Using fractal geometry to make rapid field measurements of riverbed topography at ecologically useful spatial scales

A method is described for making rapid in situ field measurements of riverbed topography over spatial scales of ≅1–10 m. This method uses rolling balls to make quick, accurate measurements of river-bed roughness at several spatial scales. Random sampling and replication generate multiple estimates of the fractal dimension (d) that can be used to test for significant differences in the complexity of riverbed architecture between habitat types and spatial scales.

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

The relationship between muscle size and bone geometry during growth and in response to exercise

As muscles become larger and stronger during growth and in response to increased loading, bones should adapt by adding mass, size, and strength. In this unilateral model, we tested the hypothesis that (1) the relationship between muscle size and bone mass and geometry (nonplaying arm) would not change during different stages of puberty and (2) exercise would not alter the relationship between muscle and bone, that is, additional loading would result in a similar unit increment in both muscle and bone mass, bone size, and bending strength during growth. We studied 47 competitive female tennis players aged 8–17 years. Total, cortical, and medullary cross-sectional areas, muscle area, and the polar second moment of area (Ip) were calculated in the playing and nonplaying arms using magnetic resonance imaging (MRI); BMC was assessed by DXA. Growth effects: In the nonplaying arm in pre-, peri- and post-pubertal players, muscle area was linearly associated BMC, total and cortical area, and Ip (r = 0.56–0.81, P < 0.09 to < 0.001), independent of age. No detectable differences were found between pubertal groups for the slope of the relationship between muscle and bone traits. Post-pubertal players, however, had a higher BMC and cortical area relative to muscle area (i.e., higher intercept) than pre- and peri-pubertal players (P < 0.05 to < 0.01), independent of age; pre- and peri-pubertal players had a greater medullary area relative to muscle area than post-pubertal players (P < 0.05 to < 0.01). Exercise effects: Comparison of the side-to-side differences revealed that muscle and bone traits were 6–13% greater in the playing arm in pre-pubertal players, and did not increase with advancing maturation. In all players, the percent (and absolute) side-to-side differences in muscle area were positively correlated with the percent (and absolute) differences in BMC, total and cortical area, and Ip (r = 0.36–0.40, P < 0.05 to < 0.001). However, the side-to-side differences in muscle area only accounted for 11.8–15.9% of the variance of the differences in bone mass, bone size, and bending strength. This suggests that other factors associated with loading distinct from muscle size itself contributed to the bones adaptive response during growth. Therefore, the unifying hypothesis that larger muscles induced by exercise led to a proportional increase in bone mass, bone size, and bending strength appears to be simplistic and denies the influence of other factors in the development of bone mass and bone shape.

Influence of the geometry of an immersed steel workpiece on mass transfer coefficient in a chemical heat treatment fluidised bed

The mass transfer during carburising in a fluidised bed and in a steel workpiece has been studied experimentally in this work. This involved carburising experiment in an electrically heated fluidised bed at 900–970°C with natural gas and air as the atmosphere. A steel workpiece was designed to provide a range of carbon transfer surfaces of different geometries in the fluidised bed, and the carbon transfer coefficient was measured at these surfaces. The carbon transfer coefficient was determined from the carbon distribution within the diffusion layer of the sample. An empirical relationship of the carbon potential as a function of carburising atmosphere, bed temperature and fluidising velocity was determined, based on the understanding of the mass transfer mechanism and analysis of the experimental results.

A computational approach to the reconstruction of surface geometry from early temple superstructures

Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing "best-fit" constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.

Long-term effects of calcium-vitamin-D3-fortified milk on bone geometry and strength in older men

The long-term effects of calcium and vitamin D supplementation on bone material and structural properties in older men are not known. The aim of this study was to examine the effects of high calcium (1000 mg/day)- and vitamin-D3 (800 IU/day)-fortified milk on cortical and trabecular volumetric BMD (vBMD) and bone geometry at the axial and appendicular skeleton in men aged over 50 years. One hundred and eleven men who were part of a larger 2-year randomized controlled trial had QCT scans of the mid-femur and lumbar spine (L1–L3) to assess vBMD, bone geometry and indices of bone strength [polar moment of inertia (Ipolar)]. After 2 years, there were no significant differences between the milk supplementation and control group for the change in any mid-femur or L1–L3 bone parameters for all men aged over 50 years. However, the mid-femur skeletal responses to the fortified milk varied according to age, with a split of ≤62 versus >62 years being the most significant for discriminating the changes between the two groups. Subsequent analysis revealed that, in the older men (>62 years), the expansion in mid-femur medullary area was 2.8% (P < 0.01) less in the milk supplementation compared to control group, which helped to preserve cortical area in the milk supplementation group (between group difference 1.1%, P < 0.01). Similarly, for mid-femur cortical vBMD and Ipolar, the net loss was 2.3 and 2.8% less in the milk supplementation compared to control group (P < 0.01 and <0.001, respectively). In conclusion, calcium–vitamin-D3-fortified milk may represent an effective strategy to maintain bone strength by preventing endocortical bone loss and slowing the loss in cortical vBMD in elderly men.

1-Naphthyl- and mesityltellurium(IV,II) derivatives of small bite chelating organic ligands: effect of steric bulk and intramolecular secondary bonding interaction on molecular geometry and supramolecular association

The synthesis and characterization of unsymmetric diorganotellurium compounds containing a sterically demanding I-naphthyl or
mesitylligand and a small bite chelating organic ligand capable of 1,4-Te···N(O) intramolecular interaction is described. The reaction
of ArTeCl₃ (Ar = I-C_lOH₇, Np; 2,4,6-Me₃C₆H_2' Mes) with (SB)HgCI [SB = the Schiff base, 2-(4,4'-N0₂C₆H₄CH=NC₆H₃-Me)] or a methyl ketone (RCOCH₃) afforded the corresponding dichlorides (SB)ArTeCI₂ (Ar = Np, 1Aa; Mes, 1Ba) or (RCOCH₂)ArTeCl₂ (Ar = Np; R = Ph (2Aa), Me (3Aa), Np (4Aa); Ar = Mes, R = Ph (2Ba)). Reduction of 1Aa and 1Ba by Na₂S₂0₅ readily gave the tellurides (SB)ArTe (Ar = Np (1A), Mes, (1B) but that of dichlorides derived from methylketones was complicated due to partial decomposition to tellurium powder and diarylditelluride (Ar₂Te₂), resulting in poor yields of the corresponding tellurides 2A, 2B and 3A. Oxidation of the isolated tellurides with S0₂Cl₂, Br₂ and I₂ yielded the corresponding dihalides. All the synthesized compounds have been characterized with the help of IR, ¹H, ^l3C, and ¹²⁵Te NMR and in the case of 2Aa, and 2Ba by X-ray crystallography. Appearance of only one ¹²⁵Te signal indicated that the unsymmetric derivatives were stable to disproportionation to symmetric species. Intramolecular 1,4-Te· . ·0 secondary bonding interactions (SBIs) are exhibited in the crystal structures of both the tellurium(IV) dichlorides, 2Aa, and 2Ba. Steric repulsion of the mesityl group in the latter dominates over lone pair-bond pair repulsion, resulting in significant widening of the equatorial C-Te-C angle. This appears to be responsible for the lack of Te· . ·CI involved supramolecular associations in the crystal structure of 2Ba.

Design of experiments and springback prediction for AHSS automotive components with complex geometry

With the drive towards implementing Advanced High Strength Steels (AHSS) in the automotive industry; stamping engineers need to quickly answer questions about forming these strong materials into elaborate shapes.
Commercially available codes have been successfully used to accurately predict formability, thickness and strains in complex parts. However, springback and twisting are still challenging subjects in numerical simulations of AHSS components. Design of Experiments (DOE) has been used in this paper to study the sensitivity of the implicit and explicit numerical results with respect to certain arrays ofuser input parameters in the forming ofan AHSS component. Numerical results were compared to experimental measurements of the parts stamped in an industrial production line. The forming predictions of the implicit and explicit codes were in good agreement with the experimental measurements for the conventional steel grade, while lower accuracies were observed for the springback predictions. The forming
predictions of the complex component with an AHSS material were also in good correlation with the respective experimental measurements. However, much lower accuracies were observed in its springback predictions. The number of integration points through the thickness and tool offset were found to be of significant importance, while coefficient of friction and Young's modulus (modeling input parameters) have no significant effect on the accuracy of the predictions for the complex geometry.

On recovering the surface geometry of temple superstructures

The application of computational techniques to the analysis of heritage artifacts enables scholars to bring together diverse fragments of surviving evidence, construe "best-fit" strategies and unearth implicit or hidden relationships. This paper reports a hybrid approach for recovering the surface geometry of temples. The approach combines physical measurements, architectural photogrammetry and generative rules to create a parametric model of the surface. The computing of surface geometry is broken into three parts, a global model governing the overall form of the superstructure, local models governing the geometry of individual motifs and finally the global and local models are combined into a single geometry. In this paper, the technique for recovering surface geometry is applied to a tenth century stone superstructure: the temple of Ranakdevi at Wadhwan in Western India. The global model of the superstructure and the local model of one individual motif are presented.

The generation of superstructure geometry in latina temples : a hybrid approach

The Nagara tradition of temple building created a rich corpus of Latina (single-spired) temples spread across Northern India between the fifth and thirteenth centuries. Computing methods offer a distinct methodology for reconstructing the genesis and evolution of geometry in this tradition over time. This paper reports a hybrid technique, comprising three distinct computations for recovering and explaining the geometry of temples. The application of the technique enables scholars to bring together fragments of evidence, construe "best-fit" strategies and unearth implicit or hidden relationships. The advantage of this approach is that changes in assumptions and testing of geometric alternatives can be easily simulated from multiple sources of information, such as texts, sacred diagrams and individual temples.

Exploiting geometry for improved hybrid AOA/TDOA-based localization

In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of  arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

Bone geometry in response to long-term tennis playing and its relationship with muscle volume : a quantitative magnetic resonance imaging study in tennis players

The benefit of impact-loading activity for bone strength depends on whether the additional bone mineral content (BMC) accrued at loaded sites is due to an increased bone size, volumetric bone mineral density (vBMD) or both. Using magnetic resonance imaging (MRI) and dual energy X-ray absorptiometry (DXA), the aim of this study was to characterize the geometric changes of the dominant radius in response to long-term tennis playing and to assess the influence of muscle forces on bone tissue by investigating the muscle–bone relationship. Twenty tennis players (10 men and 10 women, mean age: 23.1 ± 4.7 years, with 14.3 ± 3.4 years of playing) were recruited. The total bone volume, cortical volume, sub-cortical volume and muscle volume were measured at both distal radii by MRI. BMC was assessed by DXA and was divided by the total bone volume to derive vBMD. Grip strength was evaluated with a dynamometer. Significant side-to-side differences (P < 0.0001) were found in muscle volume (+9.7%), grip strength (+13.3%), BMC (+13.5%), total bone volume (+10.3%) and sub-cortical volume (+20.6%), but not in cortical volume (+2.6%, ns). The asymmetry in total bone volume explained 75% of the variance in BMC asymmetry (P < 0.0001). vBMD was slightly higher on the dominant side (+3.3%, P < 0.05). Grip strength and muscle volume correlated with all bone variables (except vBMD) on both sides (r = 0.48–0.86, P < 0.05–0.0001) but the asymmetries in muscle parameters did not correlate with those in bone parameters. After adjustment for muscle volume or grip strength, BMC was still greater on the dominant side. This study showed that the greater BMC induced by long-term tennis playing at the dominant radius was associated to a marked increase in bone size and a slight improvement in volumetric BMD, thereby improving bone strength. In addition to the muscle contractions, other mechanical stimuli seemed to exert a direct effect on bone tissue, contributing to the specific bone response to tennis playing.