Memory effects on the statistics of fragmentation.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• Understanding material fragmentation is crucial for predicting material failure.
• Two-dimensional systems offer a simplified model to study complex fragmentation phenomena.
• Previous studies have explored fragmentation in various systems, but the role of initial macroscopic phase is less understood.

Purpose of the Study:

• To investigate the fragmentation process of two-dimensional Lennard-Jones systems.
• To determine the effect of initial temperature and impact energy on mass fragment statistics.
• To identify the relationship between the system's macroscopic phase and its fragmentation scaling behavior.

Main Methods:

• Extensive molecular dynamics simulations were performed.
• Systems were thermalized to specific temperatures before fragmentation.
• Fragmentation was initiated by increasing particle velocities radially.
• Statistical analysis of mass fragments was conducted.

Main Results:

• The cumulative distribution of fragments follows a specific scaling ansatz: F(m) ∝ m^(1-α)exp(-(m/m₀)γ).
• The scaling exponent α is dependent on the initial temperature of the system.
• A characteristic scaling exponent α was identified for each macroscopic phase (e.g., solid, liquid) of the thermalized system.

Conclusions:

• The macroscopic phase of a two-dimensional system before fragmentation dictates its nonuniversal fragmentation behavior.
• Temperature-dependent scaling exponents reveal a connection between the initial state and the fragmentation outcome.
• This work provides insights into the statistical mechanics of phase transitions during fragmentation events.