1,790 research outputs found
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
Near Sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping
We consider an -dimensional spherically symmetric, asymptotically
Euclidean manifold with two ends and a codimension 1 trapped set which is
degenerately hyperbolic. By separating variables and constructing a
semiclassical parametrix for a time scale polynomially beyond Ehrenfest time,
we show that solutions to the linear Schr\"odiner equation with initial
conditions localized on a spherical harmonic satisfy Strichartz estimates with
a loss depending only on the dimension and independent of the degeneracy.
The Strichartz estimates are sharp up to an arbitrary loss. This is
in contrast to \cite{ChWu-lsm}, where it is shown that solutions satisfy a
sharp local smoothing estimate with loss depending only on the degeneracy of
the trapped set, independent of the dimension
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
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
Competition and coexistence of antiferromagnetism and superconductivity in underdoped Ba(Fe0.953Co0.047)2As2
Neutron and x-ray diffraction studies show that the simultaneous first-order
transition to an orthorhombic and antiferromagnetic (AFM) ordered state in
BaFe2As2 splits into two transitions with Co doping. For
Ba(Fe0.953Co0.047)2As2, a tetragonal-orthorhombic transition occurs at TS = 60
K, followed by a second-order transition to AFM order at TN = 47 K.
Superconductivity (SC) occurs in the orthorhombic state below TC = 15 K and
coexists with AFM. Below TC, the static Fe moment is reduced and a 4 meV spin
gap develops indicating competition between coexisting SC and AFM order.Comment: 15 pages, 4 figure
- …