Discrete Spinning Tops -- Difference equations for Euler, Lagrange, and Kowalevski tops

Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver algorithms are discussed. New discretization method is proposed for Kowalevski top, which have properties $\boldsymbol{\gamma}^2=1$, and the Kowalevski integral $|\xi|^2=\text{const.}$ satisfied exactly. Numerical tests are done successfully.Comment: 13 pages, 4 figure

Contact dynamics, contact Poisson bracket, and symplectic integrator -- Even Arnold nodds

By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named hybrid leap-frog method, is found to be a numerical solver of equations of motion for contact dissipative systems.Comment: 16 pages, 3 figure

Prevalence of Functional Constipation and Relationship with Dietary Habits in 3- to 8-Year-Old Children in Japan

Objectives. To determine the prevalence and effect of dietary habits on functional constipation in preschool and early elementary school children in Japan. Study Design. A total of 3595 children aged 3 to 8 years from 28 nursery schools and 22 elementary schools in Yokohama City, Kanagawa Prefecture, Japan, were evaluated. The subjects were divided into a functional constipation group and a nonfunctional constipation group according to the Rome III criteria. Dietary intake data were collected using a brief-type, self-administered, diet-history questionnaire validated for Japanese preschool-aged children. Results. Of the 3595 subjects evaluated, 718 (20.0%) had functional constipation. The association between functional constipation and gender was not statistically significant (p=0.617). A decrease in bowel frequency was observed in 15.9% of those with functional constipation. There was no significant difference in the proportion of participants in the constipation group by age (p=0.112). Binomial logistic regression analysis indicated that only fat per 100 kcal positively correlated with functional constipation [odds ratio = 1.216, 95% confidence interval: 1.0476–1.412]. Conclusions. Functional constipation is common among children in preschool and early elementary school in urban areas of Japan. Parents should pay attention to constipation-related symptoms other than defecation frequency. A high-fat diet should be avoided to prevent functional constipation

Time-Dependent Orthogonal Polynomials and Theory of Soliton(New Developments in Statistical Physics Similarities in Diversities,YITP Workshop)

この論文は国立情報学研究所の電子図書館事業により電子化されました。By introducing a time variable to the theory of orthogonal polynomials, it is shown that the matrix models of two-dimensional gravity, the six vertex model of two-dimensional lattice statistics and the random matrix theory of level statistics are all described by the theory of soliton, i.e. Toda molecule equation

Thermo-hydrodynamic lubrication analysis of journal bearings using a simplified THL model and prediction of onset speed of instability (Application of adiabatic boundary condition to the journal side)

Journal bearings are an important mechanical element of rotating machines and support the rotor system by oil film reaction forces. As rotational speeds increase, the shear heat of the oil film causes a significant temperature distribution on the journal surface. As a result, bending of the shaft occurs and vibration modes called Morton effect are generated. The Thermo Hydrodynamic Lubrication (THL) model is used for analyzing of lubricant, and one of the authors has modified and applied it as a simple unsteady model to efficiently analyze the temperature, viscosity, and pressure distribution of the oil film , maintaining computational accuracy. In this paper, the simplified THL model is modified with the boundary condition that both the bearing and journal are adiabatic (ADIADI) in order to construct an accurate and efficient analytical model of the Morton effect in the rotor system. The journal vibration is assumed to be small, and dynamic coefficients of journal bearing are derived considering the temperature distribution. Eigenvalue analysis is performed using these dynamic coefficients to predict the onset speed of instability of the rotor system. The validity of the eigenvalue analysis is verified by direct numerical integration simulation

One-, Two-, and Three-Dimensional Hopping Dynamics

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