Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

On effects of thickness on ductile crack growth in mild steel

Critical crack opening displacement (COD) values have been examined for a range of specimen thicknesses. The COD at the initiation of fracture δ₁ is found to be constant, given a plane-strain crack-tip stress-state, whereas the COD at maximum load δ_max decreases with increasing thickness. The loads required to produce instability are found to vary with thickness, in a way analogous to behaviour observed under linear elastic conditions. Crack growth under constant load for a range of specimen thicknesses has been examined, and failure has been found to occur at loads below that associated with Δ_max,; the minimum load per unit thickness required to cause failure decreasing with specimen thickness.     

Note on the optimal transportation of distributions

We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property.     

Randomized Decisions in Chance-Constrained Programming

Bhattacharyya and Mukherjee have both considered a particular joint randomized decision problem in chance-constrained programming. This paper shows a general approach for solving a large class of similar problems.     

On the optimal mapping of distributions

We consider the problem of mappingXY, whereX andY have given distributions, so as to minimize the expected value of X–Y². This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of X–Y² is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.     

A Quadrupole mass spectrometer for resolution of low mass isotopes

The qualitative and quantitative identification of low mass isotopes in the mass range 1–6 u poses certain difficulties when attempting to achieve the required resolution with an instrument suitable for deployment within a process environment. Certain adjacent species present in the process sample (HT and D₂) require a resolution greater than 930 to achieve an accurate measurement. We demonstrate here through simulation techniques that this level of performance required is unachievable using commercially available instruments. Using previously reported simulation techniques, this article demonstrates how the required performance for resolving the low mass isotopes can be achieved by a quadrupole mass spectrometer (QMS), which incorporates a quadrupole mass filter (QMF) constructed from hyperbolic electrodes and operated in zone 3 of the Mathieu stability diagram.     

Effect of Sol–Gel Encapsulation on Lipase Structure and Function: A Small Angle Neutron Scattering Study

The application of small angle neutron scattering (SANS) to the characterisation of sol–gel hosts containing biomolecules offers the opportunity to explore the relationship between gel structure and catalyst. A model system involving the immobilisation of Candida antarctica lipase B (CALB) was investigated.Gels were produced by fluoride-catalysed hydrolysis of fixed ratios of tetramethylorthosilicate (TMOS) and methyltrimethoxysilane (MTMS). Phase separation between the enzyme and the evolving sol–gel matrix was minimised by incorporating glycerol into the sol–gel precursor solution. The potential stabilising effect of the NaF catalyst upon the enzyme was also investigated. Scattering studies were conducted on both immobilised lipase, and lipase in free solution. Scattering studies on free enzyme provided evidence of multiple populations of enzyme aggregates and showed that choice of solvent affected the degree of aggregation. Both NaF and glycerol affected neutron scattering, indicating changes in lipase conformation. Increasing glycerol concentration increased the degree of aggregation and produced differences in solvent packing on the surface of protein molecules. Initial evidence from SANS data indicated that the presence of the enzyme during gel formation conferred structural changes on the gel matrix. Modelling the effect of sol–gel encapsulation on lipase requires comparison of data from free enzyme to the immobilised form. Removal of the enzyme from the sol–gel structure, post gelation, is necessary to better characterise the modified matrix. This methodological problem will be the subject of future investigations.