基于分岔理论的突触可塑性对神经群动力学特性调控规律研究

神经群模型是典型的非线性系统,具有丰富而复杂的动力学行为模式.神经群兴奋性和抑制性突触具有可塑性,并对神经群动力学特性具有重要调控作用,研究突触可塑性对神经群动力学特性的调控规律具有重要意义.本文基于分岔理论,通过神经群模型兴奋性和抑制性突触增益的余维一分岔分析,分别给出了神经群运行于单稳、双稳、正常和异常极限环振荡状态的兴奋性和抑制性突触增益的单参数区间;进而通过兴奋性和抑制性突触增益的余维二分岔分析给出了神经群运行于上述多种状态的双参数区域.上述结果定量剖析了兴奋性与抑制性突触可塑性及二者的相互作用对神经群动力学特性的调控规律,揭示了兴奋性与抑制性的动态平衡在神经电活动调控中所扮演的关键角色,仿真结果验证了分岔分析的正确性.本文的研究对理解突触可塑性在脑功能的维持及各种神经疾病的诱发机制中所扮演的角色具有重要参考价值.     

小型超导电源系统退磁保护回路建模与仿真

计算了采用二极管等效电压源模型和等效电阻模型的退磁回路电流响应和二极管功耗,分析了两个模型的特点和差异,在此基础上,为了进一步提高精度,充分考虑了二极管的非线性特性,以实际二极管伏安特性进行曲线拟合建立函数关系式得到二极管非线性模型,代入回路方程并求解。综合对比各模型的仿真结果后,得出采用二极管非线性模型和等效电压源模型能更好地模拟退磁保护响应。     

基于BRDF的光学表面疵病散射特性的仿真研究

为了研究精密光学元件表面微弱疵病的散射特性,基于矢量散射理论和双向反射分布函数,建立了光学表面微弱疵病的散射理论模型.通过仿真计算了双向反射分布函数随散射角的变化情况,分析了入射角度、入射光波长以及疵病自身尺寸等因素对疵病散射光特性的影响.基于仿真数据分析,针对光源参数对散射特性的影响进行仿真分析,为使用暗场成像法进行...     

双向反射分布函数在空间目标可见光反射特性建模中的应用

针对空间目标可见光反射特性提出了一种建模方法.双向反射分布函数(BRDF)可以有效地 描述目标表面材料的空间反射特性和光谱特性.根据目标表面状况及背景辐射环境,选取合 适的双向反射分布函数模型,利用辐射理论在可见光波段建立了空间目标反射特性的数学模 型.基于轨道参数进行了仿真计算.计算结果表明太阳帆板与卫星主体相比,其在探测器入 瞳处的辐照度只小一个数量级,在目标光学特性分析时不可忽略.而且,空间目标反射特性 不仅与太阳、地球和目标三者之间的实时位置有关,还与其几何形状、表面材料等有关.仿真分析结果验证了建模的正确性.     

考虑驾驶员预估效应的交通流格子模型与数值仿真

考虑驾驶员的预估效应对车流的影响,提出了一个改进的一维交通流格子模型.基于线性稳定性理论得到了该模型的线性稳定性判据;运用非线性分析方法导出了描述交通阻塞相变时的mKdV方程.应用数值仿真验证了mKdV方程的解,研究表明适当考虑车流中预估效应的作用能够增强交通流稳定性,从而能有效抑制交通阻塞的形成. 关键词： 预估效应 交通流 格子模型 数值仿真     

具有非均匀传输和抗攻击差异的网络病毒传播模型

针对实际网络中节点存在抗攻击差异以及边的非均匀传输等情况,基于平均场理论,提出具有抗攻击差异和非均匀传输特性的网络病毒传播平均场SIR模型.该模型中,通过引入脆弱性函数和传输函数,分别描述节点的抗攻击差异以及边的非均匀传输能力.通过对所提模型的分析,得到传播阈值的理论结果.理论分析和仿真表明,节点的抗攻击差异以及边的非均匀传输,都可导致出现正的传播阈值,使得病毒传播风险有效降低.     

调制气流声源气声转换过程模型研究

为克服已有准稳态理论在高频低速条件下性能预测的偏差和在换能机理假设上的不足,同时为设计者提供预示声源结构与辐射特性之间关系的工具,提出了基于混合气动声学方法的辐射声场仿真模型,分析了典型工况下流场和声场特性,探讨了换能过程的频率相关性.内流场由瞬态可压缩雷诺时均方程描述,SST k-w湍流模型耦合增强壁面函数用于预测喉...     

一类高维相对转动非线性动力系统的Lyapunov-Schmidt约化与奇异性分析

研究一类高维相对转动非线性动力系统的降维与分岔特性. 在考虑转动系统中间隙非线性影响因素的基础上, 基于广义耗散系统拉格朗日原理, 建立了一类高维相对转动非线性系统动力学模型.采用Lyapunov-Schmidt(LS)约化方法, 通过对高维非线性动力系统进行降维处理, 得到能够揭示系统非线性动力特性与系统参数之间规律的低维等价分岔方程. 运用奇异性理论对分岔方程进行普适开折, 分析了系统的分岔特性.结合实例参数, 对分岔特性进行仿真分析, 得到相对转动非线性动力系统发生动力失稳的参数区域及系统参数对动力失稳的影响规律.     

三轴速调管放大器自激振荡诊断

为满足X波段三轴速调管放大器(TKA)各腔内部自激振荡的诊断需求,设计了一种结构简单紧凑、无需外部密封结构的新型波导耦合器。利用小孔耦合原理和CST仿真软件,针对TKA中常见的自激振荡TE61模式,对该耦合器的耦合特性进行了理论分析和仿真设计。结合PIC方法,建立了利用该耦合器诊断TKA同轴漂移管内传输微波频谱特性的物理模型。通过仿真计算,验证了所设计的耦合器用于TKA自激振荡诊断的有效性。     

带电粒子束传输的相图函数理论

带电粒子束发射相图的形状可用相图函数描述.本文利用相图函数理论和Lie代数研究非线性传输系统中束相图的变化.同时研究了它的逆问题──根据束特性选择传输系统参数.作为例子,讨论了利用非线性元素改善束质量和非线性周期场系统中的束匹配问题.     

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions.Jansen's neural mass model(NMM) was initially proposed to study the origin of alpha oscillations.Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods.In this study,we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM.First,the sigmoid nonlinear function in the NMM is approximated by its describing function,allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part.Second,by conducting a theoretical analysis,we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and,furthermore,accurately determine its amplitude and frequency.The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations.Furthermore,strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.     

Extremely selective modal oscillation of random lasing induced by strong multiple scattering

We report on a new physical aspect of random lasing, an extremely selective modal oscillation by using a two-dimensional calculation model. The developed model consists of two theoretical subsystems, two-dimensional scattering model for describing multiple scattering process and rate equation model for describing lasing process. Using this model, we show how emission spectrum behaves as the scattering state of photons inside the system changes. It is shown that specific and strong modal oscillation takes place in a closed loop path of emitted photons, efficiently supported by the background multiple scattering. With the increase of multiple scattering events around the closed loop path, the system starts to oscillate with an extremely strong mode without any ASE (amplified spontaneous emission) noise.     

Temporal Behavior of Rabi Oscillation in Nanomechanical QED System with a Nonlinear Resonator

In nanomechanical QED system,consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity,we study the temporal behavior of Rabi oscillation in the nonlinear Jaynes-Cummings model.Using microscopic master equation approach,we solve time evolution of the density operator describing this model.Also,the probability of excited state of charge qubit is calculated.These analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit-resonator system affect time-oscillating and decaying of Rabi oscillation.     

微通道脉管非线性交变振荡微观机理的分子动力学研究

采用分子动力学方法，对He在微通道脉管内的非线性交变振荡的热力学响应进行仿真，研究气体振荡诱导管内轴向压力梯度、温度场的形成，并阐述微通道长径比对温差与相位的影响.结果表明：微通道内伴随压差驱动力在管内形成类似正弦函数压力波、速度波、质量流量波与半正弦的温度波.振荡周期随脉管管径的增大而缩短，随脉管长度的增加而增长，受直径影响很小；微通道两端的时均温差随长度的增加而增大，受直径的影响很小.预测针对不同的脉管直径存在一个最佳长径比与振荡周期，其数值随直径的增大而增大，为优化脉冲管的性能提供理论依据.     

Calculation of the Scattering Cross Section of Auroral Irregularities

Calculation of the scattering cross section per unit volume of auroral irregularities requires comprehensive knowledge of the law describing the formation of irregularities at both linear and nonlinear stages. In this paper, we calculate the scattering cross section using a simple idealized nonlinear model proposed by St.-Maurice and Schlegel. It is shown that the theoretical dependence of the scattering cross section per unit volume on the radar frequency calculated in terms of this model is in good agreement with the experimental curve.     

Spontaneous soliton formation with a saturated nonlinearity in a weakly nonlinear medium

We have observed the effect of a saturated nonlinearity on the process of spontaneous soliton formation in a weakly nonlinear medium with absorption. The characteristic properties of the problem are investigated on the basis of a model equation designated as a nonlinear Schrodinger equation with small perturbations describing the saturation of the nonlinearity and the absorption. The stability of the process of decay of the initial pulse is demonstrated by computational methods for a few specific cases. An effect described as an oscillation of the amplitude maximum of the formed pulse has been discovered.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–76, June, 1995.     

Thermal effects on mass detection sensitivity of carbon nanotube resonators in nonlinear oscillation regime

A mass sensor using a nano-resonator has high detection sensitivity, and mass sensitivity is higher with smaller resonators. Therefore, carbon nanotubes (CNTs) are the ultimate materials for these applications and have been actively studied. In particular, CNT-based nanomechanical devices may experience high temperatures that lead to thermal expansion and residual stress in devices, which affects the device reliability. In this letter, to demonstrate the influence of the temperature change (i.e., thermal effect) on the mass detection sensitivity of CNT-based mass sensor, dynamic analysis is carried out for a CNT resonator with thermal effects in both linear and nonlinear oscillation regimes. Based on the continuum mechanics model, the analytical solution method with an assumed deflection eigenmode is applied to solve the nonlinear differential equation which involves the von Karman nonlinear strain–displacement relation and the additional axial force associated with thermal effects. A thermal effect on the fundamental resonance behavior and resonance frequency shift due to adsorbed mas, i.e., mass detection sensitivity, is examined in high-temperature environment. Results indicate a valid improvement of fundamental resonance frequency by using nonlinear oscillation in a thermal environment. In both linear and nonlinear oscillation regimes, the mass detection sensitivity becomes worse due to the increasing of temperature in a high-temperature environment. The thermal effect on the detection sensitivity is less effective in the nonlinear oscillation regime. It is concluded that a temperature change of a mass sensor with a CNT-based resonator can be utilized to enhance the detection sensitivity depending on the CNT length, linear/nonlinear oscillation behaviors, and the thermal environment.     

Parameterization of meandering phenomenon in a stable atmospheric boundary layer

Accounting for the current knowledge of the stable atmospheric boundary layer (ABL) turbulence structure and characteristics, a new formulation for the meandering parameters to be used in a Lagrangian stochastic particle turbulent diffusion model has been derived. That is, expressions for the parameters controlling the meandering oscillation frequency in low wind speed stable conditions are proposed. The classical expression for the meandering autocorrelation function, the turbulent statistical diffusion theory and ABL similarity theory are employed to estimate these parameters. In addition, this new parameterization was introduced into a particular Lagrangian stochastic particle model, which is called Iterative Langevin solution for low wind, validated with the data of Idaho National Laboratory experiments, and compared with others diffusion models. The results of this new approach are shown to agree with the measurements of Idaho experiments and also with those of the other atmospheric diffusion models. The major advance shown in this study is the formulation of the meandering parameters expressed in terms of the characteristic scales (velocity and length scales) describing the physical structure of a turbulent stable boundary layer. These similarity formulas can be used to simulate meandering enhanced diffusion of passive scalars in a low wind speed stable ABL.     

A Simple Model for Nonlinear Confocal Ultrasonic Beams

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov （KZK） equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.