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While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
It is shown that the critical properties of a recently studied model for non-equilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
A simple model accounting for the ejection of heavy particles from the vortical structures of a turbulent flow is introduced. This model involves a space and time discretization of the dynamics and depends on only two parameters: the…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from…
Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening…
We analyze differences in dynamics and in properties of the sampled potential energy landscape between different equilibrium trajectories, for a system of rigid water molecules interacting with a two body potential. On entering in the…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a…
We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or…
Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…
The fundamental insight into Brownian motion by Einstein is that all substances exhibit continual fluctuations due to thermal agitation balancing with the frictional resistance. However, even at thermal equilibrium, biological activity can…
We present a first-principles formalism for studying dynamical heterogeneities in glass forming liquids. Based on the Non-Equilibrium Self-Consistent Generalized Langevin Equation theory, we were able to describe the time-dependent local…
We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is…
We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to…