Array Of Cubes Research Articles

Precision crystal corner cube arrays for optical gratings formed by (100) silicon planes with selective epitaxial growth

High-quality, micrometer scale, corner cube arrays were grown on (111) silicon substrates by selective epitaxial growth (SEG) techniques. Sixteen different arrays were produced that had periodic corner spacing ranging from 3 to 50 µm. The arrays were formed by suppressing silicon SEG in a regular geometric pattern, producing the three mutually perpendicular (100) smooth crystal planes. For coherent light of 633-nm wavelengtha sharp diffraction pattern of threefold symmetry was observed out to 7 maxima, as well as a retroreflection component.

Students' Understanding of Three-Dimensional Rectangular Arrays of Cubes

The present study extends previous research in this area by providing a more elaborate and theoretical description of students' solution strategies and errors in dealing with 3-D cube arrays. It describes several cognitive constructions and operations that seem to be required for students to conceptualize and enumerate the cubes in such arrays, exploring in depth general cognitive operations such as coordination, integration, and “structuring” as they are manifested in a spatial context. It describes how, in dealing with 3-D rectangular arrays, students' spatial thinking is related to their enumeration strategies. The findings suggest that students' initial conception of a 3-D rectangular array of cubes is as an uncoordinated set of faces. Eventually, as students become capable of coordinating views, they see the array as space filling and strive to restructure it as such. Those who complete a global restructuring of the array use layering strategies. Those in transition use strategies that indicate that their restructuring is local rather than global. Finally, the data suggest that many students are unable to enumerate the cubes in a 3-D array because they cannot coordinate the separate views of the array and integrate them to construct one coherent mental model of the array.

Students' Understanding of Three-Dimensional Rectangular Arrays of Cubes

Students' Understanding of Three-Dimensional Rectangular Arrays of Cubes

Plume dispersion through large groups of obstacles—A field investigation

A set of field experiments has been conducted at the Cardington experimental site, in the United Kingdom, to investigate the dispersion of a neutrally buoyant plume released upwind of an array of cubes, each of which measured approximately 2 m × 2 m × 2 m. The plume was released below the height of the obstacle array., and a second control plume was released alongside the array. The behaviour of the plume was recorded using both flow visualisation and measurements of gas concentration. A limited number of velocity measurements was also made. It is found that, relative to the control plume, certain mean concentration statistics do not change materially as the plume passes through the obstacle array. These include the form of the cross-sectional profiles, the decay along the centre line and the lateral growth with downstream distance. However, the mean vertical extent of the plume increases by 40–50%. In addition the r.m.s. fluctuations of concentration within the the plume are reduced. A clipped normal distribution is shown to be an appropriate model for the concentration fluctuations within the array plume.

Diffusion and convective dispersion through arrays of spheres with surface adsorption, diffusion, and unequal solute partitioning

The effective diffusivity (as well as convective dispersivity) of cubical arrays of neutrally buoyant spheres on whose surfaces solute adsorbs and subsequently diffuses is derived via macrotransport (i.e., generalized Taylor dispersion) theory. The role of unequal solute partitioning in the continuous and dispersed phases is also elucidated. Solute adsorption is shown to diminish the overall diffusivity of the suspension (emulsion), while—for a fixed surface adsorption—the consequence of increasing surface diffusivity is to enhance the emulsion's effective diffusivity. As expected, the role of unequal partitioning is to monotonically vary (as the dispersed-phase partition coefficient, K, ranges from 0 to 1) the magnitude of the effective diffusivity between the zero (nonconducting) and equal (conducting) partitioning cases. On the other hand, solute adsorption onto the surfaces of solid spheres whose centers are locked into the lattice points of a cubic array—through whose interstices a Newtonian fluid flows with mean (macroscopically homogeneous) interstitial velocity v ∗—measurably influences only the purely diffusive contribution to the convective dispersivity of the fixed bed, at least for highly porous beds and small to moderate Peclet and Reynolds numbers.

Properties and ways of calculation of multi-polarity generalized Walsh transforms

A new formulation of the multi-polarity generalized Walsh transform has been introduced. The formulation allows a uniform representation of Boolean functions by a set of orthogonal and generalized Walsh spectral coefficients. Forward and inverse transformation kernels and the method of recursive generation of transform matrices by using Kronecker products of elementary matrices have been given. Mutual relations among transform matrices and spectra for arbitrary polarities have been investigated. Fast forward and inverse generalized Walsh transforms have been developed. An algorithm to calculate the generalized Walsh transform from a cube array specification of incompletely specified Boolean functions has been shown. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The computer implementation drastically reduces the required time of computation by allowing calculation of only chosen coefficients in specified polarity. The entire spectrum-if required-can be computed incrementally for groups of coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electrorotation behavior of aggregated particles. A theoretical study

Electrorotation provides a convenient method for measuring the polarizability of single particles in suspensions as a function of the frequency of an applied rotating electric field. A theoretical description is given of the electrorotation behavior of a dielectric particle with an interior consisting of a large number of smaller particles. This hypothetical “aggregate” particle consist of a three-dimensional array of cubes separated by a uniform gap. The particle contains many smaller particles or vesicles, and since each vesicle represents a polarizable element we are able to describe the electric properties of the interior by averaging the dielectric behavior of the individual elements. Using this assumption we obtained the dielectric constant and the conductivity of the interior of the particle as frequency-dependent parameters. The intensity of aggregation was expressed by the dielectric parameters in the gap between the particles. The theoretical model was used to interpret the behavior of an exocytotic cell, an aggregate of cells and an aggregate of droplets (either water in oil or oil in water).

Bounds to the conductivity of some two-component composites

Calculation of third-order bounds to the conductivity of isotropic two-component composites is discussed. Coincidence of the Beran bounds and bounds derived using trial fields based on the solution of a single-body electrostatic boundary-value problem is demonstrated for a random distribution of impenetrable ellipsoids. This extends a proof of Beasley and Torquato [J. Appl. Phys. 60, 3576 (1986)]. A structural parameter related to third-order bounds is calculated for a face-centered cubic array of cubes in a matrix. For an array of rectangular blocks an upper bound in one direction is derived. This bound, and its two-dimensional analogs, become very sharp in the limit of strong inhomogeneity. Improved third- and fourth-order bounds for the three-dimensional checkerboard are presented.

INERTIAL COUPLING IN DISPERSED POTENTIAL FLOW—USE OF THE METHOD OF IMAGES

Abstract Net first and second dipole reflections are computed for several finite and infinite arrays of cylinders or spheres held stationary in a uniform potential flow. The polarizability and resistivity, from which the macroscopic properties of a two-phase flow with corresponding microstructure can be derived, are deduced for the infinite arrays. Finite arrays resemble infinite ones apart from edge and end effects, which are small for some geometries. The added mass coefficient for a regular monolayer of spheres is obtained and shown to be very close to Smythe's (1964) solution for a sphere in a circular tube. Similar agreement is obtained between the solutions for a cubical array of spheres and for a row of spheres in a circular tube.

Significance of Local Group Combustion Number Introduced.

For sprays of practical interest, the region where vigorous vaporization occurs is confined to a thin layer on their outer edges. The cubical array of droplets occupying a semi-infinite space provides a microscopic prototype to investigate this vaporization layer structure, upon which interactive droplet vaporization/combustion characteristics are examined to derive rational boundary conditions to be imposed at the spray edge when the spray is regarded as a continuum medium on large scales. It is found that not only the local droplet number density but also the gas-to-liquid density ratio plays an important role in excitation of prevailing vaporization/combustion modes, leading to their criteria in terms of the droplet separation distance as a function of the gas-to-liquid density ratio.

Effective computer methods for the calculation of Rademacher-Walsh spectrum for completely and incompletely specified Boolean functions

A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON- and DC-cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from nondisjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The programs for both algorithms use advantages of C language to speed up the execution. The comparison of different versions of the algorithm has been carried out. The algorithm and its implementation provide the fastest and most comprehensive program (having many options) known to the authors for the calculation of the Rademacher-Walsh transform. It successfully overcomes all drawbacks in the calculation of the transform from the design automation system based on spectral method-the SPECSYS system from Drexel University, which uses fast Walsh transform.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Shear flow of periodic arrays of particle clusters: a boundary-element method

The boundary-element method is used to solve Stokes equations for periodic arrays of force-free and torque-free rigid particles. Simple cubic arrays of spheres, spheroids, cubes, and clusters of spheres are subjected to a bulk simple shearing flow. The effective volume-averaged stress tensor for the suspension and the detailed velocity and stress fields throughout the Newtonian suspending fluid are calculated. We find that even crude meshes give very good volume-averaged results, but fine meshes are required to track local minima and maxima in the stress field. For simple cubic arrays of spheres, the boundary-element results are in excellent agreement with the analytical viscosity predictions of Nunan &amp; Keller (1984). Even at the highest concentration of solids studied, no significant normal stress differences were observed, in agreement with Nunan &amp; Keller's results (1984). Up to moderate concentrations of particles, the volume-averaged properties of the suspension display only a weak dependence on the particle geometry. Suspensions of spheroids and cubes behave approximately as suspensions of spheres on the average despite large differences in the local micromechanics of stress and velocity fields. Simple cubic arrays of clusters of spheres tend to behave on a macroscopic level as a cubic array of spheres whose effective volume fraction is about 150% of the total volume fraction of the spheres in the clusters.

Modelling characteristic properties of sandstones

A computer model of a porous medium is described. Written in FORTRAN, it consists of a three-dimensional array of cubes and cylinders representing pores and throats, respectively. The pore-size distribution (p.s.d.) is calculated from the mercury porosimetry curve of Clashac outcrop sandstone, a relatively clay-free, well characterised rock. Surface area and porosity are calculated from the program and the original porosimetry curve is simulated as a check of the p.s.d. Fifty values of the tortuosity factor of the sandstone are then simulated via a weighted random walk through the model. The tortuosity is then defined as the median of the resulting distribution. The tortuosity is simulated for two different cases of an assumed potential field.

ChemInform Abstract: Superdense Carbon, C8: Supercubane or Analogue of γ‐Si?

AbstractA new crystalline allotrope of carbon, "C8", which has recently been claimed, following research on the plasma deposition of thin carbon films, and which is reported to consist of a body‐centered cubic array of C8 cubes and termed "supercubane", is reinvestigated by means of a structural analysis combined with extended Hueckel band calculations.

The structure of GP zones in Cu-10.9 at.% Be

For a series of aging treatments at 538 K of a single crystal of Cu-10.9 at.% Be, the absolute diffuse X-ray intensity was measured with a wavelength of 1.4 Å, in a volume in reciprocal space sufficient to separate the contributions from clustering and those from atomic displacements. The zones are a mixture of Be-rich single and multilayered {100} planes. As aging proceeds, the zones increase in thickness and diameter. The nearest Cu planes collapse toward the zones, but subsequent planes are further away than the average interplanar distance. These displacements fall to zero 5–7 layers into the matrix. The {110} 〈11̄0〉 shear strain in the zones is ~0.05. The stair-step arrangement of these regions reported previously is supported, and this is inherited from the 〈11̄0〉 alignment of the ellipsoidal clusters present in the as-quenched condition. The γ″ phase, which appears in addition to GP zones for long aging times, is a monoclinic ordered Cu-Be array which arises from a distortion of four b.c.t. cells in the f.c.c. matrix. The shear strain in this phase is ~0.08 on the {110} 〈11̄0〉 system.

High rejection ruby filter for laser light scattering experiments

A rejection filter against stray ruby laser light in scattering experiments is described. It consists of an array of sixty-four ruby crystal cubes with a doping of up to 2.3 wt. % of chromium oxide. The filter is 15 mm thick. Suppression factors of more than 10(6) are achieved with individual cubes (5 x 5 x15 mm(3)), the effective overall suppression of the assembled array being 10(4). The filter facilitates Raman calibration of the lidar Thomson scattering system of the JET tokamak.

Visuospatial tasks compared via activation of regional cerebral blood flow

Regional cerebral blood flow was measured in 19 subjects during the performance of three tasks thought to primarily involve right hemisphere processing: judgement of line orientation, mental rotation of three-dimensional cube arrays, and a fragment puzzle task. Asymmetries in hemispheric flow (right side greater) were only observed in the line orientation and rotation conditions and were present in both sexes. The magnitude of the asymmetry was greater in the rotation task which also showed an asymmetry in parietal flow. Thus mental rotation placed the most asymmetric demand on cerebral resources. This provides a task that more reliably activates the right hemisphere than those previously reported and suggests a truly “mental manipulative” aspect to right hemisphere advantage in visuospatial performance.

Magnetostatic interaction fields for a three-dimensional array of ferromagnetic cubes

An exact analytic formula for the magnetostatic interaction energy of a three-dimensional array of ferromagnetic cubes is presented. The magnetization within each cube is assumed constant but varies in direction from cube to cube. From the expressions for the interaction energy, exact formulas for the effective magnetostatic interaction field are derived. This provides a useful tool for three-dimensional micromagnetic calculations.

Some covering problems and their solutions in automatic logic synthesis systems

This paper describes the partitioning of the set of the Boolean equations generated by the hardware logic translator and the conversion of the subsets into cube arrays. Subsequent to this, it is aimed: (1) to find out the minimal sets of input variables; (2) to finish the logic minimization; and (3) to decompose a large logic array into smaller ones to meet the design constraints if necessary.

TFTR Lithium Blanket Module Component Development, Testing and Fabrication

A lithium blanket module (LBM), representative of a fusion reactor blanket module has been fabricated by GA Technologies Inc. via sub contract from Princeton Plasma Physics Lab under the sponsorship of the Electric Power Research Institute. The LBM consists of a cubical array of 92 cylindrical breeder rods, 2.54 cm in diameter. Each rod consists of an ∼59 cm long section of lithium oxide pellets clad in 0.03 cm wall Type 316 stainless steel tube followed by a 20 cm long stainless steel reflector rod. Reusable test rods in the 20 cm diameter central region incorporate activation foils for neutron dosimetry and aluminum clad pellets for tritium dosimetry. The breeder rods are contained in an enclosure structure which has provisions for insertion and removal of test rods and dosimeter wires. Procedures developed for fabrication and assembly of the rods and enclosure structure proved to be satisfactory and reliable and the work was done on schedule and within budget.