Mathematical Sciences: Stabilized Geometric Integrators with Applications to Molecular Simulation

研究者和合作者组成了一个来自生物化学、化学和数学的多学科团队，为分子模拟问题寻找新的、更有效的数值积分器。他们开发的时间步进方案是基于对这些分子系统的结构和力定律的详细研究，并尊重不变量和对称性，如与流程图相关的辛结构和时间可逆性。该项目通过增加允许的时间步长和提高数值积分器的稳定性，扩展了可用于模拟研究的动态现象的范围。此外，通过在分子动力学模拟中自动选择时间步长，这项工作旨在消除一个突出的低效率，并推动分子动力学软件的最新发展。考虑的具体问题包括：(1)发展联合坐标和时间变换作为稳定紧密粒子对局部动力学的工具；(2)探索分子动力学的时间步长和数值行为之间的关系以及设计时间可逆的步长变化机制；(3)研究适合自旋动力学、约束系统的时间步长方案；以及相关问题及其在化学和物理动力学问题中的应用。这些新技术被用于模拟生物大分子，研究固液界面的结构和动力学问题以及玻璃和自旋玻璃中的跃迁研究。对我们理解物理、化学和生化过程的重要挑战正在通过计算机模拟来解决，但许多难题仍然远远超出了当今硬件和软件技术的范围。即使计算机能力提高几个数量级，也无法在最长的相关时间尺度上直接模拟复杂的蛋白质或DNA链，除非计算机算法和软件也得到实质性的改进。生物化学、化学、物理和材料科学中许多大规模问题的模拟软件的关键组成部分是基本分子动力学集成方案，它近似于物质组成原子从一个时刻到下一个时刻的变化位置和速度。在这个项目中，一个来自生物化学、化学和数学的跨学科团队开发了新的分子动力学积分器，以提高模拟的效率和准确性。该项目的资金由MPS的计算数学、理论和计算化学、多学科活动办公室和BIO的计算生物学计划提供。

Leimkuhler 9627330 The investigator and collaborators form a multidisciplinary team from biochemistry, chemistry and mathematics that seeks new, more efficient numerical integrators for problems of molecular simulation. They develop timestepping schemes that are based on detailed study of the structure and force laws of these molecular systems, and that respect invariants and symmetries such as the symplectic structure and time-reversibility associated to the flow map. The project extends the range of dynamical phenomena accessible to simulation studies by increasing the allowable timestep and improving stability of numerical integrators. Moreover, by automating the selection of timestep in molecular dynamics simulations, this work seeks to remove an outstanding inefficiency and push forward the state-of-the-art in molecular dynamics software. The specific problems considered include (1) the development of combined coordinate and time-transformations as a tool for stabilizing the local dynamics of close particle pairs, (2) exploration of the relationship between timestep and numerical behavior for molecular dynamics and the design of time-reversible stepsize variation mechanisms, and (3) the study of timestepping schemes appropriate to spin dynamics, constrained systems, and related problems and their application in chemical and physical dynamics problems. The new techniques are used to simulate biological macromolecules and for problems concerning the structure and dynamics of solid-liquid interfaces as well as studies of transitions in glasses and spin-glasses. Important challenges to our understanding of physical, chemical and biochemical processes are being tackled through the use of computer simulations, but many difficult problems remain well beyond the reach of today's hardware and software technology. Even improvements in computer power of several orders of magnitude will not enable the direct simulation of complex proteins or DNA chains on the longest relevant timescales unless substantial improvements are also obtained in computer algorithms and software. A key component of simulation software for many large-scale problems in biochemistry, chemistry, physics, and materials science is the fundamental molecular dynamics integration scheme, which approximates the changing positions and velocities of the constituent atoms of a substance from one moment in time to the next. In this project an interdisciplinary team from biochemistry, chemistry and mathematics develops new molecular dynamics integrators in order to improve the efficiency and accuracy of simulations. Funding for the project is provided by programs of Computational Mathematics, Theoretical and Computational Chemistry, and the Office of Multidisciplinary Activities in MPS and by the Computational Biology program in BIO.