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High resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussianity of velocity differences statistics are quantitatively investigated. The level of statistical…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
We present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumber-frequency domain. We apply hybrid plasma simulations in a simplified two-dimensional geometry to…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are…
A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging…
Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be…
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and…
In this article, we construct two families of nonsymmetrical multifractal fields. One of these families is used for the modelization of the velocity field of turbulent flows.
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Classical shell models of turbulence do not display dual cascade - inverse of energy and direct of enstrophy - because they fail to reproduce the right thermal spectra. We propose here a multi-branch shell model, including a geometry…
We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We have carried out numerical simulations of freely decaying magnetohydrodynamic (MHD) turbulence in three dimensions, which can be applied to the evolution of stochastic magnetic fields in the early Universe. For helical magnetic fields an…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model…