Related papers: Kinetic equation model for self-gravitating system…
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…
Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly…
Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be…
BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In this paper, we address the ill-posedness problem for the BGK…
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
The resolution of the problem of cosmological singularity in the framework of gauge theories of gravitation is discussed. Generalized cosmological Friedmann equations for homogeneous isotropic models filled by interacting scalar fields and…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schr\"odinger…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
The kinetic Boltzmann equation models gas dynamics over a wide range of spatial and temporal scales. Simplified versions of the full Boltzmann collision operator, such as the classical Bhatnagar-Gross-Krook and the closely related…
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation…
Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides…
We propose a theory of quantum gravity which formulates the quantum theory as a nonperturbative path integral, where each spacetime history appears with a weight given by the exponentiated Einstein-Hilbert action of the corresponding causal…
Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modelling musculo-skeleton systems. Tensegrity mechanisms are more difficult to…
We consider the dilaton gravity models derived by reductions of generalized theories of gravity and study one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully…
We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the…
We study the quantum Ising model in the transverse inhomogeneous magnetic field. Such a system can be approached numerically through exact diagonalization and analytically through the renormalization group techniques. Basic insights into…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…