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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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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...
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Symmetry in Maxwell's Equations01:28

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Gauss's Law: Spherical Symmetry01:26

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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...
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Gauss's Law: Cylindrical Symmetry01:20

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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,...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Eccentric Axial Loading in a Plane of Symmetry01:16

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Generation of Aggregates of Mouse Embryonic Stem Cells that Show Symmetry Breaking, Polarization and Emergent Collective Behaviour In Vitro
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RMSD and Symmetry.

Evangelos A Coutsias1, Michael J Wester2

  • 1Department of Applied Mathematics and Statistics and Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794.

Journal of Computational Chemistry
|March 5, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for efficiently calculating the root-mean-square deviation (RMSD) between molecular structures, improving upon existing methods for structural comparison and alignment.

Keywords:
alignmentchiralitydegeneracyoptimal superpositionsymmetry

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Area of Science:

  • Computational Biology
  • Structural Bioinformatics
  • Numerical Algorithms

Background:

  • Comparing biomolecular or solid body structures commonly involves minimizing root-mean-square deviation (RMSD).
  • Existing algorithms may not be optimal in terms of computational efficiency or handling complex symmetries.

Purpose of the Study:

  • To present a new, robust numerical algorithm for computing RMSD between molecular structures.
  • To provide an efficient method for calculating mutual RMSDs within a list of molecules and associated rotation matrices.
  • To address and resolve issues related to symmetry in structural alignment and superposition.

Main Methods:

  • Development of a novel numerical algorithm for RMSD computation.
  • Implementation of methods to handle molecular symmetry, including geometric degeneracy and alternative alignments.
  • Calculation of RMSD gradients and rotation matrices.

Main Results:

  • The new algorithm computes RMSD and rotation matrices in a minimal number of operations compared to previous methods.
  • The algorithm effectively addresses problems of symmetry, including degenerate superpositions.
  • A software package, frmsd, has been developed and is freely available.

Conclusions:

  • The presented algorithm offers a more efficient and robust approach to structural comparison using RMSD.
  • The handling of symmetry issues provides more accurate and comprehensive structural alignments.
  • The freely available software facilitates broader application in biomolecular structure analysis.