一类描述混沌映射的符号动力系统

本文定义了符号空间上的拟移位映射,并用该类映射描述了Ｃａｎｔｏｒ集及平面Ｃａｎｔｏｒ集上的混沌映射,本文结果可看作Ｓｍａｌｅ马蹄模型的简化。     

RANS-based numerical simulation and visualization of the horseshoe vortex system in the leading edge endwall region of a symmetric body

This contribution is aimed at analyzing the capabilities of popular two-equation turbulence models to predict features of 3D flow fields and endwall heat transfer near the blunt edge of a symmetric body mounted on a plate. The configuration studied experimentally by Praisner and Smith is considered. Results obtained with the in-house CFD code SINF and the commercial package ANSYS–CFX are presented and compared. Prediction capabilities of the low-Re Wilcox turbulence model and two versions of the Menter SST model, the original and the modified one, are analyzed in comparison with the experimental data. Special attention is paid to grid sensitivity of the numerical solutions. Advanced visualization of the vortex structures computed is performed with author’s visualization tool HDVIS. It has been established that the Wilcox model is not capable of predicting the development of a multiple-vortex system observed in the experiment upstream of the body leading edge. Both versions of the MSST model produce qualitatively correct results, with a considerable superiority of the modified version when compared with the quantitative data.     

广义Taylor映射与Hénon映射具有混沌条件的改进

本文进一步讨论了近年来动力系统中关于对具有混沌现象的Taylor映射,Henon映射等函数所做的研究,并着重分析了所讨论函数的参数.     

Computer-assisted verification of chaos in the model of nuclear spin generator

In this paper, chaos in a nuclear spin generator is revisited. To confirm the numerically demonstrated chaotic behavior in the nuclear spin generator, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.     

扭管混合实验研究

本文通过实验研究扭管中的混沌现象,用烟气显示扭管截面上的混沌对流图像并和数值结果比较,分析其中的马蹄形映及其对流体混合的作用。结果表明,在实际的扭管流动中,由于在管截面上出现马蹄形映射（混沌）,使得其中的流体受到剧烈的拉伸的折叠,实现高效的混合操作。     

Bouncing Ball映射的双曲不变集

对碰撞恢复系数范围为 0 <α<1的“弹跳球 (Bouncing Ball)”映射 ,通过适当的坐标变换 ,给出了双曲不变集存在的严格条件 .     

Horseshoe in a model of artificial neural network

In this paper, we study a three-dimensional general model of artificial neural network (ANN). To confirm the chaotic behavior in this neural network demonstrated in numerical studies, we consider a cross-section properly chosen for the attractor obtained and study the dynamics of the corresponding Poincaré map, and rigorously verify the existence of horseshoe by computer-assisted verification arguments.     

Numerical simulation and control of horseshoe vortex around an appendage-body junction

The horseshoe vortex generated around the appendage-body junction of submarines strongly influences the non-uniformity of submarine wakes at the propeller discs. The flow characteristics around the appended submarine body are numerically simulated and analyzed, and a new method on the vortex control baffle is presented. Then, the influence of the vortex control baffle on the horseshoe vortex generated at the sail-body junction is numerically studied, and the flow phenomena caused by the vortex control baffle with different transverse positions is investigated further. Results show that the vortex control baffle can induce a kind of attached vortex in a rotational direction opposite to the horseshoe vortex; these two kinds of vortices undermine each other. Furthermore, when the transverse position of the vortex control baffle is close to the horseshoe vortex, the state of the horseshoe vortex is directly affected, and the flow structure becomes even more complex. We adapt the vortex control baffle for the horseshoe vortex generated at the stern foil-body junction. Results from the numerical simulation of the flow around the fully appended submarine model indicate that the effect of the vortex control baffle greatly improves the performance of the submarine wake. The circumferential non-uniformity of the axial, tangential, and radial velocity components are decreased markedly. The engineering applicability of the vortex control baffle has been well presented.     

Quasi-d-Koszul Modules and Applications

Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod（R）. As an application, it is proved that the ＂Minimal Horseshoe Lemma＂ is true in the category of quasi-d-Koszul modules under certain conditions.     

Characterization of soliton solutions in 2D nonlinear Schrödinger lattices by using the spatial disorder

In this paper, the pattern of the soliton solutions to the discrete nonlinear Schrödinger (DNLS) equations in a 2D   lattice is studied by the construction of horseshoes in _l∞$l_{\infty }$-spaces. The spatial disorder of the DNLS equations is the result of the strong amplitudes and stiffness of the nonlinearities. The complexity of this disorder is log(N+1)$\log (N+1)$ where N   is the number of turning points of the nonlinearities. For the case N=1$N=1$, there exist disjoint intervals _I0$I_0$ and _I1$I_1$, for which the state _um,n$u_{m,n}$ at site (m,n)$(m,n)$ can be either dark (_um,n∈_I0$u_{m,n}\in I_0$) or bright (_um,n∈_I1$u_{m,n}\in I_1$) that depends on the configuration _km,n=0$k_{m,n}=0$ or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed.