High Concentration Arsenic Diffusion in Crystalline Silicon: An Asymptotic Analysis

For fairly high concentrations, the effective arsenic diffusioncoefficient is known to grow linearly with the concentration.In this paper, we consider the strongly enhanced diffusion ofarsenic by asymptotic methods, and extend the results of a previouspaper (King & Please, 1987) in three ways: we characterizean additional (low-concentration) region; we consider the influenceof the initial data; and we consider the case of constant surfaceconcentration.     

Diffusion of Dopant in Crystalline Silicon: An Asymptotic Analysis

An existing model of the diffusion of dopant in crystallinesilicon is presented. The model is used in predicting semiconductordevice properties. For small concentrations of dopant, the diffusionis linear. However, at large concentrations, enhanced diffusionoccurs. This may be modelled by a concentration-dependent diffusioncoefficient that is approximately constant at small concentrationsbut increases linearly at higher concentrations. The initialdistribution of implanted dopant is confined to a small regionof the crystal, and has a high peak concentration. This initialdistribution develops into a high-concentration region withadvancing steep fronts and decaying tail regions. In the enhancedregion, the dominant balance is given by the filtration equation,and the tail regions are dominated by quasi-steady convection—diffusion.These two regions are analysed and matched together, using singularperturbation theory.     

流动环境中高浓度射流扩散实验研究

通过流动显示和定量测量对浅水流动环境条件下,高浓度流体垂体向抛射入水后形成的射流运动扩散及浓度分布特征进行了水槽实验研究。实验分析了射流入水后与环境水流条件的相互作用,通过数据分析给出了射流中心线着底点与横向扩散角的拟合公式。实验结果表明高浓度射流在近区呈现出不同于一般淹没射流的复杂流动形态及扩散特征,以异重流的形式向下游推移。     

Dopant distribution in isothermal frontal polymerization

We develop and study a mathematical model which describes how an inert species contained in the initial monomer/initiator mixture is redistributed by a propagating polymerization front. This study is relevant to the production of polymers for optical applications.     

瞬时点源分数阶超常扩散的浓度分布

利用质量守恒条件、解的时空相似性、Mellin变换以及Fox函数理论,给出n维空间中(n=1,2,3)瞬时点源分数阶超常扩散浓度分布的Fox函数表示及解析表达式,并讨论其渐近性质.     

High Accuracy Spectral Method for the Space-Fractional Diffusion Equations

In this paper, a high order accurate spectral method is presented for the space-fractional diffusion equations. Based on Fourier spectral method in space and Chebyshev collocation method in time, three high order accuracy schemes are proposed. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency compared with low-order counterparts, and a completely straightforward extension to high spatial dimensions. Some numerical examples, including Allen-Cahn equation, are conducted to verify the effectiveness of this method.     

Dopant diffusion in phases with a moving interface

We consider the diffusion of a dopant through a moving interface in the suicide film-Si system during silicide layer growth. The dopant concentration distribution is derived in analytical form by the integral Fourier transform method with subsequent reduction of the dopant redistribution problem to numerical solution of two integral equations. The results are presented in the form of curves plotting the time dependence of dopant concentration on both sides of the interface for various values of diffusion coefficients and interface velocity. The effect of physical parameters on the variation of dopant concentration near the interface is demonstrated.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 93–97, 1987.     

SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intravoxel crossing fibers, and such orientation information allows one to infer the connectivity patterns prevalent among different brain regions and possible changes in such connectivity over time for various neurodegenerative and neuropsychiatric diseases. The aim of this article is to propose a penalized multiscale adaptive regression model (PMARM) framework to spatially and adaptively infer the orientation distribution function (ODF) of water diffusion in regions with complex fiber configurations. In PMARM, we reformulate the HARDI imaging reconstruction as a weighted regularized least-square regression (WRLSR) problem. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and gray matter) of HARDI. The L₁ penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L₁ weighted estimator is calculated to correct the bias introduced by the L₁ penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models, the propagation-separation method, and Lasso (least absolute shrinkage and selection operator) to adaptively estimate ODFs across voxels. Experimental results indicate that PMARM can reduce the angle detection errors on fiber crossing area and provide more accurate reconstruction than standard voxel-wise methods. Supplementary materials for this article are available online.     

硅体中磷反应扩散系统解的整体存在性及渐近性

本文用上下解方法，研究了一类带混合非齐次边界条件的化学反应──硅体中磷反应扩散系统，采用避开△的特征函数构造上下解的方法，得到一类充分条件，以使其整体解渐近趋向于Ｓｔｅａｄｙ－ｓｔａｔｅ解．     

Extremely noncommutative elements in rings

We study rings and K-algebras in which all elements or all noncentral elements have smallest possible centralizer. Our principal result asserts that a ring R must be either finite or commutative if each noncentral element a has centralizer equal to the subring generated by a. Supported by the Natural Sciences and Engineering Research Council of Canada, Grant 3961. Authors’ addresses: Howard E. Bell, Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1; Abraham A. Klein, Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel     

Extremely noncommutative elements in rings

We study rings and K-algebras in which all elements or all noncentral elements have smallest possible centralizer. Our principal result asserts that a ring R must be either finite or commutative if each noncentral element a has centralizer equal to the subring generated by a.     

分数阶扩散方程的一个新的高阶数值格式

在时间和空间上基于有限差分法和利用待定系数法,构造了一维空间分数阶扩散方程的一个新的高阶数值格式.在理论上严格证明了此算法的稳定性和一系列的数值算例验证了理论分析的正确性,表明算法是逼近数值解的一个行之有效的方法.     

High School Biology Students' Knowledge and Certainty about Diffusion and Osmosis Concepts

The purpose of this study was to investigate students' understanding about scientifically acceptable content knowledge by exploring the relationship between knowledge of diffusion and osmosis and the student's certainty in their content knowledge. Data was collected from a high school biology class with the Diffusion and Osmosis Diagnostic Test (DODT) and Certainty of Response (CRI) scale. All data was collected after completion of a unit of study on diffusion and osmosis. The results of the DODT were dichotomized into correct and incorrect answers, and CRI values were dichotomized into certain and uncertain. Values were used to construct a series of 2 × 2 contingency tables for each item on the DODT and corresponding CRI. High certainty in incorrect answers on the DODT indicated tenacious misconceptions about diffusion and osmosis concepts. Low certainty in incorrect or correct answers on the DODT indicated possible guessing; and, therefore no understanding, or confusion about their understanding. Chi‐square analyses revealed that significantly more students had misconceptions than desired knowledge on content covering the Influence of Life Forces on Diffusion and Osmosis, Membranes, the Particulate and Random Nature of Matter, and the Processes of Diffusion and Osmosis. Most students were either guessing or had misconceptions about every item related to the concepts osmosis and tonicity. Osmosis and diffusion are important to understanding fundamental biology concepts, but the concept of tonicity not be introduced to high school biology students until effective instructional approaches can be identified by researchers.     

带间断扩散系数热传导方程的高精度数值模拟方法研究

针对热传导方程在间断扩散系数处的数值求解困难,作者已经提出了"孪生逼近"自适应方法.本文以一维问题为例,推广热传导方程解的内蕴连续性到高阶,进而研究构造了更高精度,更经济的"孪生逼近"算法,并用数值结果进行了检验.     

对流扩散问题Crank-Nicolson差分-流线扩散法的高精度分析

讨论了对流扩散问题C rank-N ico lson差分流线扩散格式,利用插值后处理技术提高了特殊网格下该格式在双线性元空间解的精度,从而按Lα(L2(Ω))模达到最优.     

求解一维非定常对流扩散反应方程的高精度紧致差分格式

提出了数值求解一维非定常对流扩散反应方程的一种高精度紧致隐式差分格式,其截断误差为O(τ~4+τ~2h~2+h~4),即格式整体具有四阶精度.差分方程在每一时间层上只用到了三个网格节点,所形成的代数方程组为三对角型,可采用追赶法进行求解,最后通过数值算例验证了格式的精确性和可靠性.     

Diffusion in turbulence

Summary We prove long time diffusive behavior (homogenization) for convection-diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices.     

Extremal Forex Returns in Extremely Large Data Sets

Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon.