非线性振动、非线性波与Jacobi椭圆函数(续)

5　正弦戈登方程、扭结、反扭结波、呼吸孤立波正弦戈登方程 (sing -Gordon方程 ,简记为SG方程 )φxx- φtt=sin φ (38)是自然科学和应用科学中出现的另一个重要的非线性发展方程 (演化方程 ) .在晶体位错的传播、磁旋波在铁磁材料中的传播、约瑟夫森 (Josephson)结中继传输线等乃至生物物理的诸多问题中都应用了这一方程 .本文从单摆弹簧链模型这一特例引入SG方程 .考虑如图 3所示的N个相连弹簧 -单摆运动方程 (称为单摆弹簧链 ) .N个单摆悬挂在横置的诸弹簧上 ,每个摆的长度和质量均相同 ,每个螺旋弹簧的长度和劲度系数也相同 ,则第i…     

参量激励型孤子的研究进展

简述了参量激励型水波孤子的最新研究结果，其中包括孤子－孤子的相互作用，稳定单孤子链的极性排列规则，以及孤子链的有序时空振荡等．数值研究表明，实验现象可由带阻尼的参量驱动非线性薛定谔方程描述和解释．     

一维分子链中激子与声子的相互作用和呼吸子解

运用连续极限近似，求解声子与激子相互作用的运动方程，得到了简谐分子链和 非简谐分子链中晶格振动的孤子解，在考虑三次非简谐势的情况下，一维分子链晶格振动具 有扭结孤子解，在考虑具有四次非简谐势的情况下，得到一维分子链晶格振动具有呼吸子解 . 关键词： 一维分子链 激子 声子 孤子 呼吸子 非线性效应     

装载于外势场中的玻色-爱因斯坦凝聚N-孤子间的相互作用

首先建立起玻色-爱因斯坦凝聚孤子链的微扰复数Toda链理论,然后深入研究玻色-爱因斯坦凝聚N-孤子间的绝热相互作用,分别通过对二次外势场、周期性外势场和二者叠加的复合外势场所引起的三类微扰,利用微扰的复数Toda链理论给出了解析处理, 并和基于分步傅里叶变换的直接数值方法进行比较,发现微扰的复数Toda链方程能够充分揭示上述三类外势场中的N-孤子链的动力学行为和特征.同时还给出了从孤子链中提取一个或多个局域态的倾斜势场或周期性势场的强度临界值,这可为玻色-爱因斯坦凝聚的实验研究 关键词： 玻色-爱因斯坦凝聚 Gross-Pitaevskii方程 物质波孤子 相互作用     

一维反铁磁链中双亚格点模型的孤子解(英文)

求出了一维反铁磁链中双亚格点模型的孤子解,并求出了孤子宽度、峰值、静止能量和有效质量.在al=bl 和al=-bl 两种情况下求方程的精确解.     

阻尼作用下带对称双阱势的原子链中的洞孤子

采用多重尺度法,研究弱阻尼作用下带有对称双阱势的原子链,导出耗散型的非线性薛定谔方程,并对方程进行解析求解,给出阻尼作用下在链中传播的耗散型的洞孤子解.     

蛋白质分子链的非线性激发的孤子模型的一个改进解

通过仔细考察蛋白质分子链中体系运动方程的非线性项,得到了一个与通常非线性Schrdinger方程不同的修正的非线性Schrdinger方程,并求得了一个改进孤子解.     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schrdinger方程,对方程进行解析求解.结果表明在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε2)级阻尼作用下,格孤波为钟状或扭结的孤子.     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schr?dinger方程,对方程进行解析求解.结果表明:在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε²)级阻尼作用下,格孤波为钟状或扭结的孤子.     

(2+1)维破裂孤子方程的多方孤子解及其混沌行为

利用投射方程法和变量分离法,得到(2+1)维破裂孤子方程的新显式精确解. 根据得到的孤立波解,利用 Weierstrassp 函数,构造出多方孤子局域结构. 利用两个混沌系统研究了破裂孤子方程的混沌行为. 关键词： 投射方程法 破裂孤子方程 多方孤子 混沌行为     

Femtosecond Transform-Limited Pulse Generation by Compensating for the Linear Chirp of SPM Spectra in Dispersion Shifted Fibers

A simple technique of pulse compression, based on the linear chirp compensation of self-phase modulation (SPM) spectra in dispersion shifted fibers, is demonstrated. The optimization procedure is carried out, for a short span of a single-mode fiber, using a parabolic law, which describes the behavior of the squared output pulse width versus the pump peak power in the case of Gaussian pulses. The experimental results give a minimum pulse duration of 233 fs, which is in good agreement with the model. Shorter and coherent pulses, down to 90 fs, have been obtained by inserting an interference filter at the optical output.     

Contrastive analysis on tone between Putonghua and Taiwan Mandarin

The differences of the pitch and duration of Chinese syllables between Putonghua （PTH） and Taiwan Mandarin （TM） were studied. The speech materials to be used are not only isolated syllables, but also sentences. The results reveal that： For the isolated syllables, T1 and T2 in TM are influenced by Minnan dialect, therefore their pitch are lower than those in PTH. T3 is fall-rise in PTH, while it is fall in TM. Moreover, the syllable duration sequence for different tone is T3〉T2〉T1〉T4 in PTH, while it is T1〉T2〉T3〉T4 in TM. For the syllables in sentences, T2 is mid-rise in PTH, while it is mid-level in TM. And the T3 is longer than T4 but shorter than T1 or T2 in PTH, while it is the shortest in TM. Furthermore the effects of prosodic phrase boundary on duration for different tones are almost the same in PTH, but the lengthening part of T1 or T2 is longer than that of T3 or T4 in TM.     

Experimental study on downstep in Chinese intonation

Downstep in pitch contour of Chinese Putonghua is examined using subtly designed sentences by controlling tone combinations. The results show both automatic and nonautomatic downstep phenomena exist in Chinese. In non-automatic downstep, low tones compress downwards the pitch range of the following syllables. and the main influence of downstep is on topline. Low tone not only lower the topline behind it, but also raise the high tones before it, the effects are compatible with each other. In automatic downstep, the topline of pitch contour in intonational phrase is presented as a linear downtrend, but it differs among speakers due to the effect of personal stress practice. In comparison with downstep phenomenon in other tone or non-tone languages, the downstep ratio in Chinese is not constant, and the domain of downstep is not limited within the adjacent tones.     

Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.     

Abelian-Higgs phase of SU(2) QCD and glueball energy

It is shown that SU(2) QCD admits an dual Abelian-Higgs phase, with a Higgs vacuum of a type-Ⅱ superconductor. This is done by using a connection decomposition for the gluon field and the random-direction approximation. Using a bag picture with soft wall, we presented a calculational procedure for the glueball energy based on the recent proof for wall-vortices [Nucl. Phys. B 741(2006)1].     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

High efficiency filtering using two-dimensional photonic crystal coupled cavity structures

Transmission spectra of coupled cavity structures (CCSs) in two-dimensional (2D) photonic crystals (PCs) are investigated using a coupled mode theory, and an optical filter based on CCS is proposed. The performance of the filter is investigated using finite-difference time-domain (FDTD) method, and the results show that within a very short coupling distance of about 3λ, where λ is the wavelength of signal in vacuum, the incident signals with different frequencies are separated into different channels with a contrast ratio of 20 dB. The advantages of this kind of filter are small size and easily tunable operation frequencies.     

Real-time restoration of rotational blurred image using gradient-loading

The key to the restoration of rotational motion blurred image is how to restore the image under a low cost and to correct the irreversibility of the degradation function matrix.Based on the special qualities of degradation function matrix and precise deduction in space-domain, we present a new approach using gradient-loading for restoration of rotational blurred image.By easily adding a gradient operator, the irreversibility of the original matrix is corrected and can be applied for inverse filtering then.Gradientloading is the optimized approach which combines the advantages of both the approaches using constrained least square filtering and traditional diagonal-loading.Compared with the approach using least square filtering, its peak signal-to-noise ratio (PSNR) is improved from 3.18 to 6.46dB, while the computing time is reduced to 1/2-1/3.Experimental results demonstrate the effectiveness, noise-resistibility, robustness, and low complexity of this approach, which make it more suitable for real-time environment.