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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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...
Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

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,...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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 uniform...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Assembly of Cytoskeletal Filaments01:18

Assembly of Cytoskeletal Filaments

Cytoskeletal filaments are polymeric forms of smaller protein subunits. However, individual cytoskeletal filaments may easily disassemble or associate with other similar filaments to form rigid structures. Microfilaments, made of actin monomers, rely on actin-binding proteins to form bundles and create networks of individual actin filaments. Microtubules rely on microtubule-associated proteins (MAPs) to form sturdy cylindrical structures. However, the proteins involved in forming complex...

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Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

Self-assembled structures of Gaussian nematic particles.

Arash Nikoubashman1, Christos N Likos

  • 1Institute of Theoretical Physics, Heinrich Heine University of Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 11, 2011
PubMed
Summary

Researchers explored stable crystalline structures in liquid crystals using genetic algorithms (GA). They discovered novel solid phases where particles often avoid aligning with standard crystallographic directions due to competing forces.

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Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives

Published on: February 7, 2017

Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Crystallography

Background:

  • Nematic liquid crystals exhibit complex phase behavior.
  • Understanding crystalline configurations is crucial for materials design.

Purpose of the Study:

  • To predict stable crystalline structures of liquid crystals composed of soft ellipsoidal particles.
  • To determine the zero-temperature phase diagram for these systems.

Main Methods:

  • Utilized genetic algorithms (GA) to explore potential solid phase candidates.
  • Simulated interactions using a repulsive, anisotropic Gaussian potential.

Main Results:

  • Identified novel crystalline arrangements not aligned with high-symmetry crystallographic directions.
  • Observed a compromise between anisotropic repulsions and crystal ordering.
  • Found that strong elongation promotes particle alignment with the unit cell axis.

Conclusions:

  • The study reveals complex crystalline structures in anisotropic particle systems.
  • Particle shape and interaction potentials dictate emergent crystal symmetries.
  • Genetic algorithms are effective for predicting solid phases in soft matter systems.