Related papers: Long time scaling behaviour for diffusion with res…
In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models.…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We consider a system of interacting diffusions labeled by a geographic space that is given by the hierarchical group $\Omega_N$ of order $N\in\mathbb{N}$. Individuals live in colonies and are subject to resampling and migration as long as…
Growth and shape formation in crowded multicellular assemblies arise from the interplay of chemical gradients, single-cell expansion and mechanical interactions, making it essential to understand how these processes jointly shape collective…
Sudden turn-on of a matter-wave source leads to characteristic oscillations of the probability density which are the hallmark feature of diffraction in time. The apodization of matter waves relies on the use of smooth aperture functions…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…
Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion…
We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the bias to take…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
"Local resetting" was recently introduced to describe stochastic resetting in interacting systems where particles independently try to reset to a common "origin". Our understanding of such systems, where the resetting process is itself…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
Adaptation to changing environments is a universal feature of life and can involve the organism modifying itself in response to the environment as well as actively modifying the environment to control selection pressures. The latter case…
We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and…
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…
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…