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

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...
Hyperbolas01:30

Hyperbolas

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 axis is...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

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...
Hyperbolic Functions01:26

Hyperbolic Functions

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...
Inverse Hyperbolic Functions and Their Derivatives01:25

Inverse Hyperbolic Functions and Their Derivatives

The shape of a suspension bridge cable hanging under its own weight is described by a catenary curve, which is modeled using the hyperbolic cosine function. This mathematical model accurately captures the balance between gravity and tension acting along the cable. When a particular vertical position on the cable is known, the corresponding horizontal position can be determined using the inverse hyperbolic cosine function, allowing for a detailed analysis of the cable's geometry.Inverse...
Protein-protein Interfaces02:04

Protein-protein Interfaces

Many proteins form complexes to carry out their functions, making protein-protein interactions (PPIs) essential for an organism's survival. Most PPIs are stabilized by numerous weak noncovalent chemical forces. The physical shape of the interfaces determines the way two proteins interact. Many globular proteins have closely-matching shapes on their surfaces, which form a large number of weak bonds. Additionally, many PPIs occur between two helices or between a surface cleft and a polypeptide...

You might also read

Related Articles

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

Sort by
Same author

Collective epithelial migration mediated by the unbinding of hexatic defects.

eLife·2026
Same author

Hidden order in active nematic defects.

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

Quasi-Long-Ranged Order in Two-Dimensional Active Liquid Crystals.

Physical review letters·2025
Same author

Homochirality in the Vicsek model: Fluctuations and potential implications for cellular flocks.

Physical review. E·2025
Same author

Confined cell migration along extracellular matrix space in vivo.

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

Lipid membranes supported by polydimethylsiloxane substrates with designed geometry.

Soft matter·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 18, 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

Hyperbolic interfaces.

Luca Giomi1

  • 1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

Fluid interfaces with orientational order can form surfaces with constant negative Gaussian curvature. This hyperbolic morphology arises from a balance between surface tension and orientational elasticity in soft and biological materials.

More Related Videos

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns
07:32

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns

Published on: April 10, 2017

Related Experiment Videos

Last Updated: May 18, 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

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns
07:32

Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns

Published on: April 10, 2017

Area of Science:

  • Soft matter physics
  • Materials science
  • Biophysics

Background:

  • Fluid interfaces like soap films and lipid membranes exhibit complex geometries.
  • Special geometries arise in soft and biological materials with ordered phases.

Purpose of the Study:

  • To demonstrate the formation of surfaces with constant negative Gaussian curvature in fluid interfaces.
  • To explore the role of orientational order in determining interface morphology.

Main Methods:

  • Investigating fluid interfaces with an embedded orientational ordered phase.
  • Analyzing the interplay between surface tension and orientational elasticity.

Main Results:

  • Identified a class of surfaces with constant negative Gaussian curvature.
  • These hyperbolic surfaces emerge in materials like nematic liquid crystals and cytoskeletal assemblies.
  • The morphology results from the competition between surface tension and orientational elasticity.

Conclusions:

  • Fluid interfaces with orientational order can spontaneously form surfaces of constant negative Gaussian curvature.
  • This phenomenon is relevant to various soft and biological materials.
  • The resulting hyperbolic morphology is a direct consequence of competing physical forces.