An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell

Over the last decade there has been renewed interest in applying exponential time differencing (ETD) time stepping schemes to the solution of stiff systems. In this paper, we present an implementation of such a scheme to the fully spectral solution of the incompressible magnetohydrodynamic equations in a spherical shell. One problem associated with ETD schemes is the accurate calculation of the necessary matrices; we implement and discuss in detail a variety of different methods including direct computation, contour integration, spectral expansions and recurrence relations. We compare the accuracy of six different second-order methods in determining the evolution of a three-dimensional magnetic field under the action of a prescribed time-dependent flow of electrically conducting fluid, and find that for the timestep restriction imposed by the nonlinear terms, ETD methods are no more accurate than linearly implicit methods which have the significant advantage of being easier to implement. However, ETD methods are more readily extendable than those which are linearly implicit and will become much more advantageous at higher order.     

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根据HCSB-DEMO堆的设计要求,对不同尺寸的聚变堆能产生的聚变功率、中子壁负载和等离子体燃烧时间等进行计算与分析,给出了符合设计要求的堆芯参数。在所选定的堆芯参数条件下进行了零维功率平衡计算分析,给出了3组HCSB-DEMO堆的等离子体初步设计参数。     

几周期余弦-高斯激光脉冲的时间重心

研究了几周期超短余弦-高斯脉冲的时间重心与绝对相位以及与余弦函数参量之间的关系．给出了几周期超短余弦-高斯脉冲时间重心的解析表达式和模拟图形．结果表明，余弦-高斯脉冲的时间重心随着绝对相位的变化而发生漂移，并且脉冲宽度对余弦-高斯脉冲时间重心的漂移量也有一定的影响．余弦函数的参量在一定取值范围内对余弦-高斯脉冲也有较大的影响，它可能导致几周期余弦-高斯脉冲的时间重心有较大的漂移．     

Tunable light emission and decaying process of photoluminescence from a nanostructured Si-in-SiNx film

Strong photoluminescence (PL) covering the green-violet band was measured at room temperature in an as-deposited amorphous Si-in-SiN_x film, which was prepared by plasma-enhanced chemical vapor deposition on cold (below 60 °C) Si(1 0 0) wafer. With an increase in photon energy of excitation, the PL shifts its peak position from 510 to 416 nm at yet-comparable intensities, thus allowing an energy-selected excitation in practical application. Also, a time-resolved analysis was performed for the emissions at various wavelengths, which showed a decay time shorter than 1.0 ns. These results indicate that the nanostructured Si-in-SiN_x can be a promising candidate material for the fabrication of silicon-based optical interconnections and switches.     

Some path properties of generalized Lévy sheet

Let X(t) be an N parameter generalized Lévy sheet taking values in ℝ^d with a lower index α, ℜ = {(s, t] = ∏ _i=1 ^N (s _i, t _i], s _i < t _i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established.     

Dielectric relaxation studies of binary mixtures of N-methylacetamide and N-methylformamide in benzene solutions using microwave absorption data

Using standard microwave X-band technique and by following Gopala Krishna's single frequency (9.90?GHz) concentration variational method, the dielectric relaxation times (τ) and the dipole moments (μ) of dilute solution of N-methylacetamide (NMA), N-methylformamide (NMF) and NMA?+?NMF binary mixtures in benzene solutions have been calculated at different temperatures. The energy parameters for the dielectric relaxation process for NMA?+?NMF binary mixture containing 30?mol% NMF have been calculated at 25, 30, 35 and 40°C and compared with the corresponding viscosity parameters. A good agreement between the free energy of activation from these two sets of values shows that the dielectric relaxation process like the viscous flow process can be treated as the rate process. From relaxation time behavior of NMA and NMF binary mixture in benzene solution, solute–solute types of the molecular association has been proposed.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Stability of low levels of perchlorate in drinking water and natural water samples

Perchlorate ion (ClO₄⁻) is an environmental contaminant of growing concern due to its potential human health effects, impact on aquatic and land animals, and widespread occurrence throughout the United States. The determination of perchlorate cannot normally be carried out in the field. As such, water samples for perchlorate analysis are often shipped to a central laboratory, where they may be stored for a significant period before analysis. The stability of perchlorate ion in various types of commonly encountered water samples has not been generally examined—the effect of such storage is thus not known. In the present study, the long-term stability of perchlorate ion in deionized water, tap water, ground water, and surface water was examined. Sample sets containing approximately 1000, 100, 1.0, and 0.5 μg l⁻¹ perchlorate ion in deionized water and also in local tap water were formulated. These samples were analyzed by ion chromatography for perchlorate ion concentration against freshly prepared standards every 24 h for the first 7 days, biweekly for the next 4 weeks, and periodically after that for a total of 400 or 610 days for the two lowest concentrations and a total of 428 or 638 days for the high concentrations. Ground and surface water samples containing perchlorate were collected, held and analyzed for perchlorate concentration periodically over at least 360 days. All samples except for the surface water samples were found to be stable for the duration of the study, allowing for holding times of at least 300 days for ground water samples and at least 90 days for surface water samples.     

Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.     

Hydrocarbon specificity in the selective catalytic reduction of NOx over Cu-ZSM-5 and Co-ZSM-5 catalysts

Transformation of surface nitrates under CH₄ (CH₄+O₂) was found to ensure steady-state activity of Co-ZSM-5 in the selective catalytic reduction of nitrogen oxides by methane (CH₄-SCR). For Cu-ZSM-5, such species are mainly converted into NO. Relaxation of the coordination sphere due to oxygen and NO adsorption, stability of C,N-containing intermediates and activation routes of hydrocarbons (methane, propane) were analyzed as factors determining catalytic properties of Cu and Co cations.