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Updated: Jun 5, 2026

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

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

Published on: March 27, 2017

Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming.

S Torquato¹, Y Jiao

¹Department of Chemistry, Princeton Center for Theoretical Science, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

This study introduces a new optimization method for creating dense sphere packings. The adaptive-shrinking cell formulation with sequential-linear-programming efficiently generates various jammed packings across multiple dimensions.

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Last Updated: Jun 5, 2026

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

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Published on: March 27, 2017

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Published on: December 28, 2021

Area of Science:

Physics
Materials Science
Computational Science

Background:

Generating dense packings of particles is crucial in various scientific fields.
Existing methods face challenges in producing diverse and stable packings efficiently.

Purpose of the Study:

To develop a novel computational framework for generating dense, nonoverlapping sphere packings.
To explore the capabilities of the adaptive-shrinking cell (ASC) formulation and sequential-linear-programming (SLP) for packing optimization.
To produce a wide spectrum of jammed sphere packings in various dimensions.

Main Methods:

Formulation of particle packing as an optimization problem using the adaptive-shrinking cell (ASC) method.
Application of sequential-linear-programming (SLP) techniques to solve the ASC optimization problem for sphere packings.
Implementation of the SLP algorithm to generate packings in d-dimensional Euclidean space (R(d)) for d=2 to 6.

Main Results:

Successfully generated a broad range of jammed sphere packings, including disordered and inherent structures.
Demonstrated the algorithm's ability to produce packings with densities spanning a wide range, up to maximal densities.
Showcased the robustness and computational efficiency of the SLP-based ASC method compared to traditional algorithms like Lubachevsky-Stillinger (LS).
Achieved faster and more reliable generation of maximally dense packings, especially in higher dimensions.

Conclusions:

The SLP-based ASC formulation provides an efficient and robust method for generating diverse jammed sphere packings.
This approach offers significant advantages in computational cost and flexibility over existing packing algorithms.
The method is effective across various dimensions and packing densities, offering new possibilities for materials design and scientific inquiry.