Related papers: Lagrangian coherent structures and plasma transpor…
We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…
Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a…
We construct a climatology of Lagrangian coherent structures (LCSs), the concealed skeleton that shapes transport, with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as…
The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inelastic collisions. These equations arise in Zel'dovich's…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem…
This Report discusses a recently developed concept of Limiting Phase Trajectories (LPTs) providing a unified description of resonant energy transport in a wide range of classical and quantum dynamical systems with constant and time-varying…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…
The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures, which are…
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of…
In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on…
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs)…
Energetic particle redistribution in the presence of multiple Alfv\'en eigenmodes is analyzed in [PPCF 58, 014019 (2016)] for the ITER 15MA baseline scenario: non-linear hybrid simulations (within their well known limits) point out that…
Disorder and coherence jointly govern wave transport in complex media. In Hermitian systems, a long-established paradigm since Anderson's work holds that disorder-induced localization relies on phase-coherent interference, and that the loss…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the…
A pluri-Lagrangian (or Lagrangian multiform) structure is an attribute of integrability that has mainly been studied in the context of multidimensionally consistent lattice equations. It unifies multidimensional consistency with the…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…