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Concave Minimization for Sparse Solutions of Absolute Value Equations

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Transactions of Tianjin University 2016年第1期22卷 89-94页

作者：刘晓红樊婕李文娟 School of Sciences Tianjin University center for applied mathematics Tianjin University

Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.

关键词： absolute value equations concave minimization sparsity linear programming range space property

Controlling Chaos Using Modified Lyapunov Exponents

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Chinese Physics Letters 1993年第6期10卷 321-324页

作者： TAN Yi HE Xiantu CHEN Shigang center for Nonlinear Studies Institute of Applied Physics and Computational MathematicsBeijing 100088

We suggested a method using a small perturbation to modify Lyapunov exponents of the unstable periodic orbit for controlling *** benefit of this control scheme is studied and the effect of noise is *** on these studie... 详细信息

关键词： chaos. Lyapunov Chaos

Effects of Electron-Ion Collisions on Stimulated Raman Backward Scattering Under Different Electron Densities

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Plasma Science and Technology 2011年第1期13卷 40-43页

作者：项江刘占军郑春阳 Institute of applied Physics and Computational mathematics center for applied Physics and Technology State Key Laboratory of Nuclear Physics and TechnologyPeking University

Effect of electron-ion collision on stimulated Raman backward scattering （SRBS） spectrum are investigated by numerical simulations. In the given parameters and plasma condition, the growth rates of SRBS are found to strongly depend on the electron density, and the gap in the SRBS spectrum corresponding to the high electron density could be explained by the collisional damping. In the low density region, a much higher Landau damping estimated by the linear theory makes the collisional damping negligible. However, the present results show that, collisions play a even more important role than known in the linear theory.

关键词： Vlasov simulation SRS electron-ion collisions laser plasma.

Design of an Indirect-Drive Pulse Shape for ~1.6 MJ Inertial Confinement Fusion Ignition Capsules

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Chinese Physics Letters 2014年第4期31卷 89-92页

作者： WANG Li-Feng WU Jun-Feng YE Wen-Hua FAN Zheng-Feng HE Xian-Tu Institute of applied Physics and Computational mathematics Beijing 100094 HEDPS Center for Applied Physics and Technology Peking Universir~y Beijing 100871

We present a design of indirect-drive pulse shape for inertial confinement fusion ignition capsules using laser energy 1.6 MJ with a moderate gain （~10） on the Shenguang 1V laser facility. The trade-off fuel compression （pressure） for resistance to the hydrodynamic instability （HI） in the recent high-foot （HF） implosion campaign [Dittrieh T t et al Phys. Rev. Lett. 112 （2014）055002] is recovered. The proposed design modifies the ＂main＂ pulse shape, which features a decompression-recompression step for the fuel shell resulting in higher areal density than that of the ＂simple＂ HF design, and thereby approaches the conditions required for ignition avoiding at the expense of more laser energy while holding the HI under control.

关键词： Capsules Design Shenguang

Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent Regime-Switching on Initial Values

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Acta Mathematica Sinica,English Series 2021年第3期37卷 389-407页

作者： Jing Hai SHAO Kun ZHAO center for applied mathematics Tianjin UniversityTianjin 300072P.R.China

This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.

关键词： Regime-switching state-dependent Euler–Maruyama’s approximation

Weak centers and Local Bifurcations of Critical Periods at Infinity for a Class of Rational Systems

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 377-390页

作者： Wen-tao HUANG Valery G.ROMANOVSKI WEI-NIAN ZHANG School of mathematics and Computing Science Guilin University of Electronic Technology center for applied mathematics and Theoretical Physics University of Maribor School of mathematics Sichuan University

We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class... 详细信息

关键词： weak center isochronicity bifurcation of critical periods

Phase Effects of Long-Wavelength Rayleigh–Taylor Instability on the Thin Shell

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Chinese Physics Letters 2020年第2期37卷 35-38页

作者： Zhi-Yuan Li Li-Feng Wang Jun-Feng Wu Wen-Hua Ye Institute of applied Physics and Computational mathematics Beijing 100094 center for applied Physics and Technology HEDPSand College of EngineeringPeking UniversityBeijing 100871

Taking the long-wavelength Rayleigh-Taylor instability(RTI) on the thin shell of inertial confinement fusion as the research object,a linear analytical model is presented to study the phase effects that are caused by the phase difference of single-mode perturbations on the two *** accuracy is tested by numerical *** analyzing the characteristic of this model,it is found that the phase difference does not change the basic RTI structure(only one spike and one bubble in a period).However,the symmetry of the spike and bubble is destroyed,which has non-expected influences on the convergent motion of ICF ***,the phenomenon that the distance between spikes and bubbles along the vertical direction of acceleration differs by π is *** is also shown that when the phase difference is large,the temporal evolution of the RTI is more serious and the thin target is easier to tend to break.

关键词： Effects bubble Rayleigh

Linear Growth of Rayleigh-Taylor Instability of Two Finite-Thickness Fluid Layers

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Chinese Physics Letters 2017年第7期34卷 146-149页

作者：郭宏宇王立锋叶文华吴俊峰张维岩 Graduate School China Academy of Engineering Physics Institute of applied Physics and Computational mathematics HEDPS Center for Applied Physics and Technology Peking University

The linear growth of Ftayleigh-Taylor instability （FtTI） of two superimposed finite-thickness fluids in a gravita- tional field is investigated analytically. Coupling evolution equations for perturbation on the upper, middle and lower interfaces of the two stratified fluids are derived. The growth rate of the RTI and the evolution of the amplitudes of perturbation on the three interfaces are obtained by solving the coupling equations. It is found that the finite-thickness fluids reduce the growth rate of perturbation on the middle interface. However, the finite-thickness effect plays an important role in perturbation growth even for the thin layers which will cause more severe RTI growth. Finally, the dependence of the interface position under different initial conditions are discussed in some detail.

关键词： Linear Growth of Rayleigh-Taylor Instability of Two Finite-Thickness Fluid Layers

Simulation of nuclei morphologies for binary alloy

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Science China mathematics 2010年第11期53卷 2927-2936页

作者： LI DaMing1, & ZHANG PingWen2 1Department of mathematics, Shanghai Jiaotong University, Shanghai 200240, China 2Key Lab of mathematics and applied mathematics, center for applied Physics and Technology and School of Mathematical Sciences, Peking University, Beijing 100871, China Department of mathematics Shanghai Jiaotong University Shanghai China Key Lab of mathematics and applied mathematics Center for Applied Physics and Technology and School of Mathematical Sciences Peking University Beijing China

We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.

关键词： nucleation crystal morphology string method