XU Bao;WU Hongye;YU Yue;

• 1:Department of Physics Science and Technology
• 2: Baotou Teachers College

Abstract：

In an ideal Galton board model, the exit distribution function represents the solution to a one-dimensional diffusion equation, providing a means to verify the correctness of the derived distribution. However, when wall rebounds are incorporated, the exit distribution function obtained through the maximum entropy principle fails to satisfy this diffusion equation. To rigorously incorporate wall rebound effects, we employ a periodic folding scheme that yields an exit distribution function satisfying the one-dimensional diffusion equation. We demonstrate that the maximum entropy-based exit distribution function serves as a unimodal approximation of the periodic folding scheme. Numerical experiments using Monte Carlo method reveal that for exit distribution functions incorporating wall rebounds, a three-peak approximation derived from the periodic folding scheme exhibits superior expressive capability compared to the unimodal approximation. Furthermore, as the number of peg layers increases, the exit distribution function undergoes a gradual transition from a normal distribution toward a uniform distribution. Using the unimodal distribution as a representative case, we present a methodology for identifying this transition point.

Key Words： Galton board;exit distribution function;maximum entropy principle;periodic folding scheme

Abstract:

Keywords:

Foundation: 教育部高等学校物理类专业教学指导委员会2023年度教学研究项目（JZW-23-GT-11）;; 包头师范学院一流本科课程项目（固体物理学）;包头师范学院教改项目（BSJG24Y14）资助

Authors: XU Bao;WU Hongye;YU Yue;

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