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Electric Field of a Non Uniformly Charged Sphere

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Updated: Jun 23, 2026

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production
07:46

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production

Published on: March 27, 2017

Dense sphere packings from optimized correlation functions.

Adam B Hopkins1, Frank H Stillinger, Salvatore Torquato

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

Researchers developed smooth functions to model jammed sphere packings, achieving a packing fraction of 0.6850. This method surprisingly allows packing fractions to approach theoretical limits with increased order.

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Assembly and Characterization of Polyelectrolyte Complex Micelles
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Assembly and Characterization of Polyelectrolyte Complex Micelles

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Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Disordered sphere packings are fundamental in materials science.
  • Understanding jamming and packing fractions is crucial for material properties.
  • Existing models often struggle to capture the complexity of jammed states.

Purpose of the Study:

  • To construct and optimize pair correlation functions for jammed disordered sphere packings.
  • To achieve higher packing fractions (φ) and average number of contacts (Z).
  • To explore the relationship between packing fraction, order, and smooth function construction.

Main Methods:

  • Utilized elementary smooth functions beyond contact to build pair correlation functions.
  • Employed the g₂-invariant optimization method for parameter tuning.
  • Applied a translational order metric to analyze packing structures.

Main Results:

  • Achieved a packing fraction (φ) of 0.6850, significantly reducing the gap between theoretical maximum and random jammed packings.
  • Demonstrated that adding smooth sinusoidal functions allows packing fractions to approach the theoretical maximum (π/√18).
  • Found a positive correlation between increased packing fraction and higher degrees of translational order.

Conclusions:

  • Smooth functions beyond contact are effective for modeling jammed sphere packings.
  • Increasing order in packings is necessary to achieve higher packing fractions.
  • The developed method offers a pathway to design materials with enhanced packing efficiency.