Complete Sphere Research Articles

Natrolite, part II: Determination of deformation electron densities by the X-X method

A single crystal of natrolite, Na2Al2Si3O10 ·2H2O (space group Fdd2), was studied by X-ray diffraction methods at room temperature. The intensities were measured in a complete sphere of reflection up to sinΘ/ λ=0.903 A−1. A refinement of high-order diffraction data yielded residuals of R/(F)=0.9%, Rw(F)=0.8%, GoF=1.40 for 1856 high-angle reflections (0.7≤sinΘ/ λ≤0.903 A−1) and R(F)=1.0%, Rw(F)=1.2%, GoF=3.07 for all 3471 independent reflections in the complete sphere of reflection. The X-X method was used to calculate deformation electron densities (DED) in natrolite. Within all tetrahedra, residual electron density-was found in the T-O bond directions indicating a considerable covalent contribution to the chemical bond. The range of the interatomic peak heights was from 0.19 to 0.34 e/A3 in the SiO4 tetrahedra and from 0.11 to 0.23 e/A3 in the AlO4 tetrahedron. The ionic contribution to the chemical bond manifests itself in the displacement of the peaks towards the oxygen atoms. Charge displacement due to interaction of nonframework cations with framework oxygen atoms as well as electron densities attributable to the lone pair orbitals in the water molecule have been observed.

GAMMASPHERE-timing and signal processing aspects of the BGO Compton shield

We describe the design of the signal processing system and considerations involved in the timing performance of the BGO scintillator Compton shield that surrounds each of the 110 large germanium detectors used in a geodesic array covering the complete sphere surrounding the target in GAMMASPHERE. It is shown that the main timing limitation results from the statistics of photoelectron emission from the photocathode of the photomultiplier tubes (PMTs) that observe the light from the scintillators and that achieving the required timing demands triggering on the first photoelectron. The circuits to do this for a single detector assembly must be able to deal with signals from 14 PMTs associated with the 7 elements of the scintillator shield surrounding each germanium detector.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of tip shape on force-distance curves for AFM in aqueous electrolytes

In this study, we calculated the force-distance curves consisting of the van der Waals force and the electric double layer force in an electrolyte in the AFM with a realistic shape tip without the approximation of a low electrostatic potential. The calculation was compared with the experimentally obtained data. A complete sphere model can be applicable when 2θ ≦ 30°, but the Derjaguin approximation is not suitable for R ≦ D. A rigorous calculation without the approximation of a low potential can lead to better fitting with the experimental data, and thus the pH dependence curve of γ 1γ 2, which gives us the isoelectric point.

The influence of material properties on the predicted behaviour of rubber-toughened polymers

The toughening of polymeric materials by filling with particulates is an accepted route to improvement in their mechanical properties. However, advancing technology is now producing toughening particles of increasingly complex and varied morphologies. The full experimental investigation of all possible materials is becoming uneconomic, so predictive modelling is becoming increasingly important as a cost-effective method of material investigation; elastic properties can be predicted and failure mechanisms can be investigated. Although such simulation can never entirely replace experimental investigation, its importance as an investigative tool is becoming apparent. An important method of predictive modelling is the finite element analysis method (see, for example [1-3]). This method is based on micromechanical modelling of a representative cell of the material. Results for the whole material are gained either by assuming a random distribution [1, 2] or a fixed uniform distribution [3] of the filler. This modelling requires the elastic properties of the constituent materials; these properties are not always well known. The purpose of this letter is to illustrate the importance of knowing the precise values of the mechanical properties of the rubbery phase used in the toughening particles. Recent developments in particle morphology include multistage particles with "core-shell" structure [4]. The morphology of two types of particle is illustrated in Fig. 1, and results for these two materials are presented here. The two-stage particles consist of a rubber sphere surrounded by a glassy annulus; the diameter of the rubber sphere is 190 nm and the diameter of the complete sphere 230 nm. The three-stage particles consist of a glassy

Horizontal and vertical MAAs for a wide range of sound source locations

Minimum audible angles (MAA) in both the horizontal and the vertical directional were measured for sound source locations distributed over virtually the complete sphere around the listener. Stimuli were noise bursts with either a fixed (flat) spectrum, or a random spectrum with 1/3-octave levels drawn from a uniform distribution with a 20-dB range. It was found that, in general, horizontal MAAs are smallest for sound sources in or near the median plane and vertical MAAs are smallest for sources around 90° azimuth. The results for the random-spectrum stimuli show some unexpected asymmetries. Though listeners were almost unable to localize sources in the median plane with elevations in excess of 30° (vertical MAAs were then 60° or more), they attained moderate MAAs for lower elevations. The MAA for frontal presentation was even similar to the result obtained with fixed-spectrum noise. Results furthermore show that horizontal MAAs for sources at 90° azimuth are much larger for positive elevations than for negative elevations. These findings indicate that localization acuity is optimal for sound sources around or below the horizontal plane.

Hipparcos on-orbit environment and performance

Hipparcos was launched on 8 August 1989 for astrometry mission on geostationary orbit. Several unsuccessful attempts to ignite the ABM resulted in a revised mission on an eccentric orbit (500 km/36,000 km). Compared with the planned geostationary orbit, this one induced a more severe environment from physical and operational points of view. It resulted in major drawbacks for the radiation environment, since the radiation belts are crossed twice per orbit (i.e. roughly 4 times per day), and the eclipse duration increased up to 50%, for an orbit period divided by a factor two. Although the ground segment was extended to include additional ground stations, the revised orbit does not allow permanent contact between the ground stations and the spacecraft. The flexibility of the on-board software has been used for programming the main housekeeping functions during the non visibility periods. The spacecraft has been operating for several months, and after the payload calibration, the scientific mission started in November 1989. The results are very encouraging and the scientific returns will reach an unexpected level compared with the initial predictions after the ABM failure. The final performance relies on two major parameters. The payload characteristics measured on orbit are very well in line with ground measurements and simulations; however, radiation affects the photometry by the optics darkening effect. The mission lifetime will depend on resources and possible failures; the power budget was considered as a limiting factor, due to the solar generator degradation, but the last predictions, which are correlated with the on-orbit behaviour, indicate a possible lifetime of 3 years; however, the severe radiation levels could cause other problems which cannot be predicted. This paper presents the spacecraft status and payload performances as observed after 10 months of scientific mission. The first, astrometry performances will be known at that time, since the complete celestial sphere will have been covered, and the expected mission performance predictions will be re-evaluated more accurately. The last available results at the time of the congress could also be presented, i.e. after almost 1 year of mission.

Antenna synthesis and optimization using generalized characteristic modes

A set of modes called generalized characteristic modes is described. Previously developed characteristic modes exhibit orthogonality properties over an obstacle surface as well as the complete sphere at infinity. The generalized characteristic modes described here also exhibit orthogonality properties over the obstacle surface, but rather than showing orthogonality over the sphere at infinity, they are orthogonal over any region of space, similar to generalized Inagaki modes. Theories developed for antenna pattern synthesis and directivity optimization using generalized Inagaki modes can be applied in an entirely parallel fashion using generalized characteristic modes. Comparisons are made between generalized characteristic modes and generalized Inagaki modes through three examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The influence of viscosity on the strength of an axially strained pendular liquid bridge

Pendular liquid bridges between two relatively moving solid particles (dynamic bridges) occur extensively throughout the powder technology industry, with a typical example being binder granulation. By means of a sensitive linear voltage differential force tranducer, the influence of viscosity on the strength of an axially, periodically strained pendular bridge was investigated where bridge strength is defined as the maximum interparticle force developed during one complete sphere oscillation. The relative importance of the theoretically derived dimensionless groups governing bridge strength is experimentally established for systems exhibiting complete solid—liquid wettability. A simplified solution of dynamic bridge strength based on the superposition of lubrication theory and circular approximation is presented. For a small gap distance with sufficient bridge volume and in the limit of small Reynolds number, a good agreement between the experimental and present theoretical axial force response is observed, indicating the importance of the capillary number Ca in determining pendular bridge strength. The present quasi-static solution is zeroeth-order in Ca and gap distance, and is expected to break down with increasing local inertial effects. Such inertial effects are governed by a modified Bond number. In the limit of low Ca, they lead to an increase in bridge strength due to an added mass effect, whereas in the limit of high Ca, they lead to a reduced, shifted force response due to an insufficient rate of vorticity propagation. Under industrially relevant conditions, the strength of the dynamic bridge was observed to exceed the static by over an order of magnitude. Since a significant number of powder processes such as granulation are not static in nature, viscous interactions between particles should be considered whenever a liquid interstitial phase is present.

An Indirect Boundary Integral Equation Applied to Nonshallow Spherical Shell Problems With Arbitrary Boundary Constraints

The fundamental singular solutions of a complete elastic spherical shell are utilized and, via the superposition principle, an indirect boundary integral equation is formulated. The singular solutions correspond to the action of normal point loads, concentrated tangential loads, and surface moments which apply in a self-equilibrating fashion over the spherical surface. With singular solutions of such property in hand, an arbitrary spherical shell with surface loading and any set of consistent boundary constraints is embedded onto the complete sphere. A set of fictitious load vectors is introduced along the boundary line which, together with the prescribed surface traction, is required to satisfy the constraints at the boundary. The idea of an auxiliary boundary is also introduced and the solution to a number of representative shell problems is shown as compared to the available analytical and finite element method results.

Complete minimal spheres and projective planes inR n with simple ends

Complete minimal spheres and projective planes inR n with simple ends

THERMAL VIBRATIONS IN Ba2YCu3O7 STUDIED BY X-RAY DIFFRACTION

Unlike neutron scattering, X-ray studies can be done on very small crystals; in the case of Ba/sub 2/YCu/sub 3/O/sub 7/, a crystal of excellent quality and dimensions of 80 x 80 x /mu/m/sup 3/ dimensions was used. To account for the wavelength dependence of absorption and extinction, two complete Ewald spheres at two wavelengths were measured (Cu/Kappa//alpha/ and Mo/Kappa//alpha/ radiation) and simultaneously refined. All measurements were carried out at ambient temperature. Only a small amount of twinning was detected and accounted for mathematically. The thermal parameters were expanded beyond second order tensors (anisotropic Debye-Waller factors) to higher orders, using the Gram-Charlier formalism. It was possible to refine up to fourth order tensors for the metal atoms in Ba/sub 2/YCu/sub 3/O/sub 7/ and second order tensors for the oxygen atoms due to their considerably smaller scattering power. In the following, the results for the second order terms are discussed separately from the higher order expansion.

My First 10 Years as Artist/Holographer (1968-1977)

but structured patterns, reminiscent of Constructivist art, though my philosophy is unlike that of Constructivism [9]. Ultimately, Holos 17 (1973), a laser transmission hologram (Fig. 3), was the result. A concave hemisphere recorded in the first exposure was turned around in the darkness between exposures so that it became a convex hemisphere. When recorded in the second exposure, the convex hemisphere met the light pattern of the concave hemisphere, whereupon we had a complete sphere, not outlined as such but formed by its own laser light pattern. We intended to use the laser transmission holograms as exhibition pieces, with the best of them as masters for white-light transmission imagery that would project frontally. Although segments of the H 1 (master) pseudoscopic design could be seen from a distance of approximately 30 ft, which I found tantalizing (and have shown this way), the total HI image was too large to emerge through the H2 plates to be seen easily at a moderate distance. Furthermore, the second-generation white-light holograms seemed to have unfathomable problems other than size. After much searching, it was finally determined that the emulsion on the secondgeneration plates was defective (we had been using Agfa-Gevaert 8E75; as all holographers know, it is not unusual to receive a batch of plates with imperfect emulsion). Since we had to redo the H2s, we put Fig. 4. Equivocal Forks I, laser transmission hologram, plate 11x 14 in, pseudoscopic image projecting in front of the plate = 24 to 30 in, 1977. (Photo: Nisham Bichajian) Using a cluster of forks as the object, I placed much effort in the frontally projected imagery so that the glass would not be an obstruc-

The effect of transverse shear onto the singular solutions of a complete spherical shell

Green's functions for the field variables of a complete sphere subjected to normal surface traction are obtained with “free space” properties. Further, self-equilibrated singular solutions of the variables associated with tangentially applied point loads and concentrated surface moments are constructed. The solution formulae are derived within the framework of the improved theory of thin shells and thus incorporate the effect of transverse shear in the equilibrium of the shell element. Despite the complex character of the solution, expressed in terms of complex Legendre functions, the closed form of it reveals the effects of the new assumptions (presence of shear strains) onto the singular behavior of the associated kernels. Numerical results for the field variables demonstrate the differences between the two theories, classical and improved.

True three-dimensional cone-beam reconstruction (TTCR) algorithm

A true three-dimensional cone-beam reconstruction (TTCR) algorithm for direct volume image reconstruction from 2-D cone-beam projections is developed for the complete sphere geometry. The algorithm is derived from the parallel-beam true three-dimensional reconstruction (TTR) algorithm and is based on the modified filtered backprojection technique, which uses a set of 2-D space-invariant filters. The proposed algorithm proved to be superior in spatial resolution to the parallel-beam TTR algorithm and to offer better computational efficiency.

Dynamic buckling of imperfection-sensitive shell structures

Structural buckling under loads may occur at load levels that are less than the corresponding static loads. Presence of local geometric imperfections may induce an early buckling for both static and loadings. The phenomenon of dynamic weakening is studied for a general class of shell structures under a general class of time-dependent loadings. A doubly curved quadrilateral Love-Kirchhoff shell finite element is used. Geometric deviations of the shell middle surface are included within the element formulation by suitably modifying the strain-displacement relations. This is accomplished by retaining additional terms that are quadratic in spatial derivatives of imperfections and displacement components. The nonlinear equations of motion are written in the Lagrangian system and are solved by using an incremental algorithm based on Newmark's generalized operator. The responses up to buckling are obtained for a perfect spherical cap and an imperfect spherical cap both under external pressure, as well as a complete imperfect sphere under external pressure. Numerical results include the effects of amplitude of imperfection and thickness of shell on the buckling loads. The formulation is general and can be applied to obtain the buckling responses of a wide variety of shell structures.

Zero-Sets of Quaternionic and Octonionic Analytic Functions with Central Coefficients

We prove that the zero set of any quaternionic (or octonionic) analytic function f with central (that is, real) coefficients is the disjoint union of codimension two spheres in R4 or R8 (respectively) and certain purely real points. In particular, for polynomials with real coefficients, the complete root-set is geometrically characterisable from the lay-out of the roots in the complex plane. The root-set becomes the union of a finite number of codimension 2 Euclidean spheres together with a finite number of real points. We also find the preimages f−1 for any quaternion (or octonion) A. We demonstrate that this surprising phenomenon of complete spheres being part of the solution set is very markedly a special ‘real’ phenomenon. For example, the quaternionic or octonionic Nth roots of any non-real quaternion (respectively octonion) turn out to be precisely N distinct points. All this allows us to do some interesting topology for self-maps of spheres.

Characteristics of polymer microspheres prepared by radiation-induced polymerization in the presence of organic solvents

Radiation-induced polymerization of diethylene glycol dimethacrylate (2G) was carried out in methyl orthoformate (MOF) in the range of 25 to −78°C, to obtain the polymeric microspheres. A transparent solution consisting of 2G and MOF showed an emulsified state after irradiation. This means that the colloidal particles of poly(2G)are deposited from monomer solution during the irradiation because of poor solubility. It was confirmed by microscopic observation that the shape of obtained polymer is composed of a complete sphere. The particle size of poly(2G) microsphere obtained by 10 kGy irradiation at temperatures of 25, 0 and −43°C was found to be 1.55±0.54, 1.75±1.09, and 1.76±1.21 μm, respectively. No formation of the microsphere occurred when irradiated at −78°C. The preparation of poly(2G) microspheres was furter tried using various organic solvents under such conditions as 10 kGy and 25°C. According to this experiment, poly(2G) microspheres of the smallest size were obtained in the presence of ethyl caproate (0.70±0.25 μm), while the largest size was obtained when tetrahydrofuran was used (8.61±4.21 μm).

Extended formulation for Rayleigh-wave computations at high frequencies in a spherical layered earth

Summary. The earlier formulation of dispersion function, amplitude response and surface ellipticity for Rayleigh waves in a spherical layered earth has been extended by the reduced-delta matrix to avoid computational instability at high frequencies. We derive a modified formulation, where the layer thickness is kept separated during matrix multiplications. The present formulations are valid for an unlimited frequency range. A numerical experiment with single precision (six decimal digits accuracy) on an IBM 360/44 computer is performed at frequencies from 0.4 to 12.5 Hz on a Shield structure down to a depth of 1090 km below which a complete sphere is assumed. The experiment shows that both reduced-delta matrix and modified formulations generate roots of the dispersion equation without any reduction of layers. However, to avoid unnecessary computation, a layer-reduction procedure has been derived from a modified formulation when the contribution of deep layers becomes insignificant on surface waves.

A simple model for the acoustic cross section of sand grains

Previous work on determining the acoustic cross section of sand grains [Geophys. Res. Lett. 9(2), 175–178 (1982)] identified a problem with the application of the simple compressible sphere model for the cross section. Use of the complete elastic sphere model [J. Acoust. Soc. Am. 34, 1582–1592 (1962)] failed to remove the conflict with observation. Application of the bistatic cross-section theorem to the angle averaged cross section shows that the appropriate cross section is the total absorption cross section, not the backscatter cross section. The total absorption cross section for the fluid sphere model is found to be in semiquantitative agreement with scattering data for sand grains.

Added mass and damping of a sphere section in heave

The Norwegian wave-power buoy 1 consists of a half-immersed floating sphere which is open to the sea at the bottom end. It is a two degree-of-freedom device involving the independent motion of the outer rigid sphere and the pressure across the internal free surface. A simpler model of the device is to represent the oscillatory flow through the bottom opening as another rigid body motion being that of the curved surface which would complete the sphere. The wave-induced forces on this surface and also the outer spherical surface due to independent oscillations of either are determined semi-analytically using a simple extension of the method of Havelock, 2 recently simplified and generalised by Hulme, 3 for the complete half-immersed sphere. In particular the 2 × 2 added mass and damping matrices are determined as a function of frequency and relative size of bottom opening to sphere radius. These quantities are essential in any theoretical analysis of a multi-degree of freedom wave-energy device.