Probing surface characteristics of diffusion-limited-aggregation clusters with particles of variable size.

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Diffusion-limited aggregation (DLA) describes pattern formation in systems driven by diffusion.
• Understanding the geometric properties of DLA clusters is crucial for various scientific fields.
• Previous methods faced limitations in accurately determining the fractal dimension.

Purpose of the Study:

• To develop a novel technique for accurately probing the harmonic measure of DLA cluster surfaces.
• To precisely determine the fractal dimension (D) of DLA clusters.
• To enhance the characterization of DLA cluster geometric properties.

Main Methods:

• Developed an original off-lattice killing-free algorithm to generate 1000 DLA clusters.
• Utilized variable-size particles for probing the cluster surface.
• Applied sequential limiting procedures for vanishing probe size and infinite cluster size.

Main Results:

• Achieved unprecedented accuracy in determining the fractal dimension.
• Precisely calculated the fractal dimension D=1.7100(2).
• Demonstrated the effectiveness of the developed probing technique.

Conclusions:

• The study provides a highly accurate value for the fractal dimension of DLA clusters.
• The developed technique offers a robust method for analyzing DLA cluster surfaces.
• This work advances the understanding of fractal geometry in complex systems.