模拟硬刚体
Simulating Hard Rigid Bodies
摘要：
凝聚态物质中的几个物理系统已经被建模，将其组成粒子近似为硬物体。硬球模型确实是凝聚态物质计算和理论描述的基石之一。下一个层次的描述是把粒子看作具有一般形状的刚性物体，这将极大地丰富可能的现象学。这种建模将被证明是有趣的，在所有这些情况下，空间效应发挥了相关的作用。这些包括生物学、软物质、颗粒材料和分子系统。为了开发硬刚体的事件驱动的分子动力学模拟的通用配方，将描述用于计算两个凸硬刚体之间的距离和两个碰撞硬刚体的接触时间的两种算法，求解非线性方程组。在这两种方法的基础上，我们将发展出一个事件驱动的分子动力学演算法来模拟凸硬刚体系统。为了优化非常细长的硬刚体之间的碰撞检测，一种新的最近邻列表方法的基础上有向包围盒将被引入和充分解释。新算法的效率和性能将被广泛测试单轴硬椭球和超二次曲面。最后将报告和讨论在各个科学领域的应用。
英文摘要：
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormously. This kind of modeling will prove to be interesting in all those situations in which steric effects play a relevant role. These include biology, soft matter, granular materials and molecular systems. With a view to developing a general recipe for event-driven Molecular Dynamics simulations of hard rigid bodies, two algorithms for calculating the distance between two convex hard rigid bodies and the contact time of two colliding hard rigid bodies solving a non-linear set of equations will be described. Building on these two methods, an event-driven molecular dynamics algorithm for simulating systems of convex hard rigid bodies will be developed and illustrated in details. In order to optimize the collision detection between very elongated hard rigid bodies, a novel nearest-neighbor list method based on an oriented bounding box will be introduced and fully explained. Efficiency and performance of the new algorithm proposed will be extensively tested for uniaxial hard ellipsoids and superquadrics. Finally applications in various scientific fields will be reported and discussed.
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