Molecular-mediated crystal growth of PbTiO3 nanostructure on silicon substrate

A simple approach based on an organically modified sol-gel process has been developed to fabricate PbTiO₃ (PT) nanocrystals on Si (1 0 0) substrate, where the amorphous powder modified by acetylacetone (acac) was used as precursor. After dropping the amorphous powder precursor prepared by freeze-drying process, PT nanocrystals on Si (1 0 0) substrate were obtained after heat treatment at 720 °C for 30 min in air. PT nanocrystals have been detected by XRD to be tetragonal perovskite structure. With the increase of acac/Pb molar ratio, the relative (1 0 0)/(0 0 1) diffraction peak intensity gradually increases, which probably suggested an oriented growth of PT nanocrystal along [1 0 0] on Si (1 0 0) substrates. In addition, Atomic force microscopy (AFM) results indicated that the height and the average lateral size of PT nanocrystal increased and then decreased as the acac/Pb molar ratio increased. Piezoelectric force microscopy (PFM) results demonstrated that all the samples show obvious piezoelectric activity. These results implied that the acetylacetone molecular mediated the growth of PT nanocrystals on Si (1 0 0) substrates possibly by the acac/Pb molar ratio. This simple method has been suggested to be attractive for tailoring an oriented growth of the nanostructures of perovskite oxide systems on Si substrates.     

Vector financial rogue waves

The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields.     

New exact solution profiles of the nonlinear dispersion Drinfel’d–Sokolov (D(m, n)) system

In this paper, to understand the role of nonlinear dispersion in the coupled systems, the nonlinear dispersion Drinfel’d–Sokolov system (called D(m, n) system) is investigated. As a consequence, many types of compacton and solitary pattern solutions are obtained. Moreover, some solitary wave solutions are also deduced for differential parameters m, n. When n = 1, the D(m, 1) system with linear dispersion is shown to possess also compacton and solitary pattern solutions, which contain the known results. Moreover, some rational solutions of D(m, n) system are also deduced.     

SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS

In this article, the authors consider a class of semilinear elliptic equations on fractal sets under some new conditions, which are more weaker than those in usual cases. The authors get the non-trivial and non-negative solution of the zero boundary Dirichlet problem using Mountain Pass Lemma.     

磁场对激波冲击R22重气柱作用过程影响的数值模拟

为研究平面入射激波与磁化R22重质圆形气柱的作用过程,首先通过数值方法得到了不同初始条件下激波诱导R22气柱的Kelvin-Helmholtz (KH)及Richtmyer-Meshkov (RM)不稳定性导致的重气柱变形过程,并详细讨论了不同情况下透射激波在气柱内聚焦诱导射流的过程;然后在加入磁场的情况下,采用CTU+CT算法进行数值模拟,以保证数值结果满足任意时刻磁场的散度为零。计算结果表明:磁场对激波诱导R22气柱不稳定性具有抑制作用;法向磁场和流向磁场都可以很好地抑制RM不稳定性;对于KH不稳定性,法向磁场的控制效果更好,不仅可以抑制界面上涡串的卷起,还可以阻止主涡的发展,而流向磁场做不到后者;磁场对射流影响不大,射流处的磁能量可以一定程度上抑制射流的衰减,同时法向磁场可以减小聚焦时压力及速度峰值。     

Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach

First, a type of Q-S (complete or anticipated) synchronization is defined in discrete-time dynamical systems. Second, based on backstepping design with a scalar controller, a systematic, concrete and automatic scheme is presented to investigate Q-S (complete or anticipated) synchronization between the discrete-time drive system and response system with strict-feedback form. Finally, the proposed scheme is used to illustrate Q-S (complete or anticipated) synchronization between the two-dimensional discrete-time Lorenz system and Fold system, as well as the three-dimensional hyperchaotic discrete-time Rossler system and generalized discrete-time Rossler system. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. Our scheme can be also extended to investigate Q-S (complete or anticipated) synchronization between other discrete-time dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller and to verify its effectiveness in computer.     

Compare the phase transition properties of VO2 films from infrared to terahertz range

VO₂ with reversible semiconductor–metal phase transition properties is particularly available for the application in smart opto-electrical devices. However, there are rare reports on comparing its phase transition properties at different ranges. In this study, the VO₂ films are designed with the similar crystalline structure and stoichiometry, but different morphologies by inorganic and organic sol-gel methods, and their phase transition characteristics are compared both at infrared and terahertz range. The results indicate that the VO₂ film prepared by inorganic sol-gel method shows more compact nanostructure. It results in larger resistivity change, infrared and terahertz switching ratio in the VO₂ film. Moreover, it presents that the phase transition intensity of VO₂ film in terahertz range is more sensitive to its microstructure. This work is helpful for understanding the susceptibility of terahertz switching properties of VO₂ to its microstructure. And it can provide insights for the applications of VO₂ in terahertz smart devices.     

Discrete asymptotic deterministic randomness for the generation of pseudorandom bits

The deterministic randomness not only can become a dominant approach in exploring the relationship between chaos and randomness, but also can be associated with some famous number theoretical concepts and open problems in number theory. Compared with chaotic sequences, asymptotic deterministic randomness sequences have the characteristic of multi-value correspondence, which makes those sequences unpredictable in short steps. In this Letter, we will propose the definition of the discrete asymptotic deterministic randomness, and then analyze the dynamical characteristics such as maximum-period and multi-value correspondence. Referring to the NIST800-22 statistical test suite, we will present and discuss two examples of PRBGs based on DADR, from the point of view of FPGA design and randomness quality.     

New binary travelling-wave periodic solutions for the modified KdV equation

In this Letter, the modified Korteweg-de Vries (mKdV) equations with the focusing (+) and defocusing (−) branches are investigated, respectively. Many new types of binary travelling-wave periodic solutions are obtained for the mKdV equation in terms of Jacobi elliptic functions such as sn(ξ,m)cn(ξ,m)dn(ξ,m) and their extensions. Moreover, we analyze asymptotic properties of some solutions. In addition, with the aid of the Miura transformation, we also give the corresponding binary travelling-wave periodic solutions of KdV equation.