处理原子-辐射场相互作用系统的变分方法

用Heisenberg-Weyl(简H-W)群直积SU(2)群上的相干态表述了原子-辐射场相互作用系统的非平衡态统计力学.引入一个新定义的含时分布函数,将非平衡态下密度矩阵所满足的von Neumann方程转化成可分离变量的偏微分方程,给出了方程的形式解,算符的平均值表示.本文还就便于作微扰展开的相互作用绘景作了讨论.     

非线性映射参数辨识的离散变分方法

提出一种辨识非线性映射系统中未知参数的离散变分方法, 对以x_k+1 = F(x_k,θ)为状态控制方程的所有映射混沌系统具有通用性. 对典型的Logistic映射和Henón映射中的未知参数进行了估计, 仿真结果表明了该方法的有效性.     

具有大范围运动和非线性变形的空间柔性梁在非惯性坐标系下的动力学分析

本文针对具有大范围运动和非线性变形的空间柔性梁, 导出其在运动规律已知的非惯性坐标系下的动力学方程. 通过计算分析, 发现在本文精确模型下, 其各矩阵项较原来的一次耦合模型增加了两类耦合项. 通过仿真研究, 发现由于这两类耦合项的作用造成了附加刚度项K₁、动力刚度项K_d 的变化, 而刚度项对结构的动力学特性具有较大的影响.     

A remark on transition probability

Uhlmann's transition probability P(ψ, φ) of two normal states of a von Neumann algebra M, which is the supremum of |(Ψ, Φ)|² for all possible choices of representative vectors Ψ and Φ of ψ and φ, is shown to be the infimum of (∫d(μ_{ψ, e})^1/2)² for the induced measures μ_{ω, e}(B)=ω(e(B)) (B: Borel set in ℝ, ω=ψ, φ) for all possible projection-valued measures e belonging to M.     

Magnetoelectric effect and toroidal ordering in Ga2−x FexO3

The field dependence of the magnetoelectric effect and longitudinal magnetostriction of Ga_2−x Fe_xO₃ single crystals is studied in magnetic fields up to 200 kOe in the temperature range from 4.2 to 300 K. It is shown that the magnetoelectric effect in these materials is determined mainly by the toroidal moment T and is not related to magnetostriction, as was previously theorized. A new method for determining the toroidal moment by measuring the electric polarization in a strong magnetic field is proposed. The value of the toroidal moment of the unit cell in Ga_1.15Fe_0.85O₃ is calculated: T=(T _a ,0,0), where T _a =24.155μ _B Å per unit cell. Experimental data are analyzed using a theory of toroidal spin ordering, which gives good agreement with experiment. Zh. éksp. Teor. Fiz. 114, 263–272 (July 1998) Deceased.     

Demonstration of the approximation of eliminating atomic excited populations in an atomben cavity system

Using the master equation approach to a V-type three-level atom inside a high-finesse single-mode cavity in the strong coupling condition, we demonstrate the approximation of eliminating populations of atomic excited states, which is widely used in the field of the atom-cavity systems [Hechenblaikner G, Gangl M, Horak P and Ritsch H 1998 Phys. Rev. A 58 3030]; Liu L W, Tan T and Xu Y 2008 J. Mod. Opt. 56 968; Cho J, Angelakis D G and Bose S 2008 Phys. Rev. A 78 062338. This is reflected in the deviation of the population δ, of which the value is 10^-3～10^-2. We further find the deviation of the dipole force and demonstrate that the deviation of atomic population will not notably affect the dipole force of the atom in the strong coupling condition. A relevant experimental case is also presented.     

z切LiTaO3单晶的冲击相变研究

利用二级轻气炮加载下的冲击Hugoniot线(冲击波速度D-粒子速度u关系)和粒子速度剖面测量，结合基于密度泛函理论的平面波赝势计算研究了z切LiTaO₃单晶的高压相变.实验发现，D-u关系在u=0.95km/s附近出现明显拐折；实测波剖面中25.9 GPa和32.6 GPa时观测到弹-塑性双波结构，而终态压力为42.7 GPa和53.0 GPa时则为三波结构.上述结果都清楚地表明z切LiTaO₃单晶冲击相变的发生，相变起始压力约为37.9 GPa.同时，理论计算的菱形相(R3c对称群)压缩线与低压实验数据符合较好，而正交相(Pbnm对称群)压缩线则与扣除热压贡献的高压实验数据相符，由此推断z-切LiTaO₃的高压相为正交结构.从实验和理论上澄清了z切LiTaO₃的相变起始压力和高压相晶体结构的认识，研究工作亦对类似单晶材料的冲击相变研究有参考价值.     

基于交通流量的病毒扩散动力学研究

不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数b_k. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值β_c, 平稳状态病毒密度ρ之间的关系. 理论分析与实验结果均表明, 当网络拓扑和路由策略一定时, 传播阈值β_c为实际介数b_k的均值<b_k>与其平方的均值<b_k²>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值<b_λ=1> 的乘积倒数存在幂率关系.     

Meson-baryon s-wave resonances with strangeness -3

Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian ( Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = - 3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2⁺ octet of the nucleon and the 3/2⁺ decuplet of the Delta. Quantum numbers I(J ^P) = 0(3/2^-) are suggested for the experimental resonances Ω ^*(2250)^- and Ω ^*(2380)^-. Among other, resonances with I = 1 are found, which minimal quark content is sssˉl', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K ^- Ξ ^- resonances with masses around 2100 and 2240MeV in the sector 1(1/2^-), and for π ^± Ω ^- and K ^- Ξ ^*- resonances with masses around 2260MeV in the sector 1(3/2^-).     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

Mean width and caliper characteristics of network polyhedra

The kinetic modelling of space-filling grain networks has been approached traditionally by representing the grains as spheres of equivalent volume. A spherical approximation used to describe polyhedral grains, unfortunately, relinquishes most geometrical and all topological details of the grain structure. Techniques developed by Hilgenfeldt et al., and by Glicksman, describe network structures comprised of space-filling irregular polyhedra and their kinetics with regular polyhedra, which act as ‘proxies’ that preserve both local topology and network constraints. Analytical formulas based on regular polyhedra and Surface Evolver simulations are used in this study to calculate the average caliper width and mean width for extended sets of polyhedra that vary systematically from convex to concave objects. Of importance, caliper width and mean width measures allow estimation of the growth rates of grains. Comparison of these calculations and simulations, however, reveal a weak dependence between average caliper width and mean width measures and the detailed shapes of polyhedra, especially their face curvatures. This finding might, in fact, affect the application and use of linear measures as kinetic tools in quantitative microstructure measurements.     

MacPherson-Srolovitz晶粒长大速率方程的仿真验证

2007年MacPherson和Srolovitz联合推导出一个三维个体晶粒长大的准确速率方程,但并未给出实验或计算机仿真的验证.采用Potts模型Monte Carlo方法对该速率方程进行了大尺度仿真验证.结果表明,仿真数据与MacPherson-Srolovitz速率方程符合很好,从而初步证实了该速率方程,即三维晶粒长大速率是晶粒棱长和晶粒平均宽度的函数. 关键词： 三维晶粒长大 速率方程 Monte Carlo仿真     

磷化铟单晶生长中的传热和流动分析

用有限元法对轴向磁场存在下3英寸磷化铟单晶液封提拉法生长中的传热和流动进行了求解．结果表明:液封改变了晶体表面被封部分的换热,进而影响生长界面的形状．增加磁场强度能有效减弱熔体和封层内的流动,并使生长界面形状发生变化。增加提拉速度,生长界面形状由凸变凹．随晶体转速的增加,多涡胞流动出现．     

晶粒尺度对延性金属材料层裂损伤的影响

微细观结构对材料动态损伤、破坏的影响是目前国内外力学领域的研究热点之一. 基于相关文献的实验结果, 通过理论分析, 给出了一个新的反映晶粒尺度效应的孔洞成核模型, 并将其耦合到延性金属材料层裂损伤模型中. 采用数值方法分析了晶粒尺度对高纯铜材料层裂损伤演化过程的影响. 计算结果显示: 随着材料平均晶粒尺度的增加, 自由面速度回跳点降低, 回跳后速度曲线的斜率增加; 损伤材料内部的孔洞数减少、平均孔洞尺寸增大.计算结果与相关文献所报道的实验 分析结果定性上符合较好. 该结果对于层裂损伤的深入研究具有一定的启发性. 关键词： 层裂 晶粒尺度 延性金属材料 冲击     

光栅卡卷尺测长技术

本文在光栅卡尺技术和力矩电机技术的基础上，把卡尺量程扩大到２０ｍ作成卡卷尺。利用力矩电机作为卡卷尺的卷紧机构和利用力矩电机作为保证光栅编码器标尺光栅平直度的施力元件，在此基础上，发展了光栅卡卷尺测长技术。基于莫尔条纹技术的光栅卡尺测长技术与其它现有长度测量技术相比成本较低、性能可靠，其测量精度可达０．０５ｍｍ甚至更高。为克服实际应用中卡卷尺的平直度对测量精度的影响，在系统设计中使力矩电机工作在堵转状态作为保证光栅卡卷尺标尺光栅平直的施力元件，并设计了线性调节的力距电机电源。对系统的检测表明，在２０ｍ测程内测量精度为０．１ｍｍ。     

晶粒棱长、尺寸与拓扑学特征之间关系的Monte Carlo仿真研究

采用Potts模型Monte Carlo方法研究了晶粒棱长、尺寸与拓扑学特征之间的统计关系.结果表明,晶粒棱长与晶粒面数之间呈线性统计关系,并且平均N面体晶粒模型和Poisson-Voronoi组织均支持该结论.不同时刻的晶粒长大仿真数据表明,在准稳态晶粒长大阶段晶粒棱长的分布具有自相似性.个体晶粒的平均棱长随晶粒面数（或晶粒尺寸）的增加而逐渐增大,这说明一些理论模型中采用的“不同面数的晶粒平均棱长均相等”的假设具有局限性.仿真数据和纯铁实验数据均表明,晶粒尺寸与晶粒面数之间的统计关系表现为一条单调递增的凸曲线. 关键词： 晶粒棱长 晶粒尺寸 拓扑学 Monte Carlo仿真     

一种凸非球面镜补偿检验的新方法

凸非球面检验是光学检验中一个比较困难的问题。结合一块Φ110mm的凸双曲面镜,在分析几种传统检验方法的基础上,提出了一种用透镜组补偿检验凸非球面的新方法。令球差系数∑S1=0,用三级像差理论求解光学系统的初始结构,并通过Zemax光学设计软件对初始结构进行优化,克服了传统检验方法的缺点和不足。从设计结果可以看出,系统的像差得到了很好的校正,使得凸双曲面达到了很高的检验精度,从而使非球面的检验更加方便。     

Modelling of austenite grain growth kinetics in a microalloyed steel (30MSV6) in the presence of carbonitride precipitates

Austenite grain growth kinetics in the presence of secondary precipitates of a microalloyed steel (30MSV6) was studied employing quantitative metallographic techniques. Austenitizing experiments were carried out at 1,000, 1,100 and 1,200?°C. According to the experimental data, abnormal grain growth behaviour is observed at 1,100?°C while it is normal at 1,000 and 1,200?°C. TEM observation represents multicomponent carbonitride precipitate, (Ti,V)(C,N), in the as-received steel with a mean radius of 35?nm. A mathematical model is proposed considering austenite grain growth along with dissolution and coarsening kinetics of the multicomponent precipitates. The austenite grain growth model for short-term non-isothermal and subsequent long-term isothermal heating stages was developed using a statistical approach. The model includes an algorithm to estimate the size distribution of austenite grains. Precipitate mean field dissolution and Lifshitz–Slyozov–Wagner coarsening models were integrated in the proposed model to calculate the pinning pressure retarding the grain boundary movement. The mean austenite grain size and the grain size distribution (normal and abnormal) calculated by the model are in good agreement with experimental data.     

Deformation-induced changes in single-phase Al-0.1Mg alloy

Al-0.1wt.%Mg has been chosen to explore the effects of deformation on the microstructure of nominally single-phase materials. For these materials, the rate of static grain growth is much higher compared to that of Zener pinned systems and dual-phase alloys, where growth is hindered due to the pinning force exerted by second-phase particles on grain boundaries. Therefore, deformation-induced microstructural changes in single-phase alloys occur without any restricting pinning pressure. This paper illustrates the complex effect of deformation on the microstructural changes mainly associated with dynamic recovery. The process affects the initial microstructure due to an intensive substructure development. Dynamic recrystallisation, associated with the formation of new grains, is considered to be a transient phenomenon that quantitatively influences the mean grain size formed during straining. This work also aims to estimate the stored energy of the deformed regions and texture components to explore their contribution to the migration of high-angle grain boundaries.