Asymptotic behaviors of solutions for dissipative quantum Zakharov equations

The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.     

Dynamics of spiral waves driven by a dichotomous periodic signal

We study the effects of a dichotomous periodic force on meandering and rigidly rotating spiral waves. For a meandering state, the periodic forcing induces more modulating frequencies according to the rules of frequency-locked relations and linear combinations. It can also generate some unique closed tip orbits. On the modulating period T-axis, there exist all kinds of resonant entrainment bands. Arnold tongues exist in the period-amplitude space. The width of entrainment bands is affected by the symmetry of positive and negative parts in each signal unit. In addition, appropriate choices of T-value can be used to eliminate spiral waves. For a rigidly rotating state, the periodic forcing can induce a transition toward meandering spiral waves via generating a transitive bidirectional spiral wave. It is very interesting that, after the transition, the meandering spiral wave has the same primary rotating period as the free meandering states.     

Local discontinuous Galerkin method for solving an N‐carrier system

In this article, we present local discontinuous Galerkin (LDG) method for solving a model of energy exchanges in an N ‐carrier system with Neumann boundary conditions. This model extends the concept of the well‐known parabolic two‐step model for microheat transfer to the energy exchanges in a generalized N ‐carrier system with heat sources. The energy norm stability and error estimate of the LDG method is proved for solving N ‐carrier system. Some numerical examples are given. The numerical results when compared with the exact solution and other numerical results indicate that the present method is seen to be a very good alternative to some existing techniques for realistic problems. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

The quasi-reversibility method to solve the Cauchy problems for parabolic equations

In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.     

多群辐射扩散方程组的分裂迭代算法收敛分析

分析了多群辐射扩散方程组的分裂迭代算法的收敛速度,证明其收敛特性,给出迭代矩阵谱半径的解析公式.对谱半径进行数值计算与分析,揭示算法的收敛速度与辐射系数之间的依赖关系,数值算例验证了理论结果,给出了该算法的适用条件.     

基于JASMIN的地下水流大规模并行数值模拟

针对具有精细网格剖分、长时间跨度特征的地下水流模拟中计算时间长、存储开销大等瓶颈问题,基于MODFLOW三维非稳定流计算方法,提出基于网格片的核心算法以及基于影像区的通信机制,并在JASMIN框架上研制了大规模地下水流并行数值模拟程序JOGFLOW.通过河南郑州市中牟县雁鸣湖水源地地下水流的模拟,对程序正确性和性能进行了验证;通过建立一个具有精细网格剖分的假想地下水概念模型对可扩展性进行测试.相对于32核的并行程序,在512以及1 024个处理机上的并行效率分别可达77.2%和67.5%.数值模拟结果表明,JOGFLOW具有较好的计算性能与可扩展性,能够有效使用数百上千计算核心,支持千万量级以上网格剖分的地下水流模型的大规模并行计算.     

Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ?¹-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ?¹-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint.     

Langmuir扰动方程和Zakharov方程:光滑性与近似

考虑了一类带参数H,用于描述Langmuir扰动的方程.研究了当参数H趋于0时,这一类扰动方程的渐近行为.通过建立一个弱收敛结果和一个强收敛结果,得到了这类扰动方程初值问题的解(EH,nH)收敛到Zakharov方程初值问题的解(E,n)的结论.     

Determining the resistance of X-pinch plasma

The current and the voltage of an X-pinch were measured. The inductance of the X-pinch was assumed to be a constant and estimated by the calculation of the magnetic field based on the well-known Biot-Savart's Law. The voltage of the inductance was calculated with L · di/dt and subtracted from the measured voltage of the X-pinch. Then, the resistance of the X-pinch was determined and the following results were obtained. At the start of the current flow the resistance of the exploding wires is several tens of Ohms, one order of magnitude, higher than the metallic resistance of the wires at room temperature, and then it falls quickly to about 1 , which reflects the physical processes occurring in the electrically exploding wires, i.e., a current transition from the highly resistive wire core to the highly conductive plasma. It was shown that the inductive contribution to the voltage of the X-pinch is less than the resistive contribution. For the wires we used, the wires' material and diameter have no strong influence on the resistance of the X-pinch, which may be explained by the fact that the current flows through the plasma rather than through the metallic wire itself. As a result, the current is almost equally divided between two parallel X-pinches even though the diameter and material of the wires used for these two X-pinches are significantly different.