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Plastic Deformations of Members with a Single Plane of Symmetry

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...

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Related Experiment Video

Updated: May 22, 2026

Imaging and Analysis of Tissue Orientation and Growth Dynamics in the Developing Drosophila Epithelia During Pupal Stages

Imaging and Analysis of Tissue Orientation and Growth Dynamics in the Developing Drosophila Epithelia During Pupal Stages

Published on: June 2, 2020

Topological singularities and symmetry breaking in development.

Valeria V Isaeva¹, Nickolay V Kasyanov, Eugene V Presnov

¹A.N. Severtsov Institute of Ecology and Evolution of the Russian Academy of Science, 119071 Moscow, Russia. vv_isaeva@mail.ru

|May 22, 2012

Summary

This review uses topology to explain biological development, revealing a "topological imperative" guiding embryogenesis. Spatial symmetry breaking is crucial for morphogenesis in development and evolution.

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Last Updated: May 22, 2026

Imaging and Analysis of Tissue Orientation and Growth Dynamics in the Developing Drosophila Epithelia During Pupal Stages

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Tracking Morphogenetic Tissue Deformations in the Early Chick Embryo

Tracking Morphogenetic Tissue Deformations in the Early Chick Embryo

Published on: October 17, 2011

Area of Science:

Developmental Biology
Mathematical Biology
Evolutionary Biology

Background:

Biological morphogenesis involves complex spatial organization.
Understanding the rules governing developmental patterns is essential.
Existing frameworks may not fully capture the constraints on embryogenesis.

Purpose of the Study:

To provide a topological interpretation of morphogenetic events.
To establish the relationship between local processes and global patterns in development.
To identify a set of topological rules directing embryogenesis.

Main Methods:

Applying well-known mathematical concepts and theorems from topology.
Analyzing the spatial organization of biological fields using topological terms.
Examining topological singularities in pattern formation.

Main Results:

Spatial organization in biology is amenable to topological analysis.
Topological singularities are inherent and transformed during morphogenesis.
A "topological imperative" of rules constrains and directs embryogenesis.
Breaking spatial symmetry is critical for morphogenesis.

Conclusions:

Topology offers a strict and adequate language for describing developmental and evolutionary transformations.
The concept of a topological imperative explains inherent developmental constraints.
Topological principles are fundamental to understanding biological pattern formation.