Related papers: Conformable Derivative Approach to Granular Gases
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
We show that the anomalous diffusion equations with a fractional derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the L\'evy stable distributions which stem from the evolution properties…
Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than…
Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees…
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian…
The simulation of granular particles in a quasi two-dimensional container under the vertical vibration as an experimental accessible model for granular gases is performed. The velocity distribution function obeys an exponential-like…
We study fluidized granular gases in a stationary state determined by the balance between an external driving and the bulk dissipation. The two considered situations are inspired by recent experiments, where the gravity plays a major role…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
We use an analogy with the statistical mechanics of gas to build the statistical mechanics of granular media. The case of an isotropic disordered packing of equal spheres submitted to an isotropic stress is considered. We use the assumption…
Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper…
Computing analytically the $n$-point density correlations in systems of interacting particles is a long-standing problem of statistical physics, with a broad range of applications, from the interpretation of scattering experiments in simple…
We study generalizations of It\^{o}-Langevin dynamics consistent within nonextensive thermostatistics. The corresponding stochastic differential equations are shown to be connected with a wide class of nonlinear Fokker-Planck equations…
Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under…
We numerically and theoretically study macroscopic properties of dense, sheared granular materials. In this process we first introduce an invariance in Newton's equations, explain how it leads to Bagnold's scaling, and discuss how it…
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against…
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
A numerical molecular dynamics experiment measuring the two-time correlation function of the transversal velocity field in the homogeneous cooling state of a granular gas is reported. By measuring the decay rate and the amplitude of the…