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

Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

547
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
547
Magnetic Vector Potential01:15

Magnetic Vector Potential

1.6K
In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...
1.6K
Symmetric Member in Bending01:07

Symmetric Member in Bending

601
In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
601
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

520
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
520
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

418
The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
418
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

1.4K
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
1.4K

You might also read

Related Articles

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

Sort by
Same author

Interfacial Active-Oxygen Transport in Inverse CuO<sub><i>x</i></sub>/Perovskite Catalysts for Low-Temperature CO Oxidation.

ACS applied materials & interfaces·2026
Same author

Oxygen vacancy-mediated photothermal CO<sub>2</sub> methanation over Ni/Ce-Zr solid solution catalysts.

Journal of colloid and interface science·2026
Same author

Self-Assembly Molecular Ordering for Strengthened Interface and Efficient Perovskite/Silicon Tandem Solar Cells.

Small (Weinheim an der Bergstrasse, Germany)·2026
Same author

Cryo-EM-guided subtractive optimization of a novel VCP/p97 inhibitor.

IUCrJ·2026
Same author

Disposal of waste printed circuit boards in molten carbonates for valorization and metal recovery.

Waste management (New York, N.Y.)·2026
Same author

A dual-layer vector map encryption scheme using 4D hyperchaos and SM4.

Scientific reports·2026
Same journal

Denoising algorithm of Φ-OTDR systems based on adaptive fractional wavelet transform denoising.

Optics express·2026
Same journal

Millisecond photon-to-photon latency and high-speed volumetric projection system for optogenetics.

Optics express·2026
Same journal

Polarization-encoded coaxial structured light for high-precision 3D surface profilometry.

Optics express·2026
Same journal

Discrete freeform optical design based on collaborative optimization of point cloud and local normals.

Optics express·2026
Same journal

Ultrafast ghost imaging with 25 GHz speckle switching and wavelength-division multiplexing.

Optics express·2026
Same journal

Atomic vapor cells fabricated by femtosecond laser welding of standard-optical-quality glass.

Optics express·2026
See all related articles

Related Experiment Video

Updated: Feb 2, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

3.6K

Vector solitons in nonparity-time-symmetric complex potentials.

Xing Zhu, Yingji He

    Optics Express
    |November 25, 2018
    PubMed
    Summary
    This summary is machine-generated.

    Vector solitons in non-parity-time (PT)-symmetric potentials are stable in both low and high power regions, even above phase transitions. Their asymmetric profiles and transverse power flow are analyzed.

    More Related Videos

    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
    12:03

    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

    Published on: May 25, 2019

    8.9K
    The Logic, Experimental Steps, and Potential of Heterologous Natural Product Biosynthesis Featuring the Complex Antibiotic Erythromycin A Produced Through E. coli
    10:41

    The Logic, Experimental Steps, and Potential of Heterologous Natural Product Biosynthesis Featuring the Complex Antibiotic Erythromycin A Produced Through E. coli

    Published on: January 13, 2013

    19.0K

    Related Experiment Videos

    Last Updated: Feb 2, 2026

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
    07:42

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

    Published on: December 15, 2021

    3.6K
    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
    12:03

    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

    Published on: May 25, 2019

    8.9K
    The Logic, Experimental Steps, and Potential of Heterologous Natural Product Biosynthesis Featuring the Complex Antibiotic Erythromycin A Produced Through E. coli
    10:41

    The Logic, Experimental Steps, and Potential of Heterologous Natural Product Biosynthesis Featuring the Complex Antibiotic Erythromycin A Produced Through E. coli

    Published on: January 13, 2013

    19.0K

    Area of Science:

    • Nonlinear optics
    • Complex photonics
    • Mathematical physics

    Background:

    • Parity-time (PT)-symmetric potentials offer unique optical properties.
    • Vector solitons are multi-component optical beams with distinct propagation characteristics.
    • Understanding soliton stability in complex potentials is crucial for optical applications.

    Purpose of the Study:

    • Investigate the existence and stability of vector solitons in non-parity-time (PT)-symmetric complex potentials.
    • Analyze the behavior of vector solitons with differing propagation constants.
    • Explore the impact of phase transitions on soliton stability and properties.

    Main Methods:

    • Numerical simulations to determine soliton existence and stability regions.
    • Analysis of vector soliton profiles and their components.
    • Study of transverse power flow within the soliton components.

    Main Results:

    • Vector solitons exhibit stability both below and above the phase transition point.
    • Below the phase transition, stability is observed in the low power regime.
    • Above the phase transition, two continuous stable intervals are identified.
    • Asymmetric profiles are characteristic of the two vector soliton components.
    • Transverse power flow in both components of non-PT-symmetric complex potentials is examined.

    Conclusions:

    • Vector solitons can be robustly stable in non-PT-symmetric complex potentials across various power regimes.
    • The phase transition significantly influences the stability landscape of vector solitons.
    • The study provides insights into the complex dynamics and potential applications of vector solitons in engineered optical systems.