Jove
Visualize
Contact Us

Related Experiment Videos

Chaotic mixing in a torus map.

Jean-Luc Thiffeault1, Stephen Childress

  • 1Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA. jeanluc@mailaps.org

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Anisotropic active Brownian particle with a fluctuating propulsion force.

Physical review. E·2022
Same author

Open-flow mixing and transfer operators.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

Flow Rectification in Loopy Network Models of Bird Lungs.

Physical review letters·2021
Same author

Unravelling hagfish slime.

Journal of the Royal Society, Interface·2019
Same author

Can phoretic particles swim in two dimensions?

Physical review. E·2017
Same author

Distribution of particle displacements due to swimming microorganisms.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
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
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

This study analyzes passive scalar advection and diffusion on a chaotic 2-torus map. It reveals a transition from constant variance to exponential decay, marked by a superexponential decay phase.

Area of Science:

  • Fluid Dynamics
  • Chaos Theory
  • Statistical Mechanics

Background:

  • Investigating passive scalar transport is crucial for understanding mixing processes in chaotic systems.
  • The behavior of scalars under advection and diffusion in turbulent or chaotic flows exhibits complex dynamics.

Purpose of the Study:

  • To analytically understand the transition in scalar variance from constant to exponential decay.
  • To characterize the superexponential decay phase and its relation to the asymptotic state.
  • To examine the influence of chaotic advection on diffusion dynamics.

Main Methods:

  • Analysis of a chaotic map on the 2-torus.
  • Consideration of the limit of almost-uniform stretching.
  • Derivation of analytic understanding for scalar variance evolution.

Related Experiment Videos

  • Identification of the asymptotic state as an eigenfunction of the advection-diffusion operator.

    • Main Results:

    • Observed a transition from constant scalar variance to exponential decay over time.
    • Identified a distinct superexponential decay phase during this transition.
    • The asymptotic state concentrates scalar variance at small scales while a large-scale mode dictates decay rate.
    • The duration of the superexponential phase correlates with the logarithm of the exponential decay rate.

    Conclusions:

    • The study provides an analytic framework for scalar transport in chaotic systems.
    • A superexponential decay phase is a key feature bridging short-time and long-time scalar behavior.
    • The interplay between small-scale variance concentration and large-scale decay modes is essential.