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Related Concept Videos

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...
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In complexation reactions, metal atoms or cations interact with ligands to form donor-acceptor adducts called metal complexes. Ligands that bind through one donor site are monodentate, ligands with two donor sites are bidentate, and those with more than two donor sites are polydentate ligands. For example, ethylene diamine is a bidentate ligand that binds through two nitrogen donor atoms, forming a five-membered ring. EDTA is a polydentate ligand that binds through four oxygen and two nitrogen...
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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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Crystal Field Theory
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CFT focuses on...
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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How clustering affects the bond percolation threshold in complex networks.

James P Gleeson1, Sergey Melnik, Adam Hackett

  • 1Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Network clustering, the presence of triangles, increases the bond percolation threshold. This means clustered networks are more vulnerable to random edge deletion, impacting resilience in various applications.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Understanding network structure is crucial for predicting system behavior.
  • The bond percolation threshold is a key metric for network resilience and function.
  • Clustering, or the tendency for nodes to form triangles, is a common network feature.

Purpose of the Study:

  • To analytically investigate the impact of network clustering on the bond percolation threshold.
  • To compare the percolation threshold in clustered versus unclustered networks with similar properties.

Main Methods:

  • Utilizing recent advances in modeling highly clustered networks.
  • Analytical study of bond percolation thresholds.
  • Comparison with unclustered network models.

Main Results:

  • The presence of triangles (clustering) significantly increases the bond percolation threshold.
  • Clustering leads to a higher threshold compared to unclustered networks with identical degree distributions and correlation structures.

Conclusions:

  • Network clustering reduces resilience to random edge deletion.
  • Increased clustering raises the epidemic threshold, making networks more susceptible to fragmentation.