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

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

The Bohr Model

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...

Van der Waals Equation

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...

Spin–Spin Coupling Constant: Overview

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...

Equilibrium Conditions for a Particle

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

You might also read

Related Articles

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

Sort by

Same author

Interaction-free ergodicity-breaking driven by temporally hyperuniform noise.

Physical review. E·2025

Same author

Erratum: Minimum Scaling Model and Exact Exponents for the Nambu-Goldstone Modes in the Vicsek Model [Phys. Rev. Lett. 133, 258301 (2024)].

Physical review letters·2025

Same author

Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces.

Physical review. E·2024

Same author

Correlated noise and critical dimensions.

Physical review. E·2024

Same author

Control parameter dependence of fluctuations near jamming.

The Journal of chemical physics·2023

Same author

Vibrational density of states of jammed packing at high dimensions: Mean-field theory.

Physical review. E·2022

Search research articles

Related Experiment Video

Updated: Jun 4, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Minimum Scaling Model and Exact Exponents for the Nambu-Goldstone Modes in the Vicsek Model.

Harukuni Ikeda¹

¹Department of Physics, <a href="https://ror.org/037s2db26">Gakushuin University</a>, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan.

Physical Review Letters

|January 3, 2025

Summary

We reveal new scaling behaviors in the Vicsek model by adding a nonlinear term to its equation of motion. This analysis precisely predicts scaling exponents in two dimensions, matching prior numerical findings.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Related Experiment Videos

Last Updated: Jun 4, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Area of Science:

Condensed Matter Physics
Statistical Mechanics
Nonlinear Dynamics

Background:

The Vicsek model describes self-propelled particles exhibiting flocking behavior.
Understanding Nambu-Goldstone modes is crucial for characterizing ordered phases in physical systems.

Purpose of the Study:

To investigate the scaling behavior of Nambu-Goldstone modes in the Vicsek model's ordered phase.
To introduce and analyze a previously overlooked nonlinear term in the model's equation of motion.

Main Methods:

Development of a phenomenological equation of motion.
Inclusion of a nonlinear term accounting for velocity field and density fluctuation interactions.
Derivation of exact scaling exponents in two dimensions.

Main Results:

The introduced nonlinear term leads to novel scaling behaviors.
Exact scaling exponents were derived for two-dimensional systems.
The derived exponents align with previously reported numerical simulation results.

Conclusions:

The study elucidates the impact of nonlinear interactions on Nambu-Goldstone mode scaling.
The findings provide a theoretical framework for understanding flocking dynamics in Vicsek-like models.
This work bridges theoretical predictions with numerical observations in statistical physics.