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

A Dialectical Basis for Software Development Tool Building

We identify typical problems in the interactions of people with current software-based systems. In particular we observe the need to expend significant on-going effort to adapt these systems to reflect changes in the world about them, the need for people to adapt their working practices to fit in with these systems, and the inflexibility of these systems when faced with unusual circumstances or the need for change. We believe that these problems follow, at least in part, from these systems being developed and evolved using mechanisms each based on one Inquiry System only. This basis leads to assumptions being embedded in the mechanisms’ analysis outputs, and in system designs and implementations. We suggest that the problems noted may be mitigated by the use of a dialectical approach to Inquiry System selection for software development, based on the work of Hegel, which places in opposition different models of a situation based on different Inquiry Systems. We claim that such a mechanism has the potential to make explicit some of the assumptions which would otherwise be embedded implicitly in the delivered system without being questioned. We outline a research programme intended to test this hypothesis, and suggest other research directions

Doping Dependence of Spin Dynamics in Electron-Doped Ba(Fe1-xCox)2As2

The spin dynamics in single crystal, electron-doped Ba(Fe1-xCox)2As2 has been investigated by inelastic neutron scattering over the full range from undoped to the overdoped regime. We observe damped magnetic fluctuations in the normal state of the optimally doped compound (x=0.06) that share a remarkable similarity with those in the paramagnetic state of the parent compound (x=0). In the overdoped superconducting compound (x=0.14), magnetic excitations show a gap-like behavior, possibly related to a topological change in the hole Fermi surface (Lifshitz transition), while the imaginary part of the spin susceptibility prominently resembles that of the overdoped cuprates. For the heavily overdoped, non-superconducting compound (x=0.24) the magnetic scattering disappears, which could be attributed to the absence of a hole Fermi-surface pocket observed by photoemission.Comment: 6 pages, 5 figures, published versio

Stabilization of Polar Nano Regions in Pb-free ferroelectrics

Formation of polar nano regions through solid-solution additions are known to enhance significantly the functional properties of ferroelectric materials. Despite considerable progress in characterizing the microscopic behavior of polar nano regions, understanding their real-space atomic structure and dynamics of formation remains a considerable challenge. Here, using the method of dynamic pair distribution function, we provide direct insights into the role of solid-solution additions towards the stabilization of polar nano regions in the Pb-free ferroelectric of Ba(Zr,Ti)O3. It is shown that for an optimum level of substitution of Ti by larger Zr ions, the dynamics of atomic displacements for ferroelectric polarization are slowed sufficiently, which leads to increased local correlation among dipoles below THz frequencies. The dynamic pair distribution function technique demonstrates unique capability to obtain insights into locally correlated atomic dynamics in disordered materials, including new Pb-free ferroelectrics, which is necessary to understand and control their functional properties

Revisiting the ground state of CoAl2_2O4_4: comparison to the conventional antiferromagnet MnAl2_2O4_4

The A-site spinel material, CoAl2O4, is a physical realization of the frustrated diamond-lattice antiferromagnet, a model in which is predicted to contain unique incommensurate or `spin-spiral liquid' ground states. Our previous single-crystal neutron scattering study instead classified it as a `kinetically-inhibited' antiferromagnet, where the long ranged correlations of a collinear Neel ground state are blocked by the freezing of domain wall motion below a first-order phase transition at T* = 6.5 K. The current paper expands on our original results in several important ways. New elastic and inelastic neutron measurements are presented that show our initial conclusions are affected by neither the sample measured nor the instrument resolution, while measurements to temperatures as low as T = 250 mK limit the possible role being played by low-lying thermal excitations. Polarized diffuse neutron measurements confirm reports of short-range antiferromagnetic correlations and diffuse streaks of scattering, but major diffuse features are explained as signatures of overlapping critical correlations between neighboring Brillouin zones. Finally, and critically, this paper presents detailed elastic and inelastic measurements of magnetic correlations in a single-crystal of MnAl2O4, which acts as an unfrustrated analogue to CoAl2O4. The unfrustrated material is shown to have a classical continuous phase transition to Neel order at T_N = 39 K, with collective spinwave excitations and Lorentzian-like critical correlations which diverge at the transition. Direct comparison between the two compounds indicates that CoAl2O4 is unique, not in the nature of high-temperature diffuse correlations, but rather in the nature of the frozen state below T*. The higher level of cation inversion in the MnAl2O4 sample indicates that this novel behavior is primarily an effect of greater next-nearest-neighbor exchange.Comment: 13 pages, 8 figures, acccepted for publication in Physical Review

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

Antiferromagnetic Order in MnO Spherical Nanoparticles

We have performed unpolarized and polarized neutron diffraction experiments on monodisperse 8 nm and 13 nm antiferromagnetic MnO nanoparticles. For the 8 nm sample, the antiferromagnetic transition temperature $T_N$ (114 K) is suppressed compared to the bulk material (119 K) while for the 13 nm sample $T_N$ (120 K) is comparable to the bulk. The neutron diffraction data of the nanoparticles is well described using the bulk MnO magnetic structure but with a substantially reduced average magnetic moment of 4.2$\pm$0.3 $\mu_B$/Mn for the 8 nm sample and 3.9$\pm$0.2 $\mu_B$/Mn for the 13 nm sample. An analysis of the polarized neutron data on both samples shows that in an individual MnO nanoparticle about 80$$ of Mn ions order. These results can be explained by a structure in which the monodisperse nanoparticles studied here have a core that behaves similar to the bulk with a surface layer which does not contribute significantly to the magnetic order.Comment: 7 pages, 5 figure