The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ, ω) where b = φ((ρ, ω) = (ρ, ρ · ρ1, …, ρ · ρm); and (2) the determination of the location of the equilibrium (ρ, ω) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ, ω), there are different ways of representing the equilibrium (ρ, ω) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.
Flux-Bridgman growth and characterization of Mn-doped ZnO single crystals
