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

Navier–Stokes Equations01:28

Navier–Stokes Equations

2.8K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.8K
Euler's Equations of Motion01:28

Euler's Equations of Motion

1.1K
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform...
1.1K
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

9.7K
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
9.7K
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

1.9K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.9K
Irrotational Flow01:28

Irrotational Flow

1.3K
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
1.3K
Damped Oscillations01:07

Damped Oscillations

6.2K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
6.2K

You might also read

Related Articles

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

Sort by
Same author

Comparison of Functional Outcomes and Safety of Acute Carotid Stent Placement versus Thrombectomy Alone in the Treatment of Patients with Tandem Occlusions in Acute Ischemic Stroke.

Journal of vascular and interventional radiology : JVIR·2026
Same author

Deep Learning for analyzing chaotic dynamics in biological time series: Insights from frog heart signals.

Neurocomputing·2026
Same author

A mechanism for growth of topological entropy.

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

Dynamics of coupled neural populations: The role of synaptic dynamics.

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

Mathematical Model of CAR T-Cell Therapy for a B-Cell Lymphoma Lymph Node.

Bulletin of mathematical biology·2025
Same author

Fast-slow analysis and bifurcations in the generation of the early afterdepolarization phenomenon in a realistic mathematical human ventricular myocyte model.

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

Dynamical thermalization and turbulence in social stratification models.

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

Endogenous regime switching driven by scalar-irreducible learning dynamics.

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

The coherence analysis and Laplacian spectrum applications of cycle-based iterative networks.

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

Hitting times, recurrence, and local dimension under nonstationary forcing with applications to climate data.

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

Multiscale deep reservoir computing for predicting chaotic dynamical systems.

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

Chaotic decoherence under finite resolution: Lyapunov-controlled interference suppression.

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

Related Experiment Video

Updated: Apr 27, 2026

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

7.6K

Unbounded dynamics in dissipative flows: Rössler model.

Roberto Barrio1, Fernando Blesa2, Sergio Serrano1

  • 1Computational Dynamics Group, Dpto. Matemática Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain.

Chaos (Woodbury, N.Y.)
|July 3, 2014
PubMed
Summary
This summary is machine-generated.

Unbounded dynamics dominate chaotic systems via boundary crisis. This occurs when a chaotic set crosses an unstable equilibrium point

More Related Videos

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.8K
Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.2K

Related Experiment Videos

Last Updated: Apr 27, 2026

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

7.6K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.8K
Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.2K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics

Background:

  • Chaotic systems exhibit transient chaos and unbounded dynamics.
  • Unbounded dynamics often dominate systems with significant positive and negative divergences.

Purpose of the Study:

  • Investigate the mechanism driving unbounded dynamics dominance in dissipative flows.
  • Detail the role of boundary crisis in generating unbounded dynamics.

Main Methods:

  • Analysis of the Rössler model.
  • Application of chaos indicators and bifurcation analysis.
  • Numerical computation of bounded regions and Fenichel's theory for large parameter values.

Main Results:

  • Identified boundary crisis as the key mechanism for unbounded dynamics.
  • Demonstrated that this crisis involves an unstable focus-node and manifold crossing.
  • Derived formulas for the slow manifold influencing early orbit evolution.

Conclusions:

  • Boundary crisis, driven by unstable equilibrium points and manifold interactions, is crucial for unbounded dynamics in chaotic flows.
  • The Rössler model exemplifies this mechanism.
  • Fenichel's theory provides insights into the initial stages of chaotic trajectories.