Axisymmetric three-dimensional finger solutions in Mullins-Sekerka equation

In this paper, we study the existence problem of axisymmetricthree-dimensional finger solutions of Mullins–Sekerkaequation. The finger solutions are travelling wave solutionswhose finger-shaped interfaces are moving along a certain directionat a constant speed within a cylindrical domain. The existenceof at least one axisymmetric three-dimensional finger solutionis obtained through a fixed-point argument of the Hilbert transformation.     

注入锁定铜蒸气激光器的实验研究

使用两台相同的望远镜式非稳腔铜蒸气激光器,通过一块45°玻璃平板作腔的耦合组成匹配的注入锁定系统,研究了同步、注入信号功率和光束孔径大小等因素对输出功率和方向性的影响,实验结果清楚地表明,注入信号的作用在于抑制腔内高阶横模(包括被放大的自发发射)的竞争,使高增益介质的激光器既提高效率又改善方向性。注入锁定器件功率水平在5左右的情况下,其结果与单独非稳腔振荡相比,输出功率增加30～40％,方向性改善一倍以上。     

A strategy for choosing Gegenbauer reconstruction parameters for numerical stability

The Gegenbauer reconstruction method was first proposed in 1992, but in early studies no attempts were made to optimize the relevant parameters of this method. These parameters were allowed to grow proportionally with the number of nodes which, in many cases, resulted in exponential convergence for a selected range of the proportionality constants. Early studies also made clear that very large error bounds could be expected if these key parameters were not chosen carefully. Subsequent studies then pointed out that, although unrelated to the method’s analytically predictable domains of poor accuracy, round-off errors could also sabotage the method’s accuracy. The challenge of successfully implementing a Gegenbauer reconstruction then rests on understanding the performance trade-offs we can expect when choosing the key parameters in accordance with different objectives.In this study, we propose a new strategy for choosing optimal parameters in the Chebyshev-Gegenbauer reconstruction method, specifically to achieve numerical stability. This strategy is based on asymptotic analysis as well as minimization problems in one and two dimensions. The effectiveness of our approach, which could also be applied to a wider selection of polynomials is then illustrated with results from numerical experiments.     

The cutoff phenomenon for randomized riffle shuffles

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

C 1,α-solutions to non-autonomous anisotropic variational problems

We establish several smoothness results for local minimizers of non-autonomous variational integrals with anisotropic growth conditions. Mathematics Subject Classification (2000) 49N60, 49N99     

Digital total variation filtering as postprocessing for Chebyshev pseudospectral methods for conservation laws

Digital total variation filtering is analyzed as a fast, robust, post-processing method for accelerating the convergence of pseudospectral approximations that have been contaminated by Gibbs oscillations. The method, which originated in image processing, can be combined with spectral filters to quickly post-process large data sets with sharp resolution of discontinuities and with exponential accuracy away from the discontinuities.     

A bidirectional hybrid DWDM-PON employing optical injection locking technique and data comparators

A bidirectional hybrid dense-wavelength-division-multiplexing (DWDM)-passive optical network (PON) employing optical injection locking technique on vertical-cavity surface-emitting lasers (VCSELs) and data comparator, as well as optical injection locking technique on distributed feedback laser diodes (DFB LDs) and amplitude/phase compensator is proposed and demonstrated. Improved performances of bit error rate (BER) and carrier-to-noise ratio/composite second order/composite triple beat (CNR/CSO/CTB) were observed in our proposed bidirectional hybrid DWDM-PON. Bidirectional transmission in bidirectional hybrid DWDM-PON architecture is a very attractive option, the capacity of the optical network can be expanded relatively easily by bidirectional transmission technology.     

一种考虑剪切变形的平行四边形厚/薄板通用单元

根据Timoshenko二广义位移梁理论，构造了深梁位移场的插值函数。利用斜坐标系与直角坐标系的变换关系、有限条带思想和深梁位移插值函数，构造了一种考虑剪切变形的平行四边形厚／薄板弯曲通用单元的位移(曲率、剪应变、转角、横向位移)插值函数，导出了刚度矩阵和非结点荷载等效力。并对简支阍支方板、Razzaque斜板、四边简支斜交板弯曲进行了数值计算。算例表明此单元有较好的精度，对于薄板不出现剪切闭锁，可适应于目前桥梁建设中大量采用的斜交板桥结构分析。     

Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at the University of Illinois at Urbana-Champaign.     

Quenching phenomenon of a time‐fractional diffusion equation with singular source term

In this paper, a time‐fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0<α ?1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time‐fractional diffusion equation presents quenching solution that is not globally well‐defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright © 2017 John Wiley & Sons, Ltd.