Electrodynamics of current-biased inductive cubic networks of Josephson junctions

The dynamical equations for the gauge-invariant superconducting phase differences across the twelve Josephson junctions placed on the sides of an inductive cubic network are derived. The electrodynamic properties of the system are studied by means of a general analytic approach. The cubic system is seen to show features similar to those of a d.c. SQUID for externally applied magnetic fields perpendicular to one cube face. Additional features are detected for different field orientations.     

Crystals with sublattices belonging to the cubic system and special features of their elementary excitation spectra

Genesis of spectra of elementary excitations of crystals comprising sublattices belonging to the cubic system is investigated. Using the methods of group theory, the Brillouin sublattice zones are transformed into the Brillouin crystal zones, and degeneration is established caused by the convolution of branches of the spectrum. The degeneration is removed with allowance for hybridization of sublattice states. The special features of the band spectra of some crystals belonging to the cubic system are discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 21–27, May, 2006.     

Solitary pulses in linearly coupled Ginzburg-Landau equations

This article presents a brief review of dynamical models based on systems of linearly coupled complex Ginzburg-Landau (CGL) equations. In the simplest case, the system features linear gain, cubic nonlinearity (possibly combined with cubic loss), and group-velocity dispersion (GVD) in one equation, while the other equation is linear, featuring only intrinsic linear loss. The system models a dual-core fiber laser, with a parallel-coupled active core and an additional stabilizing passive (lossy) one. The model gives rise to exact analytical solutions for stationary solitary pulses (SPs). The article presents basic results concerning stability of the SPs; interactions between pulses are also considered, as are dark solitons (holes). In the case of the anomalous GVD, an unstable stationary SP may transform itself, via the Hopf bifurcation, into a stable localized breather. Various generalizations of the basic system are briefly reviewed too, including a model with quadratic (second-harmonic-generating) nonlinearity and a recently introduced model of a different but related type, based on linearly coupled CGL equations with cubic-quintic nonlinearity. The latter system features spontaneous symmetry breaking of stationary SPs, and also the formation of stable breathers.     

Aspects of stochastic resonance in Josephson junction,bimodal maps and coupled map lattice

We present the results of extensive numerical studies on stochastic resonance and its characteristic features in three model systems, namely, a model for Josephson tunnel junctions, the bistable cubic map and a coupled map lattice formed by coupling the cubic maps. Some interesting features regarding the mechanism including multisignal amplification and spatial stochastic resonance are shown.     

Cubic phases of amphiphilic molecular aggregates

Stability and geometry of the lyotropic periodic cubic mesophases are considered in the framework of a general symmetry based phenomenological approach. A limited number of cubic structural types is shown to be formed by amphiphilic molecular aggregates due to the specific nature of self-organizing units. The related thermodynamic models predict topology of phase diagrams and specific features of transitions between isotropic, lamellar, cubic bicontinuous and cubic micellar phases. Received 25 February 1999 and Received in final form 29 June 1999     

Cubic superspace symmetry and inflation rules in metastable MgAl alloy

The diffraction properties of a quenched Al-Mg alloy which has been recently termed as a “cubic quasicrystal” are quantitatively reanalyzed. It is shown that the phase can be interpreted within the superspace formalism as an ordinary incommensurately modulated structure. The cubic six-dimensional superspace group that describes its symmetry properties has been determined. The additional inflation symmetry features exhibited by the diffraction diagram can be summed up by its invariance for the inflation factor , but this property has its origin in the specific value of the modulus of the modulation wave vectors, which is composition dependent. Other particular values of this modulus can give rise to similar scaling properties. Further experiments are required to ellucidate if the mentioned inflation symmetry is a fortuitous situation in a composition dependent wave vector, or has indeed the physical significance which would allow to describe the system as a “cubic quasicrystal”. Received: 25 June 1998 / Received in final form and Accepted: 23 September 1998     

Thermal properties of cubic metals in anharmonic approximation

Expressions for thermal properties such as thermal expansion, specific heat and melting point are obtained by employing the usual quadratic-quartic form of the potential energy. Computed results for nineteen cubic metals are presented and compared with the experimental values. The model describes the broad features observed in the thermal properties and an estimate of the anharmonicity in cubic metals.     

Coupled maps and pattern formation on the Sierpinski gasket

The bifurcation structure of coupled maps on the Sierpinski gasket is investigated. The fractal character of the underlying lattice gives rise to stability boundaries for the periodic synchronized states with unusual features and spatially inhomogeneous states with a complex structure. The results are illustrated by calculations on coupled quadratic and cubic maps. For the coupled cubic map lattice bistability and domain growth processes are studied.     

Dynamics of 2-D one electron quantum dots in periodically fluctuating confinement potential: Influence of size and anharmonicity

We explore the dynamics of harmonically confined single electron quantum dots as a function of dot size under periodically fluctuating confinement potential. The system of interest is a 2-D system in the presence of a perpendicular magnetic field. We show that for given strengths of the magnetic field and effective mass, a periodic variation in the strength of the confinement potential could invite interesting features in the dynamics of the system. Also, the pattern of time evolution of eigenstates of the unperturbed system reveals significant size-dependence. The fluctuation in the confinement potential from its initial value is found to modulate the dynamical aspects in a prominent way. The presence of cubic anharmonicity in the confining field brings in new features in the dot dynamics.     

Numerical results on the indirect exchange interaction in crystalline and amorphous metals

Computer simulation of the indirect exchange interaction is carried out for a single tight-binding s-band in ordered (simple cubic, body-centered cubic, face-centered cubic) and amorphous (relaxed dense-random-packed) structures. All cases show very similar features in the spatial dependence of the interaction, with no attenuation being observed in the amorphous structure. The structural dependence of the phase coherence of the electron wavefunctions is analysed. Effects due to alloying are briefly discussed.     

复变系数Ginzburg-Landau方程的啁啾组合孤波解

基于描述非均匀光纤系统的复系数Ginzburg-Landau方程,通过拟解法得到了该方程的精确啁啾组合孤波解,并分析了该解的特性.通过大量的数值模拟,发现在有限的初始扰动下这些组合孤波解是在非均匀光纤系统中稳定的.最后,为了进一步研究组合孤波解的稳定性,我们还探讨了组合孤波的相互作用.     

立方非线性Schr?dinger方程的动力学行为分析

本文采用辛算法，研究了立方非线性Schr?dinger方程在不同的空间离散下的动力学行为，并讨论了其在不同的非线性参数下的动力学性质。 我们指出，系统的守恒量在长时间的演化下保持不变，但对于强非线性，不同的空间离散精度，将导致不同的动力学行为。     

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function (PSF) caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration. This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF. Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask. The system with the novel phase mask has better performance in the modulation transfer function (MTF) especially in low-and-medium spatial frequency region. The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect. The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.     

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

<正>The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C(s).Three cases including linear delay,cubic delay and global delay in the system are considered respectively.The simulation results indicate that the linear delay enhances the fluctuation of the system (reduces the stability of the system) while the cubic delay and global delay weaken it(enforce the stability of the system),and the effect of cubic delay is more pronounced than the linear delay and global delay.     

多维正常声电光效应最佳工作模式的确定

通过对四方、立方晶系的纵向电光效应和多维正常声光效应的研究，选定了四方晶系的KDP晶体和立方晶系的GaP晶体作为多维正常声电光器件的最佳晶体，并通过计算两种晶体的声光互作用性能参量，确定了它们的二维、三维、四维正常声电光效应的最佳工作模式。研究结果为多维正常声电光器件的设计与制作打下了良好基础。多维声电光器件在多路光通信和多通道光信息处理中有应用前景。     

Formability of ABO3 cubic perovskites

In this study, 223 binary oxide systems (of which, 34 systems can form cubic perovskites) are collected to explore the regularity of cubic perovskites formability. It is found that the octahedral factor (r_B/r_O) take the same important role as the tolerance factor (t) to form cubic perovskites in complex oxide system. Regularities governing cubic perovskites formability are obtained by using empirical structure map constructed by these two parameters, on this structure map, sample points representing systems of forming (cubic structure) and non-forming are distributed in distinctively different regions. Prediction criteria for the formability of cubic perovskites are squeezed out, which may be applied to design new substrate or buffer materials with cubic perovskite structure in compound semiconductor epitaxy.     

Three-to-one internal resonances in a general cubic non-linear continuous system

A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.     

Stochastic collocation method for secondary bifurcation of a nonlinear aeroelastic system

A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems.     

Response functions for crystals and surfaces,with applications to surface scattering

A general solution of the equations of forced motion of a harmonic crystal or other vibrating system with arbitrary time-dependent forces acting on the atoms is given. The solution is given in terms of dynamical “response functions”, for which expressions in terms of the normal mode frequencies and eigenvectors (polarization vectors) are given. Numerical calculations of the response functions are described for (111) and (100) surfaces of face-centered cubic crystals interacting with Lennard-Jones 6–12 potentials, and the qualitative features of the surface and bulk response functions are discussed. The use of these functions in problems of atomic scattering from surfaces is outline, and conveneint parameterized forms for this application are given.