Related papers: Multi-multifractality and dynamic scaling in stoch…
The dynamic fragmentation of residually stressed solids involves a complex interplay between stored elastic energy, stress wave propagation, and crack instabilities. In this work, we investigate the fracture mechanics of chemically…
A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations…
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of L\'evy walks - a stochastic process that originates from the famous continuous-time random walks. It is usually defined…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…
A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
In this paper, we describe the unification and extension of multiple kinematic theories on the advection of colloidal particles through periodic obstacle lattices of arbitrary geometry and infinitesimally small obstacle size. We focus…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
Present work attempts to identify the roles of flow- and geometric-variables on the scaling factor which is a necessary parameter for modeling the apparent viscosity of non-Newtonian fluid in porous media. While idealizing the porous media…
We investigate an alternative to the Sequential Propagator Method used in Lattice QCD calculations of semileptonic form factors. We replace the sequential propagator with a stochastic propagator so that, in principle, all momentum and sink…
Stochastic porous structures are ubiquitous in natural phenomena and have gained considerable traction across diverse domains owing to their exceptional physical properties. The recent surge in interest in microstructures can be attributed…
In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional…
Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple…
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…
In the single-scattering theory of electromagnetic radiation, the {\it fractal regime} is a definite range in the photon momentum-transfer $q$, which is characterized by the scaling-law behavior of the structure factor: $S(q) \propto…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…