用分数相互作用定律模拟任意形式的多粒子碰撞动力学
Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions
摘要：
利用分子动力学方法，我们研究了三维空间中球形粒子运动的离散确定性模型。该模型考虑了任意形式的多粒子碰撞。利用分数阶微积分，我们提出了一个表达式的排斥力，这是所谓的分数相互作用定律。然后，我们说明和讨论如何控制（关联）的能量耗散和碰撞时间为一个单独的文章内多粒子碰撞。在多粒子碰撞中，我们包括了从耦合的扭转-滑动摩擦通过滚动摩擦到静摩擦的过渡所需的摩擦机制。分析简单的模拟，我们发现，在强排斥状态的二元碰撞占主导地位。然而，在多粒子碰撞中，观察到弱排斥要强得多。所提出的数值结果可以用来逼真地模拟一组碰撞粒子中单个粒子的碰撞动力学。
英文摘要：
Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.
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