Homogeneous almost complex manifolds and their compact quotients

This paper investigates the (non)existence of compact quotients of the homogeneous almost-complex strongly-pseudoconvex manifolds discovered and classified by Gaussier–Sukhov [Wong–Rosay theorem in almost complex manifolds, http:www.arXiv.org:math.CV/0307335 ; On the geometry of model almost complex manifolds with boundary, Math. Z. 254(3) (2006) 567–589] and Lee [Domains in almost complex manifolds with an automorphism orbit accumulating at a strongly pseudoconvex boundary point, Michigan Math. J. 54(1) (2006) 179–205; Strongly pseudoconvex homogeneous domains in almost complex manifolds, J. Reine Angew. Math. 623 (2008) 123–160].

Relationship between the representative element volume and discontinuity parameters

We introduce an application of the discrete fracture network (DFN) model and 3D persistence to study the relationship between the representative element volume (REV) size and discontinuity information. To avoid the influence of heterogeneity on the distribution of discontinuities, the dam abutment rock mass of the Songta hydropower station is divided into eight statistically homogeneous domains based on the discontinuity orientation and trace length. An optimum DFN model is established for each homogeneous domain. Cubes of different sizes are extracted from the centre of the corresponding DFN model. Based on the discontinuity projection method, the 3D persistence values within the DFN model and each cube are calculated separately. The relative error of persistence for each cube and the DFN model are used to evaluate the size effect and to identify the REV size. Subsequently, the relationship between the determined REV size and the corresponding discontinuity information is systematically researched. Our results show that the discontinuity diameter, the volume density and the Fisher constant have separate linear relationships with the REV size. We present the empirical formulas for estimating the REV size according to the discontinuity diameter, the volume density and the Fisher constant.

Shape-fitting analyses of two-dimensional X-ray diffraction spots for strain-distribution evaluation in a β-FeSi2 nanofilm

New fitting analyses for peak shapes in a 2D reciprocal-space map are demonstrated to evaluate the strain, strain distribution and domain size of a crystalline ultra-thin (15 Å) film of β-FeSi2(100) grown epitaxially on an Si(001) substrate, using grazing-incidence X-ray diffraction. A 2D Laue-fit analysis taking into account instrument broadening and the double-domain effect provides residual maps as a function of the inequivalent strains ∊ b and ∊ c along the b and c axes of β-FeSi2, respectively (and domain size D), reflecting the probability of existence of homogeneous domains with fixed ∊ b , ∊ c and D, in addition to the most probable minimum residual. A 2D Laue fit with an inhomogeneous domain distribution provides a population map with ∊ b and ∊ c , reflecting strain components contributing to the film. The population map also leads to a reference residual as a guide for the strains contributing to the residual map. The advantages of the 2D Laue fits are discussed by comparison with the Scherrer, Williamson–Hall and Gaussian fitting methods for equivalent systems. The analyzed results indicate that the β-FeSi2 nanofilm was considerably small strained, which was also confirmed by transmission electron microscopy, implying a weak interface interaction between the film and the substrate.

Manganiakasakaite-(La) and Ferriakasakaite-(Ce), Two New Epidote Supergroup Minerals from Piedmont, Italy

Two new monoclinic (P21/m) epidote supergroup minerals manganiakasakaite-(La) and ferriakasakaite-(Ce) were found in the small Mn ore deposit of Monte Maniglia, Bellino, Varaita Valley, Cuneo Province, Piedmont, Italy. Manganiakasakaite-(La) occurs as subhedral grains embedded in pyroxmangite. Its empirical formula is A(1)(Ca0.62Mn2+0.38) A(2)(La0.52Nd0.08Pr0.07Ce0.07Y0.01Ca0.25) M(1)(Mn3+0.52Fe3+0.28Al0.18V3+0.01) M(2)Al1.00 M(3)(Mn2+0.60Mn3+0.27Mg0.13) T(1−3)(Si2.99Al0.01) O12 (OH), corresponding to the end-member formula CaLaMn3+AlMn2+(Si2O7)(SiO4)O(OH). Unit-cell parameters are a = 8.9057(10), b = 5.7294(6), c = 10.1134(11) Å, β = 113.713(5)°, V = 472.46(9) Å3, Z = 2. The crystal structure of manganiakasakaite-(La) was refined to a final R1 = 0.0262 for 2119 reflections with Fo > 4σ(Fo) and 125 refined parameters. Ferriakasakaite-(Ce) occurs as small homogeneous domains within strongly inhomogeneous prismatic crystals, where other epidote supergroup minerals coexist [manganiandrosite-(Ce), “androsite-(Ce)”, and epidote]. Associated minerals are calcite and hematite. Its empirical formula is A(1)(Ca0.64Mn2+0.36) A(2)(Ce0.37La0.17Nd0.06Pr0.03Ca0.35□0.02) M(1)(Fe3+0.61Al0.39) M(2)Al1.00 M(3)(Mn2+0.64Mn3+0.33Fe3+0.02Mg0.01) T(1−3)Si3.01 O12 (OH), the end-member formula being CaCeFe3+AlMn2+(Si2O7)(SiO4)O(OH). Unit-cell parameters are a = 8.9033(3), b = 5.7066(2), c = 10.1363(3) Å, β = 114.222(2)°, V = 469.66(3) Å3, Z = 2. The crystal structure of ferriakasakaite-(Ce) was refined to a final R1 = 0.0196 for 1960 unique reflections with Fo > 4σ(Fo) and 124 refined parameters.