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A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
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 show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories - Levy walks - over diffusive ones. This emergent dynamical…
We establish anomalous inertial range scaling of structure functions for a model of advection of a passive scalar by a random velocity field. The velocity statistics is taken gaussian with decorrelation in time and velocity differences…
Incompressible and isotropic magnetohydrodynamic turbulence in plasms can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
We investigate the occurrence of anomalous diffusive transport associated with acoustic wave fields propagating through highly-scattering periodic media. Previous studies had correlated the occurrence of anomalous diffusion to either the…
We propose a simple stochastic model of cascading transport in wave number space to clarify the origin of intermittent behavior of fully-developed fluid turbulence. In spite of lack of nonlinearity and viscosity the model gives non-Gaussian…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…
Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation…
Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by…
Active particles (i.e., self-propelled particles or called microswimmers), different from passive Brownian particles, possess more complicated translational and angular dynamics, which can generate a series of anomalous transport phenomena.…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
Oscillating population model realistic situations in different contexts.We examine this situation with reasonable mathematical models and come to interesting conclusions,such as for example,that the population at most points of the cycle…