Circuit analysis of the compound quasi-optical power combiner

In 1991, we developed a new type of quasi-optical power combiner, called a compound quasi-optical power combiner, at Ka-band. In this paper, the circuit of such a compound quasi-optical power combiner is analysed. Its equivalent circuit model is proposed. The circuit equations, the balance condition, the injection locking and the stabilized condition of the compound quasi-optical power combiner are studed by the equivalent circuit model. As an example, a compound quasi-optical power combiner which consists of two single—cavity, two—device power combiners is analysed     

The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.     

Physically based molecular device model in a transient circuit simulator

Two efficient, physically based models for the real-time simulation of molecular device characteristics of single molecules are developed. These models assume that through-molecule tunnelling creates a steady-state Lorentzian distribution of excess electron density on the molecule and provides for smooth transitions for the electronic degrees of freedom between the tunnelling, molecular-excitation, and charge-hopping transport regimes. They are implemented in the fREEDA™ transient circuit simulator to allow for the full integration of nanoscopic molecular devices in standard packages that simulate entire devices including CMOS circuitry. Methods are presented to estimate the parameters used in the models via either direct experimental measurement or density-functional calculations. The models require 6–8 orders of magnitude less computer time than do full a priori simulations of the properties of molecular components. Consequently, molecular components can be efficiently implemented in circuit simulators. The molecular-component models are tested by comparison with experimental results reported for 1,4-benzenedithiol.     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

A novel hyperchaotic system and its circuit implementation

A four-dimensional hyperchaotic system with five parameters is proposed. Its dynamical properties such as dissipativity, equilibrium points, Lyapunov exponent, Lyapunov dimension, bifurcation diagrams and Poincare maps are analyzed theoretically and numerically. Theoretical analyses and simulation tests indicate that the new system's dynamics behavior can be periodic attractor, chaotic attractor and hyperchaotic attractor as the parameter varies. Finally, the circuit of this new hyperchaotic system is designed and realized by Multisim software. The simulation results confirm that the chaotic system is different from the existing chaotic systems and is a novel hyperchaotic system. The system is recommendable for many engineering applications such as information processing, cryptology, secure communications, etc.     

Neural spike renormalization. Part I — Universal number 1

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum's constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.     

Dynamic behaviors of a class of memristor-based Hopfield networks

In this Letter, we analyze the dynamic behaviors for a class of memristor-based Hopfield networks. Some sufficient conditions are obtained which ensure the essential bound of solutions and global exponential stability of memristor-based Hopfield networks by using analysis approaches, and the criteria act as significant values for qualitative analysis of memristor-based Hopfield networks. Finally, a numerical example is given to show the effectiveness of our results.     

Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller

In this Letter, a novel method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by three different types of switching control strategies, the equilibrium point can be extended along both xy plane and z axis direction, so as to generate grid multi-scroll chaotic attractors. The dynamical behaviors are further analyzed. Moreover, an improved module-based circuit is designed for realizing 5×3 and 4×4 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.     

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.     

感应叠加过程行波分析和模拟

 采用变换矩阵为研究工具对感应叠加过程中行波的传播、透射、反射进行了分析，得到了和集中参数分析一致的稳定解，给出了电压随时间变化的细节。建立了3.5 MeV注入器脉冲功率源和感应叠加结构的电路模型，得到的感应腔压模拟波形和实验波形基本一致，结合行波分析法基本解释了腔压波形和Blumlein线输出波形之间较大差异的成因，阴极叠加电压的模拟也反映了实验中主脉冲后的反射波形。