Related papers: Superdiffusion in a Model for Diffusion in a Molec…
We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media.…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
We investigated the energy transfer from active enzymes to their surroundings in crowded environments by measuring the diffusion of passive microscopic tracers in active solutions of ficoll and glycerol. Despite observing lower rates of…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties…