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

Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

898
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
898
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.4K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.4K
Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

2.1K
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...
2.1K
The Entropy as a State Function01:14

The Entropy as a State Function

69
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
69
Entropy02:39

Entropy

37.6K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
37.6K
Entropy01:18

Entropy

3.8K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.8K

You might also read

Related Articles

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

Sort by
Same author

Chaos-generating periodic orbits of topological defects in confined active nematics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Application of Cell-Free DNA Barcode-Enabled Single-Molecule Test for Non-Invasive Prenatal Testing of α-Thalassemia and β-Thalassemia.

Journal of clinical laboratory analysis·2026
Same author

[Glomerulopathy with fibronectin deposits caused by <i>FN1</i> gene mutation: A familial case report and literature review].

Zhong nan da xue xue bao. Yi xue ban = Journal of Central South University. Medical sciences·2026
Same author

Lignin degradation, metabolic profiling, and cold adaptation of <i>Psychrobacter</i> strain CLB018 isolated from the Antarctic fish <i>Trematomus bernacchii</i>.

3 Biotech·2026
Same author

Modeling active nematics <i>via</i> the nematic locking principle.

Soft matter·2025
Same author

General approach to the statistics of microbial orientation: Lévy walks, noise, and deterministic drift.

Physical review. E·2025

Related Experiment Video

Updated: Mar 23, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Using heteroclinic orbits to quantify topological entropy in fluid flows.

Sulimon Sattari1, Qianting Chen1, Kevin A Mitchell1

  • 1School of Natural Sciences, University of California, Merced, California 95343, USA.

Chaos (Woodbury, N.Y.)
|April 3, 2016
PubMed
Summary

Topological entropy quantifies chaotic fluid mixing. This study reveals that heteroclinic orbits, not just periodic orbits, generate topological entropy, offering a more complete understanding of mixing processes.

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

13.1K

Related Experiment Videos

Last Updated: Mar 23, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

13.1K

Area of Science:

  • Fluid dynamics
  • Chaos theory
  • Topology

Background:

  • Topological approaches are crucial for understanding chaotic fluid flows, from oceanic transport to micro-mixer design.
  • Topological entropy quantifies mixing by measuring the exponential growth rate of material lines.
  • Current methods for computing topological entropy are computationally expensive and lack insight into mixing origins.

Purpose of the Study:

  • To demonstrate that topological entropy can be generated by the braiding of ghost rods following heteroclinic orbits.
  • To provide a more accurate and insightful method for computing topological entropy in chaotic fluid flows.
  • To automate the computation of symbolic dynamics using heteroclinic orbits for general 2D fluid flows.

Main Methods:

  • Utilizing homotopic lobe dynamics to extract symbolic dynamics from stable and unstable manifolds.
  • Analyzing the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow.
  • Comparing topological entropy generated by periodic orbits versus heteroclinic orbits.

Main Results:

  • Topological entropy can be accurately computed using the braiding of heteroclinic orbits, especially when periodic orbits are absent.
  • Heteroclinic orbits explain previously unaccounted excess topological entropy even when periodic orbits exist.
  • Automated computation of symbolic dynamics via heteroclinic orbits is feasible for general 2D fluid flows.

Conclusions:

  • Heteroclinic orbits offer a powerful alternative and complementary approach to periodic orbits for understanding and quantifying topological mixing in chaotic fluid systems.
  • The developed method provides a more accurate computation and deeper insight into the sources of topological entropy.
  • The automation of this process facilitates broader application in analyzing complex fluid dynamics.