Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure

A BRAVE LEAP OR A GRADUAL CLIMB? THE DYNAMICS OF INVESTMENT IN R&D OF INTEGRATIVE TECHNOLOGIES

Our paper explores the optimal investment in integrative technologies (such as command and control systems), which are a major part of defense R&D at the beginning of the 21st century. Employing a dynamic optimization framework, we find that under linear development costs, it may be optimal or nearly optimal to build military forces using a myopic, short-termed, approach. In such cases, it would be optimal to transform an armed force into a network-centric environment within just a few years. When development costs are convex however, early investment in technological infrastructure is required, extending the transformation period over more than a decade.Technology, Defense R&D, Dynamic optimization,