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

¹H NMR: Long-Range Coupling

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.

Concept of Resonance and its Characteristics

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...

Sound Waves: Resonance

Sound Waves: Resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...

Double Resonance Techniques: Overview

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

¹H NMR: Interpreting Distorted and Overlapping Signals

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...

Forced Oscillations

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

You might also read

Related Articles

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

Sort by

Same author

Molecular Surface Chemistry Drives Anomalous Clustering of Ultrasmall Silica Nanoparticles.

The journal of physical chemistry letters·2026

Same author

Comment on "Discontinuous codimension-two bifurcation in a Vlasov equation".

Physical review. E·2026

Same author

Brownian dynamics simulations of electric double-layer capacitors with tunable metallicity.

The Journal of chemical physics·2026

Same author

Interaction between charged nanoparticles in deionized suspensions.

The Journal of chemical physics·2026

Same author

Forces between charge regulated surfaces inside an electrolyte solution.

The Journal of chemical physics·2025

Same author

Efficient method for simulating ionic fluids between polarizable metal electrodes.

The Journal of chemical physics·2024

Search research articles

Related Experiment Video

Updated: May 22, 2026

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems

Published on: April 28, 2016

Ergodicity breaking and parametric resonances in systems with long-range interactions.

Fernanda P da C Benetti¹, Tarcísio N Teles, Renato Pakter

¹Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil.

Physical Review Letters

|May 1, 2012

Summary

Systems with long-range forces can break ergodicity, trapping them in non-equilibrium states. However, satisfying a generalized virial condition allows these systems to approach ergodic behavior and Lynden-Bell statistics.

More Related Videos

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Published on: December 3, 2013

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

Related Experiment Videos

Last Updated: May 22, 2026

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems

Published on: April 28, 2016

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Published on: December 3, 2013

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

Area of Science:

Statistical Mechanics
Non-equilibrium Physics

Background:

Systems with long-range forces often fail to reach Boltzmann-Gibbs equilibrium.
They tend to get trapped in out-of-equilibrium quasi-stationary states.

Purpose of the Study:

Investigate the mechanism of ergodicity breaking in systems with long-range interactions.
Determine conditions for ergodic behavior in such systems.

Main Methods:

Analysis of systems in the thermodynamic limit.
Investigation of initial distribution constraints, specifically the generalized virial condition.

Main Results:

Ergodicity breaking occurs when the generalized virial condition is violated, exciting parametric resonances and leading to chaos.
If the generalized virial condition is met, the quasi-stationary state closely approximates ergodicity and is described by Lynden-Bell statistics.

Conclusions:

The generalized virial condition is crucial for ergodicity in long-range interacting systems.
Violation of this condition leads to chaotic dynamics and ergodicity breaking, while adherence promotes near-ergodic behavior.