Geometric Weight Research Articles

Analysis of frictional properties of cereal seeds

The thickness, width, length and weight of cereal seeds (wheat, rye, barley, oats and triticale) and their external friction angles on three types of surfaces – steel, methyl polyacrylate and rubber – were determined. The experiment was performed with the use of a new device that measures the angle of external friction and the time taken by seeds to travel a given distance, which supports the determination of the coefficient of kinetic friction. The measured parameters were used to calculate arithmetic and geometric mean diameter, aspect ratio, sphericity index, specific weight, volume and density of seeds. The correlations between the analyzed parameters were evaluated by analysis of variance, correlation analysis and linear regression analysis. The dimensions, weight and the calculated indicators of the examined seeds did not affect their angles of friction or the coefficients of static and kinetic friction. The studied parameters were significantly influenced by the type of friction surface, and significantly lower average values were reported for the steel surface. An inversely proportional correlation between static and kinetic friction coefficients was also observed for the steel surface. Key words: Physical attributes, coefficient of external friction, correlation.

Statistical Theory of Materials with Nanoscale Phase Separation

Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations. A general approach is described for treating statistical properties of such materials with nanoscale phase separation. Averaging over the random phase configurations, it is possible to reduce the problem to the set of homogeneous phase replicas, with additional equations defining the geometric weights of different phases in the mixture. The averaging over phase configurations is mathematically realized as the functional integration over the manifold indicator functions. This procedure leads to the definition of an effective renormalized Hamiltonian taking into account the existence of competing phases. Heterophase systems with mesoscopic phase separation can occur for different substances. The approach is illustrated by the model of a high-temperature superconductor with non-superconducting admixture and by the model of a ferroelectric with paraelectric random inclusions.

Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

AbstractWeighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semi-implicit integration factor method to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.

Sin2ψ-based residual stress gradient analysis by energy-dispersive synchrotron diffraction constrained by small gauge volumes. I. Theoretical concept

The influence of the gauge volume size and shape on the analysis of steep near-surface residual stress gradients by means of energy-dispersive synchrotron diffraction is studied theoretically. Cases are considered where the irradiated sample volume is confined by narrow-slit systems, in both the primary and the diffracted beam, to dimensions comparable to the `natural' 1/einformation depth τ1/eof the X-rays. It is shown that the ratio between τ1/e, defined by the material's absorption, and the immersion depthhGVof the gauge volume into the sample is the crucial parameter that shapes thedψhklor ∊ψhklversussin2ψ distributions obtained in the Ψ mode of X-ray stress analysis. Since the actual information depth 〈z〉GVto which the measured X-ray signal has to be assigned is a superposition of geometrical and exponential weighting functions, ambiguities in the conventional plot of the Laplace stressesversus〈z〉GVmay occur for measurements performed using narrow-slit configurations. To avoid conflicts in data analysis in these cases, a modified formalism is proposed for the evaluation of the real space residual stress profiles σ||(z), which is based on a two-dimensional least-squares fit procedure.

Installation and Removal Records of Field Trials for Two Mooring Dolphin Platforms with Three Suction Caissons

In 1999, two mooring dolphin platforms (MDP1 and MDP2), each with three suction caissons, were installed in the JZ9–3 field of the Bohai Sea of China. Before installation, penetration and retrieval tests for MDP1 were conducted near the design location site. In 2006, after being in service for 7 years, partial removal and repenetration prototype trials were performed for MDP2. The MDP1 platform has the same geometric structure and weight as MDP2, in which each suction caisson is 6 m in diameter and 9 m in height. Typical soil profiles at the site mainly consist of organic silt, silty clay, and clay. Records from the transducers were relevant to the installation and retrieval of the suction caissons, which were performed by controlling the pump discharge into/out of the caissons. The results show that skin friction decreases because of the seepage effect that occurs after applying the suction pressure inside the caisson. However, clayey or silty soils with low permeability required more time and suction to create a seepage flow to lower resistance in the penetration or removal phases. The setup effect caused by suction significantly increases the skin friction resistance by 62–84%, and the pump-out pressure equals 1.79–2.04 times the pump-in suction after 7 years. The on-site data are valuable for further study on the design and construction of platforms with suction caissons, especially regarding external skin friction.

Brownian Gibbs property for Airy line ensembles

Consider a collection of N Brownian bridges \(B_{i}:[-N,N] \to \mathbb{R} \), B i (−N)=B i (N)=0, 1≤i≤N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak limit as N→∞ of the collection of curves scaled so that the point (0,21/2 N) is fixed and space is squeezed, horizontally by a factor of N 2/3 and vertically by N 1/3. If a parabola is added to each of the curves of this scaling limit, an x-translation invariant process sometimes called the multi-line Airy process is obtained. We prove the existence of a version of this process (which we call the Airy line ensemble) in which the curves are almost surely everywhere continuous and non-intersecting. This process naturally arises in the study of growth processes and random matrix ensembles, as do related processes with “wanderers” and “outliers”. We formulate our results to treat these relatives as well.Note that the law of the finite collection of Brownian bridges above has the property—called the Brownian Gibbs property—of being invariant under the following action. Select an index 1≤k≤N and erase B k on a fixed time interval (a,b)⊆(−N,N); then replace this erased curve with a new curve on (a,b) according to the law of a Brownian bridge between the two existing endpoints (a,B k (a)) and (b,B k (b)), conditioned to intersect neither the curve above nor the one below. We show that this property is preserved under the edge-scaling limit and thus establish that the Airy line ensemble has the Brownian Gibbs property.An immediate consequence of the Brownian Gibbs property is a confirmation of the prediction of M. Prähofer and H. Spohn that each line of the Airy line ensemble is locally absolutely continuous with respect to Brownian motion. We also obtain a proof of the long-standing conjecture of K. Johansson that the top line of the Airy line ensemble minus a parabola attains its maximum at a unique point. This establishes the asymptotic law of the transversal fluctuation of last passage percolation with geometric weights. Our probabilistic approach complements the perspective of exactly solvable systems which is often taken in studying the multi-line Airy process, and readily yields several other interesting properties of this process.

Geometric Distribution Weight Information Modeled Using Radial Basis Function with Fractional Order for Linear Discriminant Analysis Method

Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance.

Contorting a heavy and naturally curved elastic rod

We investigate how the configurations obtained from the writhing of a heavy elastic rod are influenced by its intrinsic natural curvature. To this end, we perform a combination of numerics and precision model experiments on the compression or twisting of a thin rod. The ‘softness’ of these single elastic filaments stems from their slenderness (high aspect ratio), which allow for geometrically nonlinear compliant modes that can accommodate large deformations. We uncover the original mechanism that the presence of a body force (gravity in our case) delays the effect of natural curvature, which results from the complex interplay between geometrical constraints, elasticity and weight. We rationalize our experimental results by coupling the predictive power of a numerical method of our own, with classic theory for elastic rods under large deformations. This preponderance of geometry is relevant in systems over a wide range of length scales where curvature and body-forces often co-exist; from engineered rod-like structures such as wires, cables, and pipelines, to natural macromolecules, flagella, fibers and tendrils.

718: First trimester maternal weight in USA continues to rise

Mark Evans, Terrence Hallahan, Hsiao-Pin Liu, Jon Carmichael, David Krantz Comprehensive Genetics, Genetics, New York, NY, Perkin Elmer, NTD Labs, Melville, NY OBJECTIVE: To determine whether the average weight of pregnant women continues to increase between 2003 and 2011. STUDY DESIGN: First trimester maternal weight (MW) data (lb) were evaluated on 1,677,116 patients, collected as part of first trimester aneuploidy screening conducted between 2003 and 2011. The study population was 65% Caucasian, 12% Hispanic, 10% African American, 7% Asian, 3% Asian Indian and 3% other ethnic Groups. If a patient had more than one test during this time period data from one of their tests was selected at random. Geometric mean maternal weight values were adjusted for age, gestational age at time of test and ethnicity by determining the least-squares means based on ANOVA using log-transformed weight values. The adjusted geometric mean maternal weight values were then regressed against time (with standard error of the coefficients adjusted for autocorrelation and number of patients during each time period). RESULTS: Overall over the study time period, the average weight of the total population increased by 4.0% while the increase in the top 10% group was 7.3%. A majority of the increase occurred from 2003 to 2007 (3.0% and 4.7% for the total population and top 10%, respectively). Regression analysis determined that the increase was not linear but rather followed a polynomial quadratic pattern for both the overall population as well as the top 10% (P value of the quadratic term 0.001 for both overall and top 10% of the population). CONCLUSION: The continuous increase in the mean MW particularly the top 10% is of significant concern because of increased rate of pregnancy complications, more difficult ultrasound examinations, reduced fetal fraction of DNA leading to poorer performance of NIPT testing and the need to ensure that weight adjustment formulas used for aneuploidy screening are still applicable. The slowing of the trend in the increase in MW needs to be studied but is a positive sign for public health.

The Diet of Breeding Brown Falcons (Falco berigora) In the Canberra Region, Australia, With Comparisons To Other Regions

Brown Falcons (Falco berigora) are generalist predators that take prey from a range of different taxonomic groups. Further, this species is one of the most widespread raptors in Australasia, providing great scope for dietary flexibility. However, few studies have reported on the diet of this species, and none in any detail for the relatively dry, continental climate of the Canberra region of southeastern Australia. We therefore examined this species' diet from 29 collections of prey remains and pellets from 20 nesting territories over five breeding seasons of Brown Falcon pairs breeding within 40 km of Canberra in 2002–06 and again in 2009. A total of 307 prey items was recorded, 15 of which were novel for this species. These novel prey items largely reflected locally common species that were of a similar size and niche to prey previously recorded in other regions, such as a new prey species of quail or beetle. Unusual prey included garden snails (Helix aspersa) and an owl, the Southern Boobook (Ninox novaeseelandiae). Other infrequently captured prey items such as freshwater molluscs (Corbicula australis and Glyptophysa gibbosa) and crayfish (Cherax sp.) illustrated the extraordinary dietary flexibility of Brown Falcons. In comparison with previous detailed studies, Canberra-based pairs had a relatively small geometric mean prey weight of 7.7 g, and tended to take a higher proportion of invertebrates across a relatively narrow niche breadth. When biomass was considered, rabbits (Oryctolagus cuniculus) were an important food source, making up half of the total biomass in the diet.

Solution of Multimaterial Equilibrium Radiation Diffusion Problems by using the Discontinuous Galerkin Method

The discontinuous Galerkin method is used for solving the two-dimensional equilibrium radiation diffusion equation. We construct the weighted interior penalty method based on the geometric average weight. The semi-implicit integration factor method is applied to the nonlinear ordinary differential equations obtained by the discontinuous Galerkin spatial discretization. Numerical results are presented to demonstrate the validity and reliability of using the discontinuous Galerkin method for solving the highly nonlinear radiation diffusion equation.

Core density gradient fluctuation measurement by differential interferometry in the helically symmetric experiment stellarator

The interferometer system on the Helically Symmetric eXperiment (HSX) stellarator uses an expanded beam and linear detector array to realize a multichord measurement. Unlike conventional interferometry which determines the plasma phase shift with respect to a reference, directly evaluating the phase between two adjacent chords can be employed to measure the change in plasma phase with impact parameter. This approach provides a measure of the equilibrium density gradient or the density gradient fluctuations and is referred to as differential interferometry. For central chords, measurements are spatially localized due to a geometrical weighting factor and can provide information on core density gradient fluctuations. The measurement requires finite coherence between fluctuations in the two spatially offset chords. This technique is applied on the HSX stellarator to measure both broadband turbulence and coherent modes. Spatial localization is exploited to isolate core turbulence changes associated with change in magnetic configuration or heating location.

Scaling for a one-dimensional directed polymer with boundary conditions

We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with exponential or geometric weights is special among growth models, namely, both permit explicit calculations. With appropriate boundary conditions, the polymer with log-gamma weights satisfies an analogue of Burke's theorem for queues. Building on this, we prove the conjectured values for the fluctuation exponents of the free energy and the polymer path, in the case where the boundary conditions are present and both endpoints of the polymer path are fixed. For the polymer without boundary conditions and with either fixed or free endpoint, we get the expected upper bounds on the exponents.

On the numerical range of the weighted shift operators with geometric and harmonic weights

On the numerical range of the weighted shift operators with geometric and harmonic weights

Optimized partial semicoarsening multigrid algorithm for heat diffusion problems and anisotropic grids

The purpose of this work is to reduce the CPU time necessary to solve three two-dimensional linear diffusive problems governed by Laplace and Poisson equations, discretized with anisotropic grids. The Finite Difference Method is used to discretizate the differential equations with central differencing scheme. The systems of equations are solved with the lexicographic and red–black Gauss–Seidel methods associated to the geometric multigrid with correction scheme and V-cycle. The anisotropic grids considered have aspect ratios varying from 1/1024 up to 16,384. Four algorithms are compared: full coarsening, semicoarsening, full coarsening followed by semicoarsening and partial semicoarsening. Three new restriction schemes for anisotropic grids are proposed: geometric half weighting, geometric full weighting and partial weighting. Comparisons are made among these three new schemes and some restriction schemes presented in literature: injection, half weighting and full weighting. The prolongation process used is the bilinear interpolation. It is also investigated the effects on the CPU time caused by: the number of inner iterations of the smoother, the number of grids and the number of grid elements. It was verified that the partial semicoarsening algorithm is the fastest. This work also provides the optimum values of the multigrid components for this algorithm.

Geogenic control on soil chemistry in urban areas: A novel method for urban geochemical mapping using parent material classified data

The purpose of the study reported here is to assess whether it may in some circumstances be useful and appropriate to use a parent material (PM) soil chemistry mapping method developed for national soil chemistry data to portray spatial variation in urban soil chemistry data in Great Britain. Analysis of variance (ANOVA) of the urban soil data suggests that spatial interpolation of soil ambient background concentrations (ABCs) using PM classified soil data may be justified for those elements with strong geogenic control. The PM soil chemistry mapping method for urban soil data is demonstrated using data from the Northampton urban area, in the English Midlands. Geometric mean (GM) and inverse distance weighting (IDW) interpolations based on the nearest four topsoil samples were evaluated. Independent validation indicated that for As, Cr, Fe and to a lesser extent K, which all exhibit relatively strong geogenic control in the Northampton urban area: (i) the PM soil chemistry mapping method is more accurate and effective than the conventional IDW grid mapping and (ii) PM soil chemistry mapping based on the average of the nearest four Lne element concentrations is more accurate than mapping based on IDW values calculated from the nearest four Lne element concentrations. The variation in effectiveness of the methods can be explained by the fact that PM exerts a significant control on As, Cr, Fe and K in the Northampton area whereas anthropogenic inputs appear to be the dominant control on the spatial variation of Pb, especially at high concentrations. The PM mapping method would be expected to work efficiently in other urban areas and for those elements where a significant proportion of the variation can be explained by PM.

The combined influence of multiple sex and growth hormones on risk of postmenopausal breast cancer: a nested case-control study

IntroductionSex and growth hormones are positively associated with postmenopausal breast cancer risk. However, few studies have evaluated the influence of multiple hormones simultaneously.MethodsWe considered the roles of estrone, estradiol, estrone sulfate, testosterone, androstenedione, dehydroepiandrosterone (DHEA), DHEA sulfate and prolactin and, secondarily, insulin-like growth factor 1 (IGF-1) and c-peptide in postmenopausal breast cancer risk among 265 cases and 541 controls in the prospective Nurses' Health Study. We created several hormone scores, including ranking women by the number of hormones above the age- and batch-adjusted geometric mean and weighting hormone values by their individual associations with breast cancer risk.ResultsWomen in the top versus bottom quintile of individual estrogen or androgen levels had approximately a doubling of postmenopausal breast cancer risk. Having seven or eight compared to zero hormones above the geometric mean level was associated with total (RR = 2.7, 95% CI = 1.3 to 5.7, P trend < 0.001) and estrogen receptor (ER)-positive (RR = 3.4, 95% CI = 1.3 to 9.4, P trend < 0.001) breast cancer risk. When comparing the top versus bottom quintiles of the score weighted by individual hormone associations, the RR for total breast cancer was 3.0 (95% CI = 1.8 to 5.0, P trend < 0.001) and the RR for ER-positive disease was 3.9 (95% CI = 2.0 to 7.5, P trend < 0.001). The risk further increased when IGF-1 and c-peptide were included in the scores. The results did not change with adjustment for body mass index.ConclusionsOverall, the results of our study suggest that multiple hormones with high circulating levels substantially increase the risk of breast cancer, particularly ER-positive disease. Additional research should consider the potential impact of developing risk prediction scores that incorporate multiple hormones.

Radiative transfer in a semi-transparent medium enclosed in a cylindrical annulus

An exact analytical description of the internal radiative field inside an emitting–absorbing grey semi-transparent medium at radiative equilibrium, enclosed in a cylindrical annular cavity bounded by hot and diffusely reflecting surfaces is proposed. It is shown that the radiative field can be completely described by purely geometrical weighting coefficients which allow determining the temperature field for any combined heat transfer with radiation, so as the two-dimensional vectorial radiative flux field. It is worth noting that no ray effect occurs since the only numerical discretization is purely spatial. Some examples show that the proposed method gives perfectly smooth results of good accuracy for both the temperature and flux fields inside the medium.

Simulation and Modeling of Self-Assembled Monolayers of Carboxylic Acid Thiols on Flat and Nanoparticle Gold Surfaces

Quantitative analysis of the 16-mercaptohexadecanoic acid self-assembled monolayer (C16 COOH-SAM) layer thickness on gold nanoparticles (AuNPs) was performed using simulation of electron spectra for surface analysis (SESSA) software and X-ray photoelectron spectroscopy (XPS) experimental measurements. XPS measurements of C16 COOH-SAMs on flat gold surfaces were made at nine different photoelectron emission angles (5-85° in 10° increments), corrected using geometric weighting factors and then summed together to approximate spherical AuNPs. The SAM thickness and relative surface roughness (RSA) in SESSA were optimized to determine the best agreement between simulated and experimental surface composition. On the basis of the glancing-angle results, it was found that inclusion of a hydrocarbon-contamination layer on top the C16 COOH-SAM was necessary to improve the agreement between the SESSA and XPS results. For the 16 COOH-SAMs on flat Au surfaces, using a SAM thickness of 1.1 Å/CH(2) group, an RSA of 1.05, and a 1.5 Å CH(2)-contamination overlayer (total film thickness = 21.5 Å) for the SESSA calculations provided the best agreement with the experimental XPS data. After applying the appropriate geometric corrections and summing the SESSA flat-surface compositions, the best fit results for the 16 COOH-SAM thickness and surface roughness on the AuNPs indicated a slightly thinner overlayer with parameters of 0.9 Å/CH(2) group in the SAM, an RSA of 1.06 RSA, and a 1.5 Å CH(2)-contamination overlayer (total film thickness = 18.5 Å). The 3 Å difference in SAM thickness between the flat Au and AuNP surfaces suggests that the alkyl chains of the SAM are slightly more tilted or disordered on the AuNP surfaces.

Dynamic Analysis for Robotic Integration of Tooling Systems

This paper presents a dynamic analysis method for robotic integration of tooling systems. This development is motivated by the fact that many modern robotic automation tasks require large and heavy tooling systems. Yet, the integration of these tooling systems is usually done only considering the geometric constraints and weights without resorting to dynamic analysis. To resolve this problem, the equations of motion of a robot with inclusion of a tooling system are derived using the Lagrangian formulation. Three performance indices are introduced to evaluate the influence of the tooling system on the overall dynamics. The first index measures the energy consumption due to the tooling system’s motion, the second index evaluates the influence of the tooling system on the fundamental frequency, and the third one is the dynamic manipulability ellipsoid to measure the acceleration capability of the tool tip. Simulation studies are carried out to provide guidelines for the design of tooling systems. To demonstrate its effectiveness, the proposed method is applied to facilitate the tooling integration used in the robotic riveting for aerospace assembly.