4,317 research outputs found

    The long-time asymptotic of the derivative nonlinear Schro¨\ddot{o}dinger equation with step-like initial value

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    Consideration in this present paper is the long-time asymptotic of solutions to the derivative nonlinear Schro¨\ddot{o}dinger equation with the step-like initial value \begin{eqnarray} q(x,0)=q_{0}(x)=\begin{cases} \begin{split} A_{1}e^{i\phi}e^{2iBx}, \quad\quad x0. \end{split}\nonumber \end{cases} \end{eqnarray} by Deift-Zhou method. The step-like initial problem described by a matrix Riemann-Hilbert problem. A crucial ingredient used in this paper is to introduce gg-function mechanism for solving the problem of the entries of the jump matrix growing exponentially as t→∞t\rightarrow\infty. It is shown that the leading order term of the asymptotic solution of the DNLS equation expressed by the Theta function Θ\Theta about the Riemann-surface of genus 3 and the subleading order term expressed by parabolic cylinder and Airy functions

    Experimental Research on the Ground Surface Quality of Creep Feed Ultrasonic Grinding Ceramics (Al2O3)

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    AbstractIn order to grind the ceramic blade surface with the Numerical Control contour evolution ultrasonic grinding method using the simple shape grinding wheel, primary comparative experiments of creep feed grinding with and without ultrasonic vibration were carried out to grind Al2O3 ceramics so as to implore the effects of different process parameters on the machined surface quality. It can be concluded that when the direction of ultrasonic vibration is parallel to the direction of creep feed, the value of the surface roughness will be decreased; otherwise the surface quality will become worse. With the ultrasonic grinding method, the slower feed-rate, the smaller grinding depth, the higher grinding speed and the compound feed grinding method should be applied in order to improve the surface quality. The creep feed grinding mechanisms with and without ultrasonic vibration were analyzed theoretically from the experimental results. With the selected grinding parameters resulted from the experiments, the feasibility experiment of ultrasonic grinding ceramic blade surface was carried out
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