Related papers: Thermalization of Classical Weakly Nonintegrable M…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
We study the dynamics of systems with different time scales, when access only to the slow variables is allowed. We use the concept of Finite Size Lyapunov Exponent (FSLE) and consider both the case when the equations of motion for the slow…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
The advent of short-pulse lasers, nanotechnology, as well as shock-wave techniques have created new states of matter (e.g., warm dense matter) that call for new theoretical tools. Ion correlations, electron correlations as well as bound…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
The efficient manipulation of thermodynamic states within the finite time is fundamentally constrained by the intrinsic dissipative cost. While the slow-driving regime is well-characterized by a universal $1/\tau$-scaling of…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
We describe the application of pseudo-spectral methods to problems of holographic thermal quenches of relevant couplings in strongly coupled gauge theories. We focus on quenches of a fermionic mass term in a strongly coupled N=4…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical…
We study thermalization within a quantum system with an enhanced capacity to store information. This system has been recently introduced to provide a prototype model of how a black hole processes and stores information. We perform a…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
This article presents a modeling framework for a class of multiphase chemical systems based on non-equilibrium thermodynamics. Compartmental modeling is used to establish the dynamic properties of liquid-vapor systems operating far from…