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

Stability01:28

Stability

484
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
484
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

962
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
962
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

7.3K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
7.3K
Pole and System Stability01:24

Pole and System Stability

1.3K
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
1.3K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

434
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
434
Stability of structures01:14

Stability of structures

621
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
621

You might also read

Related Articles

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

Sort by
Same author

Integrating Direct Observation of Procedural Skills as a workplace‑based assessment tool for residents working in an intensive care unit.

African journal of thoracic and critical care medicine·2026
Same author

Radiometer calibration using machine learning.

Scientific reports·2025
Same author

Radiation exposure due to radon, thoron and their progeny in different types of dwellings in two districts of Meghalaya, India.

Isotopes in environmental and health studies·2025
Same author

Topological transitions, pinning and ratchets for driven magnetic hopfions in nanostructures.

Scientific reports·2025
Same author

Effect of carnitine on Hariana bull spermatozoa function after cryopreservation.

Cryo letters·2025
Same author

Fortification of semen extender with mifepristone improves the cryo-survival of cattle spermatozoa.

Cryo letters·2025
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Apr 10, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

10.2K

When linear stability does not exclude nonlinear instability.

P G Kevrekidis1,2, D E Pelinovsky3,4, A Saxena2

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

Physical Review Letters
|June 13, 2015
PubMed
Summary
This summary is machine-generated.

Stationary states can become unstable due to nonlinear effects, even when linearly stable. This study reveals that nonlinear coupling with internal modes causes this instability in nonlinear Schrödinger equations.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

697
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.2K

Related Experiment Videos

Last Updated: Apr 10, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

10.2K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

697
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.2K

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Quantum mechanics

Background:

  • Stationary states in nonlinear systems are typically assumed stable if linearly stable.
  • Linear stability analysis may not capture all instability mechanisms in nonlinear systems.

Purpose of the Study:

  • To describe a mechanism causing nonlinear instability in linearly stable stationary states.
  • To demonstrate this instability in a broad class of nonlinear Schrödinger equations.
  • To investigate the role of internal modes coupled to the continuous spectrum.

Main Methods:

  • Analysis of nonlinear Schrödinger equations.
  • Identification of internal modes with negative energy.
  • Coupling analysis between internal modes and the continuous spectrum.
  • Numerical simulations of specific nonlinear systems.

Main Results:

  • A mechanism for nonlinear instability in linearly stable stationary states is identified.
  • This instability arises from the coupling of negative-energy internal modes with the continuous spectrum.
  • Three case studies (antisymmetric soliton, twisted localized mode, discrete vortex) exhibit weak nonlinear instability despite linear stability.

Conclusions:

  • The presence of internal modes coupled to the continuous spectrum is a sufficient condition for nonlinear instability.
  • This mechanism provides a new perspective on the stability of localized structures in nonlinear systems.
  • Findings are broadly applicable to various nonlinear phenomena described by nonlinear Schrödinger equations.