Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L2-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.

基于变分节块法六角形Quasi-diffusion程序开发及验证

传统扩散理论在中子各向异性强的堆芯计算中具有较低的精度,Quasi-diffusion方程相比于传统扩散方程引入更少的近似,通过艾丁顿因子描述传统扩散理论不能反映的中子流各向异性特点。国内外对六角形几何三维Quasi-diffusion方程研究有所不足。针对艾丁顿因子计算的非线性特点,本文基于“两步法”的思想,将艾丁顿因子看作是一个特殊的少群参数,采用中子能谱适应性更好的蒙特卡罗程序SERPENT计算,并对传统扩散变分节块法进行拓展,开发了六角形组件堆芯计算程序VNMQD。采用3D VVER1000基准题、RBWR单组件问题、3D BN600简化模型对程序进行了验证,结果表明:VNMQD程序开发正确,对于非均匀性较强的堆芯,VNMQD比传统扩散方法计算精度更高、计算效率接近,实现了计算精度和计算效率的平衡。

Quasi-Two-Dimensional Diffusion in Adherent Cells Revealed by Three-Dimensional Single Quantum Dot Tracking

Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes.Meanwhile,the diffusion dynamics is affected by the heterogeneous cytoplasm.Previous studies on intracellular diffusion are mainly based on two-dimensional(2 D)measurements under the assumption that the three-dimensional(3 D)diffusion is isotropic.However,the real behaviors of 3 D diffusion of molecules in cytoplasm are still unclear.Here,we have built a 3 D single-particle tracking(SPT)microscopy and studied the 3 D diffusion of quantum dots(QDs)in adherent A549 cells.Notably,we found that the intracellular diffusion of QDs is quasi-2 D,with the axial motion being severely confined.Further investigations demonstrated that disrupting the cytoskeleton component or endoplasmic reticulum(ER)does not alter the quasi-2 D diffusion pattern,although ER reduces the diffusion rates and slightly relieves the constraint in the axial diffusion.The preferred quasi-2 D diffusion is quite robust and attributed to the complex cytoarchitectures in the flat adherent cells.With the aid of 3 D SPT method,the quasi-2 D diffusion in cells was revealed,shedding new light on the physical nature of cytoplasm.

UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SUPERCRITI C AL EXPONENT

A new approach, is established to show that the semigroup {S（t）≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q（Ω） （2 ≤ q 〈 ∞） with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.

THE MHD PROPERTIES OF AMBIPOLAR DIFFUSION AND QUASI - AMBIPOLAR DIFFUSION IN A PLASMA COLUMN

In the present paper, based on the conservation law of mass and momentum for ion and electron, the distribution of velocity, density of ions and electrons along radial direction are solved numerically. Furthermore, the comparison between MHD properties of ambipolar and qua- si- ambipolar diffusion is made. The numerical calculation is carried out for argon plasma. The results show that the ion density, ratio of ion and electron velocity at the cathode sheath boundary surface in- crease with the intensity of magnetic induction, meanwhile, the distance between sheaths decreases as well as the radial velocity of ion and electron at the anode sheath boundary. The ion density varies in accord with experiment qualitatively. All parameters mentioned above are not sensitive to magnetic field in ambipolar diffusion.

Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

Uniqueness of solution of a quasi-linear Reaction-diffusion system

In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.

Diffusion Process of High Concentration Spikes in a Quasi-Homogeneous Turbulent Flow

When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.

A revised jump-diffusion and rotation-diffusion model

Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.

NUMERICAL ANALYSIS OF THE DIFFERENCES IN DIFFUSION BETWEEN p－SURFACE AND σ－SURFACE

Dimensional analysis and reduction are done to two existing schemes of 4th-order linear horizontal diffusion, and detailed control experiments between them are made using a topographyincluded mesoscale model. Horizontal diffusion is calculated on the or surface in one (known as Scheme A afterwards ), and on the p-surface in another (Scheme B ). Experiments show that differences are small in smooth-terrain areas and very large in steep mountain areas, with the 24h rainfall prediction deviating by 50 mm between forecasts of the two sChemes. The reason may be that temperature and humidity are falsely diffused in Scheme A, which causes abnormal temperature and humidity, and results in the anomalies of the unstable layer and convective processes. In addition, Scheme A could also bring about circulation anomalies which assumingly have direct link to the convective anomalies in the scheme. Furthermore, perturbation may also affect surrounding areas by wave-like propagation such that precipitation anomalies may occur in the area. The analysis indicate that Scheme B is necessary and feasible for it minimizes diffusion-involved forecast abnormality in steep mountains and areas around.

基于二元三次B样条拟插值的反应-扩散方程数值解

反应-扩散方程在科学和工程的许多分支中有着重要的应用,对此类方程数值解的研究具有重要意义.鉴于计算域的复杂形状、大量的自由度等导致计算非常困难,提出张量积型二元三次B样条法求解一类分数阶反应-扩散方程和交叉反应扩散系统,首先计算得出二元三次B样条拟插值的矩阵表达式,然后利用Matlab进行数值模拟,最后将数值模拟解与精确解进行对比.研究表明,当变量t的迭代次数较低时,所提方法行之有效.

多项时间分数阶扩散方程类Carey非协调元的误差分析

基于L^(1)全离散格式,针对具有Caputo导数的二维多项时间分数阶扩散方程给出了类Carey非协调有限元方法.利用该单元的特殊性质和分数阶导数巧妙的处理技巧导出了L^(2)模和H^(1)模意义下的最优误差估计.

基于改进鹈鹕优化算法的土壤污染预测

针对传统污染扩散模型结构复杂、无法验证等问题,提出一种基于多策略改进鹈鹕优化算法的土壤污染扩散模型。引入拟蒙特卡罗序列优化鹈鹕优化算法初始种群位置,提出一种非线性收敛的e指数余弦因子改进位置更新方式,结合t-分布变异扰动策略提升算法局部寻优能力。利用改进的鹈鹕优化算法优化高斯扩散模型,构建土壤污染扩散模型。选取某地为研究区域,所构建的土壤污染扩散模型的平均绝对误差与均方根误差最低,验证该模型可以有效应用于土壤污染预测。

Dynamic behaviors of water contained in calcium-silicate-hydrate gel at different temperatures studied by quasi-elastic neutron scattering spectroscopy

The dynamic behaviors of water contained in calcium-silicate-hydrate（C-S-H） gel with different water content values from 10%to 30%（by weight）,are studied by using an empirical diffusion model（EDM） to analyze the experimental data of quasi-elastic neutron scattering（QENS） spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum（HWHM） Γ;（Q） and Γ;（Q）,the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement（MSD）(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q（≤1 A;） but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;（the MSD of bound/immobile water） as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;（Q）,a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores（LGPs） and/or small gel pores（SGPs） contained in the C-S-H gel sample with 30% water content.

An O(k²+kh²+h²) Accurate Two-level Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.

套管中环向传播的准SH波的衰减特征

套管井中的准SH波测井可有效解决声阻抗类声波仪器在低密度水泥胶结评价上的不适应性.本文结合解析计算、三维数值仿真和实验测量研究了套管中环向传播的准SH波的衰减特征.数值仿真和实验测量结果均表明准SH波的衰减主要由波传播过程中的几何扩散和向套管后胶结的固体水泥泄漏能量引起的;解析计算显示在0~300 kHz的测井频段随着频率的增加零阶准SH波的泄漏衰减逐渐增大、一阶准SH波的泄漏衰减逐渐减小,在现有油气井使用的水泥阻抗范围内,准SH波的衰减与水泥阻抗成正比.数值仿真和实验测量的零阶准SH波的衰减与解析计算结果吻合,一阶准SH波的衰减稍高于解析计算结果.另外在实验测量过程中记录了水泥从浇筑到逐渐凝固过程中准SH波测井的全波波形,可清晰观测到直达的准SH波在水泥未凝固前(仍是流体)幅度较强,随着水泥逐渐凝固强度增大准SH波的泄漏衰减逐渐增加,泄漏到水泥环中的能量越来越强,来自水泥外界面的反射波幅度逐渐增加且到时逐渐提前.通过理论计算和实验测量套管井SH横波的衰减特征,为现场应用SH横波测井评价套管井水泥胶结质量奠定基础.

矩形网格下基于准扩散的堆芯pin-by-pin计算研究

随着堆芯中子学计算对精度要求的不断提高,基于栅元均匀化的pin-by-pin方法成为国内外研究热点。由于pin-by-pin计算巨大的空间网格量及栅元层面较强的非均匀性,目前常用的SP3/GSP3方法在平衡计算精度和计算效率方面还存在一定局限性,为此有必要寻找一种同时考虑计算精度与效率的堆芯计算方法。基于准扩散的堆芯pin-by-pin计算方法从中子输运理论出发,引入艾丁顿因子推导建立三维准扩散方程及边界条件,研究该方程泄漏项的特殊处理方法,同时基于节块展开法建立堆芯pin-by-pin数值计算方法并验证。数值结果表明,对于结构复杂、中子各向异性显著的堆芯,准扩散pin-by-pin计算精度要明显优于传统扩散计算,而两者计算效率相当。该方法是一种平衡了堆芯计算效率与精度的计算方法,为准扩散理论应用于堆芯pin-by-pin计算提供了基础。

Quasi-neutral limit of the drift-diffusion model for semiconductors with general sign-changing doping profile

The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.

Domain of attraction of quasi-stationary distribution for one-dimensional diffusions

We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and ＋∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.