Related papers: Generalized fractional hybrid Hamilton Pontryagin …
We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
A generalization of the Poincar\'{e}-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct "modes" are not assumed to have constant…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
We employ Monte Carlo simulations to study a generalized three-dimensional complex $psi|^4 theory of Ginzburg-Landau form and compare our numerical results with a recent quasi-analytical mean-field type approximation, which predicts…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable…
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
We analyze common lifts of stochastic processes to rough paths/rough drivers-valued processes and give sufficient conditions for the cocycle property to hold for these lifts. We show that random rough differential equations driven by such…
This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…
This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…
The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional…