Collision Dynamics of Confined Particle Systems

The paper presents a computational study of collision dynamics in two-dimensional confined particle systems. To investigate the effects of container geometry, the authors conducted simulations across three different shapes: a square container (600×600 pixels), a rectangular container (900×400 pixels), and an elongated container (1200×300 pixels). In each case, the total area was kept constant, and the system was initialized with 10 particles having random velocities within the range of -5 to 5 pixels per time unit. Each configuration was repeated five times with different random seeds to ensure statistical reliability, resulting in 15 independent simulations for the container geometry analysis. For analyzing particle density effects, simulations were carried out using a fixed square container of size 600×600 pixels while varying the number of particles. The densities considered were low (10 particles), medium (15 particles), and high (20 particles). All simulations used the same velocity range of -5 to 5 pixels per time unit for initial conditions. Like the previous case, each configuration was repeated five times with different seeds, leading to another set of 15 independent simulation runs focused on understanding how particle density influences collision behavior. The effect of initial velocity distribution was explored using a fixed container size of 600×600 pixels and a constant particle count of 10. The initial velocities were sampled from three different ranges: low energy (-5 to 5), medium energy (-10 to 10), and high energy (-15 to 15) pixels per time unit. These settings were again tested across five independent trials for each range to account for variability due to random initialization, generating another 15 distinct simulations aimed at quantifying the impact of particle speed on collision rates. Altogether, the study conducted a total of 45 independent simulations: 15 each for container geometry, particle density, and velocity distribution effects. Each dataset recorded particle-wall collisions, particle-particle collisions, and resulting velocity distributions over the course of the simulation. These systematically varied configurations enabled a robust analysis of how geometric and dynamic parameters influence the collision dynamics in confined particle systems.本论文针对二维受限粒子系统（two-dimensional confined particle systems）中的碰撞动力学开展了计算研究。为探究容器几何形态的影响，研究者针对三种不同形状的容器开展了模拟实验：正方形容器（600×600像素）、矩形容器（900×400像素）与长条形容器（1200×300像素）。所有实验中系统总占面均保持恒定，且初始时系统内包含10个粒子，其初始速度取值范围为-5至5像素/时间单位。每组配置均采用不同随机种子重复5次以保证统计可靠性，最终用于容器几何形态分析的独立模拟共计15组。 为分析粒子密度的影响效应，研究者采用尺寸固定为600×600像素的正方形容器，改变系统内的粒子数量开展模拟。所考察的密度梯度包括低密度（10个粒子）、中密度（15个粒子）与高密度（20个粒子）。所有模拟的初始速度范围均统一设置为-5至5像素/时间单位。与前述实验一致，每组配置同样通过不同随机种子重复5次，最终得到用于探究粒子密度对碰撞行为影响的15组独立模拟数据集。 为探究初始速度分布的影响效应，研究者采用尺寸固定为600×600像素的容器，并保持粒子总数恒定为10个。初始速度分别从三个不同范围采样：低能范围（-5至5像素/时间单位）、中能范围（-10至10像素/时间单位）与高能范围（-15至15像素/时间单位）。每组速度范围同样通过5次独立重复实验以抵消随机初始化带来的变量影响，最终生成15组独立模拟，用于量化粒子速率对碰撞频次的影响。 本研究总计开展45组独立模拟：其中容器几何形态、粒子密度与初始速度分布三类实验各占15组。各数据集均记录了模拟过程中的粒子-器壁碰撞、粒子-粒子碰撞事件以及最终的速度分布情况。上述系统性变化的实验配置，为深入分析几何与动力学参数如何影响受限粒子系统内的碰撞动力学提供了坚实的研究基础。