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

Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

3.4K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.4K
Dynamic Equilibrium02:20

Dynamic Equilibrium

58.0K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
58.0K
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

4.9K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
4.9K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.9K
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.
2.9K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

537
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
537
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

373
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
373

You might also read

Related Articles

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

Sort by
Same author

Leonid Shilnikov and mathematical theory of dynamical chaos.

Chaos (Woodbury, N.Y.)·2022
Same author

Doubling of invariant curves and chaos in three-dimensional diffeomorphisms.

Chaos (Woodbury, N.Y.)·2021
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
Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

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

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

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

Related Experiment Video

Updated: Oct 29, 2025

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.1K

A criterion for mixed dynamics in two-dimensional reversible maps.

Dmitry Turaev1

  • 1Imperial College, London SW7 2AZ, United Kingdom and Higher School of Economics-Nizhny Novgorod, B. Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia.

Chaos (Woodbury, N.Y.)
|July 12, 2021
PubMed
Summary
This summary is machine-generated.

This study identifies conditions leading to non-conservative dynamics in reversible maps. It focuses on the presence of transverse and non-transverse homoclinic orbits, crucial for understanding complex system behavior.

More Related Videos

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K
Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy
07:20

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy

Published on: February 18, 2022

2.7K

Related Experiment Videos

Last Updated: Oct 29, 2025

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K
Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy
07:20

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy

Published on: February 18, 2022

2.7K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Mathematical Physics

Background:

  • Reversible maps are fundamental in classical mechanics and exhibit complex dynamics.
  • Homoclinic orbits signify chaotic behavior and are key indicators of system instability.

Purpose of the Study:

  • To establish the conditions under which reversible maps exhibit non-conservative dynamics.
  • To analyze the role of transverse and non-transverse homoclinic orbits in inducing these dynamics.

Main Methods:

  • Analysis of reversible dynamical systems.
  • Investigation of homoclinic orbit structures (transverse and non-transverse).
  • Derivation of mathematical conditions for non-conservative behavior.

Main Results:

  • Provided specific criteria for non-conservative dynamics in reversible maps.
  • Demonstrated the significance of both transverse and non-transverse homoclinic orbits.
  • Established a link between geometric structures and dynamic properties.

Conclusions:

  • The presence and type of homoclinic orbits are critical determinants of non-conservative dynamics in reversible maps.
  • Understanding these conditions advances the study of chaotic and complex systems.