Related papers: An extended transfer operator approach for time-co…
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that…
The computation of Lagrangian coherent structures (LCS) has established itself as a prominent means to reveal significant geometric structures in time-dependent vector fields. Their characterization, however, requires the selection of a…
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer…
We analyze with the tools of lobe dynamics the velocity field from a numerical simulation of the surface circulation in the Northwestern Mediterranean Sea. We identify relevant hyperbolic trajectories and their manifolds, and show that the…
We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses…
In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when…
Understanding blood transport in cardiovascular flows is important for managing patients with cardiovascular disease. In this study, three-dimensional Lagrangian coherent structures have been extracted for the first time in both healthy…
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…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
Tracking Lagrangian coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy designed to track stable and…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent…
Dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach. However, by identifying coherent structures in their state spaces, i.e., regions of uniform and simpler behavior, we could hope to…
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…
We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless…
Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal…
Lagrangian methods continue to stand at the forefront of the analysis of time-dependent dynamical systems. Most Lagrangian methods have criteria that must be fulfilled by trajectories as they are followed throughout a given finite flow…
Finite-time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations include eddies and vortices in the ocean and atmosphere,…
Accurate traffic flow estimation and prediction are critical for the efficient management of transportation systems, particularly under increasing urbanization. Traditional methods relying on static sensors often suffer from limited spatial…