Global (in Time) Solutions to the 3D-Navier-Stokes Equations on R^3

A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time solutions to the three-dimensional Navier-Stokes equations. (These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces.) A related problem is to provide conditions under which we can be assured that the numerical approximation of these equations, used in a variety of fields from weather prediction to submarine design, have only one solution. In earlier papers, we solved this problem for a bounded domain. In this paper, we use an approach based on additional physical insight, that allows us to prove that there exists unique global in time solutions to the Navier-Stokes equations on R^3

Technology survey of electrical power generation and distribution for MIUS application

Candidate electrical generation power systems for the modular integrated utility systems (MIUS) program are described. Literature surveys were conducted to cover both conventional and exotic generators. Heat-recovery equipment associated with conventional power systems and supporting equipment are also discussed. Typical ranges of operating conditions and generating efficiencies are described. Power distribution is discussed briefly. Those systems that appear to be applicable to MIUS have been indicated, and the criteria for equipment selection are discussed

Proper-time relativistic dynamics

Proper-time relativistic single-particle classical Hamiltonian mechanics is formulated using a transformation from observer time to system proper time which is a canonical contact transformation on extended phase space. It is shown that interaction induces a change in the symmetry structure of the system which can be analyzed in terms of a Lie-isotopic deformation of the algebra of observables