Numba加速的二維擴散限制聚集：實現方法與碎形特徵分析

摘要

我们推出dla-ideal-solver——一个基于Numba加速Python的高性能二维扩散限制聚集（DLA）模拟框架。通过即时编译技术，该框架在保持高级编程灵活性的同时，实现了与传统静态语言实现相媲美的计算吞吐量。我们研究了不同注入几何结构与行走者浓度下的拉普拉斯生长不稳定性，分析证实了在稀薄体系中标准分形维数D_f≈1.71的鲁棒性，符合Witten-Sander普适类规律。然而，在高密度环境中我们观察到向类伊甸园紧凑生长模式（D_f≈1.87）的显著跨域转变，这归因于屏蔽长度的饱和效应。除标准质量-半径标度分析外，我们采用广义Rényi维数与空隙度指标来量化聚集体的单分形特征与空间异质性。本研究为探索非平衡统计力学中的相变建立了可复现的开源测试平台。

English

We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput comparable to legacy static implementations while retaining high-level flexibility. We investigate the Laplacian growth instability across varying injection geometries and walker concentrations. Our analysis confirms the robustness of the standard fractal dimension D_f approx 1.71 for dilute regimes, consistent with the Witten-Sander universality class. However, we report a distinct crossover to Eden-like compact growth (D_f approx 1.87) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized Rényi dimensions and lacunarity metrics to quantify the monofractal character and spatial heterogeneity of the aggregates. This work establishes a reproducible, open-source testbed for exploring phase transitions in non-equilibrium statistical mechanics.

Numba加速的二維擴散限制聚集：實現方法與碎形特徵分析

Numba-Accelerated 2D Diffusion-Limited Aggregation: Implementation and Fractal Characterization

摘要

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