Jammed systems in slow flow need a new statistical mechanics.

Area of Science:

• Physics
• Statistical Mechanics
• Materials Science

Background:

• Static granular problems, particularly jammed states of hard, rough objects, are analyzed using statistical mechanics.
• In static granular systems, kinetic energy and elastic strain are negligible, necessitating supplementary configuration-dependent equations for stress.
• Existing literature provides these 'missing equations' for static granular configurations.

Purpose of the Study:

• To extend the statistical mechanics approach from static granular problems to the slow dynamics of granular flow.
• To identify the key variables governing slow granular flow and develop analogous equations to those used in static analysis.

Main Methods:

• Adapting statistical mechanics methods used for static granular systems to analyze slow flow regimes.
• Deriving new 'missing equations' that govern the dynamics of granular flow, analogous to those for static stress.
• Focusing on configuration-dependent equations, similar to static granular mechanics.

Main Results:

• The strain rate, representing flow, replaces stress as the key variable in slow dynamics.
• New 'missing equations' governing granular flow dynamics have been derived.
• These derived equations are dependent solely on the configurations of the granular material.

Conclusions:

• Slow granular flow can be effectively studied using statistical mechanics, extending previous work on static granular systems.
• The strain rate is the critical dynamic variable, analogous to stress in static granular mechanics.
• Configuration-dependent equations are essential for a complete description of slow granular flow dynamics.