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

Focusing of Light in the Eye01:16

Focusing of Light in the Eye

6.3K
Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...
6.3K
Light Acquisition02:16

Light Acquisition

8.0K
In order to produce glucose, plants need to capture sufficient light energy. Many modern plants have evolved leaves specialized for light acquisition. Leaves can be only millimeters in width or tens of meters wide, depending on the environment. Due to competition for sunlight, evolution has driven the evolution of increasingly larger leaves and taller plants, to avoid shading by their neighbors with contaminant elaboration of root architecture and mechanisms to transport water and nutrients.
8.0K
The Wave Nature of Light02:12

The Wave Nature of Light

46.3K
The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a "corpuscular" view of light, in which light was composed of streams of extremely tiny particles traveling at high speeds according to Newton's laws of motion.
46.3K
Anchoring Junctions01:03

Anchoring Junctions

4.3K
Anchoring junctions are multiprotein complexes that help cells connect to other cells and the extracellular matrix. Anchoring junctions are present on the lateral and basal surfaces of cells, providing strong and flexible connections. Focal adhesions are often formed due to cell interactions with the ECM substrata, which initiate signal transduction via kinase cascades and other mechanisms. Together, they provide stability and tissue integrity. There are three types of anchoring junctions:...
4.3K
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

486
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
486
Electric Field Lines01:25

Electric Field Lines

8.8K
The three-dimensional representation of the electric field of a positive point charge requires tracing the electric field vectors, whose lengths decrease as the square of their distance from the charge and which point away from the charge at each point. This vector field is no doubt challenging to visualize. The visualization of electric fields becomes quickly intractable as the number of charges increases.
The solution to this problem is to use electric field lines, which are not vectors but...
8.8K

You might also read

Related Articles

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

Sort by
Same author

Turing complete Navier-Stokes steady states via cosymplectic geometry.

PNAS nexus·2026
Same author

Nonlinear diffusion and decay of a blob of turbulence spreading into a quiescent fluid.

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

Optimal metrics for the first curl eigenvalue on 3-manifolds.

Calculus of variations and partial differential equations·2025
Same author

Melting of nonreciprocal solids: How dislocations propel and fission in flowing crystals.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Isolated steady solutions of the 3D Euler equations.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Obstructions to Topological Relaxation for Generic Magnetic Fields.

Archive for rational mechanics and analysis·2024
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: May 6, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

18.2K

Tying knots in light fields.

Hridesh Kedia1, Iwo Bialynicki-Birula, Daniel Peralta-Salas

  • 1Physics Department and the James Franck Institute, University of Chicago, 929 East 57th Street, Chicago, Illinois 60605, USA.

Physical Review Letters
|October 29, 2013
PubMed
Summary
This summary is machine-generated.

Researchers developed new analytical solutions for Maxwell's equations, revealing electromagnetic field lines that form all possible torus knots and links. This discovery preserves topological structures during field evolution, offering insights into complex field dynamics.

More Related Videos

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

27.0K
Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

9.7K

Related Experiment Videos

Last Updated: May 6, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

18.2K
A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

27.0K
Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

9.7K

Area of Science:

  • Theoretical Physics
  • Electromagnetism
  • Topology

Background:

  • Maxwell's equations describe classical electromagnetism in free space.
  • Knot theory studies the mathematical properties of knotted and linked curves.
  • Understanding complex field line structures is crucial in various physics domains.

Purpose of the Study:

  • To analytically construct novel null solutions to Maxwell's equations.
  • To demonstrate that these solutions' field lines can represent all torus knots and links.
  • To investigate the topological stability of these electromagnetic fields.

Main Methods:

  • Analytical construction of null electromagnetic fields.
  • Utilizing complex polynomials on the 3-sphere (S3).
  • Analyzing the evolution of shear-free, compressible flow-analogous fields.

Main Results:

  • A new family of null solutions to Maxwell's equations was derived.
  • The field lines of these solutions encode all possible torus knots and links.
  • The evolution of these null fields preserves the encoded topological structures.

Conclusions:

  • The study provides a direct link between electromagnetic field solutions and knot theory.
  • The findings offer a method to visualize and study complex topologies within electromagnetic fields.
  • This work opens avenues for exploring topological phenomena in electromagnetism.