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Related Concept Videos

Structure of Benzene: Kekulé Model01:07

Structure of Benzene: Kekulé Model

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In 1865, August Kekule suggested the structure of benzene according to the structural theory of organic chemistry based on the three assertions—formula of benzene is C6H6, all the hydrogens of benzene are equivalent, and each carbon must have four bonds due to its tetravalency.
He proposed that benzene has a cyclic structure of six carbon atoms attached to one hydrogen atom each, with three alternating pi bonds.
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Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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Structures of Solids02:22

Structures of Solids

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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Structural Isomerism02:34

Structural Isomerism

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Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula. Structural isomerism of coordination compounds can be divided into two subcategories, the linkage isomers and coordination-sphere isomers.
Linkage isomers occur when the coordination compound contains a ligand that can bind to the transition metal center through two different atoms. For example, the CN− ligand can bind through the carbon atom or through the nitrogen atom. Similarly, SCN− can...
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Structure of Lipids03:38

Structure of Lipids

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Lipids include a diverse group of compounds that are largely nonpolar in nature. This is because they are hydrocarbons that include mostly nonpolar carbon-carbon or carbon-hydrogen bonds. Non-polar molecules are hydrophobic (“water fearing”), or insoluble in water. Lipids perform many different functions in a cell. Cells store energy for long-term use in the form of fats. Lipids also provide insulation from the environment for plants and animals. For example, they help keep aquatic...
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Viral Structure00:56

Viral Structure

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Viruses are extraordinarily diverse in shape and size, but they all have several structural features in common. All viruses have a core that contains a DNA- or RNA-based genome. The core is surrounded by a protective coat of proteins called the capsid. The capsid is composed of subunits called capsomeres. The capsid and genome-containing core are together known as the nucleocapsid.
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Related Experiment Video

Updated: Feb 9, 2026

Design and Construction of an Urban Runoff Research Facility
13:48

Design and Construction of an Urban Runoff Research Facility

Published on: August 8, 2014

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Stochastic modelling of urban structure.

L Ellam1,2, M Girolami1,2, G A Pavliotis1

  • 1Department of Mathematics, Imperial College London, London SW7 2AZ, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|June 12, 2018
PubMed
Summary

This study introduces a new stochastic urban model to handle unpredictable events. It enables estimating spatial interaction model parameters from urban structure alone, improving city modeling.

Keywords:
Bayesian inferenceBayesian statisticsMarkov chain Monte Carlocomplexityurban modellingurban structure

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Area of Science:

  • Urban modeling
  • Spatial interaction
  • Stochastic processes

Background:

  • Mathematical and computer models of cities are established.
  • Core elements include spatial interaction and structural evolution dynamics.
  • Current models often calibrate spatial interaction independently and use simulation for dynamics.

Purpose of the Study:

  • To develop a stochastic model of urban structure accounting for uncertainty.
  • To introduce a new framework for spatial interaction model calibration.
  • To integrate structural evolution and spatial interaction modeling.

Main Methods:

  • Representing structural variables via a single potential function.
  • Developing stochastic differential equations for urban evolution.
  • Estimating spatial interaction model parameters from structure using Bayesian inference.
  • Employing Markov chain Monte Carlo (MCMC) methods for computational challenges.

Main Results:

  • A unified stochastic model for urban structure and evolution.
  • Successful estimation of spatial interaction parameters independent of flow data.
  • Demonstration of the methodology with a case study on London's retail system.

Conclusions:

  • The developed methodology offers a transformative approach to urban modeling.
  • Integrating structural potential and spatial interaction enhances model robustness.
  • The Bayesian framework with MCMC provides a viable solution for complex urban systems.