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

Torque On A Current Loop In A Magnetic Field01:13

Torque On A Current Loop In A Magnetic Field

6.3K
The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...
6.3K
Toroids01:27

Toroids

4.2K
A toroid is a closely wound donut-shaped coil constructed using a single  conducting wire. In general, it is assumed that a toriod consists of  multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in...
4.2K
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

4.1K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
4.1K
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.7K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.7K
Irrotational Flow01:28

Irrotational Flow

1.1K
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
1.1K
Theorem of Pappus01:24

Theorem of Pappus

142
The Theorem of Pappus, also known as the Pappus–Guldinus Theorem, provides a geometric method for determining the volume and surface area of solids generated by the revolution of a plane region or a plane curve about an external axis. The theorem consists of two related statements. The first addresses the volume of solids formed by rotating plane areas, while the second addresses the surface area generated by rotating plane curves. Both results depend on the location of the centroid,...
142

You might also read

Related Articles

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

Sort by
Same author

Glomerular Injury Induced by Daily Exposure to the Low-Frequency Component of Environmental Noise via Endothelin Signaling in Mice.

Environmental science & technology·2026
Same author

The Potential of Apelin-Targeted Therapeutic Lymphangiogenesis Therapy for Viral Myocarditis.

JACC. Basic to translational science·2026
Same author

Adipose-derived regenerative cell therapy mitigates sepsis-induced cardiomyopathy through the induction of cardiac reparative lymphangiogenesis.

Stem cell research & therapy·2026
Same author

JCS 2026 Guideline on Management of Large Vessel Vasculitis.

Circulation journal : official journal of the Japanese Circulation Society·2026
Same author

Pulmonary fibroblasts activated by the addition of TNF-α and IL-4 enhance lymphangiogenic capacity and ameliorate lung fibrosis in an allogeneic rat model.

PloS one·2026
Same author

Therapeutic Lymphangiogenesis Using Induced Cardiac Fibroblasts Protects the Heart From Heart Failure With Preserved Ejection Fraction Progression by Exerting Anti-Inflammatory and Antifibrotic Effects.

Circulation journal : official journal of the Japanese Circulation Society·2026
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: Mar 16, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

3.9K

Point vortex interactions on a toroidal surface.

Takashi Sakajo1, Yuuki Shimizu1

  • 1Department of Mathematics , Kyoto University , Sakyo-ku, Kyoto 606-8502, Japan.

Proceedings. Mathematical, Physical, and Engineering Sciences
|August 6, 2016
PubMed
Summary
This summary is machine-generated.

Understanding vortex dynamics on toroidal surfaces is challenging. This study formulates vortex interactions as a Hamiltonian system, revealing integrable 2-vortex problems and unique behaviors like local repulsion between identical vortices.

Keywords:
Hamiltonian dynamical systemhydrodynamic Green functionring torussymplectic geometryvortex dynamicsvortex interactions

More Related Videos

Scanning SQUID Study of Vortex Manipulation by Local Contact
06:53

Scanning SQUID Study of Vortex Manipulation by Local Contact

Published on: February 1, 2017

7.4K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K

Related Experiment Videos

Last Updated: Mar 16, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

3.9K
Scanning SQUID Study of Vortex Manipulation by Local Contact
06:53

Scanning SQUID Study of Vortex Manipulation by Local Contact

Published on: February 1, 2017

7.4K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K

Area of Science:

  • Fluid dynamics
  • Differential geometry
  • Mathematical physics

Background:

  • Vortex dynamics on curved surfaces, particularly toroidal manifolds, are complex due to non-constant curvature and topology.
  • Intuitive understanding of N-point vortex evolution on a torus is difficult compared to simpler geometries.

Purpose of the Study:

  • To develop an intuitive understanding of vortex interactions on a toroidal surface.
  • To formulate the N-point vortex evolution equation on a torus as a Hamiltonian dynamical system.

Main Methods:

  • Derivation of the N-point vortex evolution equation using Green's function and the Laplace-Beltrami operator.
  • Formulation of the system as a Hamiltonian dynamical system utilizing symplectic geometry and the uniformization theorem.
  • Analysis of the 2-vortex problem, equilibria, and interactions of vortices with equal magnitudes.

Main Results:

  • The 2-vortex problem on a toroidal surface is shown to be integrable.
  • Characteristic interactions between point vortices on the torus were identified.
  • It was found that two identical point vortices can exhibit local repulsive behavior under specific conditions.

Conclusions:

  • The Hamiltonian formulation provides a robust framework for studying vortex dynamics on toroidal surfaces.
  • The findings offer new insights into the complex behavior of vortices in non-Euclidean geometries.
  • This work lays the groundwork for further investigations into multi-vortex interactions on complex manifolds.