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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.02417 |
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| _version_ | 1866908749467222016 |
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| author | Prajapati, Satish |
| author_facet | Prajapati, Satish |
| contents | Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework reconciling its stochastic algorithm, universal fractal dimension, multifractal growth measure, and finite-size effects remains essential for applications from materials science to geomorphology. Through large-scale simulations (clusters up to $N = 10^6$ particles) in two dimensions, we perform a tripartite analysis: (1) We establish a definitive finite-size scaling collapse, extracting the universal fractal dimension $D = 1.712 \pm 0.015$ and identifying the crossover to boundary-dominated growth at a scaled mass $x_0 \approx 0.10 \pm 0.02$. (2) We quantify the full multifractal spectrum of the harmonic measure ($Δα\approx 1.13$), directly linking the stochastic algorithm to the deterministic Laplacian growth equation $\nabla^2 p = 0$ and explaining the screening effect via an exponential decay $η\sim e^{-r/ξ}$ with screening length $ξ= 22.7 \pm 0.8$ lattice units. (3) We provide a complete morphological characterization, revealing power-law branch length distributions ($τ\approx 2.1$) and angular branching preferences ($\sim 72^\circ$). This work computationally validates DLA as a robust universality class and provides a scalable methodology for analyzing diffusion-controlled pattern formation across disciplines. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_02417 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Computational Framework for Two Dimensional Diffusion Limited Aggregation via Finite-Size Scaling, Multifractality, and Morphological Analysis Prajapati, Satish Statistical Mechanics Mesoscale and Nanoscale Physics Materials Science Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework reconciling its stochastic algorithm, universal fractal dimension, multifractal growth measure, and finite-size effects remains essential for applications from materials science to geomorphology. Through large-scale simulations (clusters up to $N = 10^6$ particles) in two dimensions, we perform a tripartite analysis: (1) We establish a definitive finite-size scaling collapse, extracting the universal fractal dimension $D = 1.712 \pm 0.015$ and identifying the crossover to boundary-dominated growth at a scaled mass $x_0 \approx 0.10 \pm 0.02$. (2) We quantify the full multifractal spectrum of the harmonic measure ($Δα\approx 1.13$), directly linking the stochastic algorithm to the deterministic Laplacian growth equation $\nabla^2 p = 0$ and explaining the screening effect via an exponential decay $η\sim e^{-r/ξ}$ with screening length $ξ= 22.7 \pm 0.8$ lattice units. (3) We provide a complete morphological characterization, revealing power-law branch length distributions ($τ\approx 2.1$) and angular branching preferences ($\sim 72^\circ$). This work computationally validates DLA as a robust universality class and provides a scalable methodology for analyzing diffusion-controlled pattern formation across disciplines. |
| title | A Unified Computational Framework for Two Dimensional Diffusion Limited Aggregation via Finite-Size Scaling, Multifractality, and Morphological Analysis |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2601.02417 |