耦合发电机系统的分岔和双参数特性

在综合分析系统基本动力学特性的基础上,通过数值计算Lyapunov指数谱、分岔图等,讨论了耦合发电机系统的混沌分岔行为和周期窗口的性态变化;计算和分析了系统在二维参数空间的双参数特性.结果显示系统在倍周期分岔中会出现缺边现象,在双参数空间系统出现复杂的分岔结构,两个控制参数对系统动力学行为的影响特性有所差别. 关键词： 耦合发电机系统 分岔 周期窗口 双参数特性     

一类滞后相对转动动力学方程的分岔特性及其解析近似解

建立了一类含Davidenkov滞后环的非线性相对转动动力学方程.分别分析了该非线性相对转动自治方程和微外扰下非自治方程的分岔特性,并采用KBM法求解了滞后环指数n=2时该非线性相对转动方程在周期激励下的解析近似解.通过数值仿真,得到了几种分岔结构及外扰下全局分岔图,同时将数值解与本文KBM法求解结果进行比较,证明本文求解结果有较高的精度,为研究这一类滞后相对转动系统提供了理论参考依据. 关键词： 相对转动 滞后环 分岔 KBM法     

一类延时系统的动力学行为研究

本文利用稳定性分析方法得到了一维延时系统定态稳定的充要条件。为研究系统的分岔和混沌行为,在长延时极限下对延时的倒数T_R^-1作渐近展开,得到的零级近似就是通常的一维映象,而T_R^-1的一级效应使系统运动的周期延长。更为有趣的现象是由更高级项带来的,T_R^-2项导致系统在每个分岔点出现滞迴过程(某种双稳现象);而T_R^-3项影响了系统的倍周期分岔行为:即分岔前后的周期之比并不是严格的二倍。高级效应还表明,在混沌带的合并点存在着不稳定窗口,并由此带来一些锁模现象。 关键词：     

频率扫描法研究倍周期分岔与混沌现象

在一类非线性系统中,应用频率控制方法,对倍周期分岔与混沌行为进行了研究。在V₀-ω外控参数平面上,频率扫描显示了分岔与混沌的整体结构:正的和逆的倍周期分岔序列的对称性;分岔收敛于一点的封闭性。本文中所建议的方法,将是一种研究分岔与混沌现象有效而快速的手段。它不仅能定量测量收敛比δ和标度因子α,分段展开还能定性地观察阵发混沌和嵌套在混沌带中的各种窗口等。分岔与混沌是一类非线性系统的频率响应。 关键词：     

一个小波函数指数参数变化的分岔现象

研究一个高斯小波函数产生的混沌分岔现象.随着小波函数中指数参数的增加，它的分岔图出现了倍周期分岔，然后出现混沌，经过一段混沌区域后又出现2的幂周期.在整个过程中，正分岔与逆分岔完整地结合在一起.改变小波函数的系数出现一些明显的奇数周期，如3周期、5周期等.绘制Lyapunov指数曲线及映射折射过程，对混沌现象进行研究.将小波函数展开成近似的多项式函数，对近似多项式函数的分岔图进行了分析. 关键词： 混沌 分岔 小波函数     

一类简化Lang-Kobayashi方程的Hopf分岔及其稳定性

讨论了一类简化Lang-Kobayashi方程的Hopf 分岔的性质.根据分岔理论,给出了系统产生Hopf 分岔的临界时滞条件,然后利用中心流形定理和规范型理论得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后,用数值模拟对理论结果进行了验证. 关键词： Lang-Kobayashi方程 时滞 Hopf分岔 稳定性     

参外联合激励复合非线性振子的分岔分析

讨论了参外联合激励复合非线性振子的动力学行为.对其定常解在一阶近似下的方程进行了局部分岔分析,给出了简单分岔和Hopf分岔发生的条件,并通过对近似方程和原系统的数值模拟加以验证.分析了多种参数对该振子动力学行为演化过程的影响.根据全局分岔理论探讨了该振子在不同条件下发生同宿、异宿分岔的必要条件,其结论与数值计算的结果大致符合. 关键词： 复合非线性振子 局部分岔 全局分岔 混沌     

非线性漂移波在行波扰动下的绕数分岔与超级结构

在文献[1]中,数字计算揭示出在时空周期场驱动下,有阻尼的非线性漂移波方程其分岔图显示出某种标度的超级结构。本文指出,漂移波方程的扰动解与未扰系统的解之间的共振和因此而引起的绕数分岔,是出现这种超级结构的原因。由此计算的波数与频率之间的标度关系,与数字实验结果符合。 关键词：     

开关变换器倍周期分岔精细层次结构及其普适常数研究

讨论了开关变换器倍周期分岔级联的精细层次结构和标度不变性;数值仿真得到一维、二维开关变换器倍周期分岔及混沌带合并序列的普适常数;系统谱结构可以进一步判断解的性态,显示解的结构,同时开关变换器混沌层次结构的尺度差别也反映在谱结构的精细特征上;最后实验研究了开关变换器倍周期分岔通向混沌的过程,验证了数值仿真的结论. 关键词： 开关变换器 倍周期分岔 普适常数 标度不变性     

耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解,通过讨论系统的主共振和内共振特性,分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性,得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性     

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation(LIV). As the most energetic explosions in the Universe, gamma-ray bursts(GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB,we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M_(QG) 5.05 × 10~(14) GeV in the linearly corrected case, is from GRB 140622 A. Our constraint on MQG,although not as tight as previous results, is the safest and most reliable so far.     

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10⁸ ÷10⁹ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.     

Short delay time UV preionized TEA CO2 laser operating with binary CO2/H2 and CO2/He gas mixtures

In order to obtain short tail-free output laser pulses from a TEA CO₂ laser, parametric study of the laser operation with CO₂/H₂ and CO₂/He binary gas mixtures containing high CO₂ concentrations was carried out. A small scale UV preionized short delay time TEA CO₂ laser was employed. In terms of the maximum extractable output pulse energy and power, the more conventional CO₂/He gas mixture was found to be inferior in comparison with the CO₂/H₂ mixture proposed here.     

非晶态二元合金模型偏干涉函数的计算及应用

本文从计算非晶态材料散射强度的Debye方程,推导出非晶态二元合金模型的Faber-Ziman偏干涉函数计算公式。利用这些公式,计算了Fe₈₃B₁₇和Ni₆₄B₃₆金属玻璃模型的S_FeB(Q)和S_NiB(Q),并和实验结果及模型计算的偏散射强度I_FeB(Q)和I_NiB(Q)作了比较。文中还计算了Hg₂Na液态合金模型的偏干涉函数,并把它们外推到零衍射角时的数值。最后讨论了具有化学短程序合金的全干涉函数在零衍射角附近的行为。 关键词：     

Optical delay lines using coupled slab waveguides and ring resonator with a negative refractive index core

Total delay time of a structure composed of a slab waveguide coupled with a ring resonator where negative refractive index material is replaced in the core of the structure is investigated in this work. In this paper, a two-port ring resonator (TPRR) which is made of a core with negative refractive index has been used to generate a time delay for a Gaussian-shaped pulse with 1 GHz bandwidth. It is shown that the creation of the ring how causes more n_g of a straight waveguide and results are compared with positive refractive index core TPRR. We have used metamaterial to make an n < 0 media and have used two cascaded metamaterial rings to increase the bandwidth.     

Shock-wave compression of x-cut quartz as determined by electrical response measurements

The mechanical response of x-cut quartz in the vicinity of the Hugoniot elastic limit is determined from measurements of the piezoelectric current from samples impact loaded from 26 to 130 kbar. The Hugoniot elastic limit is determined to be 60_?1·5⁺³ kbar at a compression of 0·066_?0·002^+0·004 This Hugoniot elastic limit corresponds to a shear strength of 5·5 per cent of the C₄₄ shear modulus. For stresses well above the Hugoniot elastic limit the electrical current measurements show that the material exhibits a substantial reduction of shear strength. The pressure derivative of the bulk modulus is determined to be 4·5, substantially less than the ultrasonic value. The experimental records show evidence for a time delay for reduction of shear strength which varies from about 10^?7 sec immediately above the 60 kbar Hugoniot elastic limit to about 10^?8 sec for stresses well above the Hugoniot elastic limit. The measurements also show stress relaxation below the Hugoniot elastic limit between 40 and 60 kbar.     

Numerical simulations of the ignition of n-heptane droplets in the transition diameter range from heterogeneous to homogeneous ignition

Spontaneous ignition of single n-heptane droplets in a constant volume filled with air is numerically simulated with the spherical symmetry. The volume is closed against mass, species, and energy transfer. The numerical model is fully transient. It continues calculation even after the droplet has completely vaporized, and therefore can predict pre-vaporized ignition. Initial pressure and initial air temperature are fixed at 3 MPa and 773 K, respectively. The droplet is initially at room temperature, and its diameter is between 1 and 100 μm. When the overall equivalence ratio is fixed to be sufficiently large, there exists no ignition limit in terms of initial droplet diameter d₀, and the ignition delay takes a minimum value at certain d₀. In such a case, transition from the heterogeneous ignition to the homogeneous ignition with decreasing d₀ is observed. When d₀ is fixed to be so small that the ignition would not occur in an infinite volume of air, the ignition delay takes a minimum value at certain , which is less than unity. Two-stage ignition behavior is investigated with this model. Ignition delay of a cool flame has the dependence on d₀ that is similar to that of ignition delay of a hot flame when is unity. When is almost zero, the ignition limit for cool flame in terms of d₀ is not identified unlike that for hot flame.     

Ignition limit and shock-to-detonation transition mode of n-heptane/air mixture in high-speed wedge flows

In this work, oblique detonation of n-heptane/air mixture in high-speed wedge flows is simulated by solving the reactive Euler equations with a two-dimensional (2D) configuration. This is a first attempt to model complicated hydrocarbon fuel oblique detonation waves (ODWs) with a detailed chemistry (44 species and 112 reactions). Effects of freestream equivalence ratios and velocities are considered, and the abrupt and smooth transition from oblique shock to detonation are predicted. Ignition limit, ODW characteristics, and predictability of the transition mode are discussed. Firstly, homogeneous constant-volume ignition calculations are performed for both fuel-lean and stoichiometric mixtures. The results show that the ignition delay generally increases with the wedge angle. However, a negative wedge angle dependence is observed, due to the negative temperature coefficient effects. The wedge angle range for successful ignition of n-heptane/air mixtures decreases when the wedge length is reduced. From two-dimensional simulations of stationary ODWs, the initiation length generally decreases with the freestream equivalence ratio, but the transition length exhibits weakly non-monotonic dependence. Smooth ODW typically occurs for lean conditions (equivalence ratio < 0.4). The interactions between shock/compression waves and chemical reaction inside the induction zone are also studied with the chemical explosive mode analysis. Moreover, the predictability of the shock-to-detonation transition mode is explored through quantifying the relation between ignition delay and chemical excitation time. It is demonstrated that the ignition delay (the elapsed time of the heat release rate, HRR, reaches the maximum) increases, but the excitation time (the time duration from the instant of 5% maximum HRR to that of the maximum) decreases with the freestream equivalence ratio for the three studied oncoming flow velocities. Smaller excitation time corresponds to stronger pressure waves from the ignition location behind the oblique shock. When the ratio of excitation time to ignition delay is high (e.g., > 0.5 for n-C₇H₁₆, > 0.3 for C₂H₂ and > 0.2 for H₂, based on the existing data compilation in this work), smooth transition is more likely to occur.