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

Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
Diffusion01:21

Diffusion

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Reaction Mechanisms03:06

Reaction Mechanisms

Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...

You might also read

Related Articles

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

Sort by
Same author

'Heartbreaking': Iranian scientists on losing labs, libraries and liberty.

Nature·2026
Same author

How malicious AI swarms can threaten democracy.

Science (New York, N.Y.)·2026
Same author

Ideology and polarization set the agenda on social media.

Scientific reports·2025
Same author

Rebuilding Gaza: don't sideline Palestinian scientists, say experts.

Nature·2025
Same author

How language, culture, and geography shape online dialogue: Insights from Koo.

PloS one·2025
Same author

Charting multidimensional ideological polarization across demographic groups in the USA.

Nature human behaviour·2025
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: Jul 2, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Bosonic reaction-diffusion processes on scale-free networks.

Andrea Baronchelli1, Michele Catanzaro, Romualdo Pastor-Satorras

  • 1Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
PubMed
Summary
This summary is machine-generated.

We introduce a bosonic framework for reaction-diffusion processes on complex networks, overcoming limitations of the fermionic approach. This allows modeling systems with unlimited particles per vertex, advancing network dynamics studies.

More Related Videos

High-resolution Spatiotemporal Analysis of Receptor Dynamics by Single-molecule Fluorescence Microscopy
15:13

High-resolution Spatiotemporal Analysis of Receptor Dynamics by Single-molecule Fluorescence Microscopy

Published on: July 25, 2014

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Related Experiment Videos

Last Updated: Jul 2, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

High-resolution Spatiotemporal Analysis of Receptor Dynamics by Single-molecule Fluorescence Microscopy
15:13

High-resolution Spatiotemporal Analysis of Receptor Dynamics by Single-molecule Fluorescence Microscopy

Published on: July 25, 2014

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Area of Science:

  • Complex network dynamics
  • Statistical physics
  • Computational modeling

Background:

  • Reaction-diffusion processes model network dynamics like transport and epidemics.
  • Fermionic models, limiting particles per vertex, struggle with multi-particle reactions.
  • A need exists for more flexible models on complex networks.

Purpose of the Study:

  • Develop a general framework for bosonic reaction-diffusion processes on complex networks.
  • Analyze steady-state and decaying processes with unlimited particles per vertex.
  • Compare bosonic and fermionic models to identify key differences and similarities.

Main Methods:

  • Continuous-time heterogeneous mean-field theory for theoretical analysis.
  • Development of a continuous-time Monte Carlo algorithm for simulations.
  • Analysis of one-species reaction-diffusion processes.

Main Results:

  • Bosonic and fermionic models yield identical time evolution and critical properties for particle density.
  • Differences emerge in the density of occupied vertices across degree classes.
  • Analytical predictions from mean-field theory are validated by Monte Carlo simulations.

Conclusions:

  • The bosonic framework effectively models reaction-diffusion on networks without particle limits.
  • The study provides a foundation for analyzing complex, multi-species reaction-diffusion systems.
  • This work opens new avenues for classifying dynamical systems on complex networks.