Thermodynamic ground states of platinum metal nitrides

The thermodynamic stabilities of various phases of the nitrides of the platinum-metal elements are systematically studied using density functional theory. It is shown that for the nitrides of Rh, Pd, Ir, and Pt two new crystal structures, in which the metal ions occupy simple tetragonal lattice sites, have lower formation enthalpies at ambient conditions than any previously proposed structures. The region of stability with respect to those structures extends to 17 GPa for PtN2. Calculations show that the PtN2 simple tetragonal structures at this pressure are thermodynamically stable also with respect to phase separation. The fact that the local density and generalized gradient approximations predict different values of the absolute formation enthalpies as well different relative stabilities between simple tetragonal and the pyrite or marcasite structures are further discussed.     

Killing vector fields on Riemannian and Lorentzian 3-manifolds

We give a complete local classification of all Riemannian 3-manifolds $(M,g)$ admitting a nonvanishing Killing vector field T. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are automatically nonvanishing. The two key ingredients needed in our classification are the scalar curvature S of g and the function $\text{Ric}(T,T)$, where Ric is the Ricci tensor; in fact their sum appears as the Gaussian curvature of the quotient metric obtained from the action of T. Our classification generalizes that of Sasakian structures, which is the special case when $\text{Ric}(T,T)=2$. We also give necessary, and separately, sufficient conditions, both expressed in terms of $\text{Ric}(T,T)$, for g to be locally conformally flat. We then move from the local to the global setting, and prove two results: in the event that T has unit length and the coordinates derived in our classification are globally defined on ${\mathbb{R}}^3$, we give conditions under which S completely determines when the metric will be geodesically complete. In the event that the 3-manifold M is compact, we give a condition stating when it admits a metric of constant positive sectional curvature.     

Novel swelling/shrinking behaviors of glucose-binding hydrogels and their potential use in a microfluidic insulin delivery system

Hydrogels based on lightly crosslinked poly(methacrylamidophenylboronic acid-co-acylamide) swell monototically at pH 7.4 with exposure to increasing concentrations of glucose. At pH 10 these hydrogels first shrink and then reswell with increasing glucose concentration. A mechanism for these disctinct behaviors is proposed and preliminary results validating this mechanism are presented. A simple microfabricated glucose-sensitive valve based on this hydrogel is described.