Recurrence time statistics in chaotic dynamics. I. Discrete time maps

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.     

A second-order space–time accurate scheme for nonlinear diffusion equation with general capacity term

A fully implicit finite difference (FIFD) scheme with second-order space–time accuracy is studied for a nonlinear diffusion equation with general capacity term. A new reasoning procedure is introduced to overcome difficulties caused by the nonlinearity of the capacity term and the diffusion operator in the theoretical analysis. The existence of the FIFD solution is investigated at first which plays an important role in the analysis. It is established by choosing a new test function to bound the solution and its temporal and spatial difference quotients in suitable norms in the fixed point arguments, which is different from the traditional way. Based on these bounds, other fundamental properties of the scheme are rigorously analyzed consequently. It shows that the scheme is uniquely solvable, unconditionally stable, and convergent with second-order space–time accuracy in L^∞(L²) and L^∞(H¹) norms. The theoretical analysis adapts to both one- and multidimensional problems, and can be extended to schemes with first-order time accuracy. Numerical tests are provided to verify the theoretical results and highlight the high accuracy of the second-order space–time accurate scheme. The reasoning techniques can be extended to a broad family of discrete schemes for nonlinear problems with capacity terms.     

Superconvergent estimates of conforming finite element method for nonlinear time‐dependent Joule heating equations

In this article, we study the superconvergence analysis of conforming bilinear finite element method (FEM) for nonlinear Joule heating equations. Based on the rigorous estimates together with high accuracy analysis of this element, mean value technique and interpolation postprocessing approach, the superclose and superconvergent estimates about the related variables in H¹‐norm are derived for semidiscrete and a linearized backward Euler fully discrete schemes, which extends the results of optimal estimates obtained for conforming FEMs in the previous literature. At last, a numerical experiment is performed to verify the theoretical analysis.     

A posteriori error estimates for H 1-Galerkin mixed finite-element method for parabolic problems

The purpose of this article is to derive a posteriori error estimates for the H ¹-Galerkin mixed finite element method for parabolic problems. We study both semidiscrete and fully discrete a posteriori error analyses using standard energy argument. A fully discrete a posteriori error analysis based on the backward Euler method is analysed and upper bounds for the errors are derived. The estimators yield upper bounds for the errors which are global in space and time. Our analysis is based on residual approach and the estimators are free from edge residuals.     

Fourier type analysis and the marcenko equation

For certain Fourior type operators P a transform calculus is developed and used to derive a general canonical Marcenko equation connecting P and more general Q via scattering data from Q.     

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.     

光谱开关与多色光场的奇点光学效应

推导出多色高斯光束和高斯-谢尔模型光束通过杨氏实验双缝传输的谱强度公式.对完全空间相干光和部分空间相干光照明杨氏实验装置出现的光谱开关作了详细研究,并判断其是否属于奇点光学效应. 结果表明：多色场奇点光学效应的判据应当是光谱开关出现时的谱强度极小值S_min=0,而不是总光强极小值I_min=0. 当用多色高斯-谢尔模型光束照明杨氏实验装置时,在近场和远场产生的光谱开关都不属于奇点光学效应. 当用多色高斯光束照明杨氏实验装置时,只有远场产 关键词： 光谱开关 奇点光学效应 完全相干和部分相干 多色光场     

Rate coefficients for reactions of OH radicals with CH3D,CH2D2, CHD3, and CD4

Fourier transform infrared (FTIR) smog chamber techniques were used to investigate the atmospheric chemistry of the isotopologues of methane. Relative rate measurements were performed to determine the kinetics of the reaction of the isotopologues of methane with OH radicals in cm³ molecule⁻¹ s⁻¹ units: k(CH₃D + OH) = (5.19 ± 0.90) × 10⁻¹⁵, k(CH₂D₂ + OH) = (4.11 ± 0.74) × 10⁻¹⁵, k(CHD₃ + OH) = (2.14 ± 0.43) × 10⁻¹⁵, and k(CD₄ + OH) = (1.17 ± 0.19) × 10⁻¹⁵ in 700 Torr of air diluent at 296 ± 2 K. Using the determined OH rate coefficients, the atmospheric lifetimes for CH_4–xD_x (x = 1–4) were estimated to be 6.1, 7.7, 14.8, and 27.0 years, respectively. The results are discussed in relation to previous measurements of these rate coefficients.     

Poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethylmethacrylate))] thermoresponsive microspheres: An accurate method based on solute exclusion technique to determine the volume phase transition temperature

Poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethylmethacrylate))] [poly(NIPAAm-co-AAm-co-HEMA)] copolymer was synthesized as a new thermoresponsive material possessing a lower critical solution temperature (LCST) around 37 °C in phosphate buffer, pH 7.4, at a solution concentration of 1%, w/v. The influence of polymer concentration on LCST was determined by cloud point measurements and by microcalorimetric analysis. The copolymer was transformed in hydrogel microspheres by suspension reticulation of OH groups with glutaraldehyde. The volume phase transition temperature (VPTT) of microspheres was determined by a new approach, which involves measurement of the increase in concentration of a blue dextran (BD) solution at different temperatures in the presence of dry microspheres. The minimum BD concentration that gives reliable and reproducible results was determined to be 1 mg/ml. However, the higher is the concentration of BD in solution the smaller is the error. Contrary to solution of the linear polymer which displays a sharp phase transition temperature, the dependence of water regain of the hydrogel with temperature lasts from 4 °C to 50 °C.     

一类不可压缩材料平面应力问题的裂纹尖端场

本文采用完全非线性弹性理论,研究了一类不可压缩橡皮类材料[1]在Ⅰ型荷载作用下的平面应力问题.指出裂尖变形由两个收缩区和一个扩张区三部分组成.裂纹尖端应力、应变分别具有R-1、R-1/n的奇异性,当趋近裂尖时,厚度以R1/4n的方式趋于零,n为材料常数.