Riemannian and teleparallel descriptions of the scalar field gravitational interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.

An example of cognitive obstacles in advanced integration: the case of scalar line integrals

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.

Scalar considerations in carrying capacity assessment : an Australian example

Regional resource self-sufficiency has been proposed as a way to improve food security by lessening the demand on long-distance transport. An online tool, the Carrying Capacity Dashboard, was developed for Australian conditions in order to gauge self-sufficiency at three different scales: regional, state and national. It allows users to test a variety of societal behaviours such as diet, biofuel production, farming systems and ecological protection practices. Analysis developed from the Dashboard tests the effects of various resource consumption patterns on land carrying capacity. Findings reveal that Australia’s current carrying capacity is estimated to be over 40 million, but if calculated on a regional basis, this is reduced by almost half.

Spine curvature analysis between participants with obesity and normal weight participants: A biplanar electromagnetic device measurement

To analyse and compare standing thoracolumbar curves in normal weight participants and participants with obesity, using an electromagnetic device, and to analyse the measurement reliability. Material and Methods. Cross-sectional study was carried out. 36 individuals were divided into two groups (normal-weight and participants with obesity) according to their waist circumference. The reference points (T1–T8–L1–L5 and both posterior superior iliac spines) were used to perform a description of thoracolumbar curvature in the sagittal and coronal planes. A transformation from the global coordinate system was performed and thoracolumbar curves were adjusted by fifth-order polynomial equations. The tangents of the first and fifth lumbar vertebrae and the first thoracic vertebra were determined from their derivatives. The reliability of the measurement was assessed according to the internal consistency of the measure and the thoracolumbar curvature angles were compared between groups. Results. Cronbach’s alpha values ranged between 0.824 (95% CI: 0.776–0.847) and 0.918 (95% CI: 0.903–0.949). In the coronal plane, no significant differences were found between groups; however, in sagittal plane, significant differences were observed for thoracic kyphosis. Conclusion. There were significant differences in thoracic kyphosis in the sagittal plane between two groups of young adults grouped according to their waist circumference.

Scalar connectivity measures from fast-marching tractography reveal heritability of white matter architecture

Recent advances in diffusion-weighted MRI (DWI) have enabled studies of complex white matter tissue architecture in vivo. To date, the underlying influence of genetic and environmental factors in determining central nervous system connectivity has not been widely studied. In this work, we introduce new scalar connectivity measures based on a computationally-efficient fast-marching algorithm for quantitative tractography. We then calculate connectivity maps for a DTI dataset from 92 healthy adult twins and decompose the genetic and environmental contributions to the variance in these metrics using structural equation models. By combining these techniques, we generate the first maps to directly examine genetic and environmental contributions to brain connectivity in humans. Our approach is capable of extracting statistically significant measures of genetic and environmental contributions to neural connectivity.

An alternative approach to describing agility in sports through establishment of a relationship between velocity and radius of curvature

Agility is an essential part of many athletic activities. Currently, agility drill duration is the sole criterion used for evaluation of agility performance. The relationship between drill duration and factors such as acceleration, deceleration and change of direction, however, has not been fully explored. This paper provides a mathematical description of the relationship between velocity and radius of curvatures in an agility drill through implementation of a power law (PL). Two groups of skilled and unskilled participants performed a cyclic forward/backward shuttle agility test. Kinematic data was recorded using motion capture system at a sampling rate of 200 Hz. The logarithmic relationship between tangential velocity and radius of curvature of participant trajectories in both groups was established using the PL. The slope of the regression line was found to be 0.26 and 0.36, for the skilled and unskilled groups, respectively. The magnitudes of regression line slope for both groups were approximately 0.3 which is close to the expected 1/3 value. Results are an indication of how the PL could be implemented in an agility drill thus opening the way for establishment of a more representative measure of agility performance instead of drill duration.

Arterial luminal curvature and fibrous-cap thickness affect critical stress conditions within atherosclerotic plaque: An in vivo MRI-based 2D finite-element study

High mechanical stress in atherosclerotic plaques at vulnerable sites, called critical stress, contributes to plaque rupture. The site of minimum fibrous cap (FC) thickness (FCMIN) and plaque shoulder are well-documented vulnerable sites. The inherent weakness of the FC material at the thinnest point increases the stress, making it vulnerable, and it is the big curvature of the lumen contour over FC which may result in increased plaque stress. We aimed to assess critical stresses at FCMIN and the maximum lumen curvature over FC (LCMAX) and quantify the difference to see which vulnerable site had the highest critical stress and was, therefore, at highest risk of rupture. One hundred patients underwent high resolution carotid magnetic resonance (MR) imaging. We used 352 MR slices with delineated atherosclerotic components for the simulation study. Stresses at all the integral nodes along the lumen surface were calculated using the finite-element method. FCMIN and LCMAX were identified, and critical stresses at these sites were assessed and compared. Critical stress at FC MIN was significantly lower than that at LCMAX (median: 121.55 kPa; inter quartile range (IQR) = [60.70-180.32] kPa vs. 150.80 kPa; IQR = [91.39-235.75] kPa, p < 0.0001). If critical stress at FCMIN was only used, then the stress condition of 238 of 352 MR slices would be underestimated, while if the critical stress at LCMAX only was used, then 112 out of 352 would be underestimated. Stress analysis at FCMIN and LCMAX should be used for a refined mechanical risk assessment of atherosclerotic plaques, since material failure at either site may result in rupture.

Radiative decay of quarkonium into Higgs scalar

A relativistic bound-state formalism is used to calculate the branching ratio Γ(V→H+γ)/Γ(V→e+e-) where H is a Higgs scalar and significant relativistic effects have been obtained compared to the nonrelativistic calculation originally due to Wilczek

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

Laminar flow of a suspension in a curved pipe with varying curvature

The laminar flow of a fairly concentrated suspension (in which the volume fraction Z of the solid particles < 0.4) in a spatially varying periodically curved pipe has been examined numerically. Unlike the case of interacting suspension flows, the particles are found to flow in a well-mixed fashion, altering both the axial and circumferential velocities and consequently the fluid flux in the tube, depending on their diffusivity and inertia. The magnitude of shear stress at the wall is enhanced, suggesting that, if applied to vascular system, the vascular wall could be prone to ulceration during pathological situations like polycythemia. The delay in adaptation of the deviation in Poiseuille flow velocity to the curvature changes is also discussed in detail.

The possible influence of curvature and rotation on ocean currents

Recent laboratory investigations have shown that rotation and (streamwise) curvature can have spectacular effects on momentum transport in turbulent shear flows. A simple model that takes account of these effects (based on an analogy with buoyant flows) utilises counterparts of the Richardson number Rg and the Monin-Oboukhov length. Estimates of Rg for meanders in ocean currents like the Gulf Stream show it to be of order 1 or more, while laboratory investigations reveal strong effects even at |Rg|∼0·1. These considerations lead to the conclusion that at a cyclonic bend in the Gulf Stream, a highly unstable flow in the outer half of the jet rides over a highly stable flow in the inner half. It is conjectured that the discrepancies noticed between observation and the various theories of Gulf Stream meanders, and such phenomena as the observed detachment of eddies from the Gulf Stream, may be due to the effects of curvature and rotation on turbulent transport.