方腔内双扩散混合对流非线性格子Boltzmann研究

采用格子Boltzmann方法对方腔内双扩散混合对流的非线性特性进行数值模拟.发热圆位于方腔中心,流体从方腔左侧底部流进,流出位置分别为顶部右侧、中间和左侧三种情况.结果表明,不同参数下的双扩散混合对流存在稳态定常解、周期性振荡解和非周期性振荡解,监测点速度相图分别表现为最终到达一个点、一个封闭环和没有规律的曲线.     

方腔内竖直板自然对流分岔现象的数值研究

采用非稳态数学模型通过数值模拟研究了具有对称结构的封闭方腔内竖直板自然对流换热中的非线性现象。数值结果表明,Ra在4×104-7×104之间,会出现定常解、周期性振荡解和非周期性振荡解,即解存在分岔;初始条件与解的分岔相关;网格Pe数的考核表明,本文所考虑的解的振荡不是由于数值解的不稳定而引起的振荡,而是客观存在的物理振荡。     

封闭圆内开缝圆自然对流换热的振荡特性

本文通过数值计算探讨了封闭圆内开缝圆自然对流换热的振荡特性。数值计算以整个圆为计算区域,采用了非稳态的数学模型和具有QUICK差分格式的SIMPLE算法。在相同条件下计算结果和实验结果符合很好。数值结果显示, 当几何结构一定时,Rayleigh数Ra小于某个临界值时,流动和换热处于稳态,并且关于垂直中心线对称;Ra大于这个临界值时,流动和换热是振荡的,非对称的。数值实验还表明,流动和换热出现振荡时的临界Rayleigh数Rac与开缝圆的开缝度有关,且流动和换热的振荡会出现对称振荡和非对称振荡两种情形。     

圆内开缝圆自然对流的Ruelle-Takens混沌道路

使用热格子Boltzmann方法针对圆内开缝圆自然对流的流动与换热进行数值模拟,通过相空间、功率谱等进行非线性动力学特性分析,研究其流动与换热的稳定性.结果表明：随着瑞利数Ra的增加,流场的相图从开始稳定的平衡点经历Hopf分岔后转变为极限环,表明流场进入一个倍周期性振荡状态;随着瑞利数进一步增加,稳定的极限环分岔为二维环面,系统相空间结构复杂化;当瑞利数Ra大于某一临界值时,二维环面分岔突变进入混沌状态,系统在相空间中出现非常复杂的轨线结构.总体上,通过系统不同瑞利数所对应的非线性动力学特性的表现形式,表明系统经过Ruelle-Takens道路到达混沌,展现出自然对流从稳定的流动和换热发展到非线性运动特征的混沌历程.     

锯齿型通道湍流流动和换热的自维持振荡

采用RNG k-ε湍流模型对锯齿形通道内流动和换热进行了数值模拟。对以时均方程法模拟得到的流场、温度场以及U-V相图、Nu-θ相图进行了分析。研究表明,在本文计算的Re范围内,数值计算结果仍能反映出周期性通道内流动和换热的自维持振荡特性,无量纲速度U,通道平均Nu数随时间作周期性振荡,并且振荡幅度、频率随Re数的增大而增大。     

恒热流锯齿型通道流动和换热的非稳态特性

本文对恒热流边界条件下锯齿型通道内流动与换热的非稳态特性进行了数值模拟.在本文计算的Re范围内,流动和换热随时间发生振荡,且U-V和Nu-θ相图表明,振荡是周期性的;在入口段后,发生振荡的各几何周期的流场、温度场随时间变化的规律基本相同,不同周期对应点的U、θ相同,只是在时间上不完全同步,U-V和Nu-θ相图上的曲线重合良好,因此仍具有周期性充分发展的特性.     

锌锅中低Pr流体混合对流的数值模拟

以带钢连续热镀锌生产工艺为背景,对抽象出的低Pr数流体混合对流流动和换热模型进行了数值模拟,给出了在不同Re、Ra及Ri时的流场和温度场.数值结果表明,当Re、Ra都不等于0时,在所考虑的参数范围内,流动和换热受自然对流和强制对流两种机理控制.Re不变,增大Ri,自然对流作用加强,并且当Ri增加到一定值时,流动和换热发生振荡.所给出的速度相图显示,对应不同的Re、Ra及Ri,流动和换热会出现稳态解、周期性振荡解和混沌.     

色散吸收非对称介质光腔系统中光场量子起伏的功率谱

借助系统格林函数和色散吸收介质中电磁场量子化过程,通过数值计算研究非对称色散吸收介质光腔系统中光场量子起伏的功率谱.结果表明,介质的折射和吸收性质分别对真空场起伏功率谱的振荡频率、振幅产生影响,腔两侧介质折射系数的对称性能更有效地抑制腔外空间场起伏功率谱的振荡;介质折射系数愈大,则其中光场起伏功率谱振荡中心愈低、振荡频率愈大,与此同时,光腔内真空场起伏功率谱振荡幅度加大.     

锌锅中低Pr流体混合对流的自维持振荡

本文对以带钢连续热镀锌为背景抽象出的锌锅中低Pr流体的流动和传热进行了数值模拟.数值结果显示,对Re=0的纯自然对流,Ra在104和105间时数值解由稳态解分岔为振荡解;对于Ra=0的纯强制对流,Re在4×103和5x1003之间时,数值解从稳态解分岔为振荡解;当Ra和Re均小于自然对流和强制对流单一机制作用时发生振荡的临界值时,混合对流的流动和传热为稳态;当Ra和Re中的一个参数大于单一机制作用发生振荡的临界值时,另一个参数由小于增加到大于单一机制作用发生振荡的临界值时,数值解由振荡解变为稳态解.     

外强迫作用下正压大气非线性特征数值模拟

在两种边界条件下用正压大气非线性位势涡度方程模拟了强迫、耗散和非线性共同作用下大气运动的若干特征.在南北两端为齐次边界条件时，单纯的热力强迫下只出现了波状定常解；在只有经向加热和波状地形共同强迫下出现了在两种基本流型之间振荡的准周期解，十分类似于旋转地球上大气运动的纬向和经向流型之间的准周期循环，前者对应于强的西风环流，后者对应于弱西风流型.在周期边界条件下，弱的下垫面加热导致定常解，较强的加热强迫可以得到周期解.尽管下垫面的波状地形也能强迫一个类似的准周期振荡，但弱西风流型是对称的，不像大气中的弱西风流型.因此，在周期边界条件下用低阶截谱模式求出的解析或数值解，不一定适合描述中高纬度大气的非线性动力特征. 关键词： 正压大气 热力强迫 地形起伏 周期解 准周期振荡     

Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes

The analysis of different types of non-periodic multi-cavity laser structures will be presented. Deterministic non-periodic cavity concepts such as self-similar Cantor- or quasi-periodic Fibonacci sequences offer a distinct mode selectivity whilst having a significantly lower number of coupled cavities compared to an equivalent periodic solution. A heuristic numerical optimization procedure based on a breeder genetic algorithm scheme is favoured, also to give a sort of general information as to which kind of structures are well suited in terms of our requirements. By investigating the evolutionary optimized laser topologies according to the evolution of characteristic patterns, we propose a sort of superior meta-optimization strategy which relies on a population based information gathering.     

Self-oscillations and critical fluctuations

An active system is analyzed whose parameter space contains a bistable region of stationary states bounded by a cuspidal point. This point is somewhat analogous to the critical point of a non-symmetry-breaking phase transition (in terms of high low-frequency susceptibility, fluctuation growth, etc.). The system has not only stationary states, but also periodic oscillatory ones. When parameters change so that the oscillatory instability threshold passes through the cuspidal point, the continuous spectrum of fluctuations transforms into the discrete spectrum of periodic oscillations. The dynamics associated with this transformation are examined.     

Effects of a locally injected signal on phase synchronization in a network of self-excited cells

We consider in this paper the problem of phase synchronization in a network of coupled self-excited cells with free-end boundary conditions. The eigenvalues properties are used to perform the stability boundaries of the synchronization process for pure sinusoidal and quasi-sinusoidal oscillatory states. In the case where the cells’ oscillatory states are quasi-periodic, more energy and time are required for the network to become fully synchronized, compared to the case where each cell exhibits a periodic oscillation. The influence on the stability boundaries of a periodic external excitation locally injected in the network is tackled. For both cases (with and without local injection), numerical simulations are used to check the accuracy and to complement the results derived from the analytical treatment. In this configuration, the local injection helps to drastically increase the range of the coupling parameter for which all cells become synchronized.     

Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.     

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincar'e map of the system is constructed. Using the Poincar'e map and the Gram-Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.     

Numerical simultation of quantum dots; quasi-periodic conductance fluctuations and ‘scarred’ wave-functions

Simulating ballistic transport through square quantum dots, we find quasi-periodic conductance fluctuations and power spectra containing few frequencies, indicating few periodic orbits participate, in very good agreement with some recent experiments. We also find corresponding scar-like features in the wave functions. To reproduce these effects classically, the electrons must be restricted to acollimated beamwhich enters the dot at anangle.     

Phase Transition and Semi-Global Reducibility

For 1D continuous Schödinger operators with large analytic quasi-periodic potentials of two frequencies, one knows that the spectral measure is singular at the bottom of the spectrum and purely absolutely continuous in the upper part of the spectrum, so there is a phase transition when energy increases. In this paper, we obtain the exact power-law for the phase transition in energy by the semi-global reducibility theory of analytic quasi-periodic linear systems.     

Nonlinear spring model for frictional stick-slip motion

Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k₀. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k₀. The system also displays resonance at fractional frequencies of the oscillator.     

Nonlinear dynamics and manipulation of dripping in capillary flow focusing

In this study, we carried out experimental and numerical investigations on the dripping dynamics in axisymmetric capillary flow focusing. For the direct numerical simulations, we solved the Navier-Stokes equations coupled with a diffuse interface method.For the experiments, we observed both periodic and non-periodic dripping modes at different focused and focusing liquid flow rates. The non-periodic dripping that results in polydispersed droplets downstream the orifice can be attributed to the nonlinear dynamics of the flow; thus, we constructed numerical plots of the streamlines and temporal evolutions of the focused liquid cone in different modes. We identified a phase diagram of the dripping regimes in the plane of mainly dimensionless parameters, which led us to further investigate the effects of liquid physical properties, such as viscosity and interface tension, on the mode transition.For suppression of the nonlinear dynamics, we proposed a geometrical optimization that imports a guiding rod positioning along the axis of the capillary tube. Here, we conducted a numerical analysis on the manipulation of the dripping process, as well as scaling analysis on the appearance of the nonlinear dripping. We expect this study to provide an insight into the underlying physical mechanisms of dripping in flow focusing, which are advantageous in the generation of monodispersed microdroplets for various applications.