Finite dimension and particle heterogeneous DLAs

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Diffusion Limited Aggregates (DLAs) are fractal structures formed by particles aggregating under diffusion control.
• Understanding DLA formation is crucial in fields ranging from material science to biology.
• Previous studies primarily focused on homogeneous DLAs composed of a single particle type.

Purpose of the Study:

• To investigate the fractal properties of heterogeneous DLAs formed by mixtures of 4-legged and 2-legged particles.
• To analyze how varying proportions of these particles affect the finite dimension of the resulting aggregates.
• To explain the underlying mechanisms behind the observed counter-intuitive behavior in heterogeneous DLA complexity.

Main Methods:

• Simulating the formation of heterogeneous DLAs with varying ratios of 4-legged and 2-legged particles.
• Calculating the finite dimension, a measure of fractal complexity, for each DLA configuration.
• Analyzing the structural changes and growth patterns associated with different particle proportions.

Main Results:

• Heterogeneous DLAs exhibit a non-monotonic trend in their finite dimension as particle proportions change.
• Maximum complexity is observed when the ratio of 4-legged to 2-legged particles is approximately 30:70.
• DLAs transition from complex, nature-like structures to lattice-dominated forms as the proportion of 2-legged particles increases.

Conclusions:

• The finite dimension of heterogeneous DLAs does not decrease monotonically with increasing proportions of 2-legged particles.
• An unexpected peak in complexity arises from specific mixing ratios, challenging previous assumptions.
• The study provides insights into the mechanisms governing the formation and structural properties of complex, mixed-particle fractal systems.