Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

General oblique projections for model reduction via spectral submanifolds.

Chaos (Woodbury, N.Y.)·2026
Same author

Globalizing manifold-based reduced models for equations and data.

Nature communications·2025
Same author

Data-driven nonlinear model reduction to spectral submanifolds via oblique projection.

Chaos (Woodbury, N.Y.)·2025
Same author

Data-driven modeling of subharmonic forced response due to nonlinear resonance.

Scientific reports·2024
Same author

Data-driven linearization of dynamical systems.

Nonlinear dynamics·2024
Same author

Nonautonomous spectral submanifolds for model reduction of nonlinear mechanical systems under parametric resonance.

Chaos (Woodbury, N.Y.)·2024
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: May 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Computing Lagrangian coherent structures from their variational theory.

Mohammad Farazmand1, George Haller

  • 1Department of Mathematics and Statistics, McGill University, 817 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada.

Chaos (Woodbury, N.Y.)
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

This study presents a new computational method for identifying hyperbolic Lagrangian coherent structures (LCSs) in fluid flows. The approach accurately detects attracting and repelling LCSs as smooth curves, improving flow analysis.

More Related Videos

Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Related Experiment Videos

Last Updated: May 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Fluid Dynamics
  • Dynamical Systems Theory
  • Computational Mathematics

Background:

  • Lagrangian Coherent Structures (LCSs) are key features in fluid flows, revealing transport barriers and mixing patterns.
  • Traditional methods for LCS detection often struggle with accuracy, leading to false positives and negatives.
  • Hyperbolic LCSs, specifically, require robust methods for accurate identification and analysis.

Purpose of the Study:

  • To introduce a novel computational approach for identifying hyperbolic Lagrangian coherent structures (LCSs).
  • To render attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows.
  • To enhance the accuracy and reliability of LCS detection in fluid dynamics.

Main Methods:

  • Utilized a variational theory of hyperbolic Lagrangian coherent structures (LCSs).
  • Developed a computational method based on trajectories of an ordinary differential equation for Cauchy-Green strain tensor lines.
  • Separated true exponential stretching from shear in a frame-independent manner.

Main Results:

  • Successfully rendered attracting and repelling hyperbolic LCSs as smooth, parametrized curves.
  • Eliminated false positives and negatives in LCS detection.
  • Demonstrated the method's efficacy on a kinematic model flow and 2D turbulence simulation.

Conclusions:

  • The proposed computational approach provides an accurate and robust method for identifying hyperbolic LCSs.
  • Parametrized hyperbolic LCSs facilitate in-depth analysis and accurate advection as material lines.
  • This method advances the study of fluid transport and mixing phenomena.