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Variational collision integrator for polymer chains

机译：聚合物链的可变碰撞积分仪

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摘要

The numerical simulation of many-particle systems (e.g. in molecular dynamics) often involves constraints of various forms. We present a symplectic integrator for mechanical systems with holonomic (bilateral) and unilateral contact constraints, the latter being in the form of a non-penetration condition. The scheme is based on a discrete variant of Hamilton's principle in which both the discrete trajectory and the unknown collision time are varied (cf. [R. Fetecau, J. Marsden, M. Ortiz, M. West, Nonsmooth Lagrangian mechanics and variational collision integrators, SIAM J. Appl. Dyn. Syst. 2 (2003) 381-416]). As a consequence, the collision event enters the discrete equations of motion as an unknown that has to be computed on-the-fly whenever a collision is imminent. The additional bilateral constraints are efficiently dealt with employing a discrete null space reduction (including a projection and a local reparametrisation step) which considerably reduces the number of unknowns and improves the condition number during each time-step as compared to a standard treatment with Lagrange multipliers. We illustrate the numerical scheme with a simple example from polymer dynamics, a linear chain of beads, and test it against other standard numerical schemes for collision problems.
机译：多粒子系统的数值模拟（例如分子动力学）通常涉及各种形式的约束。我们提出了具有完整（双边）和单边接触约束的机械系统的辛积分器，后者是非渗透条件。该方案基于汉密尔顿原理的离散变体，其中离散轨迹和未知碰撞时间均发生变化（参见[R. Fetecau，J. Marsden，M. Ortiz，M. West，非光滑拉格朗日力学和变分碰撞集成商，SIAM J.Appl.Dyn.Syst.2（2003）381-416]。结果，碰撞事件作为未知数进入离散运动方程，每当即将发生碰撞时，都必须即时计算。与采用拉格朗日乘数的标准处理方法相比，采用离散的零空间缩减（包括投影和局部重新设置参数步骤）可以有效地解决附加的双边约束，从而极大地减少了未知数，并在每个时间步内提高了条件数。 。我们用一个简单的例子来说明数值方案，该实例来自聚合物动力学，珠的线性链，并针对碰撞问题针对其他标准数值方案进行了测试。

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