Weak temperature gradient effect on the stability of the circular Couette flow

We have investigated the influence of a weak radial temperature gradient in a wide gap and large aspect ratio Couette-Taylor system. The inner cylinder is rotating and can be heated or cooled, the outer cylinder is at rest and immersed in a large thermal bath. We found that a radial temperature gradient destabilizes the Couette flow leading to a pattern of traveling helicoidal vortices occurring only near the bottom of the system. The size of the pattern increases as the rotation frequency of the cylinder is increased. We have characterized the spatiotemporal properties of the pattern and we have shown that it behaves as a wall mode found in the simulation of the complex Ginzburg-Landau equation with homogeneous boundary conditions.     

Laser-induced pattern formation from homogeneous polyisoprene solutions

This paper reports that the pattern formation in homogeneous solutions of polyisoprene in toluene saturated with C60 induced by a continuous-wave visible laser is observed experimentally. The transmitted beam patterns change with the increase of the laser irradiation time. In the initial phase, the patterns with concentric ring-shaped structure are formed. In the end, the patterns become speckle-shaped. The incubation time of the transmitted beam widening is inversely proportional to the laser power density and solution concentration. The pattern formation results from the optical-field-induced refractive index changes in the solutions, but the mechanism of optical-field-induced refractive index changes in the polymer solutions needs to be further studied.     

Research on identifying the order of fringe pattern traces using angular scan and zone search method

A method for automatically identifying the order of fringe pattern traces is presented. It uses the simplified Otsu algorithm for obtaining the threshold, the angular scan in the range of 45~ for searching the trace positions, and the zone search technique for identifying different traces. Experimental results show that the proposed method may reliably obtain the order of fringe pattern traces orientating from almost 45° to 90°.     

On 321-Avoiding Permutations in Affine Weyl Groups

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type A _{n – 1} by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for a 321-avoiding element of W (considered as a Coxeter group) may be obtained from each other by repeated applications of short braid relations.Using Shi's characterization of the Kazhdan–Lusztig cells in the group W, we use our main result to show that the fully commutative elements of W form a union of Kazhdan–Lusztig cells. This phenomenon has been studied by the author and J. Losonczy for finite Coxeter groups, and is interesting partly because it allows certain structure constants for the Kazhdan–Lusztig basis of the associated Hecke algebra to be computed combinatorially.We also show how some of our results can be generalized to a larger group of permutations, the extended affine Weyl group associated to GL _n ()     

Domain Investigation by the Conventional Bitter Pattern Technique with Digital Image Processing

In the cases of soft magnetic materials or complex domain configurations, investigations of the domain structure by the conventional Bitter pattern technique are generally difficult. It is demonstrated in this paper, referring to the examples of domain images of thin permalloy films and the basal surface of bulk cobalt single crystals, that this problem can be overcome by the application of digital image processing (DIP) system. In particular, the visibility limit in domain observation was expanded by an order of magnitude and high quality domain images could be obtained. Improvements over earlier results were achieved.     

相移测量技术中相移器研究

本文介绍一种用于相移测量技术的相移器。该相移器由计算机通过Ｄ／Ａ接口板自动控制输出电压幅度，其电路采用闭环控制，位移由压电晶体产生，具有很高的电压稳定度（０１％）和较小的相移误差（小于３°）。描述相移器的结构、驱动源工作原理及相移器标定方法     

Nonlinear competition between asters and stripes in filament-motor systems

A model for polar filaments interacting via molecular motor complexes is investigated which exhibits bifurcations to spatial patterns. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become either unstable with respect to an orientational instability of a finite wave number or with respect to modulations of the filament density, where long-wavelength modes are amplified as well. Above threshold nonlinear interactions select either stripe patterns or periodic asters. The existence and stability ranges of each pattern close to threshold are predicted in terms of a weakly nonlinear perturbation analysis, which is confirmed by numerical simulations of the basic model equations. The two relevant parameters determining the bifurcation scenario of the model can be related to the concentrations of the active molecular motors and of the filaments, respectively, which both could be easily regulated by the cell.     

On a superlinear elliptic p-Laplacian equation

We prove the existence of four solutions for the p-Laplacian equation

     

Phase dynamics in the complex Ginzburg-Landau equation

For αβ>−1, stable time periodic solutions A(X,T)=A_qe^iqX+iω_qT are the locally preferred planform for the complex Ginzburg-Landau equation