Related papers: Visualizing the Phase Space of the HeI_2 van der W…

Trajectory design in highly-perturbed environments like binary asteroids is challenging. It typically requires using realistic, non-autonomous dynamical models in which periodic solutions derived in autonomous systems vanish. In this work,…

Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…

A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two-…

Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material…

Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…

We present a methodology for detecting non-linearities in data sets based on the characterization of the structural features of the Fourier phase maps. A Fourier phase map is a 2D set of points $M= \{(\phi_{\vec{k}}, \phi_{\vec{k} +…

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…

We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…

Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…

In this paper, we study non-stationary filtration of real gases in porous media. Thermodynamic state of the medium is given by van der Waals state equations. Solutions for non-stationary filtration equation are obtained by means of finite…

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural…

For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce…

Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…

We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…

The reduction of dimensionality of physical systems, specially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant…

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…

We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the…

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…