Related papers: Transport Equations for Subdiffusion with Nonlinea…

When colloids flow in a narrow channel, the transport efficiency is controlled by the non-equilibrium interplay between colloid-wall interactions and hydrodynamics. In this paper, a general, unifying description of colloidal dispersion flow…

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…

One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…

Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…

We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a…

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…

Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modeling approaches combine the impact of slow advection and diffusion into a hydrodynamic dispersion coefficient and many…

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our…

This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…

Turbulent transport near the X-point of a large tokamak is examined using local, gradient-driven simulations that determine the saturated plasma profiles. The distribution of a representative set of particle tracers evolving within these…

A common wisdom posits that transports of conserved quantities across clean nonintegrable quantum systems at high temperatures are diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter…

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions.…

Non-reciprocal interactions play a key role in shaping transport in active and passive systems, giving rise to striking nonequilibrium behavior. Here, we study the dynamics of a tracer -- active or passive -- embedded in a bath of active or…

Nonlinear effects in emission and absorption spectra of gaseous systems are considered. It is shown that level splitting can be detected spectroscopically even if it is below the Doppler width. Conditions for distinguishing interference…

Colloids coupled to a bath of swimming cells generically display enhanced diffusion. This transport dynamics stems from a subtle interplay between the active and passive particles that still resists our understanding despite decades of…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…

A review of non-diffusive transport in fluids and plasmas is presented. In the fluid context, non-diffusive chaotic transport by Rossby waves in zonal flows is studied following a Lagrangian approach. In the plasma physics context the…

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…