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Related Concept Videos

Stereoisomerism02:52

Stereoisomerism

Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.

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Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
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Published on: November 4, 2021

Complex-anisotropy-induced pattern formation in bistable media.

Zhi Zhu He1, Jing Liu

  • 1Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

Complex anisotropy in bistable media can significantly alter pattern formation and wave propagation. This study introduces a novel method to model these anisotropic effects, revealing rich spatiotemporal behaviors and instabilities.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Chemical Engineering

Background:

  • Bistable media exhibit pattern formation driven by reaction-diffusion processes.
  • Anisotropy, or directional dependence, influences wave propagation and pattern evolution.
  • Understanding anisotropic effects is crucial for controlling pattern dynamics.

Purpose of the Study:

  • To develop a model for characterizing anisotropy in bistable media.
  • To investigate the impact of complex anisotropy on pattern formation and wave propagation.
  • To analyze the stability of wave patterns under anisotropic conditions.

Main Methods:

  • Adopting a construct of anisotropy in bistable media.
  • Deriving a velocity curvature relation for anisotropic wave propagation.
  • Performing stability analysis of transverse perturbations.
  • Conducting numerical simulations of reaction-diffusion models.

Main Results:

  • Complex anisotropy can induce dynamical instabilities and pattern breakup.
  • Anisotropic line tension significantly affects pattern formation.
  • Anisotropic wave propagation is accurately described by the derived relation.
  • Numerical simulations reveal rich spatiotemporal behaviors due to complex anisotropy.

Conclusions:

  • The developed method successfully incorporates complex anisotropy into reaction-diffusion models.
  • The findings have general significance for understanding pattern formation in anisotropic media.
  • Complex anisotropy offers a mechanism to control and induce instabilities in pattern dynamics.