Abstract Space plasmas can be described as conducting flows in a turbulent state, where
fluid motion is determined by a host of kinetic and magnetic coherent structures of different …

Physics-informed neural networks (PINNs) are a recent trend in scientific machine learning
research and modeling of differential equations. Despite progress in PINN research, large …

Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature.
While the more familiar turbulent flows promote efficient transport and mixing by their …

Lagrangian coherent structures (LCSs) are time-varying entities which capture the most
influential transport features of a flow. These can for example identify groups of particles …

The finite-time Lyapunov exponent (FTLE) method is a mature and practical method for
analyzing the characteristics of Lagrangian coherent structures. It can be used for studying …

Transport barriers are observed inhibitors of the spread of substances in flows. The
collection of such barriers offers a powerful geometric template that frames the main …

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 …

The output of spectral clustering is a collection of eigenvalues and eigenvectors that encode
important connectivity information about a graph or a manifold. This connectivity information …

In cardiovascular flows, Lagrangian coherent structures have been used to explore the
skeleton of blood transport. Revealing these transport barriers is instrumental to quantify the …

Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic
Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid …