Professor Ben Leimkuhler
School of Mathematics
University of Edinburgh

I moved to Edinburgh in 2006, following stints at the Universities of Leicester and Kansas. I obtained my PhD from the University of Illinois in 1988 under the joint supervision of Bill Gear and Linda Petzold, and followed this with a postdoctoral research period in Helsinki, Finland. Since then I have worked on various challenges related to the numerical solution of differential equations, including some fundamental work on symplectic methods for constrained systems and other topics in geometric integration. I authored a book on this subject jointly with Sebastian Reich (Simulating Hamiltonian Dynamics, Cambridge University Press, 2005). My recent research has focused primarily on challenges related to molecular dynamics simulation, including methods for rigid body systems, ferromagnetic systems, temperature control (thermostats) e.g., the Nosé-Poincaré method, and methods for Feynman path integrals. With former student C. Sweet (Notre Dame) I introduced a new class of dynamical thermostats based on Hamiltonian Recursive Multiple Thermostats (SIAM J. Appl. Dyn. Syst., 4:187--216, 2005). These methods have already been implemented successfully for simulation of crystalline materials. Other recent work has provided tools for applying thermostats in multiple scale simulation, in collaboration with materials scientists (Phys. Rev. B, 73(184304), 2006). In 2007, together with former student S. Bond (Illinois), I analyzed the accuracy of averages from thermally regulated molecular dynamics (Acta Numerica, 16:1-65, 2007). At large time-step, dynamics methods introduce a substantial bias; a posteriori reweighting corrections can be determined to correct for this error. Also with S. Bond, I have suggested a family of integrators for molecular dynamics simulation with hard sphere inequality constraints, based on continuously extending the backward error analysis for smooth Hamiltonian dynamics to collisional (impulse-driven) dynamics, in modified potentials, with dramatic stability improvement (SIAM J. Sci. Comput., to appear, 2008). Just accepted for publication is a new adaptive temperature control method for nonequilibrium simulation (systems subject to nonadiabatic perturbation) with F. Legoll (ENPC) and my current student E. Noorizadeh (J. Chem. Phys., to appear, 2008).