Solitons and kinks in a general car-following model

We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of that dependence. The velocity of uniform steady flow is found implicitly from the acceleration function, and its linear stability criterion can be expressed simply in terms of it. Crucially, unlike in previously analyzed car-following models, the threshold of absolute stability does not generally coincide with an inflection point in the steady velocity function. The Burgers and KdV equations can be derived under the usual assumptions, but the mKdV equation arises only when absolute stability does coincide with an inflection point. Otherwise, the KdV equation applies near absolute stability, while near the inflection point one obtains the mKdV equation plus an extra, quadratic term. Corrections to the KdV equation "select" a single member of the one-parameter set of soliton solutions. In previous models this has always marked the threshold of a finite- amplitude instability of steady flow, but here it can alternatively be a stable, small-amplitude jam. That is, there can be a forward bifurcation from steady flow. The new, augmented mKdV equation which holds near an inflection point admits a continuous family of kink solutions, like the mKdV equation, and we derive the selection criterion arising from the corrections to this equation.Comment: 25 page

College, Career, and Community Writer’s Program (C3WP) Data-driven Reports of Literacy Growth

Through the implementation of mini-units in from the C3WP, a teacher demonstrates that routine argument writing leads to great gains in argument writing literacy

Corrugation of Roads

We present a one dimensional model for the development of corrugations in roads subjected to compressive forces from a flux of cars. The cars are modeled as damped harmonic oscillators translating with constant horizontal velocity across the surface, and the road surface is subject to diffusive relaxation. We derive dimensionless coupled equations of motion for the positions of the cars and the road surface H(x,t), which contain two phenomenological variables: an effective diffusion constant Delta(H) that characterizes the relaxation of the road surface, and a function alpha(H) that characterizes the plasticity or erodibility of the road bed. Linear stability analysis shows that corrugations grow if the speed of the cars exceeds a critical value, which decreases if the flux of cars is increased. Modifying the model to enforce the simple fact that the normal force exerted by the road can never be negative seems to lead to restabilized, quasi-steady road shapes, in which the corrugation amplitude and phase velocity remain fixed.Comment: 20 pages, 8 figures, typos correcte

Noise and Dynamical Pattern Selection in Solidification

The overall goal of this project was to understand in more detail how a pattern-forming system can adjust its spacing. "Pattern-forming systems," in this context, are nonequilibrium contina whose state is determined by experimentally adjustable control parameter. Below some critical value of the control system then has available to it a range of linearly stable, spatially periodic steady states, each characterized by a spacing which can lie anywhere within some band of values. These systems like directional solidification, where the solidification front is planar when the ratio of growth velocity to thermal gradient is below its critical value, but takes on a cellular shape above critical. They also include systems without interfaces, such as Benard convection, where it is the fluid velocity field which changes from zero to something spatially periodic as the control parameter is increased through its critical value. The basic question to be addressed was that of how the system chooses one of its myriad possible spacings when the control parameter is above critical, and in particular the role of noise in the selection process. Previous work on explosive crystallization had suggested that one spacing in the range should be preferred, in the sense that weak noise should eventually drive the system to that spacing. That work had also suggested a heuristic argument for identifying the preferred spacing. The project had three main objectives: to understand in more detail how a pattern-forming system can adjust its spacing; to investigate how noise drives a system to its preferred spacing; and to extend the heuristic argument for a preferred spacing in explosive crystallization to other pattern-forming systems

Explosive crystallization mechanism of ultradisperse amorphous films

The explosive crystallization of germanium ultradisperse amorphous films is studied experimentally. We show that crystallization may be initiated by local heating at the small film thickness but it realizes spontaneously at the large ones. The fractal pattern of the crystallized phase is discovered that is inherent in the phenomena of diffusion limited aggregation. It is shown that in contrast to the ordinary crystallization mode the explosive one is connected with the instability which is caused by the self-heating. A transition from the first mechanism to the second one is modelled by Lorenz system. The process of explosive crystallization is represented on the basis of the self-organized criticality conception. The front movement is described as the effective diffusion in the ultrametric space of hierarchically subordinated avalanches, corresponding to the explosive crystallization of elementary volumes of ultradisperse powder. The expressions for the stationary crystallization heat distribution and the steady-state heat current are obtained. The heat needed for initiation of the explosive crystallization is obtained as a function of the thermometric conductivity. The time dependence of the spontaneous crystallization probability in a thin films is examined.Comment: 22 pages, 5 figures, LaTe

Surface Instability in Windblown Sand

We investigate the formation of ripples on the surface of windblown sand based on the one-dimensional model of Nishimori and Ouchi [Phys. Rev. Lett. 71, 197 (1993)], which contains the processes of saltation and grain relaxation. We carry out a nonlinear analysis to determine the propagation speed of the restabilized ripple patterns, and the amplitudes and phases of their first, second, and third harmonics. The agreement between the theory and our numerical simulations is excellent near the onset of instability. We also determine the Eckhaus boundary, outside which the steady ripple patterns are unstable.Comment: 23 pages, 8 figure

Yang-Lee Edge Singularity on a Class of Treelike Lattices

The density of zeros of the partition function of the Ising model on a class of treelike lattices is studied. An exact closed-form expression for the pertinent critical exponents is derived by using a couple of recursion relations which have a singular behavior near the Yang-Lee edge.Comment: 9 pages AmsTex, 2 eps figures, to appear in J.Phys.

Reliability and validity of the international physical activity questionnaire in the Nord-Trøndelag health study (HUNT) population of men

<p>Abstract</p> <p>Background</p> <p>There is no standardized method for the assessment of physical activity (PA). Therefore it is important to investigate the validity and comparability of different measures. The International Physical Activity Questionnaire (IPAQ) has been developed as an instrument for cross-national assessment of PA and has been validated in 12 countries. These instruments have acceptable measurement properties for monitoring population levels of PA among 18–65 year-old adults in diverse settings. However, there are some concerns that IPAQ may over-report PA.</p> <p>The purpose of this study is to evaluate the reliability and validity of IPAQ, short version, last 7-days in the Nord-Trøndelag Health Study (HUNT) population of men.</p> <p>Methods</p> <p>The questionnaire was administered twice to a random sample of 108 men aged 20–39 and validity by comparing results with VO_2maxand ActiReg, an instrument that measures PA and energy expenditure (EE). ActiReg discriminates between the body positions: stand, sit, bend forward and lie and also registers if there is motion or not in each of them or both.</p> <p>Results</p> <p>Our results for reliability of the IPAQ short version were good for vigorous and fair for moderate activities. Intraclass correlations ranged from a low of 0.30 for moderate activity hours, to a high of 0.80 for sitting hours. Concerning validity, our results suggest that total IPAQ vigorous PA was a moderately good measure of vigorous activity, having moderately strong, significant correlations with VO_2max, r = 0.41 (p ≤ 0.01), but correlated not with metabolic equivalent (METs) values of 6 or more measured with ActiReg. Only total IPAQ walking was fair correlated with METs 1–3 and METs 3–6, respectively r = -0.27 and 0.26 (p ≤ 0.05). The index for IPAQ sitting hours per week was moderate correlated with METs values of 1–3 and negatively correlated with METs values of 3–6. Classification of PA in three levels (low, moderate and high) correlated also most strongly with VO_2max(0.31 p ≤ 0.01) and METs 3–6 and METs 1–3 from ActiReg (r = 0.32 and -0.31, p ≤ 0.01). Classification of BMI in three levels (normal, overweight and obese) correlated most strongly negative with VO_2max(-0.42 p ≤ 0.01) and MJ from ActiReg (r = 0.31 p ≤ 0.01).</p> <p>Conclusion</p> <p>Our results indicate that IPAQ short version for men has acceptable reliability and criterion validity for vigorous activity and sitting. Walking has moderate reliability. Only the IPAQ for walking had a fair correlation with METs 6+. The questions about moderate activity had fair reproducibility and correlated poorly with most comparison measures.</p