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Free keywords. Physical Sciences, Quantum Field Theory, Computational Physics, Elementary Particle Physics, Hadron Physics, Lattice QCD, Computational Mathematics, Computer Hardware, Software Development. Abstract: The research aims at a deeper understanding of properties of strongly interacting matter. This is mainly done by means of numerical simulations of the underlying theory (QCD) on super- computers (Lattice QCD). We wish to understand QCD for its own sake and as a prototype of a strongly interacting fundamental theory. Therefore we will calculate the spectrum of mesons, baryons and of exotic states, their decays and their internal structure. We will also address questions of a purely quantum field theoretical nature that are also of interest to string theorists. In order to forward our understanding of matter under extreme conditions, i.e. at high temperatures like in the early universe and at high densities such as those inside of neutron stars, we will calculate the phase diagram of QCD with light sea quarks and the equation of state at high temperatures.
Free keywords. Biomedical engineering; Neuroengineering; Multielectrode Arrays; Neuroprosthetics; In vitro neuronal networks PART B:
Free keywords. Pattern formation, N -body problem, Total Collapses, Dynamical Systems, Partial Differential Equations, Non- linear Schr¨odinger equations, Competition-diffusion Systems, Optimal Partitions, Nonlinear Analysis, Varia- tional Methods, Spatial Segregation, Xxxxx Theory, Singular Hamiltonian Systems, Free boundary problems, Entire solutions, Asymptotic estimates, Singular perturbation problems.
Free keywords. Pattern formation, N -body problem, Total Collapses, Dynamical Systems, Partial Differential Equations, Nonlinear Schr¨odinger equations, Competition-diffusion Systems, Optimal Partitions, Nonlinear Analysis, Variational Methods, Spatial Segregation, Xxxxx Theory, Singular Hamiltonian Systems, Free boundary prob- lems, Entire solutions, Asymptotic estimates, Singular perturbation problems, Monotonicity Formulae. Research and technological achievements and the impact and use of them. To depict the outcome of our research, I felt it appropriate to select, and describe in full details, the five topics that I consider most innovative in relation to the originally programmed objectives. Complex Dynamics for the classical N -body problem Scattering parabolic solutions for the spatial N -centre problem. Most dynamical systems of inter- acting particles in Celestial and other areas of Classical Mechanics are governed by singular forces. We are concerned with potential of n-body type having the form n

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