Monte Carlo simulation of grain growth in polycrystalline materials

Understanding the kinetics of grain growth, under the influence of second phase (such as impurities, voids and bubbles) is fundamental to advances in the control of microstructural evolution. As a precursor to this objective, we have investigated the grain growth kinetics in a polycrystalline material using a standard Q-state Potts’ model under Monte Carlo settings. Based on physical reasoning, new modifications are suggested to circumvent some of the disadvantages in the basic Potts model. The efficacy of these modifications vis-à-vis the basic model is verified. The influence of second phase particles on the impurity loaded grain boundaries is investigated for the study of grain growth kinetics.     

监测Lévy稳定过程均值变点的平均运行时间估计

平均运行长度(时间)(ARL)是判断一控制图监测变点效果好坏的一个重要工具.本文主要研究Lévy稳定过程的均值变点监测问题.我们给出了三个控制图,即EWMA,GEWMA和GLR的ARL估计,并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

生长曲线模型中回归系数阵的极大似然估计的精确分布

对于生长曲线模型,基于理论发展和应用效果的考虑,本文引入了Gauss型误差．在此误差下,本文研究了模型中回归系数阵的极大似然估计的精确分布,求出了此分布的密度和特征函数．     

Dependence of calculated electron effective attenuation lengths on transport mean free paths obtained from two atomic potentials

We report changes in electron effective attenuation lengths (EALs) resulting from use of transport mean free paths (TMFPs) obtained from the Dirac–Hartree–Fock (DHF) potential instead of the Thomas–Fermi–Dirac (TFD) potential in an algorithm used in the National Institute of Standards and Technology (NIST) Electron Effective‐Attenuation‐Length Database (SRD 82). TMFPs from the former potential are believed to be more reliable than those obtained from the latter potential. We investigated changes in the EALs for selected photoelectron and Auger‐electron lines in four elemental solids (Si, Cu, Ag, and W), for Si 2p photoelectrons of varying energy in SiO₂, and for photoelectrons excited by Al Kα X rays in four candidate gate‐dielectric materials (HfO₂, ZrO₂, HfSiO₄, and ZrSiO₄). For each material, we computed the change in the average EAL for a range of overlayer‐film thicknesses from zero to a maximum value corresponding to attenuation of the substrate signal to 10% of its original value. This EAL change was a maximum for electrons emitted normally from the surface and decreased monotonically with increasing emission angle. The maximum EAL change varied between ?4.4% and 2.6% for the three groups of materials. We found that the maximum EAL change correlated mainly with the TMFP change. We found that TMFP changes in other solids could generally lead to maximum EAL changes between ?2.6% and 1.9% for electron energies between 500 and 2000 eV. For lower energies, the maximum EAL changes could be larger for some solids. Our revised EALs for Si 2p photoelectrons in SiO₂ excited by Mg and Al Kα X rays agree within 0.5% with values reported by Seah and Spencer from a detailed analysis of SiO₂ film‐thickness measurements by XPS and other techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.