Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Group structure of the membrane shape equation.

Tao Xu1, Zhong-Can Ou-Yang

  • 1College of Electric and Electronic Engineering, Huazhong University of Science and Technology, 430074 Wuhan, PRC. xutao@mail.hust.edu.cn

The European Physical Journal. E, Soft Matter
|September 28, 2004
PubMed
Summary

This study explores the geometry of membrane shapes using Lie group theory. It introduces a generalized geometry for membrane analysis, revealing how shape variations relate to structural parameters.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

[Expression and clinical significance of glycoprotein non-metastatic melanoma protein B in human renal cell carcinoma].

Beijing da xue xue bao. Yi xue ban = Journal of Peking University. Health sciences·2013
Same author

DNA binding, DNA cleavage and BSA interaction of a mixed-ligand copper(II) complex with taurine Schiff base and 1,10-phenanthroline.

Journal of photochemistry and photobiology. B, Biology·2013
Same author

Angiotensin IV upregulates the activity of protein phosphatase 1α in Neura-2A cells.

Protein & cell·2013
Same author

Ultrafast, accurate, and robust localization of anisotropic dipoles.

Protein & cell·2013
Same author

Three-dimensional conducting oxide nanoarchitectures: morphology-controllable synthesis, characterization, and applications in lithium-ion batteries.

Nanoscale·2013
Same author

[Pharmacokinetics of tramadol hydrochloride in the extracellular fluid of mouse frontal cortex studied by in vivo microdialysis].

Yao xue xue bao = Acta pharmaceutica Sinica·2013

Area of Science:

  • Differential Geometry
  • Lie Group Theory
  • Continuum Mechanics

Background:

  • Membrane equations describe the shape of thin, flexible surfaces.
  • Understanding membrane geometry is crucial in various engineering applications.
  • Invariance under contact transformations is a key property for analyzing geometric structures.

Purpose of the Study:

  • To investigate the plane geometry of general membrane shapes.
  • To apply Cartan's theory of Lie groups to membrane equations.
  • To define a generalized geometry for membrane analysis.

Main Methods:

  • Utilizing Cartan's theory of Lie groups.
  • Analyzing invariance under contact transformations.
  • Defining a generalized geometric space with second-order contact elements.

Related Experiment Videos

Main Results:

  • Relative invariance in membrane geometry does not vanish.
  • A generalized geometry is defined using specific contact elements and a five-parameter group.
  • Axisymmetric membrane shapes are characterized by a five-parameter group and twelve structure parameters.

Conclusions:

  • Membrane shape is intricately linked to a five-parameter group and its structure parameters.
  • Variations in membrane or environmental conditions alter structure constants, affecting symmetric groups and shape.
  • The study provides a framework for understanding membrane shape dynamics through group theory.