Universality in boundary domain growth by sudden bridging

Area of Science:

• Physics
• Statistical Mechanics
• Materials Science

Background:

• Cluster aggregation is a fundamental process in various scientific fields.
• Understanding boundary domain growth is crucial for predicting material properties and system behavior.
• Maximum concentration limits simplify aggregation dynamics to percolation processes.

Purpose of the Study:

• To investigate the universality of boundary domain growth in cluster aggregation.
• To determine the scaling behavior of boundary interface width at maximum concentration.
• To identify the universal exponent governing this growth process.

Main Methods:

• Simulations of cluster aggregation on two-dimensional square lattices.
• Analysis of boundary domain growth dynamics at maximum concentration.
• Calculation of susceptibility (χ) as a measure of boundary interface width.

Main Results:

• Boundary domain growth exhibits universal scaling behavior.
• The susceptibility (χ) scales with lattice size (L) as χ ~ L(γ).
• A universal exponent γ = 1 was determined, independent of the specific aggregation models studied.

Conclusions:

• The rapid growth of boundary domains at the percolation threshold drives universal scaling.
• The determined universal exponent (γ = 1) provides a fundamental insight into aggregation phenomena.
• This universality has implications for diverse systems exhibiting cluster aggregation and percolation.