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The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics,…
Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We study non-equilibrium velocity fluctuations in a model for the sedimentation of non-Brownian particles experiencing long-range hydrodynamic interactions. The complex behavior of these fluctuations, the outcome of the collective dynamics…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
We investigate the dynamic behavior of optical vortices, or phase singularities, in random wavefields and demonstrate the direct experimental observation of the anomalous diffusion of optical vortices. The observed subdiffusion of optical…
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…
Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…
We decompose the anomalous diffusive behavior found in a model of aging into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
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…
We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law,…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…