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We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics…
The open problem of derivation of the relativistic Vlasov equation for the systems of charged particles moving with the velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the…
We correct an error that occurs with certain frequency in popular literature of Special Relativity, namely that supposedly that mass of moving objects depends on the relative velocity of the object and the observer. In this pedagogical…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force…
The problem is to evaluate the behavior of an object when primary sources of information about the object become unavailable, so that any information must be obtained from the intelligent use of available secondary sources. This evaluative…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena.…
We present a fully covariant transport framework for Molecular Dynamics that enables a consistent description of the evolution of relativistic N-body systems. For the first time, we derive relativistic equations of motion incorporating both…
The concept of velocity dependent mass, relativistic mass, is examined and is found to be inconsistent with the geometrical formulation of special relativity. This is not a novel result; however, many continue to use this concept and some…
How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…
The geodesics equations on de Sitter and anti-de Sitter spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the…
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…