Cu/PMMA复合材料的声速与冲击响应行为

基于熔融共混法,制备了一系列不同配比且随机分散的Cu/PMMA复合材料,重点研究了Cu颗粒含量对PMMA基体声速与冲击压缩行为的影响。超声测试结果表明,随着Cu颗粒含量的增加,声波的衰减使材料的横、纵波声速皆呈缓慢下降趋势,由此使体积声速亦呈减小趋势。基于平板撞击实验,获得了冲击压力在1.1~6.0 GPa范围内各复合材料的冲击波速度-粒子速度方程。Cu/PMMA复合材料声阻抗的升高使Hugoniot参数λ逐渐增大,而零压体积声速减小,与常压体积声速所表现出的变化趋势一致。结合已有的压力-粒子速度关系模型,对各材料的压力-粒子速度曲线进行了讨论。在此基础上,归纳出一种基于上述模型的用于预测金属粒子填充聚合物基复合材料压力-密度关系的可靠方法。     

Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unrsagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coeiffcient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effecta of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.     

Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unmagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coefficient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effects of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.     

Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

嵌入随机多项式的抛物方程不确定声场快速算法

为了得到准确且高效计算起伏海洋介质中随机声场的算法,本文将随机多项式展开嵌入到宽角抛物方程声场计算模型(简称RAM模型)中,发展了一种不确定声场的快速算法。其计算结果比使用嵌入随机多项式的窄角抛物方程准确,计算时间小于作为参考的蒙特卡洛方法。在仿真算例中,随机多项式展开法对声强均值、方差、概率密度的计算准确;在一定的随机变量维度和随机多项式展开截断幂次内,其计算效率比蒙特卡洛方法至少提高一个数量级。     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx (um) which is a generalized model of Boussinesq equation uts = (u2)xx u and modified Bousinesq equation utt = (u3)xx uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.``     

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m,n) equations) u_tt=(uⁿ)_xx+(u^m)_xxxx, which is a generalized model of Boussinesq equation u_tt=(u²)_xx+u_xxxx and modified Bousinesq equation u_tt=(u³)_xx+u_xxxx, are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1,n) equations and B(m,m) equations, respectively.     

Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation

In this paper,the (2+1)-dimensional generalization of shallow water wave equation,which may be used to describe the propagation of ocean waves,is analytically investigated.With the aid of symbolic computation,we prove that the (2+1)-dimensional generalization of shallow water wave equation possesses the Painlev property under a certain condition,and its Lax pair is constructed by applying the singular manifold method.Based on the obtained Lax representation,the Darboux transformation (DT) is constructed.The first iterated solution,second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT.Relevant properties are graphically illustrated,which might be helpful to understanding the propagation processes for ocean waves in shallow water.     

Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation

In this paper, the (2+1)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the (2+1)-dimensional generalization of shallow water wave equation possesses the Painlevé property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation (DT) is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water.     

New Symmetry Reductions,Dromions—Like and Compacton Solutions for a 2D BS（m,n） Equations Hierarchy with Fully Nonlinear Dispersion

We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation.