We consider a coupled PDE model of various fluid-structure interactions seen in nature. It has recently been shown by the authors [Contemp. Math. 440, 2007] that this model admits of an explicit semigroup generator representation A : D(A) ⊂ H → H, where H is the associated space of fluid-structure initial data. However, the argument for the maximality criterion was indirect, and did not provide for an explicit solution Φ ∈ D(A) of the equation (λI − A)Φ = F for given F ∈ H and λ > 0. The present work reconsiders the proof of maximality for the fluid-structure generator A, and gives an explicit method for solving the said fluid-structure equation. This involves a nonstandard usage of the Babuška-Brezzi Theorem. Subsequently, a finite element method for approximating solutions of the fluid-structure dynamics is developed, based upon our explicit proof of maximality.

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PbZrO3 undergoes a phase transition to a paraelectric phase at 230°C. During this phase transition the unit cell changes from orthorhombic to cubic. Structural changes of PbZrO3 have been monitored using solid state NMR by measuring the variation in the 207Pb chemical shielding tensor as a function of temperature. The two distinct lead sites show rather different behavior as a function of temperature. The less shielded lead maintains an almost constant asymmetry parameter η = 0.2 from 0°C to 200°C while the more shielded lead resonance becomes more axially symmetric as the temperature is raised going from η = 0.24 at 0°C to [.eta] = 0.08 at 200°C. Powder pattern singularities become less distinct near the phase transitions, but the temperature dependence of the chemical shift tensor principal values remains continuous, and there is no evidence of an intervening higher-symmetry phase. At the phase transition, both resonances collapse into a single narrow line characteristic of a nucleus at a high-symmetry site. Results of a preliminary study of the PbZr1−xTixO3 solid solutions by 207Pb solid state NMR are also presented.