The Forces Method on Fekete Problems E. Bendito, A. Carmona, A. M. Encinas, A. Medina Departament de Matemtica Aplicada III UPC The Fekete Problem Logarithmic energy: Newtonian energy: Best-packing problem: General case : Rieszs energies: + return algorithm The algorithm Advance direction and disequilibrium degree: The Forces Method The coefficient The stop criteria The cost of a local minimum Logarithmic kernel Sample information Newtonian kernel The line-search procedure : minimize the energy in the advance direction. Energy + return algorithm The algorithm : Smooth surfaces and W-compact set The coefficient on W-compact sets In each case the coefficient seems to be a sort of average of the coefficient associated to the line-search procedure. The relation on W-compact sets The Finisterrae challenge MareNostrum Minimizing the Action The forces method in dynamical systems The algorithm on manifolds: The algorithm on free space: + return algorithm The forces method in dynamical systems Minimizing the action on Stability of the trajectories under time refinament Minimizing the action on Minimizing the action on manifolds How is the iterative process? Minimizing the action on manifolds The energy of the system remains constant during the motion The Forces Method in Molecular Dynamics The algorithm: Time assingment in an atomic model The Forces Method in Molecular Dynamics