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 Concept Videos

Equation of the Elastic Curve01:23

Equation of the Elastic Curve

1.1K
The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
1.1K
Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

557
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.
The important part of bending analysis for such a member...
557
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

969
One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
969
Curvilinear Motion: Normal and Tangential Components01:27

Curvilinear Motion: Normal and Tangential Components

1.0K
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
1.0K
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

553
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...
553
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

1.0K
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
1.0K

You might also read

Related Articles

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

Sort by
Same author

Connecting pathways between mineralized fibrocartilage and bone at the Achilles tendon insertion.

Journal of structural biology·2026
Same author

Shaping tissues with defects.

Science (New York, N.Y.)·2026
Same author

Cortical tension links curvature to tissue growth in the cellular Potts model.

Physical review. E·2026
Same author

The human osteocyte lacunocanalicular network structure in osteons of the iliac crest of elderly women depends on mineral content but not individual age.

Acta biomaterialia·2025
Same author

The mineralization of osteonal cement line depends on where the osteon is formed.

JBMR plus·2025
Same author

Deceptive Ceropegia sandersonii uses an arabinogalactan for trapping its fly pollinators.

The New phytologist·2025
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Feb 26, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.9K

Curvature-controlled defect dynamics in active systems.

Sebastian Ehrig1, Jonathan Ferracci1, Richard Weinkamer1

  • 1Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14482 Potsdam, Germany.

Physical Review. E
|July 16, 2017
PubMed
Summary
This summary is machine-generated.

Active particles on curved surfaces form vortices near points of constant curvature. This collective motion, especially on four-umbilic ellipsoids, offers insights into how living cells navigate complex geometries.

More Related Videos

Tuning the Contractility and Deformation Modes of Active Actin-Based Assemblies In Vitro: From Two-Dimensional Active Networks to Liquid Crystal Drops
06:48

Tuning the Contractility and Deformation Modes of Active Actin-Based Assemblies In Vitro: From Two-Dimensional Active Networks to Liquid Crystal Drops

Published on: July 11, 2025

955
The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
08:50

The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton

Published on: March 10, 2023

1.2K

Related Experiment Videos

Last Updated: Feb 26, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.9K
Tuning the Contractility and Deformation Modes of Active Actin-Based Assemblies In Vitro: From Two-Dimensional Active Networks to Liquid Crystal Drops
06:48

Tuning the Contractility and Deformation Modes of Active Actin-Based Assemblies In Vitro: From Two-Dimensional Active Networks to Liquid Crystal Drops

Published on: July 11, 2025

955
The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
08:50

The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton

Published on: March 10, 2023

1.2K

Area of Science:

  • Physics
  • Biophysics
  • Materials Science

Background:

  • Active matter systems exhibit complex emergent behaviors.
  • Geometric constraints significantly influence particle dynamics.
  • Cell migration is a fundamental biological process influenced by substrate topography.

Purpose of the Study:

  • To investigate the collective motion of polar active particles on ellipsoidal surfaces.
  • To understand how geometric constraints dictate emergent vortex patterns.
  • To explore the implications for biological cell migration on curved substrates.

Main Methods:

  • Computational modeling of polar active particles.
  • Analysis of particle trajectories and collective motion patterns.
  • Topological analysis of surface curvature and vortex formation.

Main Results:

  • Vortices form and encircle surface points of constant curvature (umbilics).
  • Collective motion patterns are particularly rich on ellipsoids with four umbilics.
  • Vortices preferentially form near pairs of umbilics to minimize interaction energy.

Conclusions:

  • The geometry of curved surfaces dictates the collective motion of active particles.
  • Cellular migration may be guided by substrate geometry, utilizing information from curved surfaces.
  • This work provides a framework for understanding active matter on curved manifolds.