Population dynamics in a random environment (original) (raw)

Proliferation assisted transport in a random environment

Journal of Physics A: Mathematical and General, 2001

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 appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory-like argument to understand qualitatively this nontrivial diffusive behaviour. A renormalization group analysis close to the critical dimension d c = 2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

Physical Review Letters, 2016

It is recognised now that a variety of real-life phenomena ranging from diffuson of cold atoms to motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Diffusion in randomly perturbed dissipative dynamics

EPL (Europhysics Letters), 2014

Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic Continuous Time Random Walk theory.

Scaling laws in the diffusion limited aggregation of persistent random walkers

Physica A: Statistical Mechanics and its Applications, 2011

We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and diffusion limited aggregation models. A non-trivial scaling relation ξ ∼ 1.25 between the characteristic size ξ, in which the cluster undergoes a morphological transition, and the persistence length , between ballistic and diffusive regimes of the random walk, is observed.

Anomalous diffusion of self-propelled particles in directed random environments

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

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 individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.

From Random Walk to Single-File Diffusion

Physical Review Letters, 2005

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the 1D mobility in the SFD on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] leads to the hard rod SFD theory for a Tonks gas.