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Lin’an, China

Dai C.-Q.,Zhejiang Agriculture And forestry University | Yu F.-B.,Zhejiang iversity
Wave Motion

With the help of a modified mapping method, we re-study the (3 + 1)-dimensional Burgers equation and derive three families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss interaction behaviors among flat-top rectangle-soliton and ring-soliton, embedded rectangle-soliton and embedded ring-soliton in a periodic wave background. All interaction behaviors among them are completely elastic, and no phase shift appears after the interaction. These results might be helpful to the understanding of the propagation processes for nonlinear water waves in fluid mechanics such as diverse nonequilibrium, nonlinear phenomena in turbulence and inter-face dynamics. © 2013 Elsevier B.V. Source

Zhang J.-F.,Zhejiang University of Media and Communications | Dai C.-Q.,Zhejiang iversity
Wuli Xuebao/Acta Physica Sinica

We study a (1+1)-dimensional variable-coefficient Gross-Pitaevskii equation with parabolic potential. A similarity transformation connecting the variable-coefficient Gross-Pitaevskii equation with the standard nonlinear Schrödinger equation is constructed. According to this transformation and solutions of the standard nonlinear Schrodinger equation, we obtain exact rogue wave solutions of variable-coefficient Gross-Pitaevskii equation with parabolic potential. In this solution, a Galilean transformation is used such that the center of optical pulse is Xc = v(T - T0) while the Galilean transformation was not used in previous analysis. By the Galilean transformation, the parameter T0 is added into the solution. It is found that the parameter T0 is important to control the excitations of rogue waves. Moreover, the parameters a1 and a2 in solution are complex parameters which can modulate the behaviors of rogue waves. If they are restricted to real numbers, we can obtain some well-known rogue wave solutions. If the parameter a2 = -1/12, we can have a second-order rogue wave solution. If the parameter a2 is a complex number, the solution can describe rogue wave triplets. Here two kinds of rogue wave triplets, namely, rogue wave triplets I and II are presented. For rogue wave triplet I, at first, two first-order rogue waves on each side are excited, and then a first-order rogue wave in the middle is excited with the increase of time. On the contrary, for rogue wave triplet II, a first-order rogue wave in the middle is initially excited, and then two first-order rogue waves on each side are excited with the increase of time. From these solutions, the controls for the excitations of rogue waves, such as the restraint, maintenance and postponement, are investigated in a system with an exponential-profile interaction. In this system, by modulating the relation between the maximum of accumulated time Tmax and the peak time T0 (or TI; TII), we realize the controls of rogue waves. When Tmax > T0 (or TI; TII), rogue wave is excited quickly, and the atom number of condensates increases; when Tmax = T0 (or TI; TII), rogue wave is excited to the maximum amplitude, then maintains this magnitude for a long time, and the atom number of condensates also increases; when Tmax < T0 (or TI; TII), the threshold of exciting rogue wave is never reached, thus the complete excitation is restrained, and the atom number of condensates reduces. These results can be used to understand rogue waves better, that is, besides their "appearing from nowhere and disappearing without a trace", rogue waves can be controlled as discussed by a similar way in this paper. These manipulations for rogue waves give edification on theory and practical application. © 2016 Chinese Physical Society. Source

Zhang J.,Shanghai University | Zhang J.,Zhejiang iversity | Gu C.,Shanghai University
BIT Numerical Mathematics

For nonsymmetric saddle point problems, Pan et al. (Appl Math Comput 172:762–771, 2006) proposed a deteriorated positive-definite and skew-Hermitian splitting (DPSS) preconditioner. In this paper, a variant of the DPSS preconditioner is proposed to accelerate the convergence of the associated Krylov subspace methods. The new preconditioner is much closer to the coefficient matrix than the DPSS preconditioner. The spectral properties of the new preconditioned matrix are analyzed. Theorem which provides the dimension of the Krylov space for the preconditioned matrix is obtained. Numerical experiments of a model Navier–Stokes problem are presented to illustrate the effectiveness of the new preconditioner. © 2015 Springer Science+Business Media Dordrecht Source

Duan X.,Yancheng Institute of Technology | He J.,Zhejiang iversity
Journal of Information and Computational Science

Convex optimization algorithm is strongly proposed to be applied in the source localization as the convergence to the global minimum is guaranteed. By relaxing the nonlinear and nonconvex optimization localization model, Second-order Cone Programming (SOCP), Semi-definite Programming (SDP) and mixed SOC/SDP algorithms are proposed for TOA-based source localization. The simulations show that the SDP and the mixed SOC/SDP provide a better localization accuracy than the SOCP due to the tighter relaxation. The proposed SOC/SDP algorithm has less variables and equality constraints and runs faster than the SDP. As a result, the mixed SOC/SDP provides a tradeoff between the computational complexity and localization accuracy. © 2015 by Binary Information Press Source

Liang L.,Zhejiang iversity | Zhou M.,Zhejiang iversity
Shengwu Gongcheng Xuebao/Chinese Journal of Biotechnology

Long terminal repeat (LTR) retrotransposons are mobile DNA sequences that ubiquitously exist in eukaryotic genomes. They replicate themselves in the genome by copy-paste mechanism with RNA as medium. In higher plants, many active LTR retrotransposons have been applied to analyze molecular marker technology, genetic tagging, insertion mutation and gene function. Here, we systematically review the characteristics of plant active LTR retrotransposons, including their structures, copy numbers and distributions. We further analyzed the gag (group-specific antigen) and pol (polymerase) sequence features of different plants active LTR retrotransposons and the distribution patterns of the cis-acting elements in LTR regions. The results show that autonomous active LTR retrotransposons must contain LTR regions and code Gag, Pr, Int, Rt, Rh proteins. Both LTR regions are highly homologous with each other and contain many cis-regulatory elements; RVT and RNase_H1_RT domain are essential for Rt and Rh protein respectively. These results provide the basis for subsequent identification of plant active LTR retrotransposons and their functional analysis. © 2016 Chin J Biotech, All right reserved. Source

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