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Related Concept Videos

Pore Size Distribution01:23

Pore Size Distribution

In concrete, the pore size distribution significantly influences the material's properties. Capillary pores, markedly larger than gel pores, form a vast network within partially hydrated cement paste, reducing the concrete's strength and increasing its permeability. This heightened permeability leads to a greater risk of damage from environmental factors like freeze-thaw cycles and chemical attacks, with the extent of vulnerability also being tied to the water-to-cement ratio.
Adequate...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Poisson Probability Distribution01:09

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
Ostwald’s Dilution Law01:25

Ostwald’s Dilution Law

Consider a binary electrolyte AB with a concentration ‘c’ that reversibly dissociates into its constituent ions. The degree of this dissociation is represented by ⍺. This means that the equilibrium concentration of each ionic species can be expressed as ⍺c. As well as this, the fraction of the electrolyte that remains undissociated at equilibrium is given by (1−⍺). The corresponding equilibrium concentration for this undissociated portion is then calculated as (1−⍺)c. For such solutions,...
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...

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Related Experiment Video

Updated: Jun 14, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Biased percolation on scale-free networks.

Hans Hooyberghs1, Bert Van Schaeybroeck, André A Moreira

  • 1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

Biased percolation strategically alters network robustness by modifying edge retention probabilities based on node degree. This study details biased edge percolation on scale-free networks, offering insights into network fragility and resilience.

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Last Updated: Jun 14, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Biased percolation offers strategies to control network robustness.
  • Scale-free networks are prevalent in various complex systems.

Purpose of the Study:

  • To present detailed results for biased edge percolation on scale-free networks.
  • To investigate network properties under degree-dependent edge retention.

Main Methods:

  • Analytical and numerical investigations.
  • Generating-functions method for critical exponents.
  • Extension of the Fortuin-Kasteleyn construction.

Main Results:

  • Degree-dependent edge retention probability proportional to (k(i)k(j))^(-alpha).
  • Analysis of sequential and simultaneous network reconstruction methods.
  • Agreement between theoretical predictions and simulation results.

Conclusions:

  • Biased percolation effectively modifies network fragility and robustness.
  • The q-->1 limit of the q-state Potts model describes biased percolation with inhomogeneous couplings.