Perfect Parallel Research Articles

The dressing factor and crossing equations

We utilize the DHM integral representation for the BES dressing factor of the world-sheet S-matrix of the AdS5 × S5 light-cone string theory, and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus. The results obtained are further used, in conjunction with the fusion procedure, to determine the bound state dressing factor of the mirror theory. We convincingly demonstrate that the mirror bound state S-matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure. This welcome feature is in perfect parallel to string theory, where the corresponding bound state S-matrix has no bearing on bound state constituent particles as well. The mirror bound state S-matrix we found provides the final missing piece in setting up the TBA equations for the AdS5 × S5 mirror theory.

Lattice Boltzmann simulation on Nvidia and AMD GPUs

General purpose computing on graphic processing units (GPUs) has received great attention re-cently. Both Nvidia and AMD have announced their own SDK, CUDA and ASC, respectively. Com-pared with CPUs, many applications can achieve high speed-up on GPUs. As a mesh-based particle method for flow simulation, lattice Boltzmann method (LBM) has perfect intrinsic parallelism that is very suitable for large-scale parallel computing. In this article, we put forward an algorithm for LB simulation of flow in grooved channel using the D2Q9 model, running on both Nvidia and AMD GPUs in the multi-program multi-data (MPMD) mode through message passing interface (MPI). The capability of hybrid GPU clusters can thus be fully utilized. The correctness and performance of the computation is analyzed through comparison with corresponding CPU implementation and significant speed-up of the GPU implementation has been demonstrated. The results provide valuable references to the establishment of GPU-based high performance computing (HPC) systems.

BRAITHWAITEITE, NaCu5(TiSb)O2(AsO4)4[AsO3(OH)]2(H2O)8, A NEW MINERAL SPECIES FROM LAURANI, BOLIVIA

Braithwaiteite, NaCu 5 (Ti 4+ Sb 5+ )O 2 (As 5+ O 4 ) 4 [As 5+ O 3 (OH)] 2 (H 2 O) 8 , is a new and very rare secondary mineral of copper, discovered in the supergene zone of an epithermal Cu–Au–Ag deposit at Laurani, near Sica Sica, Bolivia. This deposit is the type locality for lammerite, described as a new species in 1981. Braithwaiteite is closely associated with lammerite, lavendulan– lemanskiite and quartz. It formed by oxidation of Sb-bearing enargite in an arid environment. Traces of pyrite, covellite, anatase, albite–oligoclase, kaolinite and a mineral of the chlorite group are present as well. Electron-microprobe analysis gives Na 2 O 1.7, CuO 25.8, FeO 0.2, TiO 2 4.5, Sb 2 O 5 11.7, As 2 O 5 42.3, H 2 O (calc.) 10.17, for a total of 96.37 wt.%. The empirical formula based on the results of crystal-structure solution and refinement [34 anions and 2(OH) + 8H 2 O] is Na 0.87 Cu 2+ 5.17 (Ti 4+ 0.90 Sb 5+ 1.15 ) ∑2.05 O 2 (As 5+ 0.98 O 4 ) 4 [As 5+ 0.98 O 3 (OH)] 2 (H 2 O) 8 . The simplified formula is NaCu 5 (TiSb)O 2 (AsO 4 ) 4 [AsO 3 (OH)] 2 (H 2 O) 8 , which requires Na 2 O 2.04, CuO 26.13, TiO 2 5.25, Sb 2 O 5 10.63, As 2 O 5 45.30, H 2 O 10.65, total 100.00 wt.%. Infrared spectroscopy indicates the presence of H 2 O and OH, and As–O and As–OH stretching vibrations. Single-crystal X-ray studies show braithwaiteite to be triclinic, space group P 1, a 7.0308(4), b 9.8823(5), c 10.6754(6) A, α 106.973(1), β 104.274(1), γ 93.839(1)°, V 679.76(11) A 3 , Z = 1, and a:b:c = 0.7115:1:1.0803. The strongest seven X-ray powder-diffraction lines [ d in A(I)( hkl )] are: 9.825(100)(001), 5.887(50)(011), 4.635(30)(102), 3.354(30)(122), 3.232(30)(211), 2.947(60)(022), 2.736(30)(222). Two crystals of braithwaiteite were found, one on matrix and the other loose, each of them less than 1 mm in size, plus a few very minute fragments. The forms that could be determined with certainty include the following pinacoids: {001} dominant, {010} less prominent, {100}, {103} and {203}, all subordinate. The crystals are transparent and have a sky-blue color, a vitreous luster and a very pale blue streak. Braithwaiteite is brittle and has a perfect cleavage parallel to {001}. Optically, braithwaiteite is biaxial negative, 2 V meas 59(2), 2 V calc 65°. Indices of refraction are α 1.698(2), β 1.757(5), γ 1.783(5) at 589.3 nm. The mineral is weakly pleochroic with pale blue to greenish blue hues. The hardness (Mohs) is ~2. Using the empirical formula and the unit-cell parameters derived from the single-crystal study, the calculated density is 3.753 g cm −3 . Braithwaiteite is named after Dr. Richard S.W. Braithwaite (born 1930), prominent chemist and mineralogist at the University of Manchester, U.K. The mineral and mineral name have been approved by the Commission on New Minerals, Nomenclature and Classification, IMA (2006–050).

Mining tree-structured data on multicore systems

Mining frequent subtrees in a database of rooted and labeled trees is an important problem in many domains, ranging from phylogenetic analysis to biochemistry and from linguistic parsing to XML data analysis. In this work we revisit this problem and develop an architecture conscious solution targeting emerging multicore systems. Specifically we identify a sequence of memory related optimizations that significantly improve the spatial and temporal locality of a state-of-the-art sequential algorithm -- alleviating the effects of memory latency. Additionally, these optimizations are shown to reduce the pressure on the front-side bus, an important consideration in the context of large-scale multicore architectures. We then demonstrate that these optimizations while necessary are not sufficient for efficient parallelization on multicores, primarily due to parametric and data-driven factors which make load balancing a significant challenge. To address this challenge, we present a methodology that adaptively and automatically modulates the type and granularity of the work being shared among different cores. The resulting algorithm achieves near perfect parallel efficiency on up to 16 processors on challenging real world applications. The optimizations we present have general purpose utility and a key out-come is the development of a general purpose scheduling service for moldable task scheduling on emerging multicore systems.

Folding transformations for quantum Painlevé equations

We examine a special property of Painlevé equations, namely possessing folding transformations. The latter are relations of the solution of a given Painlevé equation to the square of that of some other, which can be the same as the initial one. They generally exist only for special values of the parameters of a given equation. The present setting will be that of the quantum Painlevé equations, which are systems where the dependent variables are noncommuting objects. Both continuous and discrete cases are analysed and the folding transformations are established in a perfect parallel between continuous and discrete systems.

Electrochemical and Spectral Properties of Ferrocene (Fc) in Ionic Liquid: 1-Butyl-3-methylimidazolium Triflimide, [BMIM][NTf2]. Concentration Effects

Several earlier studies of the electrochemical oxidation of ferrocene (Fc) in room-temperature ionic liquids revealed an essentially nonlinear dependence of the oxidation current on the Fc concentration in its relatively dilute solutions, with its formally calculated diffusion coefficient strongly increasing with the concentration. Since no plausible mechanism leading to this very unusual finding had been proposed, our study of Fc solutions in 1-butyl-3-methylimidazolium triflimide, [BMIM][NTf(2)], was performed to verify whether the above observation originated from an incorrect determination of the dissolved Fc concentration. Our observations have demonstrated that reliable control of the Fc concentration in solution is complicated by factors such as the low amount of Fc used to prepare small-volume solutions or the great difficulty to dissolve completely a solid powder in a solvent with an extremely high viscosity. An unexpected additional complication is related to a sufficiently high volatility of Fc which manifests itself even at room temperature and especially at elevated temperatures or/and in the course of vacuum treatment of its solutions or its solid powder. Parallel measurements of electrochemical responses and UV-visible spectra for several series of Fc solutions of various concentrations (prepared with the use of different procedures) have shown a perfect parallelism between the peak current and the intensity of the absorption band in the range of 360-550 nm, leading us to the conclusion of a linear relationship between the oxidation current and the molecularly dissolved Fc concentration. The relations of these measured characteristics with the estimated Fc concentration in these solutions have demonstrated a much greater dispersion (attributed to the difficulty of a precise measurement of the latter) but without a significant deviation from the linearity in general. This finding has allowed us to estimate the diffusion coefficient of this species: D = (1.7 +/- 0.2) x 10(-7) cm(2)/s. The extinction coefficients for the maximum of the absorption band (at 440 nm) of Fc have been compared for a series of solvents: [BMIM][NTf(2)], acetonitrile, THF, heptane, CH(2)Cl(2), ethanol, and toluene. A simple method to estimate reliably the concentration of solute Fc in ionic liquids based on spectroscopic measurements has been proposed, owing to the proximity of Fc absorption properties for a great variety of solvents.

Mass formula for quasi-black holes

A quasi-black hole, either nonextremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.

Second-order Bayesian revision of a generalised linear model

It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned.

Typomorphism and parasteresis of Yushkinite, the Pai-Khoi anticlinorium

Yushkinite found in quartz-calcite hydrothermal veins in the Pai-Khoi Anticlunorium (the middle reaches of the Silova-Yakha River) is associated with fluorite, sphalerite, and sulvanite and occurs as fine-lamellar aggregates. The mineral is pinkish purple, with perfect cleavage parallel to (0001). The Moh hardness is lower than 1. In reflected light, yushkinite is anisotropic, with strong bireflectance. It is uniaxial and optically negative. Yushkinite was discovered and approved by the Commission on New Minerals and Mineral Names, International Mineralogical Association, in 1983. Twenty years later, reexamination of yushkinite and associated minerals gave rise to the discovery of a new carbonate phase and specification of the physical properties and chemical composition of yushkinite.

A tearing-based hybrid parallel banded linear system solver

A new parallel algorithm for the solution of banded linear systems is proposed. The scheme tears the coefficient matrix into several overlapped independent blocks in which the size of the overlap is equal to the system’s bandwidth. A corresponding splitting of the right-hand side is also provided. The resulting independent, and smaller size, linear systems are solved under the constraint that the solutions corresponding to the overlap regions are identical. This results in a linear system whose size is proportional to the sum of the overlap regions which we refer to as the “balance” system. We propose a solution strategy that does not require obtaining this “balance” system explicitly. Once the balance system is solved, retrieving the rest of the solution can be realized with almost perfect parallelism. Our proposed algorithm is a hybrid scheme that combines direct and iterative methods for solving a single banded system of linear equations on parallel architectures. It has broad applications in finite-element analysis, particularly as a parallel solver of banded preconditioners that can be used in conjunction with outer Krylov iterative schemes.

Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum state, a perfect parallel repetition theorem holds in the following sense. The prover's optimal success probability for simultaneously playing a collection of XOR proof systems is exactly the product of the individual optimal success probabilities. This property is remarkable in view of the fact that, in the classical case (where the provers can only utilize classical information), it does not hold. The theorem is proved by analyzing parities of XOR proof systems using semidefinite programming techniques, which we then relate to parallel repetitions of XOR games via Fourier analysis.

Epidote-(Sr), CaSrAl2Fe3+(Si2O7)(SiO4)(OH), a new mineral from the Ananai mine, Kochi Prefecture, Japan

Epidote-(Sr), CaSrAl2Fe3+(Si2O7)(SiO4)(OH), the Sr-analog of epidote, was found in the Nagakawara and Hohnomori deposits at the Ananai mine, Kochi Prefecture, Japan. It occurs in the form of prismatic crystals up to 1 cm in length in the tinzenite veins or the fine crystal aggregates in piemontite breccia. Epidote-(Sr) is optically biaxial negative, α = 1.737(2), β = 1.780 (2), γ = 1.792 (2), and 2Vcalc = 62° and has perfect cleavage parallel to {001}. It exhibits pleochroism—X: pale greenish yellow, and Y and Z: pale reddish brown to brownish pink. Its calculated density is 3.74 g/cm3, and it has a Mohs' hardness of 6.5. The representative empirical formula of epidote-(Sr) from the Nagakawara deposit is (Ca1.10Sr0.90)Σ2.00 (Al1.92Fe3+0.87Mn3+0.20)Σ2.99Si3.01O12(OH) on the basis of OH = 1 and O = 12 per formula unit. The mineral is monoclinic with a space group of P21/m, a = 8.928 (5), b = 5.652 (1), c = 10.244 (5) Å, β = 114.46 (4)°, V = 470.5 (3) Å3, and Z = 2. The strongest seven lines in the X-ray powder diffraction pattern [d in Å (I/I0) (hkl)] were 2.92 (100) (11-3), 2.58 (49) (202), 3.50 (42) (21-1), 2.61 (42) (31-1), 2.72 (41) (013), 2.83 (32) (020), and 3.26 (23) (201). Epidote-(Sr) from the Nagakawara deposit may have been formed from the residual hydrothermal fluid after the crystallization of tinzenite.

Contiguity relations for discrete and ultradiscrete Painlevé equations

We show that the solutions of ultradiscrete Painlevé equations satisfy contiguity relations just as their continuous and discrete counterparts. Our starting point are the relations for q-discrete Painlevé equations which we then proceed to ultradiscretise. In this paper we obtain results for the one-parameter q-PIII, the symmetric q-PIV and the q-PIV. These results show that there exists a perfect parallel between the properties of continuous, discrete and ultradiscrete Painlevé equations.

Phosphoinnelite, Ba4Na3Ti3Si4O14(PO4,SO4)2(O,F)3, a new mineral species from peralkaline pegmatite of the Kovdor pluton, Kola Peninsula

Phosphoinnelite, an analogue of innelite with P > S, has been found in a peralkaline pegmatite vein crosscutting calcite carbonatite at the phlogopite deposit, Kovdor pluton, Kola Peninsula. Cancrinite (partly replaced with thomsonite-Ca), orthoclase, aegirine-augite, pectolite, magnesioarfvedsonite, golyshevite, and fluorapatite are associated minerals. Phosphoinnelite occurs as lath-shaped crystals up to 0.2 × 1 × 6 mm in size, which are combined typically in bunch-, sheaf-, and rosettelike segregations. The color is yellow-brown, with vitreous luster on crystal faces and greasy luster on broken surfaces. The mineral is transparent. The streak is pale yellowish. Phosphoinnelite is brittle, with perfect cleavage parallel to the {010} and good cleavage parallel to the {100}; the fracture is stepped. The Mohs hardness is 4.5 to 5. Density is 3.82 g/cm3 (meas.) and 3.92 g/cm3 (calc.). Phosphoinnelite is biaxial (+), α = 1.730, β = 1.745, and γ = 1.764, 2V (meas.) is close to 90°. Optical orientation is Z^c ∼ 5°. Chemical composition determined by electron microprobe is as follows (wt %): 6.06 Na2O, 0.04 K2O, 0.15 CaO, 0.99 SrO, 41.60 BaO, 0.64 MgO, 1.07 MnO, 1.55 Fe2O3, 0.27 Al2O3, 17.83 SiO2, 16.88 TiO2, 0.74 Nb2O5, 5.93 P2O5, 5.29 SO3, 0.14 F, −O=F2 = −0.06, total is 99.12. The empirical formula calculated on the basis of (Si,Al)4O14 is (Ba3.59Sr0.13K0.01)Σ3.73(Na2.59Mg0.21Ca0.04)Σ3.04(Ti2.80Fe 0.26 3+ Nb0.07)Σ3.13[(Si3.93Al0.07)Σ4O14(P1.11S0.87)Σ1.98O7.96](O2.975F0.10)Σ3.075. The simplified formula is Ba4Na3Ti3Si4O14(PO4,SO4)2(O,F)3. The mineral is triclinic, space group P \(\overline 1 \) or P1. The unit cell dimensions are a = 5.38, b = 7.10, c = 14.76 A; α = 99.00°, β = 94.94°, γ = 90.14°; and V = 555 A3, Z = 1. The strongest lines of the X-ray powder pattern [d, A in (I)(hkl)] are: 14.5(100)(001), 3.455(40)(103), 3.382(35)(0\(\overline 2 \)2), 2.921(35)(005), 2.810(40)(1\(\overline 1 \)4), 2.683(90)(200, \(\overline 2 \)01), 2.133(80)(\(\overline 2 \) \(\overline 2 \)2), 2.059(40)(204, 1\(\overline 3 \)3, 221), 1.772(30)(0\(\overline 4 \)1, 1\(\overline 2 \)7, 2\(\overline 3 \)2, 2\(\overline 3 \)3). The infrared spectrum is demonstrated. An admixture of P substituting S has been detected in the innelite samples from the Inagli pluton (South Yakutia, Russia). An innelite-phosphoinnelite series with a variable S/P ratio has been discovered. The type material of phosphoinnelite has been deposited at the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.

Chesnokovite, Na2[SiO2(OH)2] · 8H2O, the first natural sodium orthosilicate from the Lovozero alkaline pluton, Kola Peninsula: Description and crystal structure of a new mineral species

Chesnokovite, a new mineral species, is the first natural sodium orthosilicate. It has been found in an ussingite vein uncovered by underground mining at Mt. Kedykverpakhk, Lovozero alkaline pluton, Kola Peninsula, Russia. Natrolite, sodalite, vuonnemite, steenstrupine-(Ce), phosinaite-(Ce), natisite, gobbinsite, villiaumite, and natrosilite are associated minerals. Chesnokovite occurs as intergrowths with natrophospate in pockets up to 4 × 6 × 10 cm in size consisting of chaotic segregations of coarse lamellar crystals (up to 0.05 × 1 × 2 cm in size) flattened along [010]. The crystals are colorless and transparent. The aggregates are white to pale brownish yellowish, with a white streak and a vitreous luster. The cleavage is perfect parallel to (010) and distinct to (100) and (001). The fracture is stepped. The Mohs’ hardness is 2.5. The measured density is 1.68 g/cm3; the density calculated on the basis of an empirical formula is 1.60 g/cm3 and 1.64 g/cm3 on the basis of an idealized formula. The new mineral is optically biaxial, positive, α = 1.449, β = 1.453, γ = 1.458, 2Vmeas = 80°, and Z = b. The infrared spectrum is given. The chemical composition (Si determined with electron microprobe; Na, K, and Li, with atomic emission analysis; and H2O, with the Alimarin method) is as follows, wt %: 21.49 Na2O, 0.38 K2O, 0.003 Li2O, 21.42 SiO2, 54.86 H2O, total is 98.153. The empirical formula calculated on the basis of O2(OH)2 is as follows: (Na1.96K0.02)Σ1.98Si1.005O2(OH)2 · 7.58H2O. The simplified formula (Z = 8) is Na2[SiO2(OH)2] · 8H2O. The new mineral is orthorhombic, and the space group is Ibca. The unit-cell dimensions are: a = 11.7119, b = 19.973, c = 11.5652 A, and V = 2299.0 A3. The strongest reflections in the X-ray powder pattern [d, A (I, %)(hkl)] are: 5.001(30)(211), 4.788(42)(022), 3.847(89)(231), 2.932(42)(400), 2.832(35)(060), 2.800(97)(332, 233), and 2.774(100)(341, 143, 114). The crystal structure was studied using the Rietveld method, Rp = 5.77, Rwp = 7.77, RB = 2.07, and RF = 1.74. The structure is composed of isolated [SiO2(OH)2] octahedrons and the chains of edge-shared [Na[H2O)6] octahedrons. The Si and Na polyhedrons are linked only by H-bonds, and this is the cause of the low stability of chesnokovite under atmospheric conditions. The new mineral is named in memory of B.V. Chesnokov (1928–2005), an outstanding mineralogist. The type material of chesnokovite is deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.

EEG Arousal Norms by Age

Brief arousals have been systematically scored during sleep for more than 20 years. Despite significant knowledge concerning the importance of arousals for the sleep process in normal subjects and patients, comprehensive age norms have not been published. Seventy-six normal subjects (40 men) without sleep apnea or periodic limb movements of sleep, aged 18 to 70 years, slept in the sleep laboratory for 1 or more nights. Sleep and arousal data were scored by the same scorer for the first night (comparable to clinical polysomnograms) and summarized by age decade. There were no statistically significant differences for sex or interaction of sex by age (p > .5 for both). The mean arousal index increased as a function of age. Newman-Keuls comparisons (.05) showed arousal index in the 18- to 20-year and 21- to 30-year age groups to be significantly less than the arousal index in the other 4 age groups. Arousal index in the 31-to 40-year and 41-to 50-year groups was significantly less than the arousal index in the older groups. The arousal index was significantly negatively correlated with total sleep time and all sleep stages (positive correlation with stage 1 and wake). Brief arousals are an integral component of the sleep process. They increase with other electroencephalographic markers as a function of age. They are highly correlated with traditional sleep-stage amounts and are related to major demographic variables. Age-related norms may make identification of pathologic arousal easier.

Coplanar and coaxial orientations of RNA bases and helices

Electrostatic interactions, base-pairing, and especially base-stacking dominate RNA three-dimensional structures. In an A-form RNA helix, base-stacking results in nearly perfect parallel orientations of all bases in the helix. Interestingly, when an RNA structure containing multiple helices is visualized at the atomic level, it is often possible to find an orientation such that only the edges of most bases are visible. This suggests that a general aspect of higher level RNA structure is a coplanar arrangement of base-normal vectors. We have analyzed all solved RNA crystal structures to determine the degree to which RNA base-normal vectors are globally coplanar. Using a statistical test based on the Watson-Girdle distribution, we determined that 330 out of 331 known RNA structures show statistically significant (p < 0.05; false discovery rate [FDR] = 0.05) coplanar normal vector orientations. Not surprisingly, 94% of the helices in RNA show bipolar arrangements of their base-normal vectors (p < 0.05). This allows us to compute a mean axis for each helix and compare their orientations within an RNA structure. This analysis revealed that 62% (208/331) of the RNA structures exhibit statistically significant coaxial packing of helices (p < 0.05, FDR = 0.08). Further analysis reveals that the bases in hairpin loops and junctions are also generally planar. This work demonstrates coplanar base orientation and coaxial helix packing as an emergent behavior of RNA structure and may be useful as a structural modeling constraint.

Allanpringite, Fe3(PO4)2(OH)35H2O, a new ferric iron phosphate from Germany, and its close relation to wavellite

Allanpringite is a new ferric iron phosphate with the ideal formula Fe3(PO4)2(OH)3·5H2O, and is closely related to wavellite, Al3(PO4)2(OH)3·5H2O. Type locality is the dump of the abandoned Grube Mark near Essershausen, ca. 5 km SE of Weilburg/Lahn, Taunus, Hesse, Germany. The mineral occurs as pale brown-yellow, 010] acicular, invariably twinned (by non-merohedry) crystals which are always intergrown to form bundles of subparallel individuals. The maximum length of crystals is ca. 1.5 mm (usually much smaller); bundles can reach up to about 2 mm. The mineral is associated with beraunite (reddish “oxiberaunite” variety), cacoxenite, strengite and cryptomelane. Allanpringite is translucent to transparent, its streak is white with a pale yellowish tint, and it has a vitreous lustre. It shows a perfect cleavage parallel to the morphological elongation and one good cleavage parallel to {010}. It is brittle and has an uneven fracture, a Mohs hardness of ~3, and D (meas.) = 2.54(2) g/cm3, D (calc.) = 2.583 g/cm3 (for empirical formula). Optically, it is biaxial positive, with α = 1.662(5), β = 1.675(5), γ = 1.747(5), 2 Vγ (calc.) = 48°; pleochroism is strong: X colourless, Y colourless, Z dark yellow; absorption Z>>X~Y; orientation XYZ = ** b (pseudo-orthorhombic); no visible dispersion. Electron microprobe analysis yielded (wt.%): Fe2O3 47.84, Al2O3 0.34, Mn2O3 0.04; CuO 0.08, P2O5 28.56, F 0.02, H2Ocalc 23.49, less O≡F 0.01, total 100.36. The empirical formula is (Fe2.98Al0.03)(PO4)2(OH3.02F0.01)·4.97H2O, based on 16 O atoms. Allanpringite is monoclinic, space group P 21/ n , with a = 9.777(3), b = 7.358(2), c = 17.830(5) A, β = 92.19(4)°, V = 1281.7(6) A3 (single-crystal data) and Z = 4. Strongest lines in the X-ray powder diffraction pattern are [ d (A), I , hkl ]: 8.90 (100) (002), 8.41 (60) (10-1, 101), 5.870 (50) (110), 3.600 (50) (021, 02-1), 3.231 (80) (204, 12-2). The crystal structure has been determined using single-crystal X-ray diffraction data (Mo K α radiation, CCD area detector) obtained from a twinned fragment ( R ( F ) = 13.3%). The structure of allanpringite is a monoclinically distorted, pseudo-orthorhombic variant of the orthorhombic structure of its Al-analogue wavellite, Al3(PO4)2(OH,F)3·5H2O. Chains of corner-sharing, distorted Fe(O,OH,H2O)6 octahedra parallel to [010] are corner-linked by PO4 tetrahedra. Channels, also parallel to [010], host a positionally split water molecule. Average Fe-O distances of the three non-equivalent Fe atoms range between 2.014 and 2.021 A. Single-crystal laser-Raman spectroscopy confirms an overall weak hydrogen bonding scheme. The structure of allanpringite is also related to those of kingite and mitryaevaite. The amorphous santabarbaraite has a chemical formula basically identical to that of allanpringite. The name honours Dr. Allan Pring, eminent Australian mineralogist.

Crystallization of orbicular rocks exemplified by the Slättemossa occurrence, southeastern Sweden

The orbicular rock at Slättemossa, southeastern Sweden, has a quartz monzodioritic composition. The cores of the orbicules crystallized directly from the orbicule-forming magma; cores made up of xenoliths have not been observed. Outside the core follow first an inner mafic, a felsic and then an outer mafic shell. The orbicules occur in a matrix, which is similar to the core. They grew simultaneously and show an almost perfect parallelism in evolution. After initial ‘normal’ crystall-ization of the magma, superheating probably triggered by a sudden addition of volatiles destroyed earlier formed nuclei and also affected the already crystallized part of the rock. Cooling caused heterogeneous nucleation and rapid crystallization, which formed the inner mafic shell. This is enriched in mafic minerals, especially biotite, compared to the core. At the same time the grain size becomes significantly smaller. Depletion in mafic components, possibly intensified by a sudden change in physical conditions, destabilized biotite and amphibole crystallization, causing oversaturation in plagioclase components, forming a felsic shell having a sharp boundary with the mafic shell. Plagioclase is extremely altered. Mafic minerals were then stabilized, probably due to depletion of plagioclase components, and an outer mafic shell formed. With the return to homogeneous nucleation, matrix formation concluded the crystallization. Orbicules might have moved in the magma causing some squeezing of magma surrounding the orbicules, but major movements involved the settling of the whole package of orbicules and matrix in the surrounding non-orbicular magma.

Capacitance of spherical dielectric layers

A capacitor device is modeled consisting of a close-packed arrangement of spheres as the dielectric layer. The top electrode is deposited directly on the upper half of the top layer of spheres and bottom electrode is a flat conductor. Expressions are derived for the capacitance for both single and multiple layers of spheres. It is found that a single layer of spheres has the largest increase in capacitance over that of a perfect parallel plate capacitor that has a dielectric thickness equal to the diameter of the spheres. The model predicts a decrease in capacitance as the number of sphere layers increases. The relative uncertainty in capacitance equals the relative uncertainty in the diameter of the spheres for both single and multiple layers.