Tight-binding study of high-pressure phase transitions in titanium: alpha to omega and beyond

We use a tight-binding total energy method, with parameters determined from a fit to first-principles calculations, to examine the newly discovered gamma phase of titanium. Our parameters were adjusted to accurately describe the alpha Ti-omega Ti phase transition, which is misplaced by density functional calculations. We find a transition from omega Ti to gamma Ti at 102 GPa, in good agreement with the experimental value of 116 GPa. Our results suggest that current density functional calculations will not reproduce the omega Ti-gamma Ti phase transition, but will instead predict a transition from omega Ti to the bcc beta Ti phase.Comment: 3 encapsulated Postscript figures, submitted to Phyical Review Letter

Measurement of the Mass Splittings between the bbˉχb,J(1P)b\bar{b}\chi_{b,J}(1P) States

We present new measurements of photon energies and branching fractions for the radiative transitions: Upsilon(2S)->gamma+chi_b(J=0,1,2). The masses of the chi_b states are determined from the measured radiative photon energies. The ratio of mass splittings between the chi_b substates, r==(M[J=2]-M[J=1])/(M[J=1]-M[J=0]) with M the chi_b mass, provides information on the nature of the bbbar confining potential. We find r(1P)=0.54+/-0.02+/-0.02. This value is in conflict with the previous world average, but more consistent with the theoretical expectation that r(1P)<r(2P); i.e., that this mass splittings ratio is smaller for the chi_b(1P) triplet than for the chi_b(2P) triplet.Comment: 11 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Kodaira Dimension and the Yamabe Problem

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M. (To be absolutely precise, one only considers constant-scalar-curvature metrics which are Yamabe minimizers, but this does not affect the sign of the answer.) If M is the underlying smooth 4-manifold of a complex algebraic surface (M,J), it is shown that the sign of Y(M) is completely determined by the Kodaira dimension Kod (M,J). More precisely, Y(M) 0 iff Kod (M,J)= -infinity.Comment: LaTeX file. With minor typographical errors correcte