Geometric numerical integrators fr quantum problems, celestial mechanics and Monte Carlo

Objective:

This subproject constitutes part of the coordianted proposal GEOMETRIC NUMERICAL INTEGRATORS FOR QUANTUM PROBLEMS, CELESTIAL MECHANICS AND MONTE CARLO SIMULATIONS (GNI-QUAMC), devoted to the design, analysis, and implementation of special purpose geometric numerical integration schemes, with particular emphasis on the application to simulation of complex physical systems. It will mainly focus on the development of new and more efficient integration schemes to be applied in (i) hybrid Monte Carlo methods, and (ii) problems in celestial mechanics and astrodynamics. Although the implementation of related software ready to be exploited by practitioners will be mainly addressed by members of this subproject, the design and analysis of the underlying geometric numerical algorithms will be pursued with high degree of collaboration with members of the subproject I. The collaboration with members of subproject I will be also extended to other areas of interest of the coordinated project. It is also intended: (i) to continue collaborating with leading experts in areas of application of hybrid Monte Carlo technics such as multiscale modeling of advanced energy materials, dynamic modeling of forming latex particles morphologies, tracking development of resistance to anti-cancer therapy, and (ii) to strengthen the contact and collaboration with experts in celestial mechanics and astrodynamics. In summary, the impact of the project is assured by fully covering all three principle stages, from high-level mathematical theory to its implementation in professional software and subsequent application to the frontline research in Life and Physical Sciences using High Performance Computers. In summary, the impact of the project is assured by fully covering all three principle stages, from high-level mathematical theory to its implementation in professional software and subsequent application to the frontline research in Life and Physical Sciences using High Performance Computers.