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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...
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 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,...
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.
Unsoundness of Aggregate due to Volume Change01:26

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Unsoundness in aggregates due to volume changes is primarily caused by the physical alterations aggregates undergo, such as freezing and thawing, thermal changes, and wetting and drying. Unsound aggregates, when subjected to these changes, result in volume change upon disintegration. This, in turn, contributes to the deterioration of concrete, including scaling, pop-outs, and cracking. Particular types of aggregates, such as porous flints, cherts, and those containing clay minerals, are...
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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...

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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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Linear aggregation beyond isodesmic symmetry.

J R Henderson1

  • 1School of Physics and Astronomy and Centre for Self-Organising Molecular Systems, University of Leeds, Leeds LS2 9JT, United Kingdom. j.r.henderson@leeds.ac.uk

The Journal of Chemical Physics
|February 5, 2009
PubMed
Summary
This summary is machine-generated.

Researchers have identified exactly solvable models for linear aggregation, extending beyond Ising's original model. These new models account for broken isodesmic symmetry found in real-world systems.

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Area of Science:

  • Physics
  • Chemistry
  • Materials Science

Background:

  • Exactly solvable models of linear aggregation, like Ising's one-dimensional model, are foundational.
  • Ising's model exhibits isodesmic symmetry, where bond strength is independent of cluster length.
  • Real-world linear aggregation often deviates from isodesmic symmetry.

Purpose of the Study:

  • To demonstrate that important real-world linear aggregation systems can be modeled using exactly solvable approaches.
  • To extend the applicability of exactly solvable models beyond strict isodesmic symmetry.

Main Methods:

  • Mapping complex linear aggregation systems to a class of one-dimensional models.
  • Utilizing analytical techniques to solve these mapped models.

Main Results:

  • Established that systems with broken isodesmic symmetry can be analyzed using exactly solvable models.
  • Provided a framework for understanding linear aggregation phenomena with variable bond strengths.

Conclusions:

  • The study expands the scope of exactly solvable models in aggregation processes.
  • This work offers new analytical tools for studying complex linear aggregation in various scientific domains.