13,190 research outputs found
Topological entropy and blocking cost for geodesics in riemannian manifolds
For a pair of points in a compact, riemannian manifold let
(resp. ) be the number of geodesic segments with length
joining these points (resp. the minimal number of point obstacles
needed to block them). We study relationships between the growth rates of
and as . We derive lower bounds on
in terms of the topological entropy and its fundamental group. This
strengthens the results of Burns-Gutkin \cite{BG06} and Lafont-Schmidt
\cite{LS}. For instance, by \cite{BG06,LS}, implies that is
unbounded; we show that grows exponentially, with the rate at least
.Comment: 13 page
Rate dependent shear bands in a shear transformation zone model of amorphous solids
We use Shear Transformation Zone (STZ) theory to develop a deformation map
for amorphous solids as a function of the imposed shear rate and initial
material preparation. The STZ formulation incorporates recent simulation
results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state
effective temperature is rate dependent. The resulting model predicts a wide
range of deformation behavior as a function of the initial conditions,
including homogeneous deformation, broad shear bands, extremely thin shear
bands, and the onset of material failure. In particular, the STZ model predicts
homogeneous deformation for shorter quench times and lower strain rates, and
inhomogeneous deformation for longer quench times and higher strain rates. The
location of the transition between homogeneous and inhomogeneous flow on the
deformation map is determined in part by the steady state effective
temperature, which is likely material dependent. This model also suggests that
material failure occurs due to a runaway feedback between shear heating and the
local disorder, and provides an explanation for the thickness of shear bands
near the onset of material failure. We find that this model, which resolves
dynamics within a sheared material interface, predicts that the stress weakens
with strain much more rapidly than a similar model which uses a single state
variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate
strengthening vs. rate weakening material
Vigorous and High Intensity Training with an Anti-Gravity Treadmill
Muñoz, E., Figueroa, M., Manning, J.,William Paterson University, Wayne, NJ
Purpose: The purpose of this study was to compare two different training intensities on and anti-gravity treadmill and to determine whether or not one elicited changes that were more favorable. Methods: Pre and post measures of oxygen consumption (VO2peak), body fat (BF)% and body mass index (BMI) were collected on twelve subjects, which were divided into 2 groups. Group 1 trained at 80% body weight (BW) 3 x / week, for 8 weeks, at 70% heart rate reserve (HRR) for 30 minutes. Group 2 trained at 90% BW, 2 x / week, for 6 weeks, using an interval protocol of high intensity. This protocol consisted of a 30 second sprint, followed by a 1.5 minute walk, which was repeated for a total of 8 sets. Results: No significant differences were found between groups prior to or after training. Weight, absolute VO2 (L×min-1), BF% and BMI were significantly different after training within group 1, but not group 2. Conclusion: Training on an anti-gravity device was able to maintain and/or improve weight, aerobic capacity and body composition values using a lower percentage of BW. This is favorable for individuals who are either injured or require lower impact training
Transonic pressure measurements and comparison of theory to experiment for an arrow-wing configuration. Volume 1: Experimental data report, base configuration and effects of wing twist and leading-edge configuration
A wind tunnel test of an arrow-wing-body configuration consisting of flat and twisted wings, as well as a variety of leading- and trailing-edge control surface deflections, was conducted at Mach numbers from 0.4 to 1.1 to provide an experimental pressure data base for comparison with theoretical methods. Theory-to-experiment comparisons of detailed pressure distributions were made using current state-of-the-art attached and separated flow methods. The purpose of these comparisons was to delineate conditions under which these theories are valid for both flat and twisted wings and to explore the use of empirical methods to correct the theoretical methods where theory is deficient
Superintegrability on the two-dimensional hyperboloid
In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras
Transonic pressure measurements and comparison of theory to experiment for an arrow-wing configuration. Volume 2: Experimental data report, effects of control surface deflection
For abstract, see N76-11034
Strain localization in a shear transformation zone model for amorphous solids
We model a sheared disordered solid using the theory of Shear Transformation
Zones (STZs). In this mean-field continuum model the density of zones is
governed by an effective temperature that approaches a steady state value as
energy is dissipated. We compare the STZ model to simulations by Shi, et
al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates
solutions that fit the data,exhibit strain localization, and capture important
features of the localization process. We show that perturbations to the
effective temperature grow due to an instability in the transient dynamics, but
unstable systems do not always develop shear bands. Nonlinear energy
dissipation processes interact with perturbation growth to determine whether a
material exhibits strain localization. By estimating the effects of these
interactions, we derive a criterion that determines which materials exhibit
shear bands based on the initial conditions alone. We also show that the shear
band width is not set by an inherent diffusion length scale but instead by a
dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte
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