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Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
We consider many-particle diffusion in one spatial dimension modeled as Random Walks in a Random Environment (RWRE). A shared short-range space-time random environment determines the jump distributions that drive the motion of the…
It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on "intermediate" time scales before diffusion sets in.…
A driven Brownian particle (e.g. an adatom on a surface) diffusing on a low-viscosity, periodic substrate may execute multiple jumps. In the presence of an additional periodic drive, the jump lengths and time durations become statistically…
Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…
We use large scale molecular dynamics simulations of the isomerizations of azobenzene molecules diluted inside a simple molecular material, to investigate the effect of a modification of the cis isomer shape on the induced diffusion…
We discuss the results of simulations of an intruder pulled through a two-dimensional granular system by a spring, using a model designed to lend insight into the experimental findings described by Kozlowski et al. [Phys. Rev. E, 100,…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
In absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present and can be parameterised in terms of effective or turbulent…
The novel species injector of a recently developed research burner, consisting of an array of hypodermic needles, which allows to produce quasi one-dimensional unstrained diffusion flames has been improved. It is used in a new symmetric…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
Molecular diffusion measurements are widely used to probe microstructure in materials and living organisms noninvasively. The precise relation of diffusion metrics to microstructure remains a major challenge: In complex samples, it is often…