Sharp bounds on enstrophy growth in the viscous Burgers equation

We use the Cole--Hopf transformation and the Laplace method for the heat equation to justify the numerical results on enstrophy growth in the viscous Burgers equation on the unit circle. We show that the maximum enstrophy achieved in the time evolution is scaled as $\mathcal{E}^{3/2}$, where $\mathcal{E}$ is the large initial enstrophy, whereas the time needed for reaching the maximal enstrophy is scaled as $\mathcal{E}^{-1/2}$. These bounds are sharp for sufficiently smooth initial conditions.Comment: 12 page

Exact shock solution of a coupled system of delay differential equations: a car-following model

In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called {\it the car-following model}. We use the Hirota method, originally developed in order to solve soliton equations. %While, with a periodic boundary condition, this system has % a traveling-wave solution given by elliptic functions. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with a periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure

Measuring chocolate craving in adults

Present research finds that the experience of chocolate craving is unique from other foods (Bruinsma & Taren, 1999). Only two measures on chocolate craving exist, the Attitudes to Chocolate Questionnaire (ACQ; Benton et al., 1998) and the Orientation to Chocolate Questionnaire (OCQ; Cartwright et al., 2007). Both measures theoretically vary and include subscales that measure other eating components, such as guilt-driven restrictive eating. A need for a measure that focuses on the characteristics of chocolate craving and consumption exists. Thus, the Chocolate Craving Inventory (CCI; Whitham & Reynolds, 2014) was created. The purpose of the present study was to examine the reliability and validity of this new scale. A sample of 530 participants completed the survey both in-person and online. As hypothesized, the CCI is a sound measure that exhibited a high internal consistency reliability of .95. The Craving subscale of the ACQ demonstrated strong relationship with the CCI and Approach subscale of the OCQ demonstrated a strong relationship with the CCI. Further evidence for convergent validity was verified by the following measures: the Dutch Eating Behavior Questionnaire (DEBQ; Van Strien et al., 1986) and the Food Cravings Questionnaire-Trait-revised (FCQ-T-r; Cepeda-Benito et al., 2001). Discriminant validity was found between the CCI and measures of depression and social desirability. An exploratory factor analysis revealed a three-factor solution of craving, emotional eating, and daily interference

Upper Body Characteristics Related To Double Pole Performance in Female Cross Country Skiers

The purpose of the current study was to correlate upper body (UB) lean mass (UBLM), UB maximal strength (UBMS), and average power production during a 3-min ski ergometer (SERG) test to predict the dependent variable, a one-kilometer uphill double pole time trial (DPTT) on snow. We hypothesized UBLM would be most important to performance. All tests were conducted within four weeks of completing the championship phase of a Division I cross country (XC) ski season. Skiers (n=10; all females) performed the mass-start DPTT on snow (i.e., criterion measure), SERG, and UBMS separated by at least a few days recovery. Lastly, body composition was determined via dual-energy x-ray absorptiometry (DXA) with a focus on UB mass characteristics (i.e., trunk + arm lean mass). A significant (p = 0.02) correlation was observed between DPTT and UBLM. No significant (p \u3e 0.05) correlations were observed for UBMS or SERG vs. DPTT. Thus, our hypothesis was supported and we suggest female, competitive cross country skiers work to build functional UB lean mass to best prepare for utilizing the ever popular and evolving double pole technique

Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.Comment: 4 pages, 3 figure

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Renormalized waves and thermalization of the Klein-Gordon equation: What sound does a nonlinear string make?

We study the thermalization of the classical Klein-Gordon equation under a u^4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear behavior in a renormalized wave basis. The renormalized basis is defined locally in time by a linear transformation and the requirement of vanishing wave-wave correlations. We show that the renormalized waves oscillate around one frequency, and that the frequency dispersion relation undergoes a nonlinear shift proportional to the mean square field. In addition, the renormalized waves exhibit a Planck like spectrum. Namely, there is equipartition of energy in the low frequency modes described by a Boltzmann distribution, followed by a linear exponential decay in the high frequency modes.Comment: 13 pages, 13 figure

Weakly versus highly nonlinear dynamics in 1D systems

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order parameter, or a concentration profile. We show that two types of dynamics occur around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics. The conditions under which highly nonlinear evolution equations appear are determined, and their generic form is derived. Finally, examples are discussed.Comment: to be published in Europhys. Let

Soybean mosaic virus: A successful potyvirus with a wide distribution but restricted natural host range

Taxonomy. Soybean mosaic virus (SMV) is a species within the genus Potyvirus, family Potyviridae that includes almost a quarter of all known plant RNA viruses affecting agriculturally important plants. The Potyvirus genus is the largest of all genera of plant RNA viruses with 160 species. Particle. The filamentous particles of SMV, typical of potyviruses, are about 7,500 Å long and 120 Å in diameter with a central hole of about 15 Å in diameter. Coat protein residues are arranged in helice of about 34 Å pitch having slightly less than 9 subunits per turn. Genome. The SMV genome consists of a single-stranded positive-sense polyadenylated RNA of approximately 9.6 kb with a virus-encoded protein (VPg) linked at the 5\u27 terminus. The genomic RNA contains a single large open reading frame (ORF). The polypeptide produced from the large ORF is processed proteolytically by three viral-encoded proteinases to yield about 10 functional proteins. A small ORF, partially overlapping the P3 cistron, pipo, is encoded as a fusion protein in the N-terminus of P3 (P3N+PIPO). Biological properties. SMV’s host range is restricted mostly to two plant species of a single genus; Glycine max (cultivated soybean) and G. soja (wild soybean). SMV is transmitted by aphids non-persistently and by seeds. Variability of SMV is recognized by reactions on cultivars with dominant resistance (R) genes. Recessive resistance genes are not known. Geographical distribution and economic importance. As a consequence of its seed transmissibility, SMV is present in all soybean growing areas of the world. SMV infections can reduce significantly seed quantity and quality (e.g., mottled seed coats, reduced seed size and viability, and altered chemical composition). Control. The most effective means of managing losses from SMV are planting virus-free seeds and cultivars containing single or multiple R genes. Key attractions. The interactions of SMV with soybean genotypes containing different dominant R genes and understanding functional role(s) of SMV-encoded proteins in virulence, transmission and pathogenicity have been intensively investigated. The SMV-soybean pathosystem has become an excellent model for examining the genetics and genomics of uniquely complex gene-for-gene resistance model in a crop of worldwide importance

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur