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We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…

Behavior of the mixture of particles and dimers moving with different jump rates at reconstructed surfaces is described. Collective diffusion coefficient is calculated by the variational approach. Anisotropy of the collective particle…

Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger…

We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a…

The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the…

Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…

Heavy particles in turbulent flows have been shown to accumulate in regions of high strain rate or low vorticity, a process otherwise known as preferential concentration. This can be observed in geophysical flows, and is inferred to occur…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…

The lack of a simple operable method for longitudinal dynamic self-assembly of particles in a microchannel is one of the main problems in applying this technology to a wide range of researches, such as biomedical engineering, material…

We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…

Brownian diffusion subject to stochastic resetting to a fixed position has been widely studied for applications to random search processes. In an unbounded domain, the mean first-passage time at a target site can be minimized for a…

We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…

Particles are injected to a large planar rectangle through the boundary. Assuming that the particles move independently from one another and the boundary is also absorbing, we identify a set of abstract conditions which imply the local…

Dynamical clustering represents a characteristic feature of active matter consisting of self-propelled agents that convert energy from the environment into mechanical motion. At the micron scale, typical of overdamped dynamics, particles…

We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…

Rectification and diffusion of non-interacting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient.…