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We show that the fractonic dipole-conserving algebra can be obtained as an Aristotelian (and pseudo-Carrollian) contraction of the Poincar\'e algebra in one dimension higher. Such contraction allows to obtain fracton electrodynamics from a…
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different…
A new approach to calculate the vibrational distribution function of molecules in a medium providing energy for vibrational excitation is proposed and demonstrated. The approach is an improvement of solution methods based on the…
Diffusion coefficients are obtained from linear response functions and from the quantal fluctuation dissipation theorem. They are compared with the results of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well as…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
Many features of granular media can be modelled as a fluid of hard spheres with {\em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a…
A continuum model of fracture that describes, in principle, the propagation and interaction of arbitrary distributions of cracks and voids with evolving topology without a fracture criterion is developed. It involves a 'law of motion' for…
This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive…
We present two observations related to theapplication of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE.…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The…
The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate…
We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard-Balescu equations from the Klimontovich formalism. These equations take into account…
Starting with a formally exact diagrammatic kinetic theory for the equilibrium correlation functions of particle density and current fluctuations for a monatomic liquid, we develop a theory for high density liquids whose interatomic…
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a…
We present a general approach for obtaining the generalized transport equations with fractional derivatives using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev non-equilibrium…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
Non-Newtonian rheology is widely acknowledged in subsurface fluids, yet its presence and effects are largely ignored in current fracture-flow studies. Here, we simulate fracture flow of non-Newtonian polymer solutions on a several…
The relativistic kinetic equations describing time evolution and space dependence of the density matrices of polarized photons and electrons interacting via Compton scattering are deduced from the quantum Liouville equation. The induced…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…