Propagation and collision of soliton rings in quantum semiconductor plasmas

The intrinsic localization of electrostatic wave energies in quantum semiconductor plasmas can be described by solitary pulses. The collision properties of these pulses are investigated. In the present study, the fundamental model includes the quantum term, degenerate pressure of the plasma species, and the electron/hole exchange–correlation effects. In cylindrical geometry, using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations and the analytical phase shifts after the collision of two soliton rings are derived. Typical values for GaSb and GaN semiconductors are used to estimate the basic features of soliton rings. It is found that the pulses of GaSb semiconductor carry more energies than the pulses of GaN semiconductor. In addition, the degenerate pressure terms of electrons and holes have strong impact on the phase shift. The present theory may be useful to analyze the collision of localized coherent electrostatic waves in quantum semiconductor plasmas.     

Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.     

Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.     

New exact solutions of Einstein—Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

227-W output all-fiberized Tm-doped fiber laser at 1908 nm

In this paper, we report that a diode-pumped thulium-doped double clad silica fiber laser can provide powers of up to 227 W at 1908 nm, corresponding to a slope efficiency of 54.3%, and an optical-to-optical efficiency of 51.2%. The output power, to the best of our knowledge, is the highest output at 1908 nm. The beam quality M2 factor is about 1.56. Also discussed in this paper is the dependence of the laser performance on fiber length.     

基于线性方程组数学分离模型建立光纤传感过程检测复方缬沙坦氢氯噻嗪片溶出度

基于线性方程组数学分离模型建立在线过程检测复方缬沙坦氢氯噻嗪片溶出度方法。分别扫描缬沙坦和氢氯噻嗪的紫外吸收光谱,两组分在最大吸收波长处完全重叠。根据朗伯比尔定律吸光度加和性原理,分别测定两组分在最大吸收波长处的吸光系数,建立线性方程组数学分离模型,采用光纤传感过程分析技术(FODT)检测缬沙坦氢氯噻嗪片的溶出度,并与HPLC法相比较。在规定的溶出介质中,两种成分同时实时测定,并且FODT累积溶出度与HPLC法相比较结果无显著性差异(p>0.05)。不同批次药物的溶出行为一致,说明制剂工艺稳定,均匀度好。溶出曲线显示缬沙坦溶出快于并高于氢氯噻嗪,且30 min时两组分的溶出度均大于80%符合美国药典规定。结果表明,应用线性方程组数学分离模型结合FODT法可实现复方缬沙坦氢氯噻嗪片中双组分溶出度的同时检测,并可提供双组分的溶出过程曲线和全部溶出数据,直观反映各组分在各溶出时段的快慢,为此药建立标准提供依据。与HPLC法单点数据相比优势明显,更有利于药品评价和抽验质量分析。     

The master equation for a two-level atom in a laser field with squeezing-like terms

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a strong classical field and damped into a “modelled” reservoir with non-flat density of modes. The effects of different parameters on the atomic inversion, the von Neumann entropy and the entropy squeezing are discussed.