Helping Kindergarteners Make Sense of Numbers to 100

The authors share what was learned about kindergarteners\u27 abilities to make sense of numbers to 100 when one of the authors, Linda Jaslow, took over a kindergarten class from February through the end of the school year. Through examples of how she engaged her students in nine weeks of problem solving and discussions focused on making sense of the number system, we provide evidence that the children grew substantially in their ability to count and show understanding when counting by 10\u27s and using 10\u27s during problem solving. Suggestions for tasks to promote continued growth are also provided. Throughout this teaching experience, Mrs. Jaslow was reminded of the complexity of making sense of our number system, and this article showcases her instructional decision making that was based on inquiry into children\u27s thinking. By valuing children\u27s existing ideas, Mrs. Jaslow could use that thinking to help guide her instruction

Description and simulation of an integrated power and attitude control system concept for space-vehicle application

An Integrated Power and Attitude Control System (IPACS) concept with potential application to a broad class of space missions is discussed. A description is given of the basic concept of combining the onboard energy storage and attitude control functions by storing energy in spinning flywheels which are used to provide control torques. A shuttle-launched Research and Applications Module (RAM) A303B solar-observatory mission having stringent pointing requirements (1.0 arc second) is selected to investigate possible interactions between energy storage and attitude control. A simulation of this spacecraft involving actual laboratory-model control-system hardware is presented. Simulation results are discussed which indicate that the IPACS concept, even in a failure-mode configuration, can readily meet the RAM A303B pointing requirements

Thermal noise influences fluid flow in thin films during spinodal dewetting

Experiments on dewetting thin polymer films confirm the theoretical prediction that thermal noise can strongly influence characteristic time-scales of fluid flow and cause coarsening of typical length scales. Comparing the experiments with deterministic simulations, we show that the Navier-Stokes equation has to be extended by a conserved bulk noise term to accomplish the observed spectrum of capillary waves. Due to thermal fluctuations the spectrum changes from an exponential to a power law decay for large wavevectors. Also the time evolution of the typical wavevector of unstable perturbations exhibits noise induced coarsening that is absent in deterministic hydrodynamic flow.Comment: 4 pages, 3 figure

Coarsening Dynamics of Granular Heaplets in Tapped Granular Layers

A semi-continuum model is introduced to study the dynamics of the formation of granular heaplets in tapped granular layers. By taking into account the energy dissipation of collisions and screening effects due to avalanches, this model is able to reproduce qualitatively the pattern of these heaplets. Our simulations show that the granular heaplets are characterised by an effective surface tension which depends on the magnitude of the tapping intensity. Also, we observe that there is a coarsening effect in that the average size of the heaplets, V grows as the number of taps k increases. The growth law at intermediate times can be fitted by a scaling function V ~ k^z but the range of validity of the power law is limited by size effects. The growth exponent z appears to diverge as the tapping intensity is increased.Comment: 4 pages, 4 figure

Alternating magnetic anisotropy of Li2_2(Li1−xTx_{1-x}T_x)N with TT = Mn, Fe, Co, and Ni

Substantial amounts of the transition metals Mn, Fe, Co, and Ni can be substituted for Li in single crystalline Li$_2$(Li$_{1-x}T_x$)N. Isothermal and temperature-dependent magnetization measurements reveal local magnetic moments with magnitudes significantly exceeding the spin-only value. The additional contributions stem from unquenched orbital moments that lead to rare-earth-like behavior of the magnetic properties. Accordingly, extremely large magnetic anisotropies have been found. Most notably, the magnetic anisotropy alternates as easy-plane $\rightarrow$ easy-axis $\rightarrow$ easy-plane $\rightarrow$ easy-axis when progressing from $T$ = Mn $\rightarrow$ Fe $\rightarrow$ Co $\rightarrow$ Ni. This behavior can be understood based on a perturbation approach in an analytical, single-ion model. The calculated magnetic anisotropies show a surprisingly good agreement with the experiment and capture the basic features observed for the different transition metals.Comment: 5 pages, 3 figures, published as PRB Rapid Communication, Fig. 3 update

Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. By use of the higher order corrections to the probability density we derive an expression for the spatially dependent diffusion coefficient D(x) which substitutes the constant diffusion coefficient present in the common Fick-Jacobs equation. In addition, we show that in the diffusion dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient . The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel.Comment: 9 pages, 3 figure

Extended symmetrical classical electrodynamics

In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field E and B. It is shown that the vectors E and B can be defined in terms of two 4-potentials and the components of k are the components of the 4-tensor of the third rank. The Lagrangian of modified electrodynamics is defined. The conditions are derived at which only one 4-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of the electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy and angular momentum of the monopole are found for different eigenvalues of k

A model to predict the conditions for liquid drop breakup and the resultant mean fragment size

The potential significance of drop fragmentation in sprays and other propulsion-related multiphase flows has been noted in the literature. This has motivated recent experimental and theoretical works to: better understand the fundamentals of physics of drop breakup processes, and develop models of drop fragmentation suitable for use in multiphase flow codes. The works summarized below aim to contribute to both sides of this two-pronged attack

Nitrogen Fertiliser Effects on Perennial Ryegrass Nutritive and Nitrate Content during the Cool Season

A study was undertaken to determine the effects of differing levels of nitrogen (N) application (0 (N1), 25 (N2), 50 (N3) and 75 kgN/ha (N4)) during late autumn (T1), early (T2) and late winter (T3) on the nutritive characteristics and nitrate content of perennial ryegrass. Changes in crude protein (CP) for all treatments at each application time were similar irrespective of level of N application. At the commencement of all treatments, the existing CP content was highest in N3, followed by N2, N1 and N0. Nitrate content decreased throughout T1 primarily due to dry conditions, whilst during T2, levels for N3 and N2 were significantly (P \u3c 0.05) higher than N1 and N0. During T3, nitrate content increased for all treatments throughout the 28 day period, with highest nitrate levels being observed during T3. The findings indicate that N fertiliser did not elevate nitrate content in perennial ryegrass to levels considered toxic. It is likely that environmental effects (rain and temperature) impacting on soil N mineralisation may have a greater impact on nitrate content than fertiliser N

Nitrogen Response Efficiencies from Grazed Dairy Pastures under Dry Conditions

Experiments were conducted within a long-term nitrogen (N) fertiliser experiment under grazing. The objective was to examine N response efficiencies (kg dry matter (DM)/kg N) and herbage crude protein (CP) content to fertiliser N applied under dry soil conditions (gravimetric soil moisture content of 17% at 10cm; soil field capacity = 38% and wilting point = 11%) during autumn (April 1999) and late spring (November 1999) in southeastern Australia. Visually, N treated plots were greener in colour than control (no N) plots. No differences were recorded in primary or residual DM yields, N response efficiencies, and pasture growth rates between N fertilised plots and control plots for both autumn and late spring applications. Fertiliser N, however, had increased herbage CP content six weeks after application in autumn, but had no effect on primary (autumn and late spring applications) or residual CP content in late spring. It was concluded that N fertiliser applications under dry soil conditions are economically and environmently questionable