Fundamental challenges in packing problems: from spherical to non-spherical particles.

Area of Science:

• Physics and Materials Science
• Statistical Mechanics
• Disordered Systems

Background:

• Random packings of objects are common in science and engineering but lack systematic theoretical descriptions.
• Jammed matter states are difficult to analyze due to complex positional and orientational correlations.
• Previous theoretical treatments have not fully captured the behavior of these disordered systems.

Purpose of the Study:

• To develop a fundamental theoretical description for jammed matter states.
• To establish a predictive framework for calculating packing fractions.
• To extend the understanding of disordered matter to both spherical and non-spherical particles.

Main Methods:

• Utilized a constant volume ensemble, inspired by conventional statistical mechanics.
• Adapted and extended the Edwards' ensemble approach, first proposed over two decades ago.
• Developed a predictive framework based on statistical mechanical principles.

Main Results:

• Successfully cast the constant volume ensemble approach into a predictive framework.
• Demonstrated the ability to calculate packing fractions for random packings.
• Validated the framework for both spherical and non-spherical particles.

Conclusions:

• A fundamental description of jammed matter is achievable using statistical mechanics.
• The developed framework provides a systematic method for predicting packing fractions.
• This work advances the theoretical understanding of disordered and jammed materials.