Oscillation of the scattering time in a 2D electron system with oval antidots

Electron scattering by a single barrier is predicted to reveal singularities as the magnetic field is changed, because the number of electron collisions with the barrier dramatically increases as chaotic orbits around the barrier are changed into periodic orbits. To test this experimentally we have measured the magnetoresistance of AlGaAs/GaAs heterostructures with a two-dimensional electron gas and a lateral lattice containing a macroscopic number of oval-shaped antidots fabricated using electron lithography. Reproducible fluctuations in the magnetoresistance are observed at low field, which are due to the oscillations of the number of electron collisions with the antidots. The number of collisions N before the electron escapes from the antidot has been calculated as a function of B in an electric field. The position of the maxima in N(B) obtained from calculations and experiment are in reasonable agreement.     

Band structure of monolayer of graphene,silicene and silicon-carbide including a lattice of empty or filled holes

We have developed a π-orbital tight-binding Hamiltonian model taking into account the nearest neighbors to study the effect of antidot lattices (two dimensional honeycomb lattice of atoms including holes) on the band structure of silicene and silicon carbide (SiC) sheets.We obtained that the band structure of the silicene antidot superlattice strongly depends on the size of embedded holes,and the band gap of the silicene antidot lattice increases by increasing of holes diameter.The band gap of SiC antidot lattice,except for the lattice of the small unit cell,is independent of the holes diameter and also depends on the distance between holes.We obtained that,the band gap of the SiC antidot lattice is the same as the band gap of the corresponding sheet without hole.Also,the electronic properties of the SiC antidot superlattice occupied either by carbon or by silicon atoms are investigated,numerically.Furthermore,we study the effect of occupation of graphene antidot by Si atoms and vice versa.Also,we have calculated the band structure of graphene and silicene antidot lattice filled by Si + C atoms.Finally,we compute the band structure of the SiC antidot lattice including the holes which are filled by C or by Si atoms.Really,in this paper we have generalized the method of paper[38] about graphene antidot with empty holes to the cases of filled holes by different atoms and also to the case of silicene and silicon carbide antidot lattices.     

Quantum corrections to the conductivity of a two-dimensional system with antidots

The quantum corrections to the conductivity of a two-dimensional electron system with antidots in the limit of a small antidot density are investigated. The corrections to the conductivity and magnetoconductivity due to the presence of antidots in a magnetic field perpendicular to the plane of the system are considered. It is assumed that the mean free path l of electrons on the impurities is far smaller than the antidot radius. Fiz. Tekh. Poluprovodn. 32, 1461–1466 (December 1998)     

Intersubband optical absorption coefficients and refractive index changes in spherical hydrogenic antidots

In this work, we have studied the optical absorption coefficients and refractive index changes in spherical quantum antidots with hydrogenic donor impurity at the center. For this purpose, the energy spectrum and wavefunctions are first determined, analytically. Then, we have used analytical expressions for the intersubband absorption coefficients and refractive index changes obtained by the compact density matrix formalism. The results show that i—total absorption coeficient increase with increasing size of antidot, ii—the refractive index changes decrease with decreasing antidot size.     

Observation of and noise reduction by vortex lattice matching in YBa2Cu3O7 thin films and rf SQUIDs with regular arrays of antidots

We report on the detection of matching effects between antidot and Abrikosov vortex lattices for fields far below the matching field B_m using rf SQUIDs and demonstrate, that antidots can strongly reduce the low-frequency l/f noise in active devices in unshielded environment. Square lattices of submicron holes (antidots) with diameters of 250–450 nm and lattice parameters ranging from 0.5–5 μm are patterned into optimized sputtered YBa₂Cu₃O₇ thin films on CeO₂-buffered sapphire substrates without deterioration of superconducting properties. A special experimental set-up consisting of an antidot lattice in flip-chip configuration with a bicrystal rf-SQUID has been used for the measurements. Thus, two different matching conditions are exposed upon the vortex lattice defined by the vortex–antidot interaction and the vortex–grain boundary interaction at the grain boundary in the washer. Vortices within the vicinity of the grain boundary of the washer can either be trapped (reduction of l/f noise) or exposed to a kind of double potential (increase of l/f noise) depending upon the magnitude of the applied magnetic induction and the geometrical arrangement between antidot array and grain boundary in the washer. Matching effects between vortex and antidot lattice could be observed in the form of minima in the noise spectrum for magnetic inductions much smaller then the matching field, e.g. for B^*=(1/18)²B_m. The maxima in the low-frequency noise are a result of the existence of two matching conditions, i.e. caused by the presence of the grain boundary in the SQUID washer. The experiments demonstrate that thermally activated hopping of vortices can strongly be reduced by antidots in the superconducting layer. The resulting reduction of the low frequency excess noise bears a great potential for applications of active high-T_c superconducting devices if other matching conditions are avoided, e.g. by using step-edge type rf-SQUIDs.     

Magnetic quantum oscillation in a monolayer insulator

The Shubnikov-de Haas(SdH)oscillation,as evidenced by the oscillating resistivity as a function of magnetic field at sufficiently low temperature,is not uncommon in metals,semi-metals and narrow gap semiconductors at their conducting state.The origin of SdH oscillation is associated with Landau quantization,at which the cyclotron orbits of electrons are quantized.In other words,electrons can only occupy dis-crete energy levels,which are called the Landau levels.As the magnetic field increases,the split,quantized Landau levels move across the Fermi level and hence the material's trans-port properties start to oscillate periodically.     

Transport anomalies in electron billiards with a lack of symmetry

Magnetotransport properties of two-dimensional electron gas in low-symmetry periodic lattices of antidots have been investigated. The comparison of resistivity tensor components has shown that the magnetoresistance features of this system originate from the electron trajectories running along the lattice arrays. Deviations in the Hall resistance, connected with a lack of symmetry in the system, have been found which were absent in the square lattices with the same ratio of the period to the antidot radius.     

Ballistic magnetotransport in a suspended two-dimensional electron gas with periodic antidot lattices

The magnetoresistance of suspended semiconductor nanostructures with a two-dimensional electron gas structured by periodic square antidot lattices is studied. It is shown that the ballistic regime of electron transport is retained after detaching the sample from the substrate. Direct comparative analysis of commensurability oscillations of magnetoresistance and their temperature dependences in samples before and after suspension is performed. It is found that the temperature dependences are almost identical for non-suspended and suspended samples, whereas significant differences are observed in the nonlinear regime, caused by direct current passage. Commensurability oscillations in the suspended samples are more stable with respect to exposure to direct current, which can be presumably explained by electron–electron interaction enhancement after detaching nanostructures from the high-permittivity substrate.     

Critical conditions of saddle-node bifurcations in switching DC–DC converters

Although existence of multiple periodic orbits in some DC–DC converters have been known for decades, linking the multiple periodic orbits with the saddle-node bifurcation (SNB) is rarely reported. The SNB occurs in popular DC–DC converters, but it is generally reported as a strange instability. Recently, design-oriented instability critical conditions are of great interest. In this article, average, sampled-data and harmonic balance analyses are applied and they lead to equivalent results. Many new critical conditions are derived. They facilitate future research on the instability associated with multiple periodic orbits, sudden voltage jumps or disappearances of periodic orbits observed in DC–DC converters. The effects of various converter parameters on the instability can be readily seen from the derived critical conditions. New Nyquist-like plots are also proposed to predict or prevent the occurrence of the instability.     

Large constellations for fast acquisition and delivery of information: Design and analysis by stereographic projection onto the equatorial plane

Recent space projects are designed by satellite constellations with a large number of spacecraft, a global character (i.e., from equatorial to high inclination orbits), and the possibility to transfer information to different satellites of the constellation (inter satellite link) in order to deliver the information to the ground as soon as possible. To cope with a large number of parameters, a fast tool for constellation design, performance evaluation and networking strategies is needed. The aim of this paper is to obtain the performance of any constellation in less than 1 s, even when the number of satellites in the constellation and the duration of the analysis is large (e.g., more than 200 satellites in a period of some days). The proposed algorithm is based on analytical formulae obtained by using the stereographic projection on the equatorial plane of the satellite orbits and the projection of the target and ground station orbits. It is believed that the two-dimensional projection proposed here can offer some advantages with respect to the spatial analysis of satellite orbits and their ground tracks, such as the reduction in time required to calculate station/satellite and satellite/satellite encounter conditions, and the clear and simple representation of the motion of the satellite of the constellation and of the ground stations of interest.     

带电粒子在二维中心势和磁通规范场中的运动和分数角动量

以二维中心势和磁通规范势场形成的多连通空间为例，从经典和量子两方面研究了带电粒子的运动轨道和波函数，结果表明：波函数几率云的空间分布与经典轨道完全相同；此外，角动量的分数量子化可以通过量子-经典对应条件唯一确定，而磁通规范势仅使所有波函数产生一共同的拓扑相位，并不改变量子化条件。     

用变量旋转变换实现声光双稳系统的混沌控制

设计了一种控制非线性系统混沌的变量旋转变换(VRT)方法。介绍了变量旋转变换方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性。利用计算机仿真模拟了受控后声光双稳系统的动力学行为。模拟结果显示,旋转变换的关联系数cosθ,sinθ为系统的控制参数,通过恰当地选择旋转变换的关联系数,使受控后系统的李雅普诺夫(Lyapunov)指数λ由正值转变为负值,系统由混沌态转变为周期态,周期态不但有稳定的原系统存在的倍周期2np轨道,而且还有3mp,2n×3mp(n,m为整数)这样原系统以外的周期轨道。     

Complex dynamics of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight: Coexistence of multiple attractors and remerging Feigenbaum trees

This contribution investigates the nonlinear dynamics of a model of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight. The investigations show that the proposed HNNs model possesses three equilibrium points (the origin and two nonzero equilibrium points) which are always unstable for the set of synaptic weights matrix used to analyze the equilibria stability. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents graph, phase portraits and frequency spectra, are used to highlight the rich and complex phenomena exhibited by the model. These rich nonlinear dynamic behaviors include period doubling bifurcation, chaos, periodic window, antimonotonicity (i.e. concurrent creation and annihilation of periodic orbits) and coexistence of asymmetric self-excited attractors (e.g. coexistence of two and three disconnected periodic and chaotic attractors). Finally, PSpice simulations are used to confirm the results of the theoretical analysis.     

Nonlinear oscillators, iterated maps, symbolic dynamics, and knotted orbits

We illustrate some recent developments in the theory of dynamical systems. Concentrating on periodically forced second-order ordinary differential equations, and using the Josephson (pendulum) and Duffing equations as examples, we show how the method of symbolic dynamics allows one to study complicated (chaotic) invariant sets in the Poincaré maps of such systems. Under certain conditions, these two-dimensional invertible maps can be reduced to one-dimensional (noninvertible) maps on the interval or circle. In this situation, a fairly complete kneading theory is available and one can use it to study bifurcation sequences occurring as parameters vary. We apply these ideas to the Josephson equation. In contrast to reducing the flow to a lower dimensional Poincaré map, Birman and Williams have exploited reduction to a semiflow on a branched two-dimensional manifold by collapsing orbits along stable contracting directions. Using their fundamental result that the knot types of periodic orbits (closed curves in 3-space) are preserved under this collapse--we study some of the knots arising in the Duffing equation. Since the knot type of a periodic orbit is invariant under continuous deformations, one can use it to characterize families of such orbits in parameterized equations. This notion permits us to follow bifurcating sequences of orbits for Poincaré maps of heavily damped (almost one-dimensional) and lightly damped (almost area-preserving) systems and to show that certain "universal," one-dimensional bifurcation sequences are completely reversed for area-preserving maps.     

A global message network employing low Earth-orbiting satellites

A global message communication network for low-density traffic, using satellites at low altitudes, is described. This network affords around-the-clock service to any part of the globe, including the polar regions. Such a network can accommodate static and mobile user terminals simultaneously. The oblate globe is modeled as a regular polyhedron with 12 facets for setting up the orbits. Satellites are positioned uniformly in low-altitude symmetrical orbits. The symmetrical orbits are those whose axes are symmetrical in the three-dimensional space. The authors study the coverage aspects of the 6-orbit scheme and the 10-orbit scheme, each with satellites deployed at an altitude of 5000 km. At this altitude, the terrestrial user terminals can access satellites at a grazing angle of 45°. The method of access over the crosslinks is the slotted ALOHA scheme. For low-density traffic, the downlink and uplink throughput rates are estimated. Simulation results agree with these analytical estimates for low values of network offered load     

混沌理论在测量中的应用

提出了一种在极不稳定的混沌系统中进行信号测量的方法，将敏感元件作为混沌电路的一部分，在初值一定的条件下，利用混沌系统的参数敏感性，敏感元件的参数随待测信号变化并使系统的混沌轨道变化，定义了轨道距离。从理论上和特定电路实验上论证了混沌测量方法是可行的。     

分段线性动态系统周期轨道的时域法求解及其稳定性分析

该文提出了分段线性动态系统周期轨道的时域法求解及稳定性判断的新方法。分段线性动态系统的状态空间被切换面分割成若干个线性子区间。借助MATLAB,联合求解周期轨道在各子区间的状态转移方程,可得该周期轨道在各切换面的切换点坐标及在各子区间的运行时间,从而得到该周期轨道的分段时间表达式。由该表达式,可导出该周期轨道在某一切换面的庞加莱映射方程及其雅可比矩阵,根据其特征值可判断周期轨道的稳定性。以三阶、四阶蔡氏电路为例,用该方法求出了它们的多个周期轨道,进行了稳定性判断,数字仿真表明该文所提出的新方法是可行的和正确的。     

Computing call-blocking probabilities in LEO satellite networks:the single-orbit case

We study the problem of carrying voice calls over a low-Earth-orbit satellite network and present an analytical model for computing call-blocking probabilities for a single orbit of a satellite constellation. We have devised a method to solve the corresponding Markov process efficiently for orbits of up to five satellites. For orbits consisting of a larger number of satellites, we have developed an approximate decomposition algorithm to compute the call-blocking probabilities by decomposing the system into smaller subsystems and iteratively solving each subsystem in isolation using the exact Markov process. Our approach can capture blocking due to handoffs for both satellite-fixed and Earth-fixed constellations. Numerical results demonstrate that our method is accurate for a wide range of traffic patterns and for orbits with a number of satellites that is representative of commercial satellite systems     

Mobile internet access using satellite networks

Satellites offer a promising alternative for mobile access to the Internet by both pedestrians, and more importantly, from vehicles. As such, satellites provide an essential complement to the cellular radio (UMTS) infrastructure in sparsely populated areas where high bandwidth UMTS cells cannot be economically deployed. In this paper, we analyse various mobile Internet applications in representative urban scenarios for two LEO constellations (one with polar orbits and the other with inclined orbits), as well as for some simple GEO configurations. To this end, we develop a satellite channel propagation model that includes shadowing from surrounding building skylines based on actual data in a built‐up area. Using these tools, we analyse various Internet applications and the performance of various TCP schemes in different topologies. Copyright © 2004 John Wiley & Sons, Ltd.     

Gray codes and 1D quadratic maps

The authors show how the symbolic sequences of same period superstable orbits in 1D quadratic maps are ordered according to Gray codes. Next, the Gray ordering number is introduced, in the interval (0, 1), allowing the simultaneous ordering of symbolic sequences of different period superstable orbits. Likewise, it is shown that Gray ordering number manipulation can determine whether or not a given symbolic sequence exists