The crystal structure of an isotropic, single phase, Ti-rich schorlomite garnet, ideally Ca3Ti4+ 2(Fe3+ 2Si)O12, from Magnet Cove, Arkansas was refined with the Rietveld method, space group $Ia\overline 3 d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction data. Electron-microprobe analysis gave an average composition {Ca2.92Na0.04Mn2+ 0.03Mg0.01}Σ3[Ti1.04Fe3+ 0.46Mg0.18Fe2+ 0.16Zr4+ 0.13V3+ 0.04]Σ2(Si2.21Fe3+ 0.71Al0.07)Σ3O12, and corresponds to the general garnet formula of [8] X 3 [6] Y 2 [4] Z 3 [4]O12. Schorlomite is the dominant component, but the composition contains significant amounts (>15 mol.%) of andradite, Ca3(Fe3+ 2)Si3O12, morimotoite, Ca3(Ti4+Fe2+)Si3O12, and morimotoite-(Mg), Ca3(Ti4+Mg)Si3O12. The crystal structure model was refined well using isotropic and anisotropic displacement parameters. Using isotropic displacement parameters, the χ 2 and R (F 2) Rietveld refinement values are 1.148 and 0.0742, respectively. The unit-cell parameter, a = 12.18599(1) (Å), is large for a natural schorlomite for which complete structural data are available. The bond distances are average <Ca–O> = 2.4461, Ti–O = 2.0085(5), Si–O = 1.7022(5) Å, and site occupancy factors (sofs) for Ca(sof) = 0.963(1), Ti(sof) = 1.045(1), and Si(sof) = 1.150(2). Comparison of schorlomite data from the type locality in Magnet Cove with morimotoite from Ice River, Canada and the type locality in Japan show that they are quite similar and cast doubts as to morimotoite being different from schorlomite.

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

Previous studies have shown that a dilute dispersion of fine particles can either augment or attenuate the gas-phase turbulent kinetic energy (TKE). However, such turbulence modification is not accurately captured by numerical simulation models. A critical reason is that the models do not incorporate flow distortion occurring at small scales on the order of the particle diameter or the Kolmogorov scale. These scales are too small to be resolved by most experiments and simulations, so the small-scale effects remain poorly understood. The main objective of this study is to investigate experimentally the small-scale turbulence structures that affect the overall turbulence modification to improve understanding and prediction of the macroscopic turbulence modification. A high resolution particle image velocimetry (PIV) system was developed that provided two-dimensional velocity field measurements with a sub-Kolmogorov vector spacing of 60 μm. Measurements of gas-phase isotropic turbulence were performed in the facility developed by Hwang & Eaton (Exp. Fluids, vol. 36 (3), 2004a, p. 444) in the presence of dispersed 500 μm glass, 250 μm glass or 250 μm polystyrene particles at mass loading ratio up to 0.45. The Reynolds number based on the Taylor microscale was 130 for the unladen case. The TKE was attenuated by up to 25 % in the presence of particles. The high-resolution measurements of the dissipation rate show that changes in the dissipation rate are smaller than changes to the TKE, in contrast to previous underresolved experiments. An analysis of a large set of PIV images allowed calculation of the average turbulence distortion around particles. The measurements also showed strong damping of the TKE and strong augmentation of the dissipation rate in a roughly spherical region surrounding the particles.

The two-dimensional space spanned by the velocity gradient invariants Q and R is expanded to three dimensions by the decomposition of R into its strain production −1/3sijsjkski and enstrophy production 1/4ωiωjsij terms. The {Q; R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martín et al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence of Reλ ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to the Q–R plane. The relatively weak cyclic evolution in the Q–R space is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian of Aij, on the other hand, seems the main responsible for intermittently alternating between low and high intensity Aij states.

This paper presents a new planar particle that shows negative effective permittivity under irradiation by an electromagnetic wave. The mutual coupling between the couples of these particles is studied in particular. The response of this particle sensitive to an electric field is strongly anisotropic. The particle is aimed to be used to compose an isotropic epsilon-negative metamaterial in two forms. First, a unit cell of the metamaterial consists of a cube bearing six particles on its faces, located with specific orientations. The experiments showed that this unit cell is suitable for manufacturing an isotropic epsilon-negative metamaterial obtained by arranging these cells in a 3D cubic periodic system. The second form of an epsilon-negative metamaterial with an isotropic response consists of the planar particles themselves, distributed quasi-randomly, composing a 2D system and/or of particles placed in spherical shells and distributed fully randomly in a hosting material forming a 3D system. The isotropy of these systems was verified by measurements in a rectangular waveguide.

A theorem on the existence of moduli spaces of compact complex isotropic submanifolds in complex contact manifolds is established.

Variograms and covariance functions are the fundamental tools for modeling dependent data observed over time, space, or space-time. This paper aims at constructing nonseparable spatio-temporal variograms and covariance models. Special attention is paid to an intrinsically stationary spatio-temporal random field whose covariance function is of Schoenberg-Lévy type. The correlation structure is studied for its increment process and for its partial derivative with respect to the time lag, as well as for the superposition over time of a stationary spatio-temporal random field. As another approach, we investigate the permissibility of the linear combination of certain separable spatio-temporal covariance functions to be a valid covariance, and obtain a subclass of stationary spatio-temporal models isotropic in space.

Variograms and covariance functions are key tools in geostatistics. However, various properties, characterizations, and decomposition theorems have been established for covariance functions only. We present analogous results for variograms and explore the connections with covariance functions. Our findings include criteria for covariance functions on intervals, and we apply them to exponential models, fractional Brownian motion, and locally polynomial covariances. In particular, we characterize isotropic locally polynomial covariance functions of degree 3.