一种适用于大幅值Quasi周期轨道的数值构造方法

针对现有方法在构造大幅值quasi周期轨道时收敛性和通用性不足等问题,提出一种适用于大幅值quasi周期轨道的数值构造方法。首先针对2维不变环面的计算问题,设计了映射间隔约束的环面多步微分修正算法。在此基础上,采用自然参数延拓法和伪弧长延拓法两种不同的思路构造等映射间隔的quasi周期轨道族。接着以quasi-Vertical为对象分析了两种思路各自的特点。最后以quasi-Axial,quasi-DRO等为对象验证了方法对三角平动点及多对复特征值情况的适用性。仿真结果表明,所提出的方法能够简单有效地解决多种类型幅值比超过1.2的大幅值quasi周期轨道的数值计算问题。

Geometric Aspects of Quasi-Periodic Property of Dirichlet Functions

The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.

Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid.

Studies of Optical Properties of Symmetrical Quasi-Periodic Photonic Crystals

Using the transfer matrix method approach (TMM), the present paper attempts to determine the optical properties of quasi-periodic symmetric one-dimensional photonic systems. In addition, it studies hybrid hetero-structure systems constructed by using periodic and quasi-periodic multilayer systems. The effect of symmetry applied to symmetric multilayer systems results in the appearance of optical windows at the photonic band gaps (PBG) of the system. The use of hybrid symmetric systems, at normal incidence in the visible range, show that the complete photonic band gap is the sum of bands from individual systems. The results show also that the width of the PBG depends on the parameters and nature of the built system.

Real-Space Renormalization Group Approach of the Potts Model on the Octagonal Quasi-Periodic Tiling

A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the correlation length in the q =1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice(SQL).

Quasi-periodic events on structured earthquake models

There has been much interest in studying quasi-periodic events on earthquake models.Here we investigate quasiperiodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform.For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system.Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena.Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system,there is evidence that it depends on the time series of the average force of the system.

Band structures of elastic waves in two-dimensional eight-fold solid–solid quasi-periodic phononic crystals

Combined with the supercell method, band structures of the anti-plane and in-plane modes of two-dimensional （2D） eight-fold solid-solid quasi-periodic phononic crystals （QPNCs） are calculated by using the finite element method. The influences of the supercell on the band structure and the wave localization phenomenon are discussed based on the modal distributions. The reason for the appearance of unphysical bands is analyzed. The influence of the incidence angle on the transmission spectrum is also discussed.

Boundedness in Asymmetric Quasi-periodic Oscillations

In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation x′′+ ax;-bx;+φ（x） = p（t）, where a≠b are two positive constants and φ（s）, p（t） are real analytic functions. Moreover, the p（t） is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions,the quasi-periodic oscillator has the Lagrange stability.

Quasi-periodic Solutions of the General Nonlinear Beam Equations

In this paper, one-dimensional （1D） nonlinear beam equations of the form utt - uxx ＋ uxxxx ＋ mu = f （u） with Dirichlet boundary conditions are considered, where the nonlinearity f is an analytic, odd function and f（u） = O（u3）. It is proved that for all m ∈ （0, M＊] R （M＊ is a fixed large number）, but a set of small Lebesgue measure, the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.

Stability and Robustness Analysis of an Adaptive Algorithm for Quasi-periodic Disturbances Rejection

Winding and web transport systems are subjected to quasi-periodic disturbances of the web tension due to the eccentricity and the non-circularity of the reel and rolls. The disturbances induced by the non-circularity and eccentricity of the rolls are quasi-periodic with a frequency that varies with their rotation speed. An adaptive method of rejection of these disturbances is proposed in this paper. It is based on a phase-locked loop structure that estimates simutaneously the phase and magnitude of the perturbation and then cancels it. This algorithm can be plugged in an existing industrial controller. The stability and robustness of the algorithm are also discussed. The ability of the algorithm to reject quasi-periodic disturbances with slowly varying frequencies is shown through simulation results.

Periodic,quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein-Gordon lattice

We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.

Reducibility of Periodic Quasi-Periodic Systems

In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.

近136年(1885~2020年)长江中下游伏旱期划分及其演变分析

少雨高温的伏旱期对长江中下游地区农业、水利和人体健康等具有重要影响,但目前缺乏对该地区伏旱期的历史划分,对其长期变化规律也缺乏充分认识。本文利用1885年以来已划定的长江中下游沿江五站(上海、南京、芜湖、九江和汉口)梅雨期和夏季日气温、降水资料,对出梅后的少雨高温时段分别确定了少雨和高温的定量标准,划定出1885~2020年长江中下游伏旱期,并用统一气温标准结合伏旱期长度,综合确定了近136 a(1885~2020年)伏旱期强度指数。这136 a(包含有16个无伏旱年及10个入秋伏旱年)里伏旱期的年平均长度为21.6 d,呈现出3~6 a、36 a和84 a周期。1951年以来,1959~1978年是伏旱期长度的主要峰期,1980~1987年是伏旱期长度的下降谷期,之后缓慢增加;1980年代之后虽然大于30 d的长伏旱期有减少趋势,但是15~30 d且高强度的伏旱期频现;1995年之后秋伏旱明显增多,夏季延迟。136 a里最长且强的伏旱期依次出现于1934、1967、1978和2013年;最早的伏旱期出现在6月中旬,最晚在9月中下旬。近40 a来,伏旱期高温(≥35.0°C)日数大幅提高,伏旱期高温发生率从1980年代的30%左右上升到近年的50%以上,对人体健康构成威胁。长(强)伏旱期的副热带环流特征为西太平洋副热带高压稳定控制长江中下游区,而短(弱)伏旱期西太平洋副热带高压多偏东或偏南,入秋伏旱与副热带高压稳定西伸有关。伏旱期内高温日数的演变受到双重人类活动的制约,它不仅与人类活动导致的全球海陆升温有关,并且因地而异,即受到局地生态环境演变和城市热岛效应增减的人为作用影响。印度—太平洋季风区陆海温差对长江中下游伏旱期长度年代际变化有重要调制作用。

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.

天线引向器阵列的准周期布局优化方法

准周期电磁金属阵列已被成功应用于机载旋罩天线等多种类型的电子器件中,用以提升电磁辐射性能。与周期阵列相比,准周期阵列不再受到周期性的限制,其设计自由度大幅增加,但也导致布局形式的描述参数规模更大且相互独立。同时,在准周期阵列的布局优化中,各个阵元间存在非规律耦合效应,耦合效应随着布局形式的变化而发生变化,该非规律变耦合效应需要在布局优化的迭代过程中严格考虑,以实现性能的精准设计。提出一种基于阵元几何移动、考虑变耦合效应的准周期电磁金属阵列布局优化方法,并将其用于求解天线引向器阵列的准周期布局。数值算例表明,通过引向器阵列中各个阵元尺寸和布置位置的协同优化,能够实现天线辐射波束性能的提升。

黑龙江省准对称混合训练期MOS气温预报性能分析

本文选取ECMWF细网格地面2 m气温要素预报产品作为预报因子,选取中国气象局陆面数据同化系统(CLDAS-V2.0)地面2 m气温格点实况数据作为预报量,应用准对称混合训练期MOS方法,建立黑龙江省格点气温MOS方法,并对MOS方法在24 h预报时效内间隔3 h的格点气温预报性能进行检验分析。结果表明:MOS平均绝对误差≤1.5℃;MOS夏半年≤2℃预报准确率为84.1%,比ECMWF提高7.6%;冬半年预报准确率为71.5%,比ECMWF提高18.3%;预报技巧夏半年为14.2%,冬半年为29.8%。MOS夏半年预报效果好于冬半年,冬半年预报改善效果好于夏半年。大、小兴安岭和东南部山区MOS预报效果不如平原地区好,但是MOS改善效果明显好于平原地区。

制度型开放对企业投资效率的影响研究——以自由贸易试验区建设为例

选取2009—2022年沪深A股上市公司为样本,运用多时点双重差分法检验自贸区建设对企业投资效率的影响。研究表明:自贸区建设能够有效改善企业投资不足和过度投资的情况,进而促进企业投资效率提高;机制检验发现,自贸区建设可以通过创新水平提升效应、税收优惠提高效应、融资环境改善效应和融资约束缓解效应提高企业投资效率;异质性检验发现,自贸区建设能够显著提升民营企业、非资本密集型行业、低层级城市企业的投资效率。基于此,进一步深化制度型对外开放,加强制度型开放政策之间的联动性,因地制宜加强自贸区建设、制定区内政策,对促进企业投资效率提高有重要作用。

重构谐波平衡法及其求解复杂非线性问题应用

谐波平衡法是求解非线性动力学系统周期解的最常用方法,但对非线性项进行高阶近似需要庞杂的公式推导,限制了该方法的超高精度解算.通过对频域非线性量的时域等价重构,提出了重构谐波平衡法(RHB法),解决了经典谐波平衡法超高阶次计算难题.然而,上述两种方法均要求动力学系统为多项式型非线性,且无法直接用来求解非线性系统的拟周期解.针对上述问题,文章提出一种将RHB法和复杂非线性系统等价重铸法相结合的计算方法,首先将一般非线性问题无损重铸为多项式型非线性系统,然后用RHB法进行高精度求解;针对拟周期响应求解问题,提出基于“补频”思想的RHB方法,通过基频的优化筛选,实现拟周期响应的快速精准捕捉.选取非线性单摆、相对论谐振子和非线性耦合非对称摆等典型系统进行仿真计算,仿真结果表明,所提出的RHB-重铸法在解非多项式型非线性系统的稳态响应时精度保持为10^(-12)量级,达计算机精度,远超现有方法水平.补频RHB法则实现了对拟周期问题的高效解算,拓宽了方法对真实物理响应的求解范围.

准周期激励Duffing系统中奇异非混沌吸引子的判别方法

奇异非混沌动力学是非线性动力学领域中的新课题。本文以准周期激励Duffing振子为例,对其产生的奇异非混沌吸引子(strange nonchaotic attractors,SNAs)进行分析。通过三维庞加莱截面和定量方法如傅里叶变换、李雅普诺夫指数、李雅普诺夫维数、关联维数和盒维数检测SNAs是否存在。研究结果表明,傅里叶变换无法判断混沌与奇异非混沌行为。而李雅普诺夫指数、李雅普诺夫维数可以作为检测系统混沌与非混沌指标。关联维数和盒维数显著表明系统奇异与非奇异性,从而阐明适用于准周期驱动Duffing振子中存在SNAs的判别方法,并为其他类似系统检测SNAs提供指导。

基于渐近均匀化方法的准周期梁结构等效刚度数值实现方法研究

相比周期梁结构,准周期梁结构沿轴向梯度变化,具有更大的设计自由度,能够获得更好的结构性能。由于其非均质性,一般将其均匀化为具有等效性质的均质梁结构,但现有工作很少涉及准周期梁结构等效性质的计算。本文针对由周期梁结构映射而成的准周期梁结构,通过引入雅可比矩阵,基于渐近均匀化方法推导的单胞方程及其等效性质计算列式,并建立了其单胞方程及等效刚度的有限元求解列式。该方法可以处理沿轴向变形的任意微单胞构型,数值算例验证了其正确性和有效性。