This will include an analytical description of two similar species competition without mutations, two species competitions with mutations including similar and dissimilar species, sticky phases, transition times, and scaling, and three species competitions both with and without mutations. Finally a plethora of future research directions will be discussed. Phase Transitions in finite systems Phase transitions in thermodynamics are ordinarily defined for infinite, homogenous systems, making use of the singular behavior of e.g. the specific heat at the phase tranistion temperature. For finite systems this singular behavior dwindles to a nonspectacular hump until for a single atom thermodynamics can no longer be applied. Modern theoretical physics concepts are presented for the quantum statistics and thermodynamics of finite systems.
Phase transitions show up again as singular structures, but now in the complex temperature plane.
The whole bouquette of unique other features of the thermodynamic of small systems is demonstrated and the respective tools such as path integral formalism, recursive partition functions, shell model theory, are revealed. 18 Apr 25 Prof. Dr. Ross Angel , Virginia Tech Geological Sciences Ferroic phase transitions at high pressure While structural phase transitions as a function of temperature have been studied extensively, relatively little work has been performed at high pressures. In addition, pressure couples linearly with the strain in the expression of the free energy of the solid, through the PV term. Thus, unlike temperature, pressure can drive transitions directly through the strain, or by inducing changes in the elastic constants. The use of internal diffraction standards to measure pressure yields a precision in pressure measurement of better than 0.01 GPa over the pressure range of 0-10 GPa.