Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Dynamics of a small vibro-impact pile driver

A mathematical model is developed to study periodic-impact motions and bifurcations in dynamics of a small vibro-impact pile driver. Dynamics of the small vibro-impact pile driver can be analyzed by means of a three-dimensional map, which describes free flight and sticking solutions of the vibro-impact system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the Poincaré map. The piecewise property is caused by the transitions of free flight and sticking motions of the driver and the pile immediately after the impact, and the singularity of map is generated via the grazing contact of the driver and the pile immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularities and parameter variation on the performance of the vibro-impact pile driver is analyzed. The global bifurcation diagrams for the impact velocity of the driver versus the forcing frequency are plotted to predict much of the qualitative behavior of the actual physical system, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocity and shorter impact period of such response.     

由三氯丙烷粗馏分制取三醋酸甘油酯

三醋酸甘油酯工业上历来是用甘油与醋酸酯化制得[1],三醋酸甘油酯用作纤维素树脂和乙烯基聚合物、共聚物的增塑剂。主要用于增塑醋酸纤维素作卷烟过滤嘴,可提供良好的弹性、透气性和合适的硬度。工业上由氯丙烯生产环氧氯丙烷过程中,生产相当量的三氯丙烷(以下简称ＴＣＰ),1,3二氯2丙醇等副产品[2]。以齐鲁石化公司氯碱厂3.2×104ｔ/ａ环氧氯丙烷装置为例,副产物ＴＣＰ达2000ｔ/ａ。它们在生产中成为一个馏分分离出来。这一馏分没有什么用处,用燃烧法处理时还生成ＨＣｌ等废气污染环境[3],我们考虑将它转化为三醋酸甘油酯,既可以变废为宝又…     

Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x₀ of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x₀ as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem.     

Crowding with nearest neighbors replacement for multiple species niching and building blocks preservation in binary multimodal functions optimization

This paper introduces a novel niching scheme called the q-nearest neighbors replacement (q-NNR) method in the framework of the steady-state GAs (SSGAs) for solving binary multimodal optimization problems. A detailed comparison of the main niching approaches are presented first. The niching paradigm and difference of the selection-recombination genetic algorithms (GAs) and the recombination-replacement SSGAs are discussed. Then the q-NNR is developed by adopting special replacement policies based on the SSGAs; a Boltzmann scheme for dynamically sizing the nearest neighbors set is designed to achieve a speed-up and control the proportion of individuals adapted to different niches. Finally, experiments are carried out on a set of test functions characterized by deception, epistasis, symmetry and multimodality. The results are satisfactory and illustrate the effectivity and efficiency of the proposed niching method.     

On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras

In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.     

Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision

This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Balance Method (HBM). As the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these oscillation are also clarified.     

Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations

This paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects. The main results here are the generalization of Jiang [Daqing Jiang, On the existence of positive solutions to second order periodic BVPs, Acta Math. Sci. 18 (1998) 31–35] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.     

Extension of statistical replacement to systems with time-correlated fluctuations

Nonlinear systems with correlated stochastic parameters are approximated by simpler systems. This method is an extension of an earlier version of statistical replacement and statistical linearization. The extended method is applicable to systems with correlated fluctuations. We show how this general method reduces to the earlier methods in special cases.     

Fabrication of urchin‐like Ag/ZnO hierarchical nano/microstructures based on galvanic replacement mechanism and their enhanced photocatalytic properties

Urchin‐like Ag/ZnO hierarchical nano/microstructures have been synthesized through a facile low‐temperature hydrothermal growth method based on galvanic replacement mechanism. The experimental results show that the urchin‐like Ag/ZnO heterostructures are formed through the epitaxial growth of ZnO nanorods on the {111} facets of Ag nanoparticles along their own c‐axis. The photocatalytic properties of the products were evaluated by the degradation of RhB dye solution under ultraviolet irradiation, and the results show that the products exhibit significantly enhanced photocatalytic properties comparing with pure ZnO nanorods. The products with a Ag content of 35.64 atom % prepared with a Ag⁺ concentration in solution of 5 mM exhibit surprisingly high degradation rate (99.5%) for RhB dye solution (4 mg/L) after photocatalytic reaction for only 14 min under ultraviolet irradiation. The Schottky barrier formed at the metal‐semiconductor interfaces improves the segregation of charges and prevents the charge recombination, and thus significantly enhances the photocatalytic activities of the products. On the other hand, the high stability of the urchin‐like Ag/ZnO hierarchical nano/microstructures can effectively prevent the aggregation of nanostructures with simultaneously preserving high photocatalytic properties due to the existence of nanosized unites. Copyright © 2016 John Wiley & Sons, Ltd.