Problems and Proposed Solutions for MD and HMC

Here our work towards multiscale MTS integrators is presented in more detail. In Section 2.1 it is shown how our methods can be extended to handle more complex systems in an efficient manner. Section 2.2 introduces extensions of MOLLY to constant temperature and pressure ensembles, which are interesting from both theoretical and practical points of view. Integration in these ensembles is more stable than in constant energy simulations, and it can also be related more easily to experiments. Section 2.3 presents an exciting application of MOLLY to hybrid Monte Carlo methods, which will be used to compute free energies for flexible docking methods. Finally, ideas for efficiently-parallelizable, linear-complexity algorithms for fast electrostatics of both periodic and non-periodic boundary conditions are presented in Section 2.4.