相关论文: Lagrangian Descriptors for Stochastic Differential…

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the…

The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…

In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic maps. In order to illustrate its use, we apply it to a…

Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in…

Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work…

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at…

In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four generic model problems--a hyperbolic saddle point for a…

We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…

We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian…

This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…

We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…

Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when…

We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for…

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as…

The identification of invariant objects and Lagrangian coherent structures is a cornerstone of dynamical systems. As a consequence, several diagnostic indicators have been established over time, such as the fast Lyapunov indicator, the…

In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…

This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the…