Stabilized generation of three phase sinewaves

The paper deals with the derivation of a three phase oscillator model. The model is unusual in embracing a third order three-dimensional dynamics. Another feature of the model is in enabling an undistorted generation of precise sinewaves. The oscillator is in this latter respect similar to the well known two phase precise quadrature oscillators, which are also characterized in possessing a method of amplitude stabilization which does not distort the oscillator waveforms. The main effort of the present work has been, therefore, in extending the fundamental principles of the second order quadrature oscillator system from a two dimensional space into a three dimensional space.The paper concludes in suggesting possible applications of the present model.     

Local solutions of the Hamilton-Jacobi-Bellman equation for some stochastic problems

Consideration is given to the control problem of motion of a linear oscillator, which is subject to the external Gaussian and Poisson random actions, with the aim to minimize the mean energy with the aid of the external bounded control force. The hybrid solution method is suggested for the solution of the stated problem. This method relies on the search in a portion of the phase space for the exact analytical solution of the appropriate Hamilton-Jacobi-Bellman (HJB) equation and the numerical solution of this equation in the remaining (bounded) portion of the space. It is proved that the found analytical solutions represent the asymptotics of solutions of the Hamilton-Jacobi-Bellman equation. With the aid of the decomposition method, the obtained results are applied to the problem for the suppression with the aid of the actuator of vibrations of an elastic rod (plate) that is found to be under the action of Gaussian random actions. Results of the numerical modeling are given.     

基于Duffing振子的铁路轨道移频信号测量系统设计

铁路轨道作为移频信号的传输载体,其对于信号对象传输轨迹疏密度的辨别能力,决定了轨道体系对移频信号的测量准确性。为实现对信号对象传输频率的准确辨别,设计基于Duffing振子的铁路轨道移频信号测量系统。将电源模块输出的电量信号,按需分配至STM32F103 微处理器、移频信号辨别模块与DSP测量单元之中,完善各级应用部件之间的连接关系,实现铁路轨道移频信号测量系统的硬件方案设计。确定移频信号的Duffing振子描述条件,针对其定义形式,构造移频信号的相空间,完成对铁路轨道移频信号的提取。求解铁路轨道的Lyapunov指数,并构建移频信号的Duffing方程,确定混沌测量参数的取值范围,实现对铁路轨道移频信号的测量,联合各级应用部件,完成基于Duffing振子的铁路轨道移频信号测量系统设计。实验结果表明,上述系统测量所得信号传输轨迹疏密度与真实轨迹疏密度相似度较高,能够实现对铁路轨道移频信号的准确测量。     

弱非线性耦合二维各向异性谐振子的动力学行为

研究了弱非线性耦合二维各向异性谐振子的奇点稳定性及其在相空间中的轨迹.首先,求得弱非线性耦合二维各向异性谐振子的奇点;其次,分别利用Lyapunov间接法和梯度系统方法讨论该系统的平衡点稳定性;最后,用Matlab方法对系统进行数值模拟,并运用庞加赖截面观察系统在相空间的运动轨迹,发现随着能量的增加系统经历规则运动、规则运动与混沌并存等阶段,最后出现了混沌现象.     

时变耦合神经振子集群刺激依赖性相响应同步

考虑时变耦合情形下,利用相位响应曲线建立谐波刺激作用下耦合神经振子集群活动的动力学模型.引入相位概率密度函数导出描述神经振子集群活动序参数的演化方程.数值模拟结果表明高频谐波刺激可产生相位同步周期振荡,同步振荡周期与刺激频率有关,刺激频率越高神经振子群同步振荡频率也越高;同步强度与刺激强度有关,刺激越强同步程度越高.     

Rotor pole design of IPM motors for a sinusoidal air-gap flux density distribution

This study presents optimization methods for the design of rotor poles in interior permanent magnet machines, which aim to effectively obtain a sinusoidal distribution of the air-gap flux density. A sinusoidal field in the air-gap offers several advantages, such as reduction of torque ripple when using sinusoidal phase currents, and reduction in cogging torque and higher harmonic components of back electromotive force. In this study, the optimization process is achieved based on a phase field method using an Allen-Cahn equation. For the optimization problem we address, regions with meaningful design sensitivity values may exist outside the interfacial layer, which makes design variable updating impossible. To resolve this problem, the design sensitivities are diffused in the radial direction, using a diffusion equation. The time evolution of the design variables is based on the implicit finite element method, and the augmented Lagrangian method is used to deal with the volume constraint.     

Momentum-time flux conservation method for one-dimensional wave equations

We present a conservation element and solution element method in time and momentum space. Several paradigmatic wave problems including simple wave equation, convection-diffusion equation, driven harmonic oscillating charge and nonlinear Korteweg-de Vries (KdV) equation are solved with this method and calibrated with known solutions to demonstrate its use. With this method, time marching scheme is explicit, and the nonreflecting boundary condition is automatically fulfilled. Compared to other solution methods in coordinate space, this method preserves the complete information of the wave during time evolution which is an useful feature especially for scattering problems.     

Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation

The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol s...     

Obtaining real solutions for non-linear systems using certain transformation techniques†

Certain non-linear systems can be transformed into equivalent linear systems using power law transformations of the dependent variable. The conditions for obtaining a real solution using this technique are examined for an example non-linear oscillator. Although the requirement of a real solution can place restrictions on the parameters of the equation, a technique is suggested whereby a real solution can be obtained to an approximating equation which differs from the actual equation by an arbitrarily small amount.     

Topology optimization using a reaction–diffusion equation

This paper presents a structural topology optimization method based on a reaction–diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction–diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction–diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method’s effectiveness and utility.     

Quasi-linear modeling of gyroresonance between different MLT chorus and geostationary orbit electrons

The contributions of dayside and nightside gyroresonance of chorus waves to electron radiation belt evolution at L = 6.6 are detailedly differentiated via fully solving the two-dimensional Fokker-Plank equation.The numerical results show that the chorus waves at different regions play signiffcantly different roles.The dayside chorus waves can cause obvious loss of energetic electrons at lower pitch angles and weak energization at larger pitch angles.The nightside chorus waves can yield significant energization at larger pitch angles,but cannot efficiently resonate with the energetic electrons at lower pitch angle.Due to the numerical difficulty in fully solving Fokker-Planck equation,the cross diffusion terms are often ignored in the previous work.Here the effect of cross diffiusion at different regions is further analyzed.On the dayside,ignoring cross diffusion overestimates the electron phase space density by several orders of magnitude at lower pitch angles,and consequently the dayside chorus waves are incorrectly regarded as an effective energization mechanism.On the nightside,ignoring cross diffusion overestimates the electron phase space density(PSD) by about one order of magnitude at larger pitch angles.These numerical results suggest that cross diffusion terms can significantly affect gyroresonance of chorus waves on both the dayside and nightside,which should be included in the future radiation belt models.     

Design and optimization of a tunable W‐band subharmonic cavity based Gunn diode oscillator using computer‐aided design technique

In this work, a systematic computer‐aided design technique is proposed to minimize the fabrication iteration for the design and development of W‐band subharmonic Gunn diode oscillator with wideband tunable bandwidth at W‐band. Gunn diode based single diode oscillator structure was divided into passive and active parts to facilitate the modeling of the component on appropriate simulation environment. Resonating structure and package of Gunn diode are modeled as passive circuit in high frequency structure simulator (HFSS). To satisfy the oscillator design equation, disc‐post resonating structure is tuned in HFSS and its S‐parameters are collaborated with the model of Gunn diode in advanced design system. Magnitude and phase of reflection coefficient (S11) is observed to ascertain the desired frequency of oscillation. Proper tuning of disc‐post structure is done on simulation platform, which reduces the fabrication complexity and cost as well. The measurement results validate the models designed using EM and circuit simulator. The measured maximum stable RF power without any fabrication iteration is 14.2 dBm. A tunable bandwidth of 4 GHz with power output ripple of ±1 dB is measured by using a movable backshort.     

A Global Minimization Algorithm Based on a Geodesic of a Lagrangian Formulation of Newtonian Dynamics

The global minimum search problem is important in neural networks because the error cost involved is formed as multiminima potential in weight parametric space. Therefore, parameters that produce a global minimum in a cost function are the best values for enhancing the performance of neural networks. Previously, a global minimum search based on a damped oscillator equation known as the heavy ball with friction (HBF) was studied. The kinetic energy overcomes a local minimum if the kinetic energy is sufficiently large or else the heavy ball will converge into a local minimum due to the action of friction. However, an appropriate damping coefficient has not been found in the HBF; therefore, the ball has to be shot again after it arrives at each local minimum until it finds a global minimum. In order to solve this problem, we determined an adaptive damping coefficient using the geodesic of Newtonian dynamics Lagrangian. This geometric method produces a second-order adaptively damped oscillator equation, the damping coefficient of which is the negative time derivative of the logarithmic function of the cost potential. Furthermore, we obtained a novel adaptive steepest descent by discretizing this second-order equation. To investigate the performance of this novel steepest descent, we applied our first-order update rule to the Rosenbrock- and Griewank-type potentials. The results show that our method determined the global minimum in most cases from various initial points. Our adaptive steepest descent may be applied in many fields related to global minimum search, such as neural networks, game theory, and economics.     

Calculation of atomic hydrogen and its photoelectron spectra in momentum space

An essential modification to the kernel in the numerical calculation of hydrogenic momentum wave functions, is presented in this paper. Using only 256 grid points, the calculated eigenvalues, eigenfunctions and the oscillator strengths are shown to be in excellent agreement with the exact analytic results. The reliable pseudocomplete set of momentum space eigenfunctions is then applied to the time-dependent calculation of intense laser pulse on the hydrogen atom. With the advantage of having no boundary reflection during the time evolution, like that inherent in the coordinate space method, the photoelectron spectra of above-threshold-ionization (ATI) are elucidated for four cases. Some of which are not feasible or very difficult to solve with the coordinate space method. Generalization of the method to single-active electron systems is straightforward. Due to the good accuracy with a reasonably small-sized basis set, applications to the currently interested intense case of laser pulse on atom or molecule are expected.     

Comparison of Eulerian Vlasov solvers

Vlasov methods, which instead of following the particle trajectories, solve directly the Vlasov equation on a grid of phase space have proven to be an efficient alternative to the Particle-In-Cell method for some specific problems. Such methods are useful, in particular, to obtain high precision in regions where the distribution function is small.Gridded Vlasov methods have the advantage of being completely free of numerical noise, however the discrete formulations contain some other numerical artifacts, like diffusion or dissipation. We shall compare in this paper different types of methods for solving the Vlasov equation on a grid in phase space: the semi-Lagrangian method, the finite volume method, the spectral method, and a method based on a finite difference scheme, conserving exactly several invariants of the system. Moreover, for each of those classes of methods, we shall first compare different interpolation or reconstruction procedures. Then we shall investigate the cost in memory as well as in CPU time which is a very important issue because of the size of the problem defined on the phase space.     

用Duffing振子阵列解调微弱π/4-DQPSK信号

首次提出了微弱π/4-DQPSK信号Dumng振子阵列的解调算法,并用计算机对此算法进行了相应的仿真验证,同时还创造性地提出了星座图重叠划分,功率谱熵计算阵列和Dumng振子码元分界点搜寻器。先将π/4-DQPSK星座图的8个点划分成相重叠的四个区域,然后用功率谱熵来判定不同区域内Dumng振子的不同响应,最后依据当前时刻Duffing振子阵列的不同响应来断定所传送的数字信息。计算机仿真结果表明,本算法切实可行,在高斯信道中解调信噪比最低可达-15.6 dB。     

Design of MMIC oscillators using GaAs 0.2 μm PHEMT technology

We propose a feedback type oscillator and two negative resistance oscillators.These microwave oscillators have been designed in the S band frequency.A relatively symmetric resonator is used in the feedback type oscillator.The first negative resistance oscillator uses a simple lumped element resonator which is substituted by a microstrip resonator in the second oscillator to improve results.The negative resistance oscillator produces 4.207 dBm and 7.124 dBm output power with the lumped element resonator and microstrip resonator respectively,and the feedback type oscillator produces ?10.707 dBm output power.The feedback type oscillator operates at 3 GHz with phase noise levels at-83.30 dBc/Hz and-103.3 dBc/Hz at 100 kHz and 1 MHz offset frequencies respectively.The phase noise levels of the negative resistance oscillator with the lumped element resonator are-94.64 dBc/Hz and-116 dBc/Hz at 100 kHz and 1 MHz offset frequencies respectively,at an oscillation frequency of 3.053 GHz.With the microstrip resonator the phase noise levels are-99.49 dBc/Hz and-119.641 dBc/Hz at 100 kHz and 1 MHz offset frequencies respectively,at an oscillation frequency of 3.072 GHz.The results showed that both the output power and the phase noise of the negative resistance oscillators were better than those of the feedback type oscillator.