Related papers: Diffusion in a rough potential revisited
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
Diffuse scattering of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several diffuse scattering models based on different approaches have…
High-dimensional networks producing oscillatory dynamics are ubiquitous in biological systems. Unravelling the mechanism of oscillatory dynamics in biological networks with stochastic perturbations becomes paramountly significant. Although…
Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes…
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the…
Recently, it was shown that the probability distribution function (PDF) of the free energy of a single continuum directed polymer (DP) in a random potential, equivalently of the height of a growing interface described by the…
In this paper, phenomenological developments are used to explore several aspects of the relative particle dispersion (RPD) in different physical fully-developed turbulence (FDT) situations. The role played by the FDT cascade physics…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
Laplace's first law of errors, which states that the frequency of an error can be represented as an exponential function of the error magnitude, was overlooked for many decades but was recently shown to describe the statistical behavior of…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We extend the statistical field-theoretical framework of rough surface contact mechanics to characterize the interfacial gap between an elastic half-space and a randomly rough surface incorporating exponential repulsion. Building upon a…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
The temperature dependence of the diffusion coefficient of particles is studied on lattices with disorder. A model is investigated with both trap and barrier disorder that was introduced before by Limoge and Bocquet (1990 Phys. Rev. Lett.…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…
We study the steady-state distribution function of a run-and-tumble particle evolving around a repulsive hard spherical obstacle. We show that the well-documented activity-induced attraction translates into a delta peak accumulation at the…