Assessment in Music Education: Relationships between Classroom Practice and Professional Publication Topics

The purpose of this study was to investigate the relationship between actual current assessment practices of elementary music teachers and the assessment topics as published in the literature aimed at those teachers. Specifically, this study sought to: 1) identify the current assessment techniques utilized by elementary music teachers; 2) identify the types of assessment techniques included in the current music teacher literature, and 3) identify any relationships between the assessment techniques that are most frequently utilized by teachers and those that are most frequently included in teacher-focused music education publications. The researchers first examined data collected from the 100 elementary general music educators from the Northwestern United States who participated in a survey designed to identify the assessment practices of elementary general music teachers. The researchers next reviewed ten years (1999 – 2009) of the national publications Teaching Music and Music Educators Journal searching for articles that addressed the topic of classroom music assessment. Finally, the researchers ranked both the classroom and literature assessment techniques by frequency of use and frequency of inclusion in the literature and then examined the results in order to identify possible relationships. The researchers found that there is a possible disconnect between the assessment strategies reported as used by the classroom music educators participating in this study and the major professional publications in the music education field

Association between urinary sodium, creatinine, albumin, and long term survival in chronic kidney disease

Dietary sodium intake is associated with hypertension and cardiovascular risk in the general population. In patients with chronic kidney disease, sodium intake has been associated with progressive renal disease, but not independently of proteinuria. We studied the relationship between urinary sodium excretion and urinary sodium:creatinine ratio and mortality or requirement for renal replacement therapy in chronic kidney disease. Adults attending a renal clinic who had at least one 24-hour urinary sodium measurement were identified. 24-hour urinary sodium measures were collected and urinary sodium:creatinine ratio calculated. Time to renal replacement therapy or death was recorded. 423 patients were identified with mean estimated glomerular filtration rate of 48ml/min/1.73m<sup>2</sup>. 90 patients required renal replacement therapy and 102 patients died. Mean slope decline in estimated glomerular filtration rate was -2.8ml/min/1.73m<sup>2</sup>/year. Median follow-up was 8.5 years. Patients who died or required renal replacement therapy had significantly higher urinary sodium excretion and urinary sodium:creatinine but the association with these parameters and poor outcome was not independent of renal function, age and albuminuria. When stratified by albuminuria, urinary sodium:creatinine was a significant cumulative additional risk for mortality, even in patients with low level albuminuria. There was no association between low urinary sodium and risk, as observed in some studies. This study demonstrates an association between urinary sodium excretion and mortality in chronic kidney disease, with a cumulative relationship between sodium excretion, albuminuria and reduced survival. These data support reducing dietary sodium intake in chronic kidney disease but further study is required to determine the target sodium intake

Computational probes of molecular motion in the Lewis and Whanstrom model for ortho-terphenyl

We use molecular dynamics simulations to investigate translational and rotational diffusion in a rigid three-site model of the fragile glass former ortho-terphenyl, at 260 K < T < 346 K and ambient pressure. An Einstein formulation of rotational motion is presented, which supplements the commonly-used Debye model. The latter is shown to break down at supercooled temperatures as the mechanism of molecular reorientation changes from small random steps to large infrequent orientational jumps. We find that the model system exhibits non-Gaussian behavior in translational and rotational motion, which strengthens upon supercooling. Examination of particle mobility reveals spatially heterogeneous dynamics in translation and rotation, with a strong spatial correlation between translationally and rotationally mobile particles. Application of the Einstein formalism to the analysis of translation-rotation decoupling results in a trend opposite to that seen in conventional approaches based on the Debye formalism, namely an enhancement in the effective rate of rotational motion relative to translation upon supercooling.Comment: 11 pages, 8 figures, 1 tabl

Multiscale Modeling of Binary Polymer Mixtures: Scale Bridging in the Athermal and Thermal Regime

Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling procedure is presented for the efficient calculation of the static structural properties of binary homopolymer blends. The procedure combines computer simulations of polymer chains on two different length scales, using a united atom representation for the finer structure and a highly coarse-grained approach on the meso-scale, where chains are represented as soft colloidal particles interacting through an effective potential. A method for combining the structural information by inverse mapping is discussed, allowing for the efficient calculation of partial correlation functions, which are compared with results from full united atom simulations. The structure of several polymer mixtures is obtained in an efficient manner for several mixtures in the homogeneous region of the phase diagram. The method is then extended to incorporate thermal fluctuations through an effective chi parameter. Since the approach is analytical, it is fully transferable to numerous systems.Comment: in press, 13 pages, 7 figures, 6 table

Renormalized one-loop theory of correlations in polymer blends

The renormalized one-loop theory is a coarse-grained theory of corrections to the self-consistent field theory (SCFT) of polymer liquids, and to the random phase approximation (RPA) theory of composition fluctuations. We present predictions of corrections to the RPA for the structure function $S(k)$ and to the random walk model of single-chain statics in binary homopolymer blends. We consider an apparent interaction parameter $\chi_{a}$ that is defined by applying the RPA to the small $k$ limit of $S(k)$. The predicted deviation of $\chi_{a}$ from its long chain limit is proportional to $N^{-1/2}$, where $N$ is chain length. This deviation is positive (i.e., destabilizing) for weakly non-ideal mixtures, with \chi_{a} N \alt 1, but negative (stabilizing) near the critical point. The positive correction to $\chi_{a}$ for low values of $\chi_{a} N$ is a result of the fact that monomers in mixtures of shorter chains are slightly less strongly shielded from intermolecular contacts. The depression in $\chi_{a}$ near the critical point is a result of long-wavelength composition fluctuations. The one-loop theory predicts a shift in the critical temperature of ${\cal O}(N^{-1/2})$, which is much greater than the predicted ${\cal O}(N^{-1})$ width of the Ginzburg region. Chain dimensions deviate slightly from those of a random walk even in a one-component melt, and contract slightly with increasing $\chi_{e}$. Predictions for $S(k)$ and single-chain properties are compared to published lattice Monte Carlo simulations.Comment: submitted to J. Chem. Phy

Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution

A First Principle Approach to Rescale the Dynamics of Simulated Coarse-Grained Macromolecular Liquids

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as a bead-and-spring model and molecular as a soft-colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse-graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse-graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.Comment: 21 pages, 6 figures, 6 tables. Submitted to Phys. Rev.

Phonon Band Structure and Thermal Transport Correlation in a Layered Diatomic Crystal

To elucidate the relationship between a crystal's structure, its thermal conductivity, and its phonon dispersion characteristics, an analysis is conducted on layered diatomic Lennard-Jones crystals with various mass ratios. Lattice dynamics theory and molecular dynamics simulations are used to predict the phonon dispersion curves and the thermal conductivity. The layered structure generates directionally dependent thermal conductivities lower than those predicted by density trends alone. The dispersion characteristics are quantified using a set of novel band diagram metrics, which are used to assess the contributions of acoustic phonons and optical phonons to the thermal conductivity. The thermal conductivity increases as the extent of the acoustic modes increases, and decreases as the extent of the stop bands increases. The sensitivity of the thermal conductivity to the band diagram metrics is highest at low temperatures, where there is less anharmonic scattering, indicating that dispersion plays a more prominent role in thermal transport in that regime. We propose that the dispersion metrics (i) provide an indirect measure of the relative contributions of dispersion and anharmonic scattering to the thermal transport, and (ii) uncouple the standard thermal conductivity structure-property relation to that of structure-dispersion and dispersion-property relations, providing opportunities for better understanding of the underlying physical mechanisms and a potential tool for material design.Comment: 30 pages, 10 figure

Asymmetries in symmetric quantum walks on two-dimensional networks

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast, directed transport through the network to the opposite corner. This transport is not ballistic in nature, but rather produced by quantum mechanical interference. In the long time limit, certain walks show an asymmetric limiting probability distribution; this feature depends on the starting site and, remarkably, on the precise size of the network. The limiting probability distributions show patterns which are correlated with the initial condition. This might have consequences for the application of continuous time quantum walk algorithms.Comment: 9 pages, 12 figures, revtex