We review, systematize and discuss models of diffusion in neuronal tissue, by putting them
into an overarching physical context of coarse‐graining over an increasing diffusion length …

The subject of this paper is the evolution of Brownian particles in disordered environments.
The “Ariadne's clew” we follow is understanding of the general statistical mechanisms which …

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media,
composite materials and biological tissues. A major challenge is to characterize the …

We review the application of field-theoretic renormalization group (RG) methods to the study
of fluctuations in reaction–diffusion problems. We first investigate the physical origin of …

We present a comprehensive study of the motion of a damped Brownian particle evolving in
a static, one dimensional gaussian random force field. We provide both a clear physical …

Quantum disordered problems with a direction (imaginary vector potential) are discussed
and mapped onto a supermatrix σ model. It is argued that the 0D version of the σ model may …

We study spectral properties of the Fokker-Planck operator that describes particles diffusing
in a quenched random velocity field. This random operator is non-Hermitian and has …

We consider the long-time behavior of a diffusion process on $\mathbb {R}^ d $ advected by
a stationary random vector field which is assumed to be divergence-free, dihedrally …

A numerical study of Brownian motion of noninteracting particles in random potentials is
presented. The dynamics are modeled by Langevin equations in the high friction limit. The …

A renormalisation group analysis of anomalous diffusion in a random medium with
constrained long-range correlations is carried out to two-loop order. The crossover between …