A point is normal for almost all maps βx+α mod 1 or generalized β-transformations

We consider the map Tα,β(x):=βx+αmod1, which admits a unique probability measure μα,β of maximal entropy. For x[0,1], we show that the orbit of x is μα,β-normal for almost all (α,β)[0,1)×(1,∞) (with respect to Lebesgue measure). Nevertheless, we construct analytic curves in [0,1)×(1,∞) along which the orbit of x=0 is μα,β-normal at no more than one point. These curves are disjoint and fill the set [0,1)×(1,∞). We also study the generalized β-transformations (in particular, the tent map). We show that the critical orbit x=1 is normal with respect to the measure of maximal entropy for almost all

Social rules govern vocal competition in the barn owl

To resolve the share of limited resources, animals often compete through exchange of signals about their relative motivation to compete. When two competitors are similarly motivated, the resolution of conflicts may be achieved in the course of an interactive process. In barn owls, Tyto alba, in which siblings vocally compete during the prolonged absence of parents over access to the next delivered food item, we investigated what governs the decision to leave or enter a contest, and at which level. Siblings alternated periods during which one of the two individuals vocalized more than the other. Individuals followed turn-taking rules to interrupt each other and momentarily dominate the vocal competition. These social rules were weakly sensitive to hunger level and age hierarchy. Hence, the investment in a conflict is determined not only by need and resource-holding potential, but also by social interactions. The use of turn-taking rules governing individual vocal investment has rarely been shown in a competitive context. We hypothesized that these rules would allow individuals to remain alert to one another's motivation while maintaining the cost of vocalizing at the lowest level

COMPLIANCE TESTING OF IOWA’S SKID-MOUNTED SIGN DEVICE

A wide variety of traffic control devices are used in work zones, some of which are nont ormally found on the roadside or in the traveled way outsideofthe work zones. These devices are used to enhance the safety of the work zones by controlling the traffic through these areas. Due to the placement of the traffic control devices, the devices themselves may be potentially hazardous to both workers and errant vehicles. The impact performance of many work zone traffic control devices is mainly unknown and to date limited crash testing has been conducted under the criteria of National Cooperative Highway Research Program (NCHRP) Report No. 350, Recommended Procedures for the Safety Performance Evaluation of Highway Features. The objective of the study was to evaluatethe safety performance of existing skid-mounted sign supports through full- scale crash testing. Two full-scale crash tests were conducted on skid-mounted sign supports to determine their safety performance according to the Test Level 3 (TL-3) criteria set forth in the NCHRP Report No. 350. The safety performancevaluations indicate that these skid-mounted sign supports did not perform satisfactorily in the full-scale crash tests. The results of the crash tests were documented, and conclusions and recommendations pertaining tothe safety performance of the existing work zone traffic control devices were made

Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.Comment: 7 pages, 6 figure

On the Significance of the Weyl Curvature in a Relativistic Cosmological Model

The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.Comment: 15 pages, incorporating proof correction

Exploring Spirituality in Teaching Within a Christian School Context Through Collaborative Action Research

This article reports on a collaborative action research project conducted in New Zealand, during 2012, exploring spirituality in teaching within a Christian school context. The experienced primary school teacher participant chose to take action around the issue of personal fear and insecurity which were believed to be hindering professional growth and relationships. Through self-directed inquiry, critical reflective journaling, Bible study, fellowship and prayer with trusted friends, the teacher experienced a renewed sense of peace and freedom in Christ. This personal transformation was believed to be influential on subsequent professional practice, assisting the teacher to become more relational, responsive and compassionate. The findings provide a rich description of the participant’s spirituality, the lived reality of a person’s spiritual life. This report will be of interest to teachers, teacher-leaders and teacher-educators who desire to explore Christian spirituality through practitioner-led inquiry

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references, typos removed, accepted as Rapid Commun. in Phys. Rev.

Detection, Measurement and Gravitational Radiation

Here I examine how to determine the sensitivity of the LIGO, VIRGO, and LAGOS gravitational wave detectors to sources of gravitational radiation by considering the process by which data are analyzed in a noisy detector. By constructing the probability that the detector output is consistent with the presence of a signal, I show how to (1) quantify the uncertainty that the output contains a signal and is not simply noise, and (2) construct the probability distribution that the signal parameterization has a certain value. From the distribution and its mode I determine volumes $V(P)$ in parameter space such that actual signal parameters are in $V(P)$ with probability $P$. If we are {\em designing} a detector, or determining the suitability of an existing detector for observing a new source, then we don't have detector output to analyze but are interested in the ``most likely'' response of the detector to a signal. I exploit the techniques just described to determine the ``most likely'' volumes $V(P)$ for detector output corresponding to the source. Finally, as an example, I apply these techniques to anticipate the sensitivity of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed Kerr black hole.Comment: 37 pages (plus 6 figures), LaTeX/REVTE

Growth, microstructure, and failure of crazes in glassy polymers

We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length $N$, entanglement length $N_e$ and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is $N_e/3$. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for $N/N_e\sim 10$, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theoretical models of craze widening that were based on continuum level hydrodynamics

Yield conditions for deformation of amorphous polymer glasses

Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset of shear is consistent with the pressure-modified von Mises criterion, and the pressure coefficient is nearly independent of many parameters. Under triaxial tensile loading, the mode of failure changes to cavitation.Comment: 9 pages, 8 figures, revte