Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Existence and nonexistence of curved front solution of a biological equation

This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential.     

Tokamak中自举电流的剖面准直性

利用Harris模型,通过求解等离子体平衡方程,计算俘获粒子份额,分别对常规剪切和中心负剪切下tokamak中的自举电流的大小和剖面准直性进行了计算和分析.自举电流分布与等离子体平衡电流分布之间的剖面准直性可以通过调整等离子体的密度、温度和电流分布参数,以及描述等离子体形状的拉长度k和三角变形因子d来获得.中心负剪切位形有利于自举电流产生,并有好的剖面准直性.通过计算比较,分别在常规剪切位形下和中心负剪切位形下获得了一组优化的等离子体参数,在这组参数下,自举电流有较大的份额和好的剖面准直性 关键词： tokamak 自举电流 剖面准直性     

Acoustic characterization and prediction for fan-duct-plenum-room integrations

This paper investigates mutual influence of duct and room acoustics in the whole fan-duct-plenum-room integrations. Applying the parametric design language of finite element software ANSYS (APDL), dimensional and positional influence on system acoustics has been studied. Models with different room dimensions, duct lengths, duct cross-sections, duct locations, duct discharges and duct elbow were constructed, and their characteristics were compared qualitatively. Results show that small rooms, short ducts, large duct cross-sections and bell mouth duct discharges help to increase room sound pressure levels (SPLs); SPLs in ducts and plenums are sensitive to duct dimensions and duct discharge types but insensitive to duct locations and room dimensions; duct elbows have relatively indistinct acoustic influence in each component. Based on the calculation results, a semi-experimental method was proposed for simply and approximately evaluating indoor acoustic spectra of fan-duct-plenum-room integrations, then an example was used to demonstrate the prediction process. Finally, by adopting several ideal models, sound field constitutions, duct and room wall admittances and duct end reflection were explored quantitatively. This study may give a detailed understanding of fan-duct-plenum-room acoustics for researchers, also it might provide a new, simple and approximate prediction method for professionals to evaluate and improve fan-ducted acoustics.     

Energy of formation for and liquid binary alloys

We have investigated the free energy of formation for Ag_xIn_1-x and Ag_xSn_1-x liquid binary alloys at temperatures 1173 and 1250 K, respectively. A microscopic theory based on the first order perturbation has been applied. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseudopotential. A liquid of hard spheres (HS) of two different effective diametres and charges is used to describe the reference system. The results of the calculations for energy of formation agree very well with the available experimental data. Our calculations also reveal that a simple perturbative approach along with appropriate effective pair potentials can produce nearly quantitative results for the concerned alloys.     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

Parametric multiple sequence alignment and phylogeny construction

Bounds are given on the size of the parameter-space decomposition induced by multiple sequence alignment problems where phylogenetic information may be given or inferred. It is shown that many of the usual formulations of these problems fall within the same integer parametric framework, implying that the number of distinct optima obtained as the parameters are varied across their ranges is polynomially bounded in the length and number of sequences.     

Electron–hole recombination luminescence in LiYF4:U single crystal

Photoluminescence (PL), photostimulated luminescence (PSL), thermally stimulated luminescence (TSL) and electron paramagnetic resonance (EPR) studies were carried out on LiYF₄:U⁴⁺ and pure LiYF₄ crystals. The PL and EPR investigations have identified the presence of Eu³⁺, Tb³⁺ and Gd³⁺ ions in both of these crystals possibly due to their existence in the starting materials. The luminescence observed during afterglow, PSL and TSL revealed that emission occurs at wavelength positions 382, 413, 437 and 544 nm, which are characteristic of Tb³⁺ ions. The present investigations using PSL and TSL in combination with PL studies before and after gamma irradiation have revealed that selective energy transfer to Tb³⁺ ions occurs during electron–hole recombination processes like PSL and TSL. Even though other luminescent ions (U⁴⁺ and Eu³⁺) are present in the system and U⁴⁺/U³⁺ ions are participating in electron capture/release processes, the selective energy transfer results in Tb³⁺ ions acting as luminescence centers.     

低阻抗二极管产生的强流电子束能谱分布的数值模拟

 给出了低阻抗二极管产生的电子束能谱分布及外加磁场对二极管阻抗影响的数值模拟研究结果。结果表明，即使在外加电压恒定的条件下，二极管产生的电子束也具有一定的能谱分布，这说明用二极管电压、电流波形计算脉冲电子束能谱分布是不正确的。另外,外加磁场对低阻抗二极管的阻抗特性具有较大影响，其阻抗随外加磁场的增大而减小。分析认为这是由于外加磁场强度的变化改变了二极管中束电子的运动轨迹。当没有外加磁场或外加磁场较小时，低阻抗二极管产生的电子束发生自箍缩，此时二极管电流是自箍缩饱和顺位流；当外加磁场足够强时，电子束的自箍缩被抑制，二极管电流是没有箍缩时的空间电荷限制电流。束电流小于自箍缩临界电流的二极管其阻抗将不随外加磁场的变化而变化。     

A surface-mounted device assembly technique for small optics based on laser reflow soldering

The three-dimensional miniaturized optical surface-mounted device (TRIMO-SMD) is a new flexible and automated assembly technique for small optical components (maximum diameter for a lens is 2 mm) based on laser reflow soldering technique. This technology can be compared to the electronic SMD technique but applied to micro-optical devices. We present some recent developments of TRIMO-SMD in its application to industrial products.