Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

Expansion-based algorithms for finding single pair shortest path on surface

Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorithms must traverse the entire polyhedral surface. With the rapid advance in areas like Global Positioning System (CPS), Computer Aided Design (CAD) systems and laser range scanner, surface models axe becoming more and more complex. It is not uncommon that a surface model contains millions of polygons. The single pair shortest path problem is getting harder and harder to solve. Based on the observation that the single pair shortest path is in the locality, we propose in this paper efficient methods by excluding part of the surface model without considering them in the search process. Three novel expansion-based algorithms are proposed, namely, Naive algorithm, Rectangle-based Algorithm and Ellipse-based Algorithm. Each algorithm uses a two-step approach to find the shortest path. (1) compute an initial local path. (2) use the value of this initial path to select a search region, in which the global shortest path exists. The search process terminates once the global optimum criteria are satisfied. By reducing the searching region, the performance is improved dramatically in most cases.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

On a Two-Dimensional Search Problem

In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.

Data structures for highly efficient querying of spatial data

The virtual quadrilateral is the coalescence of novel data structures that reduces the storage requirements of spatial data without jeopardizing the quality and operability of the inherent information. The data representative of the observed area is parsed to ascertain the necessary contiguous measures that, when contained, implicitly define a quadrilateral. The virtual quadrilateral then represents a geolocated area of the observed space where all of the measures are the same. The area, contoured as a rectangle, is pseudo-delimited by the opposite coordinates of the bounding area. Once defined, the virtual quadrilateral is representative of an area in the observed space and is represented in a database by the attributes of its bounding coordinates and measure of its contiguous space. Virtual quadrilaterals have been found to ensure a lossless reduction of the physical storage, maintain the implied features of the data, facilitate the rapid retrieval of vast amount of the represented spatial data and accommodate complex queries. The methods presented herein demonstrate that virtual quadrilaterals are created quite easily, are stable and versatile objects in a database and have proven to be beneficial to exigent spatial data applications such as geographic information systems. ^

Aboveground plant biomass from the Jena Experiment (Monocultures, year 2010)

This data set contains aboveground plant biomass in 2010 (Sown plant community, Weed plant community, Dead plant material, and Unidentified plant material; all measured in biomass as dry weight) of the monoculture plots of a large grassland biodiversity experiment (the Jena Experiment). In the monoculture plots the biomass of the sown plant community contains only a single species per plot and this species is a different one for each plot. Which species has been sown in which plot is stated in the plot information table for monocultures (see further details below). The monoculture plots of 3.5 x 3.5 m were established for all of the 60 plant species of the Jena Experiment species pool with two replicates per species. One of the replicate plots per species was given up after the vegetation period of 2007 for all but the nine species belonging also to the so called dominance experiment in Jena. These nine species are: Alopecurus pratensis, Anthriscus sylvestris, Arrhenatherum elatius, Dactylis glomerata, Geranium pratense, Poa trivialis, Phleum pratense, Trifolium repens and Trifolium pratense.In 2010 plot size was reduced to 1 x 1 m. These 60 species comprising the species pool of the Jena Experiment belong to four functional groups (grasses, legumes, tall and small herbs). Plots were sown in May 2002 and are since maintained by bi-annual weeding and mowing. Aboveground plant biomass was harvested twice in 2010 just prior to mowing (during peak standing biomass in early June and in late August) on all experimental plots of the monocultures. This was done by clipping the vegetation at 3 cm above ground in 1 rectangle of 0.2 x 0.5 m per plot. The location of this rectangle was in the center of the plot area. The positions of the rectangles within plots were identical for all plots. The harvested biomass was sorted into categories: sown plant species, weed plant species (species not sown at the particular plot), detached dead plant material (i.e., dead plant material in the data file), and remaining plant material that could not be assigned to any category (i.e., unidentified plant material in the data file). All biomass was dried to constant weight (70°C, >= 48 h) and weighed.

TRIPPy: Trailed Image Photometry in Python

Photometry of moving sources typically suffers from a reduced signal-to-noise ratio (S/N) or flux measurements biased to incorrect low values through the use of circular apertures. To address this issue, we present the software package, TRIPPy: TRailed Image Photometry in Python. TRIPPy introduces the pill aperture, which is the natural extension of the circular aperture appropriate for linearly trailed sources. The pill shape is a rectangle with two semicircular end-caps and is described by three parameters, the trail length and angle, and the radius. The TRIPPy software package also includes a new technique to generate accurate model point-spread functions (PSFs) and trailed PSFs (TSFs) from stationary background sources in sidereally tracked images. The TSF is merely the convolution of the model PSF, which consists of a moffat profile, and super-sampled lookup table. From the TSF, accurate pill aperture corrections can be estimated as a function of pill radius with an accuracy of 10 mmag for highly trailed sources. Analogous to the use of small circular apertures and associated aperture corrections, small radius pill apertures can be used to preserve S/Ns of low flux sources, with appropriate aperture correction applied to provide an accurate, unbiased flux measurement at all S/Ns.

Approximation limits of linear programs (beyond hierarchies)

We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^1/2-ε)-approximations for CLIQUE require LPs of size 2^nΩ(ε). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov's [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.

Stilling Basin Scour Remediation Using Air Injection and Flat Plate Extension

The South Florida Water Management District (SFWMD) is responsible for managing over 2500 miles of waterways and hundreds of water control structures. Many of these control structures are experiencing erosion, known as scour, of the sediment downstream of the structure. Laboratory experiments were conducted in order to investigate the effectiveness of two-dimensional air diffusers and plate extensions (without air injection) on a 1/30 scale model of one of SFWMD gated spillway structures, the S65E gated spillway. A literature review examining the results of similar studies was conducted. The experimental design for this research was based off of previous work done on the same model. Scour of the riverbed downstream of gated spillway structures has the potential to cause serious damage, as it can expose the foundation of the structure, which can lead to collapse. This type of scour has been studied previously, but it continues to pose a risk to water control structures and needs to be studied further. The hydraulic scour channel used to conduct experiments contains a head tank, flow straighteners, gated spillway, stilling basin, scour chamber, sediment trap, and tailwater tank. Experiments were performed with two types of air diffusers. The first was a hollow, acrylic, triangular end sill with air injection holes on the upstream face, allowing for air injection upstream. The second diffuser was a hollow, acrylic rectangle that extended from the triangular end sill with air injection holes in the top face, allowing for vertical air injection, perpendicular to flow. Detailed flow and bed measurements were taken for six trials for each diffuser ranging from no air injection to 5 rows of 70 holes of 0.04" diameter. It was found that with both diffusers, the maximum amount of air injection reduced scour the most. Detailed velocity measurements were taken for each case and turbulence statistics were analyzed to determine why air injection reduces scour. It was determined that air injection reduces streamwise velocity and turbulence. Another set of experiments was performed using an acrylic extension plate with no air injection to minimize energy costs. Ten different plate lengths were tested. It was found that the location of deepest scour moved further downstream with each plate length. The 32-cm plate is recommended here. Detailed velocity measurements were taken after the cases with the 32-cm plate and no plate had reached equilibrium. This was done to better understand the flow patterns in order to determine what causes the scour reduction with the extension plates. The extension plate reduces the volume of scour, but more importantly translates the deepest point of scour downstream from the structure, lessening the risk of damage.