Humans, geometric similarity and the Froude number: is ''reasonably close'' really close enough?

Summary Understanding locomotor energetics is imperative, because energy expended during locomotion, a requisite feature of primate subsistence, is lost to reproduction. Although metabolic energy expenditure can only be measured in extant species, using the equations of motion to calculate mechanical energy expenditure offers unlimited opportunities to explore energy expenditure, particularly in extinct species on which empirical experimentation is impossible. Variability, either within or between groups, can manifest as changes in size and/or shape. Isometric scaling (or geometric similarity) requires that all dimensions change equally among all individuals, a condition that will not be met in naturally developing populations. The Froude number (Fr), with lower limb (or hindlimb) length as the characteristic length, has been used to compensate for differences in size, but does not account for differences in shape. To determine whether or not shape matters at the intraspecific level, we used a mechanical model that had properties that mimic human variation in shape. We varied crural index and limb segment circumferences (and consequently, mass and inertial parameters) among nine populations that included 19 individuals that were of different size. Our goal in the current work is to understand whether shape variation changes mechanical energy sufficiently enough to make shape a critical factor in mechanical and metabolic energy assessments. Our results reaffirm that size does not affect mass-specific mechanical cost of transport (Alexander and Jayes, 1983) among geometrically similar individuals walking at equal Fr. The known shape differences among modern humans, however, produce sufficiently large differences in internal and external work to account for much of the observed variation in metabolic energy expenditure, if mechanical energy is correlated with metabolic energy. Any species or other group that exhibits shape differences should be affected similarly to that which we establish for humans. Unfortunately, we currently do not have a simple method to control or adjust for size–shape differences in individuals that are not geometrically similar, although musculoskeletal modeling is a viable, and promising, alternative. In mouse-to-elephant comparisons, size differences could represent the largest source of morphological variation, and isometric scaling factors such as Fr can compensate for much of the variability. Within species, however, shape differences may dominate morphological variation and Fr is not designed to compensate for shape differences. In other words, those shape differences that are “reasonably close” at the mouse-to-elephant level may become grossly different for within-species energetic comparisons

Intrinsic Shapes of Very Flat Elliptical Galaxies

Photometric data from the literature is combined with triaxial mass models to derive variation in the intrinsic shapes of the light distribution of elliptical galaxies NGC 720, 2768 and 3605. The inferred shape variation in given by a Bayesian probability distribution, assuming a uniform prior. The likelihood of obtaining the data is calculated by using ensemble of triaxial models. We apply the method to infer the shape variation of a galaxy, using the ellipticities and the difference in the position angles at two suitably chosen points from the profiles of the photometric data. Best constrained shape parameters are found to be the short to long axial ratios at small and large radii, and the absolute values of the triaxiallity difference between these radii.Comment: Accepted in MNRA

Chatter Control by Spindle Speed Variation in High-Speed Milling

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area

Spectral Variation of the Seyfert 1 Galaxy MCG-6-30-15 observed with Suzaku

We have investigated spectral variation of the Seyfert 1 galaxy MCG-6-30-15 observed with Suzaku in January 2006 for three separate periods spreading over fourteen days. We found that the time-averaged continuum energy spectrum between 1 keV and 40 keV can be approximated with a spectral model composed of the direct power-law component, its reflection component, two warm absorbers with different ionization states, and neutral absorption. We have taken two approaches to study its spectral variation at various timescales: The first approach is to make intensity-sliced spectra and study correlation between the intensity and spectral shape. The second approach is to study spectral changes between the intervals when the source flux is above ("bright state") and below ("faint state") the average for fixed time-intervals. In both approaches, we found a clear correlation between the intensity in the 6 -- 10 keV band and the spectral ratio of 0.5 -- 3.0 keV/6.0-- 10 keV. Such a spectral variation requires change of the apparent slope of the direct component, whereas the shape and intensity of the reflection component being invariable. The observed apparent spectral change is explained by variation of the ionization degree of one of the two warm absorbers due to intrinsic source luminosity variation. Current results suggest that the warm absorber has a critical role to explain the observed continuum spectral shape and variation of MCG-6-30-15, which is essential to constrain parameters of the putatively broadened iron line emission feature.Comment: 11 pages, accepted for publication in PAS