Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Types of Damping

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Damped Oscillations

Damped Oscillations

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...

Partial Differential Equations

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...

Types of Responses of Series RLC Circuits

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.

Bessel Function of Order Zero

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...

You might also read

Related Articles

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

Sort by

Same author

Analysis of primary care electronic health record data of people living with hepatitis B virus: infection and hepatocellular carcinoma risk associated with socio-economic deprivation.

Public health·2023

Same author

Characteristics, management and outcome of a large necrotising otitis externa case series: need for standardised case definition.

The Journal of laryngology and otology·2022

Same author

The Interaction of Compliance and Activation on the Force-Length Operating Range and Force Generating Capacity of Skeletal Muscle: A Computational Study using a Guinea Fowl Musculoskeletal Model.

Integrative organismal biology (Oxford, England)·2020

Same author

The effect of size-scale on the kinematics of elastic energy release.

Soft matter·2019

Same author

Beyond power amplification: latch-mediated spring actuation is an emerging framework for the study of diverse elastic systems.

The Journal of experimental biology·2019

Same author

American Society of Biomechanics Journal of Biomechanics Award 2017: High-acceleration training during growth increases optimal muscle fascicle lengths in an avian bipedal model.

Journal of biomechanics·2018

Search research articles

Related Experiment Video

Updated: Jul 7, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Pattern formation in the damped Nikolaevskiy equation.

S M Cox¹, P C Matthews

¹School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 1, 2008

Summary

The Nikolaevskiy equation models instabilities in fronts, exhibiting spatiotemporal chaos. Weak damping transitions these instabilities to Eckhaus instability, revealing critical damping thresholds for stable solutions.

More Related Videos

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Related Experiment Videos

Last Updated: Jul 7, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Area of Science:

Fluid dynamics
Nonlinear dynamics
Pattern formation

Background:

The Nikolaevskiy equation models phenomena like seismic waves and weak turbulence.
It describes transverse instabilities of fronts, featuring a large-scale "Goldstone" mode.
Spatially periodic steady solutions are inherently unstable, leading to spatiotemporal chaos.

Purpose of the Study:

To investigate the influence of weak damping on the Nikolaevskiy equation.
To analyze the transition from inherent instabilities to Eckhaus instability.
To determine critical damping values affecting the stability of periodic solutions.

Main Methods:

Numerical calculations were employed to study the system's behavior.
Weakly nonlinear analysis was performed using coupled amplitude equations.
Asymptotically consistent methods were utilized for theoretical analysis.

Main Results:

All spatially periodic steady solutions are unstable at onset due to the Goldstone mode.
A critical damping value exists, below which periodic steady states remain unstable.
The transition to Eckhaus instability was observed as damping increased.
The last solutions to destabilize were found near the marginal stability curve.

Conclusions:

Weak damping of the Goldstone mode is crucial for understanding stability transitions.
The Nikolaevskiy equation exhibits complex dynamics, including spatiotemporal chaos and transitions to Eckhaus instability.
The study provides insights into the stability of patterned states in physical systems modeled by this equation.