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

Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

339
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
339
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.1K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
8.1K
Escape Velocity01:26

Escape Velocity

5.8K
The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is gravitationally bound and never to return. For example, what would be the minimum velocity at which a satellite should be launched from the Earth's surface such that it just escapes the Earth's gravitational field?
To calculate the escape velocity, it is assumed that no energy is lost to any frictional forces. In practice, a satellite...
5.8K
Spherical Coordinates01:23

Spherical Coordinates

11.7K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
11.7K
Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

8.7K
Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...
8.7K
Schwarzschild Radius and Event Horizon01:21

Schwarzschild Radius and Event Horizon

2.2K
No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape...
2.2K

You might also read

Related Articles

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

Sort by
Same author

The Iris billiard: Critical geometries for global chaos.

Chaos (Woodbury, N.Y.)·2020
Same author

Linear and nonlinear stability of periodic orbits in annular billiards.

Chaos (Woodbury, N.Y.)·2017
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

Chaos (Woodbury, N.Y.)·2026
Same journal

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

Chaos (Woodbury, N.Y.)·2026
Same journal

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

Chaos (Woodbury, N.Y.)·2026
Same journal

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Oct 8, 2025

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

6.6K

Spherical billiards with almost complete escape.

Carl P Dettmann1, Mohammed R Rahman1

  • 1School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, United Kingdom.

Chaos (Woodbury, N.Y.)
|January 1, 2022
PubMed
Summary
This summary is machine-generated.

Investigating particle escape from spherical billiards with multiple holes reveals that evenly spaced holes ensure almost all particles escape. The survival probability depends universally on hole area and time.

More Related Videos

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
08:19

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

2.4K
Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns
07:32

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns

Published on: April 10, 2017

9.2K

Related Experiment Videos

Last Updated: Oct 8, 2025

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

6.6K
Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
08:19

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

2.4K
Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns
07:32

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns

Published on: April 10, 2017

9.2K

Area of Science:

  • Mathematical Physics
  • Dynamical Systems
  • Chaos Theory

Background:

  • Dynamical billiards model particle motion with elastic boundary collisions.
  • Previous studies linked circular billiards escape to the Riemann Hypothesis.
  • Spherical billiards with a single hole exhibit a non-zero probability of indefinite particle confinement.

Purpose of the Study:

  • To investigate spherical billiard variants that promote near-complete particle escape.
  • To analyze the impact of multiple small holes or a thin strip on particle escape dynamics.
  • To determine the long-time survival probability and its dependence on hole configuration.

Main Methods:

  • Analytical calculations of particle trajectories and escape probabilities.
  • Numerical simulations of particle motion within modified spherical billiards.
  • Investigation of hole spacing and size effects on escape dynamics.

Main Results:

  • Equal spacing of holes around the equator significantly enhances particle escape.
  • Almost all initial conditions lead to escape in configurations with multiple small holes or a thin strip.
  • The long-time survival probability converges to a universal function dependent on hole area and time.

Conclusions:

  • Strategically placed multiple holes are effective for ensuring particle escape from spherical billiards.
  • The study provides insights into the dynamics of escape in systems with complex boundary conditions.
  • The discovered universal function offers a predictive model for survival probability in such systems.