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Related Concept Videos

Unusual Results01:16

Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
Network Covalent Solids02:18

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
Capillarity in Fluid01:19

Capillarity in Fluid

Capillarity describes the movement of liquid in small spaces without external forces acting on it. The capillarity is driven by surface tension and adhesive interactions between the liquid and surrounding solid surfaces. This effect is often seen in narrow tubes, porous materials, and fine particles.
Surface tension is crucial to capillarity. It results from cohesive forces between liquid molecules at the liquid-air boundary, forming a skin that resists external forces. When the capillary tube...
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...
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,...
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.

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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Unusual percolation in simple small-world networks.

Reuven Cohen1, Daryush Jonathan Dawid, Mehran Kardar

  • 1Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary

We solved percolation on Watts-Strogatz graphs, finding a nonclassical critical point. This reveals three distinct connectivity regimes, crucial for optimizing communication and transportation networks.

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Area of Science:

  • Complex networks
  • Statistical physics
  • Graph theory

Background:

  • Watts-Strogatz graphs offer a model for systems with both local and random connections.
  • Percolation theory studies the formation of connected clusters in random systems.

Purpose of the Study:

  • To provide an exact solution for percolation on a generalized Watts-Strogatz graph on a 1D lattice.
  • To identify and characterize critical behavior and distinct regimes of connectivity.

Main Methods:

  • Exact solution of percolation theory on a specific graph class.
  • Analysis of critical phenomena, including critical points and scaling functions.

Main Results:

  • A nonclassical critical point was found as long-range bonds approach zero.
  • Discontinuity in percolation probability and divergence in mean finite-cluster size observed.
  • Three distinct critical regimes identified based on bond proportions, unified by a single scaling function.

Conclusions:

  • The study provides a theoretical framework for understanding connectivity in complex networks.
  • Results are applicable to optimizing real-world systems like communication and transportation chains.
  • Offers insights into the 'telephone game' communication problem through network analysis.