Exponential Time Differencing Method for a Reaction-Diffusion System with Free Boundary

For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.

PERTURBATION FINITE VOLUME METHOD FOR CONVECTIVE-DIFFUSION INTEGRAL EQUATION

A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations,with the least nodes similar to the standard three-point schemes,that is,the number of the nodes needed is equal to unity plus the face-number of the control volume.For instance,in the two-dimensional(2-D)case,only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized,respectively.The PFV scheme is applied on a number of 1-D linear and nonlinear problems,2-D and 3-D flow model equations.Comparing with other standard three-point schemes,the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme(UDS).Its numerical accuracies are also higher than the second-order central scheme(CDS),the power-law scheme(PLS)and QUICK scheme.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

High-Integrated-Photosensitivity Negative-Electron-Affinity GaAs Photocathodes with Multilayer Be-Doping Structures

The effect of changing Be doping concentration in GaAs layer on the integrated photosensitivity for nega- tive-electron-affinity GaAs photocathodes is investigated. Two GaAs samples with the monolayer structure and the muhilayer structure are grown by molecular beam epitaxy. The former has a constant Be concentration of 1 × 10^19 cm^-3, while the latter includes four layers with Be doping concentrations of 1 × 10^19, 7 × 10^18, 4 × 10^18, and 1 × 10^18 cm^-3 from the bottom to the surface. Negative-electron-affinity GaAs photocathodes are fabricated by exciting the sample surfaces with alternating input of Cs and O in the high vacuum system. The spectral response results measured by the on-line spectral response measurement system show that the integrated photosensitivity of the photocathode with the muhilayer structure enhanced by at least 50% as compared to that of the monolayer structure. This attributes to the improvement in the crystal quality and the increase in the surface escape probability. Different stress situations are observed on GaAs samples with monolayer structure and muhilayer structure, respectively.

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

CHEMICAL VAPOR DEPOSITION OF DIFFUSION BARRIERS FOR ADVANCED METALLIZATION

Metalization is widely used in integrated circuit devices to connect millions of devices together. The success of metallization depends strongly on diffusion barrier technology, due to the interactions of metals with surrounding materials. As device dimension further shrinks, diffusion barrier technology is facing more challenges and opening up new opportunities, particularly for chemical vapor deposition (CVD) process technology. CVD is attracting increased attention in advanced metallization mainly due to its capability in producing conformal thin films. In this review, we will focus our discussion on CVD processes for three most important classes of diffusion barriers: Ti, W and Ta-based diffusion banters. Examples from current literature will be examined.

Time evolution of negative binomial optical field in a diffusion channel

We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.

Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model

This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.

Diffusion of Zinc in In_xGa_(1-x)As, InP and GaAs

Zinc has been diffused into n-type InxGa1-xAs, InP and GaAs in closed ampoules, and the experimental data for InxGa1-xAs rarely reported previously have been obtained. Theoretically the linear relationship between logarithmic diffusion coefficient InD and the composition x has been demonstrated, which is in good agreement with the experimental results. The calculated diffusion junction depth for InGaAs based on the diffusion model in which D∝ c2 is assumed also agrees well with that of the experiment. Finally the overall diffusion time in a multilayer heterostructure was approximated as t=(Σ )2.

Boosting rate performance of layered lithium-rich cathode materials by oxygen vacancy induced surface multicomponent integration

The rapid development of electric vehicles and portable energy storage systems demands improvements in the energy density and cost-effectiveness of lithium-ion batteries,a domain in which Lithium-rich layered cathode(LLO)materials inherently excel.However,these materials face practical challenges,such as low initial Coulombic efficiency,inferior cycle/rate performance,and voltage decline during cycling,which limit practical application.Our study introduces a surface multi-component integration strategy that incorporates oxygen vacancies into the pristine LLO material Li1.2Mn_(0.6)Ni_(0.2)O_(2).This process involves a brief citric acid treatment followed by calcination,aiming to explore rate-dependent degradation behavior.The induced surface oxygen vacancies can reduce surface oxygen partial pressure and diminish the generation of O_(2)and other highly reactive oxygen species on the surface,thereby facilitating the activation of Li ions trapped in tetrahedral sites while overcoming transport barriers.Additionally,the formation of a spinel-like phase with 3D Li+diffusion channels significantly improves Li^(+)diffusion kinetics and stabilizes the surface structure.The optimally modified sample boasts a discharge capacity of 299.5 mA h g^(-1)at a 0.1 C and 251.6 mA h g^(-1)at a 1 C during the initial activation cycle,with an impressive capacity of 222.1 mA h g^(-1)at a 5 C.Most notably,it retained nearly 70%of its capacity after 300 cycles at this elevated rate.This straightforward,effective,and highly viable modification strategy provides a crucial resolution for overcoming challenges associated with LLO materials,making them more suitable for practical application.

Solving Stiff Reaction-Diffusion Equations Using Exponential Time Differences Methods

Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Though, this paper shows that recent advance methods can be more favored. In this work, we have incorporated, throughout numerical comparison experiments, spectral methods, for the space discretization, in conjunction with second and fourth-order time integrating methods for approximating the solution of the reaction-diffusion differential equations. The results have revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of implementation, accuracy and CPU time.

Effective diffusion of a tracer in active bath:A path-integral approach

We investigate the effective diffusion of a tracer immersed in an active particle bath consisting of self-propelled particles.Utilising the Dean's method developed for the equilibrium bath and extending it to the nonequilibrium situation,we derive a generalized Langevin equation(GLE)for the tracer particle.The complex interactions between the tracer and bath particles are shown as a memory kernel term and two colored noise terms.To obtain the effective diffusivity of the tracer,we use path integral technique to calculate all necessary correlation functions.Calculations show the effective diffusion decreases with the persistent time of active force,and has rich behavior with the number density of bath particles,depending on different activities.All theoretical results regarding the dependence of such diffusivity on bath parameters have been confirmed by direct computer simulation.

EFFECTIVE SOLUTION METHOD OF CHEMICAL REACTION KINETICS WITH DIFFUSE

The time integration method with four-order accuracy, self-starting and implicit for the diffuse chemical reaction kinetics equation or the transient instantaneous temperature filed equation was presented. The examples show that both accuracy and stability are better than Runge-Kutta method with four-order. The coefficients of the equation are stored with sparse matrix pattern, so an algorithm is presented which combines a compact storage scheme with reduced computation cost. The computation of the competitive and consecutive reaction in the rotating packed bed, taken as examples, shows that the method is effective.

An Analytical Air Pollution Model with Time Dependent Eddy Diffusivity

Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

基于低温积分球的中红外陷阱探测器技术

针对中波红外辐射测量定标的需求,提出了将微型积分球与中红外探测器集成在低温环境中。验证比对了几种用于制作积分球内腔表面的材料样品,通过宽光谱反射率、特征光谱反射率、双向反射分布函数(bidirectional reflectance distribution function,BRDF),以及用激光共聚焦显微镜、扫描电子显微镜(scanning electron microscope,SEM)等进行微观表面形貌的测量,获得了适用于制作中红外积分球的内腔表面制作工艺。BRDF测试结果显示,制作的内腔表面接近朗伯反射表面。测试了积分球探测器样品的光谱与电学性能,经过表面粗糙化处理并蒸镀金属反射膜,样品的光谱波段适应性好,光强衰减比为0.0674,经计算,积分球内腔壁的反射率为96.4%;同时,低温积分球的引入,使探测器芯片的噪声由3.5×10^(-12)A·Hz^(-1/2)降低至1.0×10^(-12)A·Hz^(-1/2)。

探讨单层动态匀场弥散加权成像在提高直肠癌图像质量的应用

目的:对单层动态匀场-弥散加权成像(iShim-DWI)和单次激发平面回波成像(SS-EPI)-DWI在直肠癌MR成像中的图像质量进行对比研究。方法:共纳入31例原发性直肠癌患者,对入组患者使用iShim-DWI(b=0、800、1600mm^(2)/s)和SS-EPI-DWI(b=0、1000mm^(2)/s)进行扫描。使用Mann-WhitneyU检验比较两者的伪影和图像质量评分。使用配对样本t检验比较两者的定量指标,包括臀大肌的标准差(SD)、病变组织和正常直肠壁的信号值(SI)、表观弥散系数(ADC)、信噪比(SNR)和对比度噪声比(CNR)。结果:iShim-DWI的图像质量比SS-EPI-DWI有显著提升(P<0.01)。在iShim-DWIb1600图像和ADC图中背景SD显著降低(P<0.05)。iShim-DWI中b800和b1600图像的SNR和CNR均高于SS-EPI-DWI中的b1000图像(P<0.01)。原发性直肠癌患者在iShim-DWI扫描模式下,其b800和b1600图像中病变组织的SI值均显著高于正常直肠组织(P<0.01)。结论:与SS-EPI-DWI相比,iShim-DWI不仅可以显著提高直肠癌的图像质量,降低图像噪声,还可以更加显著区分病变与正常直肠,其应用前景具有很大的临床意义。

200 V全碳化硅集成技术

本文提出了一种基于N衬底P外延晶圆的全碳化硅(Silicon Carbide,SiC)集成工艺平台,该工艺平台兼容低压互补金属氧化物半导体场效应晶体管(Complementary Metal Oxide Semiconductor field-effect transistor,CMOS)、横向扩散金属氧化物半导体(Laterally-Diffused MOS,LDMOS)以及高压二极管等器件.采用P型缓冲层技术调节器件垂直方向电场分布,使高压器件垂直方向耐受电压提高212.4%;在1μm厚度的P型缓冲层和1μm厚度的P型外延层上,实现LDMOS、高压二级管和高侧区域耐受电压大于300 V.基于该工艺平台,搭建了SiC CMOS反相器和反相器链电路,均实现了0~20 V轨至轨的电压输出;设计了半桥驱动电路,低压侧驱动电路由四阶反相器构成;高压侧驱动电路由电平移位电路和高侧区域反相器链电路组成,实现了180~200 V浮空栅极驱动信号输出.

大口径热不敏星敏感器光机设计与分析

为满足大口径长焦距星敏感器的需求,对一种大口径热不敏星敏感器进行光机设计,根据指标要求,对热不敏系统进行光机热集成分析。使用MSC.Patran软件对主次镜结构施加温度载荷,计算出主次镜结构的热弹性变形,先利用MSC.Nastran软件计算热变形后节点的刚体位移,再利用Sigft光机接口软件分析得到变形后主次镜表面的Zernike多项式系数。将结果导入Zemax中,预判镜片面型变化以及刚体位移对弥散斑、光轴漂移量及波像差的影响。最后通过在20℃±5℃的温度范围内装调测试验证了系统性能满足指标要求以及光机热集成分析的准确性,提供了一套准确快捷的光机热集成分析流程。

基于单颗粒锂扩散模型的锂离子电池SOC估算方法改进与在线监测研究

为提高动力电池荷电状态(SOC)的预测精度,基于单颗粒锂扩散模型对锂离子电池SOC的传统安时积分估算法进行改进,利用LabVIEW软件编写了电池SOC估算的传统和改进安时积分法求解程序以及电池数据采集通信接口程序,在不同环境温度和工作电流下,分别采用传统和改进安时积分法对电池SOC进行了在线监测。结果表明,在上述充放电工况下,改进方法和传统安时积分法的最大估算误差分别为1.11%和1.89%,且在放电电流变化剧烈时改进方法得到的电池SOC估算结果波动更小。

基于创新扩散理论的武医融合高质量发展的内在逻辑、问题审视、路径优化

武医融合是健康服务供给的全新理念,对营造全民健身的良好氛围具有现实意义。文章运用文献资料法和逻辑分析法等研究方法,以创新扩散理论分析我国武医融合高质量发展的内在逻辑,提出具体路径,为营造全民健康氛围和树立全民大健康理念作出积极贡献。