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

Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

7.6K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
7.6K
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

4.2K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
4.2K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.4K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.4K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.6K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
18.6K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.4K
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...
1.4K
Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

30.2K
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
30.2K

You might also read

Related Articles

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

Sort by
Same author

Determination of topological charges of polychromatic optical vortices.

Optics express·2010
Same author

Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons.

Optics letters·2006
See all related articles

Related Experiment Video

Updated: Mar 21, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Correlation between topological structure and its properties in dynamic singular vector fields.

Vasyl Vasilev, Marat Soskin

    Applied Optics
    |May 4, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel technique for measuring topology in singular vector fields by analyzing ellipticity. Researchers discovered strict experimental rules linking optical vortices to C points, with percolation phenomena explaining long-lasting chains.

    More Related Videos

    Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
    13:02

    Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

    Published on: February 27, 2016

    13.1K
    Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
    09:39

    Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

    Published on: November 18, 2019

    6.4K

    Related Experiment Videos

    Last Updated: Mar 21, 2026

    Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
    11:00

    Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

    Published on: July 19, 2016

    12.0K
    Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
    13:02

    Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

    Published on: February 27, 2016

    13.1K
    Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
    09:39

    Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

    Published on: November 18, 2019

    6.4K

    Area of Science:

    • Physics
    • Optics
    • Complex Systems

    Background:

    • Singular vector fields are crucial in optics and fluid dynamics.
    • Understanding their topology, including C points and L lines, is essential for various applications.
    • Existing measurement techniques have limitations in precision and scope.

    Purpose of the Study:

    • To develop a new, precise technique for establishing topology measurements of static and dynamic singular vector fields.
    • To investigate the relationship between optical vortices and the morphological parameters of C points.
    • To explore the role of percolation phenomena in the behavior of singular vector fields.

    Main Methods:

    • Precise measurement of the 3D ellipticity distribution landscape in singular optical fields.
    • Identification and analysis of C points located at the peaks of ellipticity.
    • Experimental confirmation of rules governing the connection between optical vortices and C point morphology.

    Main Results:

    • A three-component topology of vector fields was identified, including right-hand (RH) and left-hand (LH) elliptical areas and L lines as singularities.
    • The azimuth map of polarization ellipses was found to be common for both RH and LH ellipses and does not sense L lines.
    • Strict experimental rules were confirmed, establishing a link between optical vortex sign and C point morphology.
    • Percolation phenomena were shown to explain the realization and long duration (up to 10^3 s) of chains in singular vector fields.

    Conclusions:

    • The new technique provides precise topology measurements for singular vector fields.
    • The confirmed rules offer a deeper understanding of the relationship between optical vortices and C points.
    • Percolation phenomena play a significant role in the observed long-duration chains within these fields.