Empty Square Research Articles

Effect of the cross-sectional shape on crash behaviour of a three dimensional space frame

This paper addresses a design aspect of a front rail structure of an automobile body from the point of view of weight efficiency and energy absorption. Various ways of reinforcing the cross-section by an internal flange or diaphragm are investigated. The results are compared with a response of the empty square profile. Also, advantages of a full or partial internal reinforcing by means of aluminium foam of three different densities are assessed. It was shown through extensive numerical simulation that a diagonally positioned internal flange with suitable triggering dents can absorb four times more energy than a referred empty member. At the same time there is 3.4-fold increase in the specific energy absorption. Using the concept of foam filling with 3Mpa foam can still raise the above numbers to six and 3.67, respectively. The above results refer to extruded aluminium profiles.

TEMPERATURE FLUCTUATION MEASUREMENTS FOR TRANSITIONAL FLOW IN A SQUARE CHANNEL

The effect of a 6.35-mm-diameter cylindrical rod on the transitional flow in a 50.8-mm square channel has been investigated experimentally. A Chromel-Constanian thermocouple with 12,7-fim-diameter leads was used to measure the temperature fluctuations of slightly heated air (5°C) flowing in the channel, over the range of Reynolds number Re = 1,500-3,500. Without the rod, laminar-to-turbulent transition occurred at Re ≈ 2,500-3,500 in the empty square channel The rod destabilized the flow and advanced the onset of fluctuations profoundly. Within the wake of the rod, large fluctuations were detected. Temperature measurements also reviewed the existence of regular vortex shedding at Re = 1,500, and the development of the wake downstream of the rod. This study confirmed the feasibility of using a fine thermocouple for studying obstructed channel flow.

O(log logn)-time integer geometry on the CRCW PRAM

We study problems in computational geometry on PRAMs under the assumption that input objects are specified by points withO(logn)-bit coordinates, or, equivalently, with polynomially bounded integer coordinates. We show that in this setting many geometric problems can be solved in time O(log logn). The following five specific problems are investigated:closest pair of points, intersection of convex polygons, intersection of manhattan line segments, dominating set, andlargest empty square. Algorithms solving them are developed which operate in time O(log logn) on the arbitrary CRCW PRAM. The number of processors used is eitherO(n) orO(n logn).

Multipolar Expansions for Multiple Scattering Theory

ABSTRACTA simple derivation (based on a derived identity of integral equation theory) of fully separable, non–muffin–tin multiple scattering theory is presented. Three multipolar representations have been proposed for use in this theory: the original representation by Williams and Morgan, a more recent one by Brown and Ciftan, and a “Bloch periodic” representation by Badralexe and Freeman (which was addressed in earlier work). We study the properties of the Williams and Morgan representation in the context of the 2D empty square lattice, where the representation of Brown and Ciftan is manifestly exact and correct (so that MST derived in terms of it is a “natural” theory). We show that the representation of Williams and Morgan contains an explict divergence predicted by its implicit use of a wrong-order Green's function expansion but that MST expressed in terms of this representation is still a fairly good asymptotic approximation to the formally exact theory.

Synthesis and structure of [NMe4][CuPt(CN)4]: an infinite three-dimensional framework related to PtS which generates intersecting hexagonal channels of large cross section

[NMe4][CuPt(CN)4] contains an infinite 3D [CuIPtII(CN)4]nn– framework related to the PtS structure, which generates two mutually perpendicular and equivalent sets of hexagonal channels of large cross-section (largest Pt ⋯ Pt diagonal, 13.50 A) together with large empty square channels perpendicular to the hexagonal channels.

A niobium phosphate bronze with a tunnel structure: KNb 3P 3O 15

A new niobium monophosphate KNb 3P 3O 15 has been isolated. Its structure was solved from a single-crystal X-ray study in the space group Pnnm with the cell parameters: a = 13.3085(9), b = 14.7382(10), c = 6.4615(2)Å, and Z = 4. The refinement by full-matrix least-squares calculations led to R = 0.029 with 3184 independent reflections. The structure is built up from corner-sharing NbO 6 octahedra and PO 4 tetrahedra which delimit five-sided tunnels containing the K ions and empty square and triangular tunnels. These tunnels are like those observed in the tetragonal tungsten bronzes.

Percolation in an interactive cluster-growth model.

Interactions are included in the standard model of site percolation by specifying two numbers, ${p}_{0}$ and ${p}_{1}$, which are the probabilities of occupying a site on a lattice if none or at least one of the neighboring sites are occupied, respectively. This is expected to be a better description of systems where interactions between neighbors can either enhance or deter site occupation. Monte Carlo methods are used to simulate the irreversible growth of clusters starting from an empty two-dimensional square lattice, and continuing through the percolation threshold. The value of the percolation threshold ${p}_{c}$ and other properties of the system depend on the parameter r=${p}_{1}$/${p}_{0}$. For r=1, the system corresponds to random percolation. As r\ensuremath{\rightarrow}\ensuremath{\infty}, compact Eden clusters are produced, which link together to form larger, fractal clusters. As r\ensuremath{\rightarrow}0, neighboring sites become less easily occupied, resulting in checked ``domains'' separated by antiphase boundaries. Several quantities are analyzed to determine the critical exponents \ensuremath{\nu}, \ensuremath{\gamma}, and \ensuremath{\beta}, including the threshold distribution width, the mean cluster size, and the infinite cluster size. For all finite values of r, the data are found to be consistent with the exponents of random percolation.