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The mass and size distributions are the key characteristics of any astrophysical objects, including the densest clumps comprising the cold phase of multiphase environments. In our recent papers, we showed how individual clouds of various…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Heteroepitaxial structures based on Bi$_{2}$Te$_{3}$-type topological insulators (TIs) exhibit exotic quantum phenomena. For optimal characterization of these phenomena, it is desirable to control the interface structure during film growth…
We report on grain dynamics versus depth for steady-state gravity-driven flow of grains along a heap formed between two parallel sidewalls. Near the surface the flow is steady and fast, while far below there is no flow whatsoever;…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
Communities of swimming microorganisms often thrive near liquid-air interfaces. We study how such `active carpets' shape their aquatic environment by driving biogenic transport in the water column beneath them. The hydrodynamic stirring…
We study the meandering instability during growth of an isolated nanostructure, a crystalline cone, consisting of concentric circular steps. The onset of the instability is studied analytically within the framework of the standard…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
Diffusion models achieve great success in generating diverse and high-fidelity images, yet their widespread application, especially in real-time scenarios, is hampered by their inherently slow generation speed. The slow generation stems…
Transport across heterogeneous, patchy environments is a ubiquitous phenomenon spanning fields of study including ecological movement, intracellular transport and regions of specialised function in a cell. These regions or patches may be…
The flow of motor proteins on a filamental track is modelled within the the framework of lattice driven diffusive systems. Motors, considered as hopping particles, perform a highly biased asymmetric exclusion process when bound to the…
Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…
Variations of transport efficiency in structured environments between distinct individuals in actively self-propelled systems is both hard to study and poorly understood. Here, we study the transport of a non-tumbling {\ecoli} strain, an…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
The evolution of the allelic proportion $x$ of a biallelic locus subject to the forces of mutation and drift is investigated in a diffusion model, assuming small scaled mutation rates. The overall scaled mutation rate is parametrized with…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…