通过分散反馈控制使稳定的Takagi-Sugeno(TS)模糊系统产生Devaney混沌

研究了利用分散状态反馈控制使稳定的Takagi-Sugeno(TS)模糊系统产生Devaney混沌的问题。所提的分散反馈控制器是由分散线性反馈控制器与2补运算的溢出非线性函数复合而成的。2补运算的溢出非线性导致了复杂动态。应用Shi-Chen定理从数学上证明了受控系统在Devaney意义下确实是混沌的。给出了计算混沌化参数的解析公式。一个数值例子被用来说明所提的理论结果。     

A novel approach for characterizing the nonlinear phase steps of the PZT in interferometry

We propose a novel approach to estimate the phase distribution in the presence of nonlinear response of the PZT. The proposed method is an outcome of two different concepts based on the discrete chirp Fourier transform (DCFT) and the maximum-likelihood estimator for the estimation of nonlinear phase step. The robustness of the proposed method is tested for various magnitudes of nonlinearity and harmonics. Comparison of our proposed method with the bench marking algorithm by Hibino et al.'s six and nine sample algorithm in the presence of noise shows that our method is highly efficient.     

Analysis of the dispersion relations of nonlinear slab-guided waves

The dispersion relations of TE-polarized nonlinear guided waves (NGW) were investigated in detail. These waves travel along a dielectric slab embedded between two different nonlinear media. A simple relation between the effective nonlinear dielectric constants was established. All dispersion curves exhibit a particular transition point, where one evanescent field maximum changes from a virtual into a real one, and vice versa. Depending on the type of the remaining invariant evanescent field maximum, all NGW's split into two families. The lowest-order membres of every family play a particular role. The power flux supported by a NGW is derived, too.Preliminary results were presented at the XVI^th European Congress of Molecular Spectroscopy, Sofia, Bulgaria (1983)     

Non-dispersive traveling waves in inclined shallow water channels

Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied.     

Spinor fields in the theory of relativity and a generalization of Heisenberg's nonlinear spinor equation

Some years ago it was shown that the nonlinear term of Heisenberg's spinor equation can be derived by torsion of the Minkowski space (Cartan space). This result is applied in the investigations of this paper. As the Heisenberg equation does not show any connection with recent phenomenological theories in high energy physics, like the parton or quark model, the problems of the metric of space-time are discussed from the aspect of fundamental axioms of topology (Hausdorff space). It will be shown that Feynman's relativistic parton theory can be derived by means of a quantised de Sitter space, where the constant curvature can assume only discrete values. It is also possible to derive the Dirac equation from the same mathematical considerations. A nonlinear spinor equation will be formulated which contains the parton theory and the nonlinear term of the Heisenberg equation as different approaches in the theory of elementary particles.     

Nonequilibrium dynamics of parametrically excited cold atoms via magnetic field-gradient modulation

We propose that the driven cold atomic system whose trap potential is periodically perturbed via parametric modulation of the magnetic field-gradien is a novel system to investigate the complex dynamics in nonlinear dynamical systems. We calculate the atomic trajectories and basins of attraction by varying the modulation amplitude and the modulation frequency. The calculation results show parametric resonance similar to those in Kim et. al.'s work [Opt. Commun. 236 (2004) 349] on cold atoms under parametric modulation of trap laser intensities in the case of small modulation amplitude or low modulation frequency. As the modulation amplitude or the modulation frequency is increased, the nonlinear effects are enhanced so that the dynamics of the system shows a wide variety of nonlinear behaviors, such as period doubling and chaos. We experimentally demonstrate the parametric resonance when the magnetic field gradient is parametrically modulated, which evidences the realization of the proposed system. We expect that this system is useful for understanding the stochastic phenomena occurring between complex basins of attraction, such as fluctuation induced transitions across the complex basin boundaries.     

掺铒光纤环镜中超短光孤子的放大与压缩Ⅱ.环镜及输入脉冲特性对放大结果的影响

最近的研究发现,用掺铒光纤环镜放大并压缩超短光孤子不仅能避免常规掺铒光纤放大器中由于非线性效应引起的孤子畸变,而且可克服绝热放大技术中放大器长度随输入脉宽增大而指数规律增大的困难。进一步研究了环镜及输入脉冲特性对放大结果的影响。数值计算表明,对于确定的输入脉冲,当环镜参量(环镜长度、增益、耦合器功率耦合系数)在较大范围内变化时,环镜放大器的孤子输出性能基本稳定。对于确定的环镜,输入脉冲形状的变化、初始输入功率的起伏以及高阶效应等因素对放大结果的影响较小;相对而言,初始频率啁啾对输出孤子宽度的影响较大,但对输出孤子质量的影响并不严重。     

Solving the phase-retrieval problem of a complex signal in the fractional Fourier domain by nonlinear least-squares

From the viewpoint of unconstrained optimization the phase-retrieval problem of a 1D complex signal in the fractional Fourier domain is formulated as a nonlinear least-squares problem. A definition of the discrete fractional Fourier transform (DFRFT) constructed by a discrete Hermite-Gaussian function is adopted here. The ill-posedness of the problem is stressed, and the Levenberg-Marquardt algorithm of Moré's form is used to solve it. In contrast to many published references, this method can reconstruct the phase accurately from the amplitude of the original signal and the one of its DFRFT at any order in the interval (0, 2). For amplitudes with low-level noise this method also works well.     

Generalized Projective Synchronization between Two Complex Networks with Time-Varying Coupling Delay

Generalized projective synchronization （GPS） between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü＇s system [Physica A 382 （2007） 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand supply of energy resource in some regions of China.     

Differential algebraic method for time of flight property of electrostatic electron lenses

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the truncation error of the computer. When applied to nonlinear dynamical systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this article, the time of flight (TOF) property of electrostatic electron lens systems is studied by differential algebraic method and their arbitrary order TOF transfer properties can be numerically calculated. As an example, Schiske's model electrostatic lens has been studied by the efficient differential algebraic TOF method.     

Bose fluids above T(c): incompressible vortex fluids and "supersolidity"

This Letter emphasizes that nonlinear rotational or diamagnetic susceptibility is characteristic of Bose fluids above their superfluid T(C)'s. For sufficiently slow rotation or, for superconductors, weak B fields, this amounts to an incompressible response to vorticity. The cause is that there are terms missing in the conventionally accepted model Hamiltonian for quantized vortices in the Bose fluid. The resulting susceptibility can account for recent observations of Chan et al. [Nature (London) 427, 225 (2004); Science 305, 1941 (2004)] on solid He and Ong et al. [Europhys. Lett. 72, 451 (2005) on cuprate superconductors.     

Calculated T1 images derived from a partial saturation-inversion recovery pulse sequence with adiabatic fast passage

Calculated T1 images of the head and abdomen have been obtained using an alternating partial saturation-inversion recovery pulse sequence. Timing parameters were adjusted to yield optimum T1 contrast-to-noise ratio for this sequence for the range of T1 studied. Adiabatic fast passage (AFP) was implemented for the nonselective inverting pulse, to reduce the sensitivity of the measurement to RF and static field inhomogeneity. A nonlinear frequency sweep was used to improve the efficiency of the AFP pulse. The effect on the T1 calculation of slice selection during the pi/2 pulses was also determined and corrected for in the image reconstruction algorithm. The T1's determined by this method show a standard deviation of less than 10%, and good agreement with the literature.     

高功率Nd:YVO_4/KTP腔内倍频晶体温度分布的半解析热分析

非线性晶体KTP采用Ⅱ类相位匹配腔内倍频时,不仅要求晶体满足基频光的偏振匹配条件,而且所选用的晶体要求符合λ/2波片的条件,才能使晶体的谐波转换效率达到最佳。由于倍频晶体吸收基频光能量引起晶体内部非均匀温升,改变晶体内部各点的折射率,也会使晶体产生不应有的热形变,破坏晶体初始的位相匹配条件,严重影响输出激光的品质和倍频效率。减弱、改善这种情况的关键是准确得出在实际工作条件下晶体内部温度场。利用半解析热分析方法得出了KTP晶体内部温度场的计算方法,分析了各种热参量变化对KTP晶体内部温度场的影响。得出的结果具有一定的普适性,可以应用到具有轴对称形式内热源的其它热模型温度场的计算分析中,对连续波腔内倍频激光系统的设计将起到指导作用。     

动力学阿尔文波及其在太阳和空间等离子体中的应用

动力学阿尔文波是短波长的色散阿尔文波,其色散主要是由于垂直波长接近离子回旋半径或电子惯性长度等微观粒子动力学特征尺度而引起的。在频率远低于离子回旋频率的低频条件下,其平行波长通常仍然远大于离子惯性长度,这导致动力学阿尔文波在电磁偏振和传播方向上呈现显著各向异性的重要特性,并因此使其在磁等离子体的粒子能化现象和结构丝化现象中起重要作用。动力学阿尔文波早期于1970年代由Chen和Hasegawa研究聚变等离子体加热问题时首先提出。随后,在1980年代受到空间等离子体、特别是电离层-磁层耦合与极光现象研究的广泛关注。进入1990年代后,由于在空间卫星探测技术和地面等离子体实验技术的不断发展,特别是一些高分辨空间等离子体探测仪器和地面大型等离子体实验设备投入工作以来,在动力学阿尔文波的实验研究上取得了一系列突破性的重要进展。这不仅导致对动力学阿尔文波在磁等离子体动力学现象中重要作用的重新估价和正视,并再次激发了对动力学阿尔文波理论及其在实验室、空间和天体环境下各类等离子体活动现象中应用研究的广泛兴趣。自1990年代中期以来,我们在中国科学院紫金山天文台的研究小组一直致力于动力学阿尔文波及其在太阳和空间等离子体粒子能化现象中应用的研究。这篇综述性报告主要介绍了有关动力学阿尔文波非线性孤波理论及其在空间和太阳等离子体粒子能化现象中应用的研究进展,也是我们这十几年来在这一领域研究工作的一个总结。报告的第一章简要介绍动力学阿尔文波的一些主要特征及其在磁等离子体动力学现象中的重要作用。然后,在第二章中利用等离子体的双流体方程、结合有关的实验观测,系统介绍了动力学阿尔文波的色散、传播、偏振等基本特性和在一维孤波与二维涡旋等非线性结构理论方面的研究进展。接下来的第三、四、五章将聚焦在动力学阿尔文波的耗散机制及其在太阳和空间等离子体粒子能化现象中的应用研究上,分别包括：动力学阿尔文孤波的耗散结构及其在极光高能电子加速现象中的应用（第三章）;动力学阿尔文孤波中重离子的各向异性能化机制及其在延伸日冕中少量重离子反常加热现象中的应用（第四章）;以及动力学阿尔文波的反常耗散机制及其在日冕磁等离子体结构非均匀加热现象中的应用（第五章）。最后的第六章是一个简要的总结和几点进一步发展的展望。     

动力学阿尔文波及其在太阳和空间等离子体中的应用(英文)

动力学阿尔文波是短波长的色散阿尔文波,其色散主要是由于垂直波长接近离子回旋半径或电子惯性长度等微观粒子动力学特征尺度而引起的。在频率远低于离子回旋频率的低频条件下,其平行波长通常仍然远大于离子惯性长度,这导致动力学阿尔文波在电磁偏振和传播方向上呈现显著各向异性的重要特性,并因此使其在磁等离子体的粒子能化现象和结构丝化现象中起重要作用。动力学阿尔文波早期于1970年代由Chen和Hasegawa研究聚变等离子体加热问题时首先提出。随后,在1980年代受到空间等离子体、特别是电离层-磁层耦合与极光现象研究的广泛关注。进入1990年代后,由于在空间卫星探测技术和地面等离子体实验技术的不断发展,特别是一些高分辨空间等离子体探测仪器和地面大型等离子体实验设备投入工作以来,在动力学阿尔文波的实验研究上取得了一系列突破性的重要进展。这不仅导致对动力学阿尔文波在磁等离子体动力学现象中重要作用的重新估价和正视,并再次激发了对动力学阿尔文波理论及其在实验室、空间和天体环境下各类等离子体活动现象中应用研究的广泛兴趣。自1990年代中期以来,我们在中国科学院紫金山天文台的研究小组一直致力于动力学阿尔文波及其在太阳和空间等离子体粒子能化现象中应用的研究。这篇综述性报告主要介绍了有关动力学阿尔文波非线性孤波理论及其在空间和太阳等离子体粒子能化现象中应用的研究进展,也是我们这十几年来在这一领域研究工作的一个总结。报告的第0章简要介绍动力学阿尔文波的一些主要特征及其在磁等离子体动力学现象中的重要作用。然后,在第1章中利用等离子体的双流体方程、结合有关的实验观测,系统介绍了动力学阿尔文波的色散、传播、偏振等基本特性和在一维孤波与二维涡旋等非线性结构理论方面的研究进展。接下来的第2、3、4章将聚焦在动力学阿尔文波的耗散机制及其在太阳和空间等离子体粒子能化现象中的应用研究上,分别包括:动力学阿尔文孤波的耗散结构及其在极光高能电子加速现象中的应用(第2章);动力学阿尔文孤波中重离子的各向异性能化机制及其在延伸日冕中少量重离子反常加热现象中的应用(第3章);以及动力学阿尔文波的反常耗散机制及其在日冕磁等离子体结构非均匀加热现象中的应用(第4章)。最后的第5章是一个简要的总结和几点进一步发展的展望。     

Exceptionally low shear modulus in a prototypical imidazole-based metal-organic framework

Using Brillouin scattering, we measured the single-crystal elastic constants (C(ij)'s) of a prototypical metal-organic framework (MOF): zeolitic imidazolate framework (ZIF)-8 [Zn(2-methylimidazolate)(2)], which adopts a zeolitic sodalite topology and exhibits large porosity. Its C(ij)'s under ambient conditions are (in GPa) C(11)=9.522(7), C(12)=6.865(14), and C(44)=0.967(4). Tensorial analysis of the C(ij)'s reveals the complete picture of the anisotropic elasticity in cubic ZIF-8. We show that ZIF-8 has a remarkably low shear modulus G(min) < or approximately 1 GPa, which is the lowest yet reported for a single-crystalline extended solid. Using ab initio calculations, we demonstrate that ZIF-8's C(ij)'s can be reliably predicted, and its elastic deformation mechanism is linked to the pliant ZnN(4) tetrahedra. Our results shed new light on the role of elastic constants in establishing the structural stability of MOF materials and thus their suitability for practical applications.     

Waveform interactions and the segregation of concurrent vowels

Two experiments investigated the effects of small values of fundamental frequency difference (delta F0) on the identification of concurrent vowels. As delta F0's get smaller, mechanisms that exploit them must necessarily fail, and the pattern of breakdown may tell which mechanisms are used by the auditory system. Small delta F0's also present a methodological difficulty. If the stimulus is shorter than the beat period, its spectrum depends on which part of the beat pattern is sampled. A different starting phase might produce a different experimental outcome, and the experiment may lack generality. The first experiment explored the effects of delta F0's as small as 0.4%. The smallest delta F0 conditions were synthesized with several starting phases obtained by gating successive segments of the beat pattern. An improvement in identification was demonstrated for delta F0's as small as 0.4% for all segments. Differences between segments (or starting phase) were also observed, but when averaged over vowel pairs they were of small magnitude compared to delta F0 effects. The nature of delta F0-induced waveform interactions and the factors that affect them are discussed in detail in a tutorial section, and the hypothesis that the improvement in identification is the result of such interactions (beat hypothesis) is examined. It is unlikely that this hypothesis can account for the effects observed. The reduced benefit of delta F0 for identification at smaller delta F0's more likely reflects the breakdown of the same F0-guided segregation mechanism that operates at larger delta F0's.     

SU(3) coupling schemes for odd-odd nuclei in the interacting boson – fermion – fermion model with both odd proton and odd neutron in natural parity orbits

The SU^BFF(3) dynamical symmetry limits of interacting boson – fermion – fermion model are identified and they are appropriate for heavy deformed odd – odd nuclei for configurations with both the odd proton and odd neutron occupying all the natural parity orbits in the corresponding valence shells. There are three symmetry limits and their correspondence with two quasi-particle (proton-neutron) Nilsson configurations is established; one of the limits mixes both Nilsson n_z's and Λ's and other two limits mix only Nilsson Λ's. The ¹⁹¹Ir (d,t) ¹⁹⁰Ir single nucleon transfer spectroscopic strengths are well described by one of the symmetry limits that mixes only Nilsson Λ's. Received: 22 June 1998     

Precision measurement of cosmic-Ray antiproton spectrum

The energy spectrum of cosmic-ray antiprotons ( &pmacr;'s) has been measured in the range 0.18-3.56 GeV, based on 458 &pmacr;'s collected by BESS in a recent solar-minimum period. We have detected for the first time a characteristic peak at 2 GeV of &pmacr;'s originating from cosmic-ray interactions with the interstellar gas. The peak spectrum is reproduced by theoretical calculations, implying that the propagation models are basically correct and that different cosmic-ray species undergo a universal propagation. Future BESS data with still higher statistics will allow us to study the solar modulation and the propagation in detail and to search for primary &pmacr; components.     

Measurements of total and positronium-formation cross sections for the scattering of positrons by alkali atoms

We present a review of our recent measurements of total cross sections (Q _T's) for the scattering of positrons by Na, K, and Rb, and positronium-formation cross sections (Q _Ps's) for Na and K. For our total cross section measurements, a beam transmission technique has been used. For ourQ _Ps measurements, our approach involves setting upper and lower limits onQ _Ps using a combination of (1) measuring the transmission of the positron beam with the angular discrimination of the apparatus made as poor as possible, and (2) measuring the 511 keV annihilation gamma rays in coincidence produced by the decay of para-Ps formed in the scattering cell. Comparison with theoretical calculations shows that our measuredQ _T's andQ _Ps's for Na and K agree reasonably well with a close coupling approximation (CCA) calculation which takes into account the formation of Ps in then=1 andn=2 states. In the 3–10 eV energy range, this calculation predicts a peak in theQ _T's andQ _Ps's for K which also appears in our measurements. The absence of such a peak in our measuredQ _T's andQ _Ps's (preliminary) for Na in this energy range is also consistent with the same theory. Comparisons with five-state CCA calculations ofQ _T which do not take Ps-formation into account also show good agreement with our positron-Na, K, and RbQ _T measurements for energies above 20 eV, but show dramatic departures from our measurements below 10 eV for K and Rb.