-time limit, the time-averaged active work quantifies how much energy is dissipated by active particles into the surrounding environment, i.e., it is a measure of the entropy production rate of active particles. Thus, by calculating the large deviation function (LDF) of the...

The effective dynamics of stochastic systems with a finite number of states where only a few degrees of freedom are accessible to observation is described in terms of coarse-grained models. Coarse graining on states typically entails non-markovianity that is recovered under physically motivated assumption, thus restricting the range of applicability of such models. We use a novel approach...

Understanding the role of active fluctuations in physics is a problem emerging both as a hot topic and a major challenge. The reason for this is their inherent non-equilibrium nature. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone. Recently a paradoxical effect has been briefly communicated in which a free particle...

A major challenge in soft matter physics is to understand the repercussions of an external shear flow on the microscopic structure of colloidal suspensions. In the case of diluted suspensions of spherical colloids, a common starting point for the theoretical treatment of the problem is the two-body Smoluchowski *convection-diffusion* equation [1]. However, solving the latter equation is...

We present two approaches to explore the dynamics of many-body localization (MBL) in disordered interacting quantum systems using experimentally measurable single- and two-site correlation functions.

First [1], we propose an algorithm based on neural networks that uses two-site correlation functions to detect ergodic bubbles, i.e., delocalized regions surrounded by a localized phase, with a...

We studied random sequential adsorption packings constructed from rectangles,

ellipses, and discorectangles, where the orientations of constituent shapes were

picked from discrete sets of values with varying spacing. It allowed us to monitor

the transition between the two edge cases: the parallel alignment and the arbitrary, continuous orientation of the shapes within the packing. The...