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We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
Second order partial differential equations which describe spherical surfaces (ss) or pseudospherical surfaces (pss) are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature $K = 1$ or $K…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
Using the general framework of quantum field theory, we derive basic equations of quantum field kinetics. The main goal of this approach is to compute the observables associated with a quark-gluon plasma at different stages of its…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic…
We propose a general hydrodynamic framework for systems with spontaneously broken approximate symmetries. The second law of thermodynamics naturally results in relaxation in the hydrodynamic equations, and enables us to derive a universal…
We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg's equation. Systems describing harmonic oscillators are given.
In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
The studies of the generalized Einstein Lagrangian densities without torsion are extended to those of the more generalized Lagrangian densities with torsion. The properties of the more generalized Lagrangian densities are studied…
The equations of fluid dynamics developed in paper I are applied to the study of the propagation of ultrasound waves. There is good agreement between the predicted propagation speed and experimental results for a wide range of Knudsen…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
A quantum-kinetic formulation of the dynamical evolution of a high-energy non-equilibrium gluon system at finite density is developed, to study the interplay between quantum fluctuations of high-momentum (hard) gluons and the low-momentum…
Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions for various families of fractional…
General features of the formalism describing hydrodynamic evolution of transversally thermalized matter possibly produced at the very early stages of ultra-relativistic heavy-ion collisions are presented. Thermodynamical consistency of the…
The spherically symmetric thin shells of the macroscopically stable quark-gluon matter are considered within the frameworks of the bag model and theory of discontinuities in general relativity. The equation of state for the two-dimensional…
The hydrodynamic equations for a crystals with interstitials, taking into account the dissipative processes of the viscosity, heat conduction and the interstitial diffusion are derived. To achieve that we use the phenomenological approach…