Elastic and anelastic anomalies associated with the antiferromagnetic ordering transition in wüstite, FexO

The elastic and anelastic properties of three different samples of Fe(x)O have been determined in the frequency range 0.1-2 MHz by resonant ultrasound spectroscopy and in the range 0.1-50 Hz by dynamic mechanical analysis in order to characterize ferroelastic aspects of the magnetic ordering transition at T(N) ~ 195 K. No evidence was found of separate structural and magnetic transitions but softening of the shear modulus was consistent with the involvement of bilinear coupling, λe(4)q, between a symmetry-breaking strain, e(4), and a structural order parameter, q. Unlike a purely ferroelastic transition, however, C(44) does not go to zero at the critical temperature, T*(c), due to the intervention of the magnetic ordering at a higher temperature. The overall pattern of behaviour is nevertheless consistent with what would be expected for a system with separate structural and magnetic instabilities, linear-quadratic coupling between the structural (q) and magnetic (m) driving order parameters, λqm(2), and T(N) > T*(c). Comparison with data from the literature appears to confirm the same pattern in MnO and NiO, with a smaller difference between T(N) and T*(c) in the former and a larger difference in the latter. Strong attenuation of acoustic resonances at high frequencies and a familiar pattern of attenuation at low frequencies suggest that twin walls in the rhombohedral phase have typical ferroelastic properties. Acoustic dissipation in the stability field of the cubic phase is tentatively attributed to anelastic relaxations of the defect ordered structure of non-stoichiometric wüstite or of the interface between local regions of wüstite and magnetite, with a rate controlling step determined by the diffusion of iron.     

Theoretical links between median and coverage location problems

The relationship between the maximal covering problem and the P-median problem is reviewed. It is shown that two multiple coverage models, themaximumexpectedcoverageproblem (MECP) and thebackupcoverageproblem (BACOP), are special cases of thevectorassignmentP-medianproblem (VAPMP). This relationship is utilized to solve both MECP and BACOP on test sets from the literature. Computational experience is reported.     

Polarization detection of trapped electrons via interaction with polarized atoms

Electrons were trapped in an electrostatic quadrupole trap with superimposed homogeneous magnetic field. The electrons were polarized by spin exchange with a polarized atomic beam. The free trapped electron polarization was converted to a change in the electron translational energy via spin-dependent inelastic collisions with the atomic beam, and the electron translational temperature was monitored. Discussed are the development of this variation of the measurement technique, characteristics of electron storage, and the electron-polarized atom inelastic interaction as a function of electron temperature and time. The method has been applied to the detection of the (g-2) resonance of free, stored electrons.     

Representation theory and homological stability

We introduce the idea of representation stability   (and several variations) for a sequence of representations _Vn$V_n$ of groups _Gn$G_n$. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Representation stability also provides a framework in which to find and to predict patterns, from classical representation theory (Littlewood–Richardson and Murnaghan rules, stability of Schur functors), to cohomology of groups (pure braid, Torelli and congruence groups), to Lie algebras and their homology, to the (equivariant) cohomology of flag and Schubert varieties, to combinatorics (the (n+1)ⁿ⁻¹${(n+1)}^{n-1}$ conjecture). The majority of this paper is devoted to exposing this phenomenon through examples. In doing this we obtain applications, theorems and conjectures.     

Designing robust coverage networks to hedge against worst-case facility losses

In order to design a coverage-type service network that is robust to the worst instances of long-term facility loss, we develop a facility location–interdiction model that maximizes a combination of initial coverage by p facilities and the minimum coverage level following the loss of the most critical r facilities. The problem is formulated both as a mixed-integer program and as a bilevel mixed-integer program. To solve the bilevel program optimally, a decomposition algorithm is presented, whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem. After sequentially solving these problems, supervalid inequalities can be generated and appended to the upper level master in an attempt to force it away from clearly dominated solutions. Computational results show that when solved to optimality, the bilevel decomposition algorithm is up to several orders of magnitude faster than performing branch and bound on the mixed-integer program.     

Charge transfer reaction of multi-charged oxygen ions with O2

The rate of transfer of electrons from O₂ to O²⁺ and O³⁺ has been measured at energies ? 2 eV using a stored ion technique. The rate for O²⁺ is k = 1.0(0.3) × 10^?9 cm³/s and for O³⁺, k = 2.5(0.3) × 10^?9 cm³/s, compared to calculated Langevin rates of 1.8 × 10^?9 cm³/s and 2.7 × 10^?9 cm³/s respectively.     

A chelating gel for collection of copper from seawater

An affinity Chromatographic gel is coupled to carboxymethyl(imino)-bis(ethyl-enenitrilo) tetraacetic acid (DTPA) by a carbodiimide reaction. This gel is successful in extracting copper from seawater with high selectivity over alkaline earths such as mag-nesium. It is useful over a wide range of pH (4–9), and is stable and reversible over a period of nine months. Up to 20 μmol of copper can be adsorbed and recovered with greater than 99% efficiency with gel—DTPA prepared from 1 g of dry gel.     

Additions of substituted phenylthiyl radicals to substituted α-methylstyrenes : Ground state and transition state electronic effects

The radical addition of substituted thiophenols to α-methylstyrene and substituted α-methylstyrenes has been investigated at 70°. Relative reactivities of pairs of thiophenols competing with individual alkenes can be utilized to obtain Hammett correlations. The interplay of substituent effects in alkene and thiyl radical leads to examples of non-linear rho values. Rationales for this behavior will be offered in terms of variable contributions from ground state and transition state electronic factors as well as in terms of possible mechanistic changes.