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Related Experiment Video

Updated: Jul 7, 2026

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Phase transitions in the Kuramoto model.

Lasko Basnarkov¹, Viktor Urumov

¹Faculty of Electrical Engineering and Information Technologies, SS. Cyril and Methodius University, P.O. Box 574, Skopje, Macedonia. lasko@feit.ukim.edu.mk

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

|February 1, 2008

Summary

This summary is machine-generated.

The Kuramoto model with specific frequency distributions exhibits a first-order phase transition. This transition

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Last Updated: Jul 7, 2026

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

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Area of Science:

Complex systems
Nonlinear dynamics
Statistical physics

Background:

The Kuramoto model is a fundamental framework for studying synchronization in coupled oscillator systems.
Understanding phase transitions in such systems is crucial for various scientific disciplines.

Purpose of the Study:

To investigate the nature of phase transitions in the Kuramoto model with a unimodal frequency distribution featuring a central plateau.
To determine the scaling laws governing the order parameter near the critical coupling strength.

Main Methods:

Analysis of the Kuramoto model with a specific unimodal natural frequency distribution.
Mathematical derivation of the order parameter and critical behavior.

Main Results:

The phase transition is identified as first-order when a finite plateau exists in the frequency distribution.
A precise scaling law, r-rc proportional, variant(K-Kc)2/(2m+3), is derived for the order parameter (r) near the critical coupling (Kc).

Conclusions:

The presence of a plateau in the natural frequency distribution fundamentally alters the phase transition characteristics.
The derived scaling law provides quantitative insights into the collective behavior of synchronized oscillators in this configuration.