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101.
We consider a weakly dissipative quasilinear system of PDEs, governingthe unsteady one-dimensional motion of a relaxing gas, and investigatethe effects ofhigher order terms and the source term, present in the differentialsystem, on the wave motion associated with it. The undisturbed stateof the medium, which is assumed to be uniform and at restadmits mixed nonlinearity, i.e., the quadratic nonlinearity parameter inherent in the system changes sign depending on the basestate. The method of multiple scales is employed to determine theevolution equation governing small perturbations to the state where is of O(), and the effects of nonlinearity arenoticeable over times of order O(–2). 相似文献
102.
Heng Zhou Mingle Liao Shu‐Wei Huang Linjie Zhou Kun Qiu Chee Wei Wong 《Laser \u0026amp; Photonics Reviews》2016,10(6):1054-1061
Nonlinear wave mixing in mesoscopic silicon structures is a fundamental nonlinear process with broad impact and applications. Silicon nanowire waveguides, in particular, have large third‐order Kerr nonlinearity, enabling salient and abundant four‐wave‐mixing dynamics and functionalities. Besides the Kerr effect, in silicon waveguides two‐photon absorption generates high free‐carrier densities, with corresponding fifth‐order nonlinearity in the forms of free‐carrier dispersion and free‐carrier absorption. However, whether these fifth‐order free‐carrier nonlinear effects can lead to six‐wave‐mixing dynamics still remains an open question until now. Here we report the demonstration of free‐carrier‐induced six‐wave mixing in silicon nanowires. Unique features, including inverse detuning dependence of six‐wave‐mixing efficiency and its higher sensitivity to pump power, are originally observed and verified by analytical prediction and numerical modeling. Additionally, asymmetric sideband generation is observed for different laser detunings, resulting from the phase‐sensitive interactions between free‐carrier six‐wave‐mixing and Kerr four‐wave‐mixing dynamics. These discoveries provide a new path for nonlinear multi‐wave interactions in nanoscale platforms.
103.
The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results. 相似文献
104.
Monotonicity,uniqueness, and stability of traveling waves in a nonlocal reaction‐diffusion system with delay 下载免费PDF全文
Hai‐Qin Zhao 《Mathematical Methods in the Applied Sciences》2017,40(18):6702-6714
The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction‐diffusion system with delay arising from the spread of an epidemic by oral‐faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c ?c ?. Then we show that the traveling wave fronts with speed c >c ? are exponentially asymptotically stable. 相似文献
105.
《Mathematische Nachrichten》2017,290(14-15):2198-2206
The aim of this work is to present results of existence of solutions for a class of superlinear asymmetric elliptic systems with resonance in the first eigenvalue. The asymmetry that we consider has linear behavior on and superlinear on . To obtain these results we apply topological degree theory. 相似文献
106.
任永华 《数学的实践与认识》2017,(1):213-220
主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性. 相似文献
107.
准确预测风电场风速是解决风能对电力系统所造成的安全、稳定运行和电能质量等问题的有效途径之一.风速的难以预测是由于它的高度随机和非线性.基于一种非参数的非线性自回归随机模型来预测风速,模型的自回归系数随模型依赖变量的变化而变化,因而它有灵活的非线性结构.数值实验和比较结果表明了这种函数系数自回归模型在风电场风速预测中的有效性. 相似文献
108.
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110.
水平地震时斜面水坝受到的非线性动水压力的全过程的解析解 总被引:1,自引:0,他引:1
本文给出在非线性Rayleigh阻尼作用下,由水平地震激发的水库内动水压力变化全过程的解析解:在激发初期其幅值较小,可用小参数法使控制方程线性化,从而求得各阶渐近控制方程的解析解;当动水压力的幅值增大到小参数展开不适用时,用van derpol法求得非线性控制方程的渐近解,从而显示了动水压力的幅值从有序变化到发生突然跳跃的多值性的非线性本质。 相似文献