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

Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

992
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...
992
Coordination Number and Geometry02:57

Coordination Number and Geometry

18.9K
For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
18.9K
Coplanar Forces01:25

Coplanar Forces

5.5K
Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium...
5.5K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

779
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
779
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

14.0K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
14.0K
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

811
In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
811

You might also read

Related Articles

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

Sort by
Same author

Aging of amorphous materials under cyclic strain.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Emergent universal long-range structure in random-organizing systems.

Nature communications·2026
Same author

PropMolFlow: property-guided molecule generation with geometry-complete flow matching.

Nature computational science·2026
Same author

Hydrodynamic spin-pairing and active polymerization of oppositely spinning rotors.

Nature communications·2025
Same author

Gyromorphs: A New Class of Functional Disordered Materials.

Physical review letters·2025
Same author

A mechanical route for cooperative transport in autonomous robotic swarms.

Nature communications·2025

Related Experiment Video

Updated: Jan 18, 2026

Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

7.1K

A geometric condition for robot-swarm cohesion and cluster-flock transition.

Mathias Casiulis1,2, Eden Arbel3, Charlotte van Waes4

  • 1Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003.

Proceedings of the National Academy of Sciences of the United States of America
|September 8, 2025
PubMed
Summary

We discovered a geometric design rule for controlling particle cluster size. Individual particle properties, like radius and a new parameter called curvity, dictate collective behaviors such as flocking and self-limiting clustering.

Keywords:
active matterdecentralized controlflockingrobot swarmself-limiting clustering

More Related Videos

Investigating Flagella-Driven Motility in Escherichia coli by Applying Three Established Techniques in a Series
07:59

Investigating Flagella-Driven Motility in Escherichia coli by Applying Three Established Techniques in a Series

Published on: May 10, 2020

8.5K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.8K

Related Experiment Videos

Last Updated: Jan 18, 2026

Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

7.1K
Investigating Flagella-Driven Motility in Escherichia coli by Applying Three Established Techniques in a Series
07:59

Investigating Flagella-Driven Motility in Escherichia coli by Applying Three Established Techniques in a Series

Published on: May 10, 2020

8.5K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.8K

Area of Science:

  • Physics
  • Robotics
  • Materials Science

Background:

  • Self-propelled particles exhibit complex collective behaviors.
  • Controlling particle clustering is crucial for applications like metamaterials.

Purpose of the Study:

  • To introduce a geometric design rule for size-controlled clustering of self-propelled particles.
  • To define and utilize a new intrinsic parameter, 'curvity', for active particles.

Main Methods:

  • Derivation of the 'curvity' parameter from first principles.
  • Experimental studies using robots.
  • Numerical simulations of particle swarms.

Main Results:

  • Curvity, an intrinsic signed parameter, quantifies particle rotational tendency.
  • Individual particle radius and curvity control pair cohesion in binary systems.
  • These properties govern flocking stability and self-limiting clustering in swarms.

Conclusions:

  • The geometric design rule enables precise control over particle cluster size and behavior.
  • Curvity is a key factor in predicting and controlling collective dynamics.
  • Applications include advanced metamaterials and decentralized robotic control systems.