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

Phase Transitions: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
Hess's Law03:40

Hess's Law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.
The Bohr Model02:18

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 the nucleus...
Phase Transitions02:31

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

You might also read

Related Articles

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

Sort by
Same author

Moon phases influence encounters of anurans in the Brazilian semi-arid region of Piauí.

Brazilian journal of biology = Revista brasleira de biologia·2026
Same author

Thermodynamic constraints and pseudotransition behavior in a one-dimensional waterlike system.

Physical review. E·2025
Same author

Thermodynamics and inhomogeneous hole distribution in an exactly solvable model of a randomly decorated CuO spin ladder.

Physical review. E·2025
Same author

Unusual low-temperature behavior in the half-filled band of the one-dimensional extended Hubbard model in atomic limit.

Physical review. E·2024
Same author

Thermodynamic analog of integrate-and-fire neuronal networks by maximum entropy modelling.

Scientific reports·2024
Same author

Crossing the Rift valley: using complete mitogenomes to infer the diversification and biogeographic history of ethiopian highlands <i>Ptychadena</i> (anura: Ptychadenidae).

Frontiers in genetics·2023
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 14, 2026

Synthetic Condensates and Cell-Like Architectures from Amphiphilic DNA Nanostructures
08:02

Synthetic Condensates and Cell-Like Architectures from Amphiphilic DNA Nanostructures

Published on: May 31, 2024

Bose-Einstein condensation in the Apollonian complex network.

I N de Oliveira1, F A B F de Moura, M L Lyra

  • 1Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Topology influences Bose-Einstein condensation (BEC) in complex networks. The BEC transition temperature and energy gap in Apollonian networks follow a scaling law, showing anomalous density dependence.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Related Experiment Videos

Last Updated: Jun 14, 2026

Synthetic Condensates and Cell-Like Architectures from Amphiphilic DNA Nanostructures
08:02

Synthetic Condensates and Cell-Like Architectures from Amphiphilic DNA Nanostructures

Published on: May 31, 2024

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Area of Science:

  • Condensed Matter Physics
  • Network Science
  • Statistical Mechanics

Background:

  • Bose-Einstein condensation (BEC) is a quantum mechanical phenomenon.
  • Complex networks exhibit unique topological properties like scale-free, small-world, and hierarchical structures.
  • Understanding BEC in non-uniform or complex systems is crucial for quantum information and materials science.

Purpose of the Study:

  • To investigate the occurrence and characteristics of topology-induced Bose-Einstein condensation (BEC) in a complex network.
  • To model BEC in an Apollonian network, a topology with scale-free, small-world, and hierarchical properties.
  • To analyze the relationship between network topology, BEC transition temperature, energy spectrum, and specific heat.

Main Methods:

  • Utilizing a tight-binding approach for noninteracting bosons.
  • Modeling the system on a deterministic Apollonian network.
  • Analyzing finite-size scaling laws for the BEC transition temperature and the energy gap.
  • Investigating the density dependence of the transition temperature and the energy spectrum's structure.
  • Calculating and analyzing the specific heat at the BEC transition.

Main Results:

  • Demonstrated topology-induced Bose-Einstein condensation in a complex network.
  • Observed that the BEC transition temperature and the ground-to-first-excited state gap follow the same finite-size scaling law.
  • Reported an anomalous density dependence of the transition temperature, linked to spectral properties.
  • Found a discontinuous specific heat at the transition, with low-temperature modulations due to a fragmented density of states.

Conclusions:

  • Network topology significantly influences Bose-Einstein condensation.
  • The Apollonian network model provides insights into BEC phenomena in complex systems.
  • Spectral properties, including gaps and degeneracies, play a critical role in anomalous BEC behavior.
  • The findings contribute to understanding quantum phenomena in complex network structures.