Abstract The variance among bin counts is one of the most effective and convenient indices to quantify the degree of spatial distributive mixing. Although it is suitable for evaluating the spatial distribution of unimodal particles, many practical particle-mixing processes involve bimodal or multimodal particle systems. Herein, the variance among bimodal bin counts is introduced as a new mixing index to quantify the degree of distributive mixing of bimodal or multimodal particles. Four bimodal particle-mixing systems are assumed and analyzed to evaluate index performance: balanced versus imbalanced and fully versus partially distributed particle systems. As a result, we suggest practical usage and the most effective variation of variances among conventional bin counts and bimodal bin counts to quantify the four bimodal particle-mixing systems. Furthermore, variations of the method for evaluating multimodal mixing are proposed.

中文翻译：

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用新型双峰箱计数方差评估多峰拉格朗日粒子分布混合的策略

摘要 箱数之间的方差是量化空间分布混合程度最有效、最方便的指标之一。虽然它适用于评估单峰粒子的空间分布，但许多实际的粒子混合过程涉及双峰或多峰粒子系统。在此，引入双峰仓计数之间的方差作为一种新的混合指标，以量化双峰或多峰粒子的分布混合程度。假设并分析了四种双峰粒子混合系统以评估指标性能：平衡与不平衡以及完全与部分分布的粒子系统。因此，我们建议实际使用和常规箱计数和双峰箱计数之间最有效的方差变化来量化四个双峰粒子混合系统。