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

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

9.7K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
9.7K
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

7.0K
A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the  symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field,...
7.0K
Spherical Coordinates01:23

Spherical Coordinates

16.8K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
16.8K
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

86
Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
86
Atomic Orbitals02:44

Atomic Orbitals

46.6K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
46.6K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

9.8K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
9.8K

You might also read

Related Articles

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

Sort by
Same author

Harmonious color pairings: Insights from human preference and natural hue statistics.

iScience·2026
Same author

Reverse Janssen effect with non-spherical grains.

Physical review. E·2026
Same author

Liquidlike Dynamics in Ordered Soft-Particle Systems.

Physical review letters·2026
Same author

Structure-dynamics decoupling in soft-colloid suspensions.

Nature communications·2025
Same author

Hidden order in active nematic defects.

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

Evaporation from spherical chitosan polymer gels.

The Journal of chemical physics·2025
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Mar 15, 2026

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.3K

Spherical nematic shells with a threefold valence.

Vinzenz Koning1, Teresa Lopez-Leon2, Alexandre Darmon2

  • 1Instituut-Lorentz for Theoretical Physics, Leiden University, Leiden NL 2333 CA, The Netherlands.

Physical Review. E
|August 31, 2016
PubMed
Summary
This summary is machine-generated.

This study reveals the stable arrangement of defects in nematic shells. The optimal configuration, with specific defect angles, explains their experimental observation and long-term stability.

More Related Videos

Fabrication of Spherical and Worm-shaped Micellar Nanocrystals by Combining Electrospray, Self-assembly, and Solvent-based Structure Control
06:16

Fabrication of Spherical and Worm-shaped Micellar Nanocrystals by Combining Electrospray, Self-assembly, and Solvent-based Structure Control

Published on: February 11, 2018

21.4K
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

8.6K

Related Experiment Videos

Last Updated: Mar 15, 2026

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.3K
Fabrication of Spherical and Worm-shaped Micellar Nanocrystals by Combining Electrospray, Self-assembly, and Solvent-based Structure Control
06:16

Fabrication of Spherical and Worm-shaped Micellar Nanocrystals by Combining Electrospray, Self-assembly, and Solvent-based Structure Control

Published on: February 11, 2018

21.4K
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

8.6K

Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Theoretical Chemistry

Background:

  • Nematic shells are fascinating structures with unique defect arrangements.
  • Understanding defect energetics is crucial for predicting shell behavior.

Purpose of the Study:

  • To theoretically investigate the energetics of thin nematic shells containing specific defect types.
  • To determine the optimal spatial arrangement of these defects.
  • To analyze the influence of thermal fluctuations and shell thickness on defect energy.

Main Methods:

  • Utilizing theoretical modeling to calculate defect energetics.
  • Determining defect configurations through energy minimization principles.
  • Analyzing thermal fluctuations and their impact on the ground state.

Main Results:

  • The optimal arrangement of two charge-one-half defects and one charge-one defect was identified.
  • These defects form an isosceles triangle on a great circle with specific angles (66° and 48°).
  • The calculated energy of this three-defect configuration is comparable to other known defect arrangements.

Conclusions:

  • The determined defect arrangement is consistent with experimental observations.
  • The energy landscape, including large energy barriers, explains the stability and observability of these nematic shell configurations.