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

Circles01:18

Circles

160
A circle in the coordinate plane is defined as the set of all points that lie at a constant distance, known as the radius, from a fixed point called the center. This relationship is captured using the distance formula. For a point (x, y) on the circle and a center (h, k), the distance between them equals the radius r. By squaring both sides of the distance formula, the equation of the circle is written in standard form:Constructing the Equation from Geometric InformationIf the center and the...
160
Circular Orbits and Critical Velocity for Satellites01:16

Circular Orbits and Critical Velocity for Satellites

5.4K
The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial satellites in orbit. One can examine the circular orbit, the simplest kind of orbit, to understand the relationship between the speed and the period of planets and satellites with respect to their positions and the bodies that they orbit.
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...
5.4K
Non-uniform Circular Motion01:22

Non-uniform Circular Motion

9.4K
In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all circular motion occurs at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of motion. In that case, the motion is called non-uniform circular motion, and an additional acceleration is introduced, which is in the direction tangential to the circle. 
For example, such...
9.4K
Uniform Circular Motion01:14

Uniform Circular Motion

21.5K
Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is undergoing uniform circular motion. The second, minute, and hour hands of a watch also undergo uniform circular motion. It is hard to believe that points on these rotating objects are actually accelerating, even though the rotation rate is constant. To understand this, we must analyze the motion in terms of...
21.5K
Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

5.5K
The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
5.5K
Mohr's Circle for Moments of Inertia: Problem Solving01:14

Mohr's Circle for Moments of Inertia: Problem Solving

3.1K
Mohr's circle is a graphical method for determining an area's principal moments by plotting the moments and product of inertia on a rectangular coordinate system. This circle can also be used to calculate the orientation of the principal axes.
Consider a rectangular beam. The moments of inertia of the beam about the x and y axis are 2.5(107) mm4 and 7.5(107) mm4, respectively. The product of inertia is 1.5(107) mm4. Determine the principal moments of inertia and the orientation of the major and...
3.1K

You might also read

Related Articles

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

Sort by
Same author

Soft-Lubrication Drainage and Rupture in Particle-Driven Vesicles.

Physical review letters·2026
Same author

Hydrodynamics of a multicomponent vesicle under strong confinement.

Soft matter·2023
Same author

A meta-analysis of cranial electrotherapy stimulation in the treatment of depression.

Journal of psychiatric research·2021
Same author

Cell-cell communication enhances bacterial chemotaxis toward external attractants.

Scientific reports·2017
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: Jan 11, 2026

Key Elements of Photo Attraction Bioassay for Insect Studies or Monitoring Programs
05:17

Key Elements of Photo Attraction Bioassay for Insect Studies or Monitoring Programs

Published on: July 26, 2018

8.1K

N bugs on a circle.

Josh Briley1, Bryan Quaife1

  • 1Florida State University, Department of Scientific Computing, Tallahassee, Florida 32306, USA.

Physical Review. E
|November 18, 2025
PubMed
Summary
This summary is machine-generated.

This study generalizes cyclic pursuit problems by constraining N bugs to a circle. Bugs can move clockwise, counterclockwise, or stay still, leading to three outcomes: coalescence, antipodal clusters, or infinite chase cycles.

More Related Videos

Insect-controlled Robot: A Mobile Robot Platform to Evaluate the Odor-tracking Capability of an Insect
09:00

Insect-controlled Robot: A Mobile Robot Platform to Evaluate the Odor-tracking Capability of an Insect

Published on: December 19, 2016

15.1K
Visualizing Efficacy of Pesticides Against Disease Vector Mosquitoes in the Field
10:49

Visualizing Efficacy of Pesticides Against Disease Vector Mosquitoes in the Field

Published on: March 16, 2019

9.0K

Related Experiment Videos

Last Updated: Jan 11, 2026

Key Elements of Photo Attraction Bioassay for Insect Studies or Monitoring Programs
05:17

Key Elements of Photo Attraction Bioassay for Insect Studies or Monitoring Programs

Published on: July 26, 2018

8.1K
Insect-controlled Robot: A Mobile Robot Platform to Evaluate the Odor-tracking Capability of an Insect
09:00

Insect-controlled Robot: A Mobile Robot Platform to Evaluate the Odor-tracking Capability of an Insect

Published on: December 19, 2016

15.1K
Visualizing Efficacy of Pesticides Against Disease Vector Mosquitoes in the Field
10:49

Visualizing Efficacy of Pesticides Against Disease Vector Mosquitoes in the Field

Published on: March 16, 2019

9.0K

Area of Science:

  • Mathematical Physics
  • Dynamical Systems
  • Computational Science

Background:

  • The classic "Four Bugs on a Square" problem involves cyclic pursuit where agents spiral towards each other.
  • Generalizations explore variations in agent movement and environmental constraints.
  • Understanding agent behavior in constrained environments is crucial for robotics and swarm intelligence.

Purpose of the Study:

  • To analyze a generalization of the cyclic pursuit problem with N bugs constrained to the perimeter of a unit circle.
  • To identify and characterize the possible steady states of this system.
  • To calculate the probabilities of reaching each steady state for random initial configurations.

Main Methods:

  • Analytical derivation of steady-state probabilities for N<=4.
  • Monte Carlo simulations for N>4 to estimate coalescence probabilities.
  • Stability analysis of identified steady states.

Main Results:

  • Three steady states were identified: single-point coalescence, two-antipodal-point clusters, and stable infinite chase cycles.
  • For N<=4, exact analytical probabilities for each state were derived.
  • For larger N, coalescence probability approximates an inverse square-root relationship with N.

Conclusions:

  • Constraining pursuit agents to a circle perimeter introduces complex dynamics absent in unrestricted problems.
  • The system exhibits rich behaviors including stable non-coalescing states.
  • This model offers insights into the long-term behavior of pursuing agents in confined spaces.