Rotating class of parametric resonance processes in coupled oscillators

We single out and elucidate basic features of strongly coupled parametric oscillators as opposed by symmetry to the type reducible to uncoupled Mathieu equations. The strongly coupled type is essential to the oscillations and waves in rotating structures and chiral systems. It exhibits only the main parametric resonance, no higher-order ones. As well, the relaxation–fluctuation behavior is unusual, characterized by a negative-energy oscillation mode that is, nonetheless, stable so the Gibbs statistics lose its force. The models presented are exactly solvable.     

Borel resummation of the ?-expansion of the dynamical exponent z in model a of the ?4(O(n)) theory

We perform the Borel resummation of the currently known terms of the ɛ-expansion up to order ɛ ⁴ of the dynamical exponent z in the critical-behavior model A. We obtain the large-order asymptotic approximation of the ɛ-expansion of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 96–108, April, 2009.     

Dynamic Monte Carlo Renormalization group. II

The dynamic Monte Carlo Renormalization group method introduced by Jan, Moseley, and Stauffer is used to determine the dynamic exponent of the Ising model with conserved magnetization in two dimensions. We present an explicit theoretical basis for the method and expand on the original results for the Kawasaki model. The new result clearly demonstrates the validity of the method and the value of the dynamic exponent,z=3.79±0.05, supports the conclusion of Halperin, Hohenberg, and Ma.     

Commutators of fractional integral operators on Vanishing-Morrey spaces

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces VL ^p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal function and the fractional maximal function and related Morrey inequalities.      

Study of a Biological Oscillation System by a Microcalorimetric Method

The power–time curves of a biological oscillation system were determined for different temperatures, acidities and carbon sources, by using a 2277 thermal activity monitor. The apparent activation energy and order of the oscillation reaction were calculated from the induction period (t _in) and the first oscillation period (t _p). The regularity of the biological oscillation system is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

一阶非线性具偏差变元脉冲微分方程

给出了具有时滞和时超的一阶非线性脉冲微分方程所有解为振动的充分条件，所得结论包含了线性情形作为其推论。     

Numerical investigation of the effect of inlet condition on self‐excited oscillation of wet steam flow in a supersonic turbine cascade

Self‐excited oscillation can be induced due to the interaction between condensation process and local transonic condition in condensing flow, which is an important problem in wet steam turbine. With an Eulerian/Eulerian numerical model, the self‐excited oscillation of wet steam flow is investigated in a supersonic turbine cascade. Owing to supercritical heat addition to the subsonic flow in the convergent part of the cascade, the oscillation frequency decreases with increased inlet supercooling. Mass flow rate increases in the oscillating flow due to the greater supersaturation in condensation process, while the increase will be suppressed with the flow oscillation. Higher inlet supercooling leads to the fact that the condensation process moves upstream and the loss increases. Moreover, some predictions of oscillation effects on outflow angle and aerodynamic force are also presented. Finally, heterogeneous condensations with inlet wetness and periodic inlet conditions, as a result of the interference between stator and rotor, are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Anti-control of chaos in Bose-Einstein condensates

The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the chaotic orbits associated with the positive Lyapunov exponents.      

Application of Complexity Theory to an Information Processing Model in Science Education

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.     

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q₀ and the critical Fujita exponent qc for the problems considered, and show that q₀=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q₀<qc for the one-dimensional case.