Related papers: Backtracking Dynamical Cavity Method
Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
Cavitation is a limiting phenomenon in many domains of fluid mechanics. Instabilities of a partial cavity developed on an hydrofoil, a converging-diverging step or in an inter-blade channel in turbomachinery, have already been investigated…
Trajectory Prediction of dynamic objects is a widely studied topic in the field of artificial intelligence. Thanks to a large number of applications like predicting abnormal events, navigation system for the blind, etc. there have been many…
The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…
We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, i.e. by a finite element method, all required…
For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of…
We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector…
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random…
A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally tree-like topology is presented. The method builds on $(a)$ a graph expansion to eliminate loops from the normalizations of each…
We study localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity…
We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean networks with self-interactions that evolve according to synchronous Glauber dynamics. Equilibrium analysis is achieved via a novel application of the…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
Dynamic facilitation theory assumes short-ranged dynamic constraints to be the essential feature of supercooled liquids and draws much of its conclusions from the study of kinetically constrained models. While deceptively simple, these…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
This paper presents the results of studies in elaboration of a mathematical model of the cavity-chain slow wave structures. Considered is the problem of coupling of an infinitely long cylindrical cavity chain coupled through centerholes in…