Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Ytterbium divalency and lattice disorder in near-zero thermal expansion YbGaGe

While near-zero thermal expansion (NZTE) in YbGaGe is sensitive to stoichiometry and defect concentration, the NZTE mechanism remains elusive. We present x-ray absorption spectra that show unequivocally that Yb is nearly divalent in YbGaGe and the valence does not change with temperature or with nominally 1% B or 5% C impurities, ruling out a valence-fluctuation mechanism. Moreover, substantial changes occur in the local structure around Yb with B and C inclusion. Together with inelastic neutron scattering measurements, these data indicate a strong tendency for the lattice to disorder, providing a possible explanation for NZTE in YbGaGe.Comment: 4 pages, 4 figure, supplementary inf

Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

Phonon self-energy and origin of anomalous neutron scattering spectra in SnTe and PbTe thermoelectrics

The anharmonic lattice dynamics of rock-salt thermoelectric compounds SnTe and PbTe are investigated with inelastic neutron scattering (INS) and first-principles calculations. The experiments show that, surprisingly, although SnTe is closer to the ferroelectric instability, phonon spectra in PbTe exhibit a more anharmonic character. This behavior is reproduced in first-principles calculations of the temperature-dependent phonon self-energy. Our simulations reveal how the nesting of phonon dispersions induces prominent features in the self-energy, which account for the measured INS spectra and their temperature dependence. We establish that the phase-space for three-phonon scattering processes, rather than just the proximity to the lattice instability, is the mechanism determining the complex spectrum of the transverse-optical ferroelectric mode

Quantum critical behavior in the heavy Fermion single crystal Ce(Ni0.935_{0.935}Pd0.065_{0.065})2_2Ge2_2

We have performed magnetic susceptibility, specific heat, resistivity, and inelastic neutron scattering measurements on a single crystal of the heavy Fermion compound Ce(Ni$_{0.935}$Pd$_{0.065}$)$_2$Ge$_2$, which is believed to be close to a quantum critical point (QCP) at T = 0. At lowest temperature(1.8-3.5 K), the magnetic susceptibility behaves as $\chi(T)-\chi (0)$ $\propto$ $T^{-1/6}$ with $\chi (0) = 0.032 \times 10^{-6}$ m$^3$/mole (0.0025 emu/mole). For $T<$ 1 K, the specific heat can be fit to the formula $\Delta C/T = \gamma_0 - T^{1/2}$ with $\gamma_0$ of order 700 mJ/mole-K$^2$. The resistivity behaves as $\rho = \rho_0 + AT^{3/2}$ for temperatures below 2 K. This low temperature behavior for $\gamma (T)$ and $\rho (T)$ is in accord with the SCR theory of Moriya and Takimoto\cite{Moriya}. The inelastic neutron scattering spectra show a broad peak near 1.5 meV that appears to be independent of $Q$; we interpret this as Kondo scattering with $T_K =$ 17 K. In addition, the scattering is enhanced near $Q$=(1/2, 1/2, 0) with maximum scattering at $\Delta E$ = 0.45 meV; we interpret this as scattering from antiferromagnetic fluctuations near the antiferromagnetic QCP.Comment: to be published in J. Phys: Conference Serie

The Strauss conjecture on asymptotically flat space-times

By assuming a certain localized energy estimate, we prove the existence portion of the Strauss conjecture on asymptotically flat manifolds, possibly exterior to a compact domain, when the spatial dimension is 3 or 4. In particular, this result applies to the 3 and 4-dimensional Schwarzschild and Kerr (with small angular momentum) black hole backgrounds, long range asymptotically Euclidean spaces, and small time-dependent asymptotically flat perturbations of Minkowski space-time. We also permit lower order perturbations of the wave operator. The key estimates are a class of weighted Strichartz estimates, which are used near infinity where the metrics can be viewed as small perturbations of the Minkowski metric, and the assumed localized energy estimate, which is used in the remaining compact set.Comment: Final version, to appear in SIAM Journal on Mathematical Analysis. 17 page