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

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.3K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.5K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.5K
Navier–Stokes Equations01:28

Navier–Stokes Equations

2.8K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.8K
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

2.6K
Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations:...
2.6K
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

1.4K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
1.4K
Carrier Transport01:21

Carrier Transport

1.2K
The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
1.2K

You might also read

Related Articles

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

Sort by
Same author

Time evolution of piglet cerebral blood volume after resuscitation from hypoxic-ischemic insult.

Scientific reports·2025
Same author

Coarse-graining of perplexity for the spatial distribution of molecules.

Physical review. E·2024
Same author

Spatial distribution of the Shannon entropy for mass spectrometry imaging.

PloS one·2023
Same author

Changes of Mass Spectra Patterns on a Brain Tissue Section Revealed by Deep Learning with Imaging Mass Spectrometry Data.

Journal of the American Society for Mass Spectrometry·2022
Same author

Diffuse optical tomography by simulated annealing via a spin Hamiltonian.

Journal of the Optical Society of America. A, Optics, image science, and vision·2021
Same author

Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation.

Journal of the Optical Society of America. A, Optics, image science, and vision·2020
Same journal

Multi-module collaborative optimization-driven fast speckle correlation imaging in variable environments.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Secrecy performance analysis of NOMA-UWOC systems over a vertically stratified WGG oceanic turbulence channel.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Backscattering of plane waves in a composite system containing a rough surface and anisotropic scatterers.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Aspherical surface construction methods based on extended Jacobi polynomials.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

OCT sidelobe suppression method based on dual-path phase sinusoidal modulation and minimum value fusion.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Optical design concepts using wavelength-selective diffractive optics to enable miniaturized multimodal endoscopic imaging across separated spectral ranges.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
See all related articles

Related Experiment Video

Updated: May 2, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.0K

Singular eigenfunctions for the three-dimensional radiative transport equation.

Manabu Machida

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |February 25, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study generalizes Case's method for solving the radiative transport equation. Elementary solutions are found for three spatial variables, extending the method to complex 3D scenarios.

    More Related Videos

    Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
    10:23

    Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

    Published on: December 1, 2023

    1.3K
    Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
    04:35

    Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

    Published on: July 5, 2024

    2.2K

    Related Experiment Videos

    Last Updated: May 2, 2026

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    9.0K
    Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
    10:23

    Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

    Published on: December 1, 2023

    1.3K
    Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
    04:35

    Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

    Published on: July 5, 2024

    2.2K

    Area of Science:

    • Physics
    • Applied Mathematics
    • Computational Science

    Background:

    • Case's method provides solutions to the radiative transport equation.
    • The method is established for specific intensity depending on one spatial variable.

    Purpose of the Study:

    • To generalize Case's method for radiative transport equation solutions.
    • To find elementary solutions for specific intensity depending on three spatial variables in 3D space.

    Main Methods:

    • Utilizing a reference frame aligned with the wave vector.
    • Analyzing the angular part of elementary solutions.
    • Connecting to singular eigenfunctions of the 1D radiative transport equation.

    Main Results:

    • Elementary solutions for the radiative transport equation in 3D space were derived.
    • The angular component of these solutions corresponds to 1D singular eigenfunctions.
    • Case's method was successfully generalized to three spatial dimensions.

    Conclusions:

    • The generalization of Case's method is validated for 3D radiative transport problems.
    • This approach simplifies solving complex radiative transfer scenarios.
    • The findings offer a powerful tool for advanced physics and engineering applications.