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

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

216
An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
216
Hyperbolas01:30

Hyperbolas

558
A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
558
Hyperbolic Functions01:26

Hyperbolic Functions

184
A flexible cable suspended between two points at the same height naturally forms a curve known as a catenary. This shape results from the balance between the cable’s weight and the tension acting along its length, representing a state of mechanical equilibrium. Unlike simpler approximations, the true shape of a hanging cable is described using hyperbolic functions.Hyperbolic functions are closely related to exponential functions and are named for their connection to the geometry of the...
184
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

626
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
626
Bending of Material: Problem Solving01:09

Bending of Material: Problem Solving

641
In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for...
641
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

10.2K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
10.2K

You might also read

Related Articles

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

Sort by
Same author

Ultrafast photoluminescence and multiscale light amplification in nanoplasmonic cavity glass.

Nature communications·2024
Same author

Functionalization of Phosphate and Tellurite Glasses and Spherical Whispering Gallery Mode Microresonators.

ACS omega·2023
Same author

Durability of SrTiO<sub>3</sub>-TiO<sub>2</sub> eutectic composite as a photoanode for photoelectrochemical water splitting.

RSC advances·2023
Same author

Surprising Eutectics: Enhanced Properties of ZnO-ZnWO<sub>4</sub> from Visible to MIR.

Advanced materials (Deerfield Beach, Fla.)·2022
Same author

Controlling Self-Assembly in Gyroid Terpolymer Films By Solvent Vapor Annealing.

Small (Weinheim an der Bergstrasse, Germany)·2018
Same author

Optically-active metastable defects in volumetric nanoplasmonic composites.

Scientific reports·2018

Related Experiment Video

Updated: Mar 31, 2026

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging
10:01

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

Published on: September 8, 2017

8.3K

Compendium of natural hyperbolic materials.

Karolina Korzeb, Marcin Gajc, Dorota Anna Pawlak

    Optics Express
    |October 20, 2015
    PubMed
    Summary

    Natural hyperbolic materials (NHMs) offer advantages over artificial hyperbolic metamaterials (HMMs). This review analyzes naturally occurring NHMs, suggesting optimal material choices based on wavelength, dielectric anisotropy, and losses.

    Area of Science:

    • Condensed matter physics
    • Materials science
    • Optics

    Background:

    • Artificial hyperbolic metamaterials (HMMs) exhibit unique electromagnetic properties due to opposite permittivity signs for ordinary and extraordinary waves.
    • Natural hyperbolic materials (NHMs) possess similar properties but remain less explored.
    • Existing literature provides data on permittivity as a function of wavelength for various materials.

    Purpose of the Study:

    • To review materials with naturally occurring anisotropy of permittivity.
    • To identify and suggest suitable natural hyperbolic materials (NHMs) for specific applications.
    • To analyze the influence of wavelength, dielectric anisotropy, and losses on NHM selection.

    Main Methods:

    • Literature review of existing data on material permittivity.

    More Related Videos

    Harmonic Nanoparticles for Regenerative Research
    09:23

    Harmonic Nanoparticles for Regenerative Research

    Published on: May 1, 2014

    12.2K
    Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging
    05:45

    Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

    Published on: March 31, 2022

    3.1K

    Related Experiment Videos

    Last Updated: Mar 31, 2026

    Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging
    10:01

    Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

    Published on: September 8, 2017

    8.3K
    Harmonic Nanoparticles for Regenerative Research
    09:23

    Harmonic Nanoparticles for Regenerative Research

    Published on: May 1, 2014

    12.2K
    Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging
    05:45

    Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

    Published on: March 31, 2022

    3.1K
  • Analysis of permittivity as a function of wavelength.
  • Evaluation of material properties including dielectric anisotropy and optical losses.

    • Main Results:

    • Identification of materials exhibiting natural hyperbolic behavior in specific wavelength ranges.
    • Characterization of the strength of dielectric anisotropy (SDA) in candidate NHMs.
    • Assessment of optical losses associated with potential NHM candidates.

    Conclusions:

    • Natural hyperbolic materials (NHMs) present a viable alternative to artificial HMMs.
    • Material selection for NHMs is critically dependent on wavelength, SDA, and losses.
    • Further research into NHMs can unlock new applications in metamaterials and optics.