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

Antiferromagnetic ordering and dipolar interactions of YbAlO3_3

In this paper we report low-temperature magnetic properties of the rare-earth perovskite material YbAlO$_3$. Results of elastic and inelastic neutron scattering experiment, magnetization measurements along with the crystalline electrical field (CEF) calculations suggest that the ground state of Yb moments is a strongly anisotropic Kramers doublet, and the moments are confined in the $ab$-plane, pointing at an angle of $\varphi = \pm 23.5^{\circ}$ to the $a$-axis. With temperature decreasing below $T_{\rm N}=0.88$ K, Yb moments order into the coplanar, but non-collinear antiferromagnetic (AFM) structure $AxGy$, where the moments are pointed along their easy-axes. In addition, we highlight the importance of the dipole-dipole interaction, which selects the type of magnetic ordering and may be crucial for understanding magnetic properties of other rare-earth orthorhombic perovskites. Further analysis of the broad diffuse neutron scattering shows that one-dimensional interaction along the $c$-axis is dominant, and suggests YbAlO$_3$ as a new member of one dimensional quantum magnets.Comment: 8 pages, 6 figure

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

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