Mathematical Sciences: Stabilized Geometric Integrators with Applications to Molecular Simulation

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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.