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Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Due to the large-scale structured galactic magnetic field this diffusion is anisotropic with respect to the local field…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
We study a model of contraction-based cell motility inside a microchannel to investigate the regulation of cell polarization and motion by the mechanical resistance of the environment. A positive feedback between the asymmetry of the…
High-resolution imaging provides dense trajectories of migrating cells, flocking animals, and synthetic active particles, from which interaction laws can be determined with a wide variety of methods. Yet, distinguishing whether front-back…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
Channel proteins, that selectively conduct molecules across cell membranes, often exhibit an asymmetric structure. By means of a stochastic model, we argue that channel asymmetry in the presence of non-equilibrium fluctuations, fueled by…
The goal of the present paper is the investigation of the evolution of anisotropic regular structures and turbulence at large Reynolds number in the multi-dimensional Burgers equation. We show that we have local isotropization of the…
We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
Simple models of interacting spins play an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, systems with gauge fields, high-Tc…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
Transport of nanoscale objects in complex, structured environments plays a key role in a wide range of processes, from biomolecular dynamics in extracellular spaces to transport in porous materials such as filters and catalysts. While…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
In densely-packed two-dimensional systems of growing cells, such as rod-shaped bacteria, a number of experimental and numerical studies report distinct patterns of nematic orientational order in the presence of confinement. So far, these…