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We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with H\"older continuous…
We obtain a Liouville property for stationary diffusions in random environment which are small, isotropic perturbations of Brownian motion in spacial dimension greater than two. Precisely, we prove that, on a subset of full probability, the…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including…
The famous Bernoulli shift (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one,…
Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential…
We study diffusion in a one-dimensional periodic array of scatterers modeled by a simple map. The chaotic scattering process for this map can be changed by a control parameter and exhibits the dynamics of a crisis in chaotic scattering. We…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…
Aging, the dependence of the dynamics of a physical process on the time $t_a$ since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…
In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical…
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that…
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…
Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the…
We investigate the long-term diffusion transport and chaos properties of single and coupled standard maps. We consider model parameters that are known to induce anomalous diffusion in the maps' phase spaces, as opposed to normal diffusion…