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We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
We employ the Full Relativistic Boltzmann Transport approach for a conformal system in 3+1D to study the universal behaviour in moments of the distribution function and anisotropic flows. We investigate different transverse system sizes $R$…
We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Liouvillian reversible dynamics. It connects the ratio between the probabilities of…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
We formulate the angular structure of Lacunarity in fractals, in terms of a symmetry reduction of the three point correlation function. This provides a rich probe of universality, and first measurements yield new evidence in support of the…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required…
Transitions from reversible to irreversible or fluctuating states above a critical density and shear amplitude have been extensively studied in non-thermal cyclically sheared suspensions and amorphous solids. Here, we propose that the same…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
The construction of attractors of a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward attractors are identical. As…
This paper presents some first results on how to perform uniform random walks (where every trace has the same probability to occur) in very large models. The models considered here are described in a succinct way as a set of communicating…
Making use of a recursive approach, derivative dispersion relations are generalized for an arbitrary number of subtractions. The results for both cross even and odd amplitudes are theoretically consistent at sufficiently high energies and…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…