Institute for Complex Systems - Sapienza - CNR

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ISC Sapienza Statistical Dynamics

Statistical Dynamics

The main scientific objectives of this research activity is the investigation and characterization of   complex dynamical evolutions and transport phenomena encountered in far-from-equilibrium systems such as turbulent flows, high dimensional chaotic, non-chaotic systems up to the formation of cosmological structures. ISC-Sapienza researchers have nowadays established a body of knowledge and tools cross-fertilizing ideas and methods coming from (non-equilibrium) statistical mechanics, dynamical systems and information theory.  For the next years, we intend to further explore the problem of transport in turbulent and stochastic flows with emphasis on the formation of structures in the distribution of non-neutral impurieties. In this respect we shall consider particles having a density different from that of the carrying flow and a finite size, in such a case inertial forces are responsible for the generation of clustered distributions, which have an important impact on applications: from cloud physics to combustion technologies.  We aim to strengthen our efforts towards the application of statistical and nonlinear physics methods to the study the nonequilibrium phase-transitions occurring in the synchronization of high-dimensional chaotic systems with emphasis also to experimentally testable systems, such as nonlinear lasers. Despite big progresses in the last years, the problem of cosmological structure formation via gravitational interaction from uniform and homogeneous initial conditions is still open. More in general the statistical physics and the dynamical evolution of particle distributions characterized by long range mutual interactions is a largely unsolved  problem which is attracting  more and more interest in the community. In this context we think to contribute by refining our interdisciplinary approach based on methods of modern statistical physics. In particular we want to tackle the problems of the large time evolution and existence or not of a sort of  thermodynamical equilibrium of such dynamical systems. With this aim we want to study the dynamical evolution of two different systems: (i) statistically translationally invariant infinite particle systems, (ii) closed spherical particle distributions. In the first case we want to proceed to the study of dimensionally reduced cases which, though strongly simplified, are able to capture important dynamical features of the original three-dimensional case. Moreover we aim to proceed to a complete classification of the long range attractive interactions with respect to the general statistical properties of the large time evolution of an arbitrarily correlated particle distribution interacting via this force. In the second case our interest focus on the so called spherical collapse model and aims to the understanding of the virialization process under the mutual gravitational interaction. In particular one would like to reach  a characterization of these virialized states  as  quasi-equilibrium thermodynamical states similarly to other toy models characterized by long range interactions as the celebrated Hamiltonian Mean-Field (HMF) model.

This section is edited by Massimo Cencini.