Related papers: Ultrametric dynamics for the closed fractal-cluste…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
It is presented the general properties of N-dimensional multi-component or many-particle systems exhibiting self-similar hierarchical structure. Assuming there exists an optimal coarse-graining scale at which the quality and diversity of…
Dynamic networks, especially those representing social networks, undergo constant evolution of their community structure over time. Nodes can migrate between different communities, communities can split into multiple new communities,…
This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport…
We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $\phi^{4}$ model using…
Granular materials are inherently out-of-equilibrium systems due to energy dissipation through inelastic collisions and friction. When driven by mechanical agitation such as vibration, they exhibit rich collective behaviors including…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…
We introduce a model for fractures in quenched disordered media. This model has a deterministic extremal dynamics, driven by the energy function of a network of springs (Born Hamiltonian). The breakdown is the result of the cooperation…
The metabolic networks are very well characterized for a large set of organisms, a unique case in within the large-scale biological networks. For this reason they provide a a very interesting framework for the construction of analytically…
In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different…
We present the results of an attempt to adapt the distribution function formalism to characterize large-scale structures like clusters of galaxies that form in a cosmological N-body simulation. While galaxy clusters are systems that are not…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…