An improved algorithm for in situ adaptive tabulation

In situ adaptive tabulation (ISAT) is a proven storage/retrieval method which efficiently provides accurate approximations to high-dimensional functions which are computationally expensive to evaluate. Previous applications of ISAT to computations of turbulent combustion have resulted in speed-ups of up to a thousand. In this paper, improvements to the original ISAT algorithm are described and demonstrated using two test problems. The principal improvements are in the table-searching strategies and the addition of an error checking and correction algorithm. Compared to an earlier version of ISAT, reductions in CPU time and storage requirements by factors of 2 and 5, respectively, are observed for the most challenging, 54-dimensional test problem.     

Effects of vapor pressure on thermodynamic equilibrium in multiphase flow for thermochemical hydrogen production

This paper examines the effects of H₂O vapor pressure on the equilibrium conditions of a CuCl₂ hydrolysis reactor in the thermochemical Cu–Cl cycle of hydrogen production. A new predictive model is developed to determine the minimum steam requirement in the reactor based on the chemical equilibrium condition, reactor pressure and fraction of gaseous reactant. Experimental data, at three separate vapour pressures of steam, compared well with the new predictive formulation.     

Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a “relativity group” which is a one-parameter family of deformations of the standard Galilei group to the Newton–Hooke group which is a Wigner–?nönü contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn’s theorem and related results. Larmor’s theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the “Eisenhart” or “lightlike” lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdi?ka–Eardley–Nappi–Witten pp-wave solution of Einstein–Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi–Jackiw group.     

Comparison of the three-phase oil relative permeability models

A comparative study of seven different methods for predicting three-phase oil relative permeabilities in the presence of gas and water phases is presented. Predicted oil relative permeabilities from these correlations have been compared with published three-phase experimental data obtained in Berea sandstone core samples. Some of the correlations under study have been recently developed and have never been tested against the laboratory data.The comparison shows that the commonly used models such as Stones' often do not give accurate predictions of the experimental data. It is concluded that the recently developed models fit the experimental data as well as or better than the previously developed and widely used three-phase oil relative permeability models.     

Experimental and computational analyses of the effects of slice distortion from a metallic sphere in an MRI phantom

Susceptibility artifacts due to metallic prostheses are a major problem in clinical magnetic resonance imaging. We theoretically and experimentally analyze slice distortion arising from susceptibility differences in a phantom consisting of a stainless steel ball bearing embedded in agarose gel. To relate the observed image artifacts to slice distortion, we simulate images produced by 2D and 3D spin-echo (SE) and a view angle tilting (VAT) sequence. Two-dimensional SE sequences suffer from extreme slice distortion when a metal prosthesis is present, unlike 3D SE sequences for which--since slices are phase-encoded--distortion of the slice profile is minimized, provided the selected slab is larger than the region of interest. In a VAT sequence, artifacts are reduced by the application of a gradient along the slice direction during readout. However, VAT does not correct for the excitation slice profile, which results in the excitation of spins outside the desired slice location and can lead to incorrect anatomical information in MR images. We propose that the best sequences for imaging in the presence of a metal prosthesis utilize 3D acquisition, with phase encoding replacing slice selection to minimize slice distortion, combined with excitation and readout gradient strengths at their maximum values.     

Self-assembly of luminescent ternary complexes between seven-coordinate lanthanide(III) complexes and chromophore bearing carboxylates and phosphonates

Luminescent lanthanide complexes have been prepared by exploiting the interaction between lanthanide DO3A complexes and chromophore bearing carboxylates or phosphonates. This interaction can be utilised to probe the choice of sensitising chromophore suited to a given lanthanide. Furthermore, ternary complexes obtained from chromophore appended carboxylates dissociate in the presence of phosphate, while those obtained from phosphonates do not.     

New Heteropolytungstates Incorporating Dioxouranium(VI). Derivatives of α-[SiW9O34]10−, α-[AsW9O33]9−, γ-[SiW10O36]8−, and [As4W40O140]28−

Reaction of uranium salts with several lacunary polyoxotungstate anions yields four new heteropolyanion assemblies in which the uranium atoms occupy pentagonal bipyramidal coordination polyhedra. Treatment of A,-[SiW₉O₃₄]^10– with UO₂(NO₃)₂ leads to Na₁₄[Na₂(UO₂)₂(SiW₉O₃₄)₂]38H₂O (1, Monoclinic, P2₁/c, a=16.5719(8) Å, b=14.1689(7) Å, c=21.2528(10) Å, =111.6670(10)°, V=4786.6(4) ų, Z=2) which proves to be isostructural with the analogous derivative of [PW₉O₃₄]^9– reported previously. Solutions of 1 exhibit the 5-line W-NMR spectrum expected for the structure of C _i point symmetry. The salt (NH₄)₁₇[(UO₂)₃(H₂O)₄As₃W₂₆O₉₄]16H₂O (2, Orthorhombic, Pnma, a=40.1747(2) Å, b=18.25840(10) Å, c=18.0817(2) Å, V=13263.4(2) ų, Z=4) was isolated in 64% yield from a reaction of UO₂(NO₃)₂ with B,-[AsW₉O₃₃]^9–. The structure of the anion in 2 has C _s symmetry and contains one -AsW₉O₃₃ and two novel -AsW₈O₃₀ units linked by the UO²⁺ ₂ groups; an additional WO₆ links the two AsW₈ fragments. Spectrophotometric titration of UCl₄ with the sodium salt of [As₄W₄₀O₁₄₀]^28– indicated the formation of a 4:1 U:As₄W₄₀ complex. During attempts to isolate a crystalline product from this reaction the uranium became oxidized and a guanidinium salt of [Na(UO₂)₃(OH)(H₂O)₆As₄W₄₀O₁₄₀(WO)]^18– (3, Orthorhombic, Fdd2, a=54.848(3) Å, b=80.809(4) Å, c=20.2874(2) Å, V=89919(7), Z=16) was isolated. The partially disordered structure of 3 shows the S₂ and adjacent sites of the lacunary As₄W₄₀ anion to be occupied by three UO₅ and one WO₅ polyhedra. A tetrameric assembly of -SiW₁₀ units linked by UO²⁺ ₂ groups occurs in [{M(OH₂)}₄(UO₂)₄(OH)₂(SiW₁₀O₃₆)₄]^22– (lithium salt, M=Na, 4a, tetragonal, P4₂/nmc, a=b=26.5285(2) Å, c=15.0463(2) Å, V=10589.0(2) ų, Z=2; sodium-potassium salt, M=K, 4b, orthorhombic, Fddd, a=24.180(5) Å, b=31.696(6) Å, c=58.012(12) Å, V=44460(15) ų, Z=8). Tungsten-183 NMR spectra show the slow transformation of the expected 5-line (1:1:1:1:1) spectrum of 4a to a new species giving a 6-line spectrum (2:2:2:1:2:1). The latter complex has not been successfully isolated.