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: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.3K
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...
9.3K
Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

1.3K
A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
1.3K
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

1.0K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.0K
Two-Dimensional Force System01:20

Two-Dimensional Force System

1.5K
A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
1.5K
Reflective Property of Parabolas01:26

Reflective Property of Parabolas

190
A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...
190
Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

464
The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...
464

You might also read

Related Articles

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

Sort by
Same author

Analytical characterization of sloppiness in neural networks: Insights from linear models.

Physical review. E·2026
Same author

Inverse design of parameter-controlled disclination paths.

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

Numerical assessment of arterial punch method and arterial reconstruction in femoral endarterectomy.

Annals of biomedical engineering·2025
Same author

Path integral approach for predicting the diffusive statistics of geometric phases in chaotic Hamiltonian systems.

Chaos (Woodbury, N.Y.)·2025
Same author

Universal Scaling Framework for Controlling Phase Behavior in Thickening and Jamming Suspensions.

Physical review letters·2025
Same author

Electronically configurable microscopic metasheet robots.

Nature materials·2024

Related Experiment Video

Updated: Jan 5, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

17.1K

Curved Geometries from Planar Director Fields: Solving the Two-Dimensional Inverse Problem.

Itay Griniasty1, Hillel Aharoni1,2, Efi Efrati1

  • 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review Letters
|October 22, 2019
PubMed
Summary

Designing materials that deform into specific shapes is now possible. This study solves the inverse problem for director fields in anisotropic materials, enabling precise shape control for advanced applications.

More Related Videos

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

16.0K
Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.6K

Related Experiment Videos

Last Updated: Jan 5, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

17.1K
High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

16.0K
Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.6K

Area of Science:

  • Materials Science
  • Solid Mechanics
  • Applied Mathematics

Background:

  • Anisotropic materials like nematic elastomers deform uniformly under actuation.
  • Director field variations dictate complex shape changes in these materials.
  • A general solution for designing director fields to achieve desired surface geometries is lacking.

Purpose of the Study:

  • To solve the inverse design problem for director fields in anisotropic materials.
  • To determine if a director field exists for a target surface geometry.
  • To develop a method for designing director fields for precise shape transformation.

Main Methods:

  • Formulating the inverse problem as a hyperbolic system of differential equations.
  • Proving local integrability of the inverse problem.
  • Developing an algorithm for integrating the hyperbolic system.
  • Deriving bounds for global solutions.

Main Results:

  • The inverse problem is proven to be locally integrable.
  • An algorithm for integrating the inverse problem is provided.
  • Bounds on global solutions for director field design are derived.
  • A classification of director fields deforming into a given surface is established.

Conclusions:

  • The study provides the first general solution to the inverse design problem for director fields.
  • The developed methods enable the design of materials with predictable anisotropic deformation.
  • This work paves the way for optimizing director fields for specific surface geometries.