Microscopic two-dimensional lattice model of dimer granular compaction with friction

Area of Science:

• Physics
• Statistical Mechanics
• Computational Physics

Background:

• Understanding granular material compaction is crucial in various scientific and engineering fields.
• Hard dimer systems provide a simplified yet relevant model for studying complex particle dynamics.

Purpose of the Study:

• To investigate the compaction dynamics of hard dimers in two dimensions.
• To analyze the effects of gravity, shaking (vertical and horizontal), and friction on dimer packing.
• To explore the influence of shaking duration and intensity on system density evolution.

Main Methods:

• Monte Carlo simulations were employed to model the system.
• Effective probabilities were introduced to represent forces, including gravity, shaking, and friction.
• Simulations were conducted for varying shaking durations (tau) and force intensities.

Main Results:

• Density evolution follows a stretched exponential behavior for shorter shaking times (tau) and a power-law tail for longer tau.
• In the absence of friction, a critical shaking time (tau*) distinguishes two regimes: power-law scaling for tau < tau* and logarithmic saturation for tau > tau*.
• Friction slows down compaction dynamics, leading to lower asymptotic densities that decrease linearly with the friction coefficient.

Conclusions:

• The study reveals distinct compaction regimes for hard dimers influenced by shaking duration and friction.
• Friction significantly impacts the final packing density, making dynamics slower and reducing overall compaction.
• Observed behaviors, particularly the inverse logarithmic density evolution under sequential tapping, align with experimental findings.