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 Experiment Videos

Introducing small-world network effects to critical dynamics.

Jian-Yang Zhu1, Han Zhu

  • 1CCAST (World Laboratory), Box 8730, Beijing 100080, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

DAQplugin: Deep Learning based Real-time Model Evaluation Plugin for ChimeraX.

bioRxiv : the preprint server for biology·2026
Same author

Interfacial Redox Decoupling via Amphiphilic Carbon Dots for Highly Efficient Biphasic Photocatalytic H<sub>2</sub>O<sub>2</sub> Production and Selective Benzyl Alcohol Oxidation.

Langmuir : the ACS journal of surfaces and colloids·2026
Same author

Beta-Adrenergic Stimulation and <i>MYH7</i> G256E Mutant Gene Dosage Drive Hypertrophic Cardiomyopathy Phenotype Penetrance.

bioRxiv : the preprint server for biology·2026
Same author

Stress-Driven Accelerated Evolution and Ecological Network Reconfiguration in Extremophilic Microbial Communities.

Biology·2026
Same author

Workload-induced changes to cell state contribute to β-cell failure in diabetes.

bioRxiv : the preprint server for biology·2026
Same author

A nomogram estimates postoperative urinary tract infection risk after upper urinary tract stone surgery with double-J stents.

Scientific reports·2026
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

This study analyzes kinetic models on small-world networks (SWN), finding mean-field behavior in Gaussian models and confirming no finite-temperature transition threshold in Ising models. SWN effects do not alter the dynamic critical exponent.

Area of Science:

  • Statistical physics
  • Complex networks
  • Computational modeling

Background:

  • Small-world networks (SWN) exhibit unique topological properties influencing system dynamics.
  • Kinetic models, like the Gaussian and Ising models, are crucial for understanding phase transitions and critical phenomena.

Purpose of the Study:

  • To analytically investigate the kinetic Gaussian and one-dimensional kinetic Ising models on two types of SWN (adding and rewiring).
  • To formulate general approaches and basic equations for these models on SWN.
  • To explore the impact of SWN topology on dynamic evolution and critical behavior.

Main Methods:

  • Analytical investigation using Glauber-type and Kawasaki-type dynamics.
  • Formulation of general approaches and basic equations for kinetic models on SWN.

Related Experiment Videos

  • Derivation of evolving equations and analysis of critical points and exponents.

    • Main Results:

    • The kinetic Gaussian model exhibits mean-field-like global influence on spin dynamics, supporting a simplified method for analyzing SWN mean-field transitions.
    • For the one-dimensional Ising model, the p dependence of the critical point was obtained, confirming no finite-temperature transition threshold.
    • Static critical exponents (gamma, beta) align with Monte Carlo simulations and mean-field behavior; the dynamic critical exponent (z=2) remains unchanged by SWN effects.

    Conclusions:

    • SWN topology significantly influences dynamic evolution and critical points in kinetic models.
    • The study confirms the robustness of the dynamic critical exponent (z=2) for the Ising model on SWN.
    • Observed influences of long-range randomness suggest distinct underlying mechanisms affecting critical points.