Abstract Large-scale behavior of a wide class spatial and spatiotemporal processes is characterized in terms informational measures. Specifically, subordinated random fields defined by nonlinear transformations on the family homogeneous isotropic Lancaster–Sarmanov are studied under long-range dependence (LRD) assumptions. In case, it shown that Shannon mutual information between field componen...

Here u= (u1, . . . , ud) :R d ×Ω→ Rd is the Eulerian velocity field of the flow. It is assumed to be a stationary, d-dimensional random vector field given over a certain probability space (Ω,V,P), and w(·) is a standard d-dimensional Brownian motion defined over another probability space (Σ,A,Q). Parameter κ, called the molecular diffusivity of the medium, is assumed to be nonnegative. The resu...

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-d...

We study the nature of non-Fickian particle transport in 3-D porous media by simulating fluid flow in the intricate pore space of real rock. We solve the full Navier-Stokes equations at the same resolution as the 3-D micro-CT (computed tomography) image of the rock sample and simulate particle transport along the streamlines of the velocity field. We find that transport at the pore scale is mar...

This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of "valid deformations" as the intersection of three subspac...

The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not absolute. Therefore, the scale variables are functions of the space-time coordinates, so that we expect a coupling between the displacement in space-time and the di...

This paper proposes the use of Gaussian random vector fields as a generative model to describe a set of observed trajectories in a 2-dimensional space. The observed trajectories are sequences of points in space sampled from continuous trajectories that are assumed to have been generated by an underlying velocity field. Given the observed velocities connecting the trajectory points, a vector fie...

We add a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential. For the resulting functional we study the asymptotic properties of minimizers and minimal energy under a rescaling in space, i.e., on the macroscopic scale. By bounding the energy f...