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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
Types of Responses of Series RLC Circuits01:11

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.
Second Order systems II01:18

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 Damping01:20

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...
Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Damped Oscillations01:07

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...

You might also read

Related Articles

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

Sort by
Same author

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit.

Physical review letters·2026
Same author

Immunological Avalanches in Renal Immune Diseases.

Biomedicines·2025
Same author

Optimal Control of an Electromechanical Energy Harvester.

Entropy (Basel, Switzerland)·2025
Same author

Inhibitory neurons and the asymmetric shape of neuronal avalanches.

Physical review. E·2025
Same author

Stochastic Model for a Piezoelectric Energy Harvester Driven by Broadband Vibrations.

Entropy (Basel, Switzerland)·2025
Same author

Positive Answer on the Existence of Correlations between Positive Earthquake Magnitude Differences.

Physical review letters·2025
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Jun 28, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Nonlinear response and fluctuation-dissipation relations.

Eugenio Lippiello1, Federico Corberi, Alessandro Sarracino

  • 1Dipartimento di Scienze Fisiche, Universitá di Napoli Federico II, Naples, Italy. lippiello@sa.infn.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
PubMed
Summary
This summary is machine-generated.

This study unifies off-equilibrium fluctuation-dissipation relations (FDRs) for various spin systems. It introduces new methods for calculating response functions and defining off-equilibrium temperature, particularly useful for glassy and coarsening systems.

Related Experiment Videos

Last Updated: Jun 28, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Off-equilibrium systems lack simple fluctuation-dissipation relations (FDRs).
  • Existing methods struggle with complex systems like spin glasses and coarsening materials.
  • Calculating response functions and effective temperatures is computationally challenging.

Purpose of the Study:

  • To provide a unified derivation of off-equilibrium FDRs for Ising and continuous spins to arbitrary order.
  • To develop efficient numerical methods for computing response functions using FDRs.
  • To explore the definition of off-equilibrium effective temperature and its consistency in coarsening systems.

Main Methods:

  • Derivation of FDRs within Markovian stochastic dynamics.
  • Development of zero-field algorithms for numerical computation.
  • Application of second-order FDRs to Edwards-Anderson spin glass models.
  • Analysis of nonlinear FDRs for defining off-equilibrium effective temperature.

Main Results:

  • A unified framework for off-equilibrium FDRs applicable to diverse spin systems.
  • Demonstrated effectiveness of second-order FDRs in detecting cooperative length scales in spin glasses.
  • Showcased consistency between second-order and linear FDRs for effective temperature in coarsening systems.

Conclusions:

  • The unified FDR derivation offers a powerful tool for analyzing complex non-equilibrium phenomena.
  • Advanced FDRs enable efficient computation and provide deeper insights into system behavior.
  • The findings contribute to a more robust understanding of effective temperature in dynamic systems.