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

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...
Spontaneity02:21

Spontaneity

A spontaneous process is one that occurs naturally under certain conditions. A nonspontaneous process, on the other hand, will not take place unless it is “driven” by the continual input of energy from an external source. Processes have a natural tendency to occur in one direction under a given set of conditions. Water will naturally flow downhill (spontaneous process), but uphill flow (nonspontaneous process) requires outside intervention such as the use of a pump. Iron exposed to the earth’s...
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...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...

You might also read

Related Articles

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

Sort by
Same author

Network clustering algorithms and preprocessing pipelines for robust cell type identification in single-cell RNA sequencing data.

Scientific reports·2026
Same author

Scale invariance and statistical significance in complex weighted networks.

Physical review. E·2026
Same author

Detectability threshold in weighted modular networks.

Physical review. E·2026
Same author

Shortest-path percolation on scale-free networks.

Physical review. E·2026
Same author

Triadic percolation on multilayer networks.

Physical review. E·2026
Same author

Modeling resource consumption in the US air transportation system via minimum-cost percolation.

Nature communications·2025
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Jun 18, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

Explosive percolation in scale-free networks.

Filippo Radicchi1, Santo Fortunato

  • 1Complex Networks and Systems Group, ISI Foundation, Torino, Italy.

Physical Review Letters
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study explores scale-free networks using a cooperative growth process, revealing a unique percolation transition. The findings show how biased link formation impacts network structure and dynamics.

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

Related Experiment Videos

Last Updated: Jun 18, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Scale-free networks are crucial in various systems, from social networks to biological systems.
  • Standard percolation theory describes random link formation, but real-world networks often exhibit biased growth.
  • Understanding biased growth processes is key to accurately modeling network properties and dynamics.

Purpose of the Study:

  • To investigate the percolation transition in scale-free networks grown via a cooperative Achlioptas process.
  • To analyze how biased link selection, based on merging cluster mass, influences network structure.
  • To compare the observed percolation behavior with standard random percolation models.

Main Methods:

  • Construction of scale-free networks using a cooperative Achlioptas growth process.
  • Introduction of links biased by the mass of the clusters they merge.
  • Analysis of the percolation transition and its dependence on the degree distribution exponent (lambda).

Main Results:

  • The biased growth process results in a percolation transition distinct from random percolation.
  • A non-vanishing percolation threshold is observed for lambda > lambda(c) ≈ 2.2.
  • The transition is continuous for lambda ≤ 3 and becomes discontinuous for lambda > 3.

Conclusions:

  • The cooperative Achlioptas growth process significantly alters network percolation behavior.
  • The nature of the phase transition (continuous vs. discontinuous) depends critically on the degree distribution exponent.
  • These findings have implications for understanding network structure and the dynamics of processes occurring on them.