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

Generalized Hooke's Law01:22

Generalized Hooke's Law

3.2K
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
3.2K
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

824
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
824
Castigliano's Theorem01:18

Castigliano's Theorem

1.4K
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
1.4K
General State of Stress01:21

General State of Stress

917
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
917
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

716
When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
716
Hooke's Law01:26

Hooke's Law

1.9K
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
1.9K

You might also read

Related Articles

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

Sort by
Same author

The effects of ionic valency and size asymmetry on counterion adsorption.

The Journal of chemical physics·2026
Same author

Sculpting 2D Crystals via Membrane Contractions before and during Solidification.

Langmuir : the ACS journal of surfaces and colloids·2026
Same author

Effect of charge regulation on the screening properties of zwitterionic macroion solutions.

Soft matter·2026
Same author

Anomalous proteinaceous shells with octagonal local order.

Physical review. E·2025
Same author

Modular programming of interaction and geometric specificity enables assembly of complex DNA origami nanostructures.

Nature communications·2025
Same author

From toroids to helical tubules: Kirigami-inspired programmable assembly of two-periodic curved crystals from DNA origami.

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

Related Experiment Video

Updated: May 4, 2026

Forming, Confining, and Observing Microtubule-Based Active Nematics
08:37

Forming, Confining, and Observing Microtubule-Based Active Nematics

Published on: January 13, 2023

2.8K

Tensorial conservation law for nematic polymers.

Daniel Svenšek1, Gregory M Grason2, Rudolf Podgornik3

  • 1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
PubMed
Summary

This study introduces a new tensorial conservation law for quadrupolar nematic polymers, distinct from polar order conservation. It reveals unique constraints on order parameters due to microscopic coupling differences.

More Related Videos

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

6.6K
High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
06:24

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

Published on: October 31, 2019

5.7K

Related Experiment Videos

Last Updated: May 4, 2026

Forming, Confining, and Observing Microtubule-Based Active Nematics
08:37

Forming, Confining, and Observing Microtubule-Based Active Nematics

Published on: January 13, 2023

2.8K
DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

6.6K
High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
06:24

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

Published on: October 31, 2019

5.7K

Area of Science:

  • Polymer physics
  • Soft matter physics
  • Theoretical chemistry

Background:

  • Nematic polymers exhibit orientational order.
  • Existing conservation laws primarily address polar order.
  • Understanding quadrupolar order is crucial for polymer dynamics.

Purpose of the Study:

  • Derive a tensorial conservation law for quadrupolar nematic polymers.
  • Contrast this with conservation laws for polar order.
  • Analyze the implications for polymer behavior and structure.

Main Methods:

  • Tensorial formulation of conservation laws.
  • Analysis of microscopic coupling between orientational fields and density variations.
  • Mathematical derivation from polymer nematic tensor field gradients.

Main Results:

  • A novel tensorial conservation law for quadrupolar nematic polymers is derived.
  • Fundamentally distinct constraints on order parameters compared to polar order are identified.
  • The law connects spatial variations of the nematic tensor field with density variations.

Conclusions:

  • Microscopic differences lead to distinct conservation laws for polar and quadrupolar nematic polymers.
  • The derived tensorial law provides new insights into the behavior of quadrupolar polymer systems.
  • Singular structures like 'hairpins' influence gradients despite not affecting local order.