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Related Concept Videos

Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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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Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

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The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
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Bending of Curved Members - Strain Analysis01:14

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The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
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Curvilinear Motion: Rectangular Components01:23

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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Updated: Jan 7, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Riemannian L-systems: modelling growing forms in curved spaces.

Christophe Godin1, Frédéric Boudon2,3

  • 1Laboratoire Reproduction et Développement des Plantes, Univ. Lyon, ENS de Lyon, UCB Lyon1, CNRS, INRAE, Inria, Lyon, France.

Quantitative Plant Biology
|December 25, 2025
PubMed
Summary
This summary is machine-generated.

This study extends L-systems to model biological growth in curved, non-Euclidean spaces, integrating differential geometry for accurate simulations of plant development and branching systems.

Keywords:
differential geometryintrinsic shapesmorphodynamic systemspatterningtropism

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Area of Science:

  • Computational Biology
  • Developmental Biology
  • Mathematical Biology

Background:

  • L-systems formalism effectively models biological growth in Euclidean spaces.
  • Many biological forms grow in curved, non-Euclidean spaces, posing a challenge for existing models.
  • Examples include plant venation, pollen tube growth, and tissue development.

Purpose of the Study:

  • To extend the L-systems formalism to model biological growth in non-Euclidean spaces.
  • To integrate differential geometry concepts into turtle geometry for curved space modeling.
  • To demonstrate applications in plant development and abstract growth modeling.

Main Methods:

  • Extension of L-systems formalism to non-Euclidean geometry.
  • Integration of differential geometry into turtle geometry.
  • Application to modeling mathematical and biological forms on curved surfaces.

Main Results:

  • Successfully extended L-systems to model growth in curved spaces.
  • Demonstrated applications in plant development, including vein networks and pollen tubes.
  • Showcased extension to abstract Riemannian spaces for modeling growth on non-embedded curved substrates.

Conclusions:

  • The extended L-systems provide a novel approach for modeling biological growth in complex, curved environments.
  • This formalism enables more accurate simulations of plant development and other biological systems.
  • The abstract extension offers potential for modeling growth in diverse, non-uniform substrates.