均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅴ 分子分凝统计结晶动力学—结晶增长速率对结晶生长机制和高聚物起始结构的依赖性

首先对结晶增长速率同浓度、分子量和链柔性依赖性进行总结，然后基于微晶核和粒——高分子键组网络结构模型和高分子分子分凝统计结晶动力学，根据高分子链组是微晶粒同连接链段复合体的结构特征及它们间存在的四个相关性（并存性、简并性、顺反式构象共存性和物料守恒性）的事实，成功地把连接链段缩短增长动力方程同微晶粒体积增大增长动力方程有机结合在一起，从理论上创建出一种微晶粒数增长速率和微晶粒尺寸增长速率表达的一般化计算法，推导出结晶体系的微晶粒数增长速率和微晶粒尺寸增长速率同四种增长机制（近邻折叠，近邻伸直，近邻折叠同近邻伸直并联并存和近邻折叠同近邻伸直串联并存）、结晶温度和高分子起始结构（分子量）间定量表达式．当把分子量的指数同链的构象分数相连后，就又从理论上得到了分子量指数同温度和链柔性间的关系式，并讨论了它们同增长机制间的关系，最后以大量结晶动力学实验数据对上述所得到的关系式进行了验证，结果表明它们均能同实验结果很好符合．     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅴ 分子分凝统计结晶动力学—结晶增长速率对结晶生长机制和高聚物起始结构的依赖性

首先对结晶增长速率同浓度、分子量和链柔性依赖性进行总结,然后基于微晶核和粒———高分子键组网络结构模型和高分子分子分凝统计结晶动力学,根据高分子链组是微晶粒同连接链段复合体的结构特征及它们间存在的四个相关性(并存性、简并性、顺反式构象共存性和物料守恒性)的事实,成功地把连接链段缩短增长动力方程同微晶粒体积增大增长动力方程有机结合在一起,从理论上创建出一种微晶粒数增长速率和微晶粒尺寸增长速率表达的一般化计算法,推导出结晶体系的微晶粒数增长速率和微晶粒尺寸增长速率同四种增长机制(近邻折叠,近邻伸直,近邻折叠同近邻伸直并联并存和近邻折叠同近邻伸直串联并存)、结晶温度和高分子起始结构(分子量)间定量表达式.当把分子量的指数同链的构象分数相连后,就又从理论上得到了分子量指数同温度和链柔性间的关系式,并讨论了它们同增长机制间的关系.最后以大量结晶动力学实验数据对上述所得到的关系式进行了验证,结果表明它们均能同实验结果很好符合.     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅵ. 分子分凝统计结晶动力学-结晶增长速率对结晶生长机制和溶液浓度和的依赖性

首先对结晶增长速率同浓度和链柔性依赖性进行总结,然后基于微晶核和粒———高分子键组网络结构模型和高分子分子分凝统计结晶动力学,根据高分子链组是微晶粒同连接链段复合体的结构特征及它们间存在的四个相关性(并存性、简并性、顺反式构象共存性和物料守恒性)的事实,成功地把连接链段缩短增长动力方程同微晶粒体积增大增长动力方程有机结合在一起,从理论上创建出一种微晶粒数增长速率和微晶粒尺寸增长速率表达式的一般化计算法,推导出结晶体系的微晶粒数增长速率、微晶粒尺寸增长速率同四种增长机制(近邻折叠,近邻伸直,近邻折叠同近邻伸直并联并存和近邻折叠同近邻伸直串联并存)、结晶温度和和结晶浓度间定量表达式.当把浓度指数同链的构象分数相连后,就又从理论上得到了浓度指数同温度和链柔性间的关系式,并讨论了它们同增长机制间的关系.最后以大量结晶动力学实验数据对上述所得到的关系式进行了验证,结果表明它们均能同实验结果很好符合.     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅳ 分子分凝统计结晶动力学~结晶增长区域的区划和它们对温度和生长机制的依赖性

首先对高分子结晶增长动力学的实验规律进行全面总结,并指出了当前高分子结晶增长动力理论中存在的难题.然后按我们建议的评估微晶粒尺寸增长速率的新方法推导出了四种不同微观生长机制(折叠、伸直、折叠同伸直并联并存和折叠同伸直串联并存等方式)下微晶粒高分子链组的微晶粒尺寸增长速率定量表征式,又导出了四种不同生长机制下微晶粒尺寸增长速率同结晶温度和过冷温度间关系的表达式.根据四种不同微观生长机制同宏观增长方式差别和它们出现的结晶温度同过冷温度之积值高低,可把结晶动力学的结晶增长区域图中三组交叉线区划为三个不同增长区域,最后又根据三个增长区的理论关系式讨论了增长区中晶体形貌同结晶温度和过冷温度间的相关性,其理论预测能同近期实验观测基本符合.     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论III. 分子分凝统计结晶动力学～熔体内结晶增长速率的一般化表征和它们对生长机制的依赖性

首先对微晶粒尺寸增长速率的表征进行总结.从微晶核和粒—高分子链组网络结构特点(高分子链组是微晶核和微晶粒同连接链段的复合体)同增长速率间的三个相关性的特征: ①晶核和晶粒加大同连接链段缩短的并存性; ②微晶核和粒表面上连接链段的缩短机制存有简并性; ③微晶粒内和粒表面上stem的反顺式构象共存性出发.建议了一种评估和计算微晶粒尺寸增长速率的新方法和原则,基于该种计算方法和原则用统计力学和动力学相结合法推导出了高分子熔体内几种不同结晶生长机制(近邻折叠、近邻伸直分凝和近邻折叠同近邻伸直分凝并存等生长方式)下微晶粒—高分子链组中微晶粒数增长速率和微晶粒尺寸增长速率动力学方程.     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅲ．分子分凝统计结晶动力学～熔体内结晶增长速率的一般化表征和它们对生长机制的依赖性

首先对微晶粒尺寸增长速率的表征进行总结．从微晶核和粒-高分子链组网络结构特点(高分子链组是微晶核和微晶粒同连接链段的复合体)同增长速率间的三个相关性的特征：①晶核和晶粒加大同连接链段缩短的并存性；②微晶核和粒表面上连接链段的缩短机制存有简并性；③微晶粒内和粒表面上stem的反顺式构象共存性出发．建议了一种评估和计算微晶粒尺寸增长速率的新方法和原则，基于该种计算方法和原则用统计力学和动力学相结合法推导出了高分子熔体内几种不同结晶生长机制(近邻折叠、近邻伸直分凝和近邻折叠同近邻伸直分凝并存等生长方式)下微晶粒-高分子链组中微晶粒数增长速率和微晶粒尺寸增长速率动力学方程．     

Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {–1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential in the limit of zero temperature; we analyze the first excursion from the metastable –1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2 is crossed.     

一类热传导问题源项识别的快速稳定算法

利用正算子的性质和Lax-Milgram定理,将一维热传导方程源项识别问题转化为适定的、第二类Volterra方程的求解,给出一个新的快速稳定算法,并进行理论分析.采用两种实现后验准则的新途径,在输入数据的误差水平已知和未知的情况下,快速地决定正则参数.数值实验证实了算法的有效性.     

40, 48Ca+90, 96Zr近垒熔合反应的动力学研究

发展了一种改进的量子分子动力学模型,并用这一模型研究了40,48Ca+90,96Zr的近垒熔合反应.改进的量子分子动力学模型能很好地描述一系列核,从6Li到208Pb,的基态性质及它们的时间演化.在相同参数下计算得到的40Ca+90Zr以及40Ca+96Zr这两个熔合反应的激发函数与实验结果都符合得相当好.在分析丰中子核熔合截面增强机制中,发现丰中子核熔合反应初始阶段颈部的N/Z值明显偏大,促使反应中动态位垒降低,从而引起了丰中子核反应熔合截面的增强. An improved Quantum Molecular Dynamics (QMD) model is proposed and the fusion reactions 40, 48Ca+90, 96Zr are studied by using this model. With our improved QMD model, the ground state properties and their time evolution of nuclei from 6Li to 208Pb can be reproduced reasonably well and the excitation functions of fusion cross section for reactions40Ca+96Zr and 40Ca+96Zr at near barrier can be reproduced remarkably well with the same set of parameters...     

Conditions for growth of columnar and filamentary crystals

The computer model of the initial stage of condensation processes is developed. The stochastic processes of adsorption, surface diffusion, and desorption occur on the 70×70 lattice of adsorption vacancies. The model was tested by an example close to water vapor sorption on a conventional crystal surface. Computed results demonstrate the processes of nucleation, growth of crystals, and developed condensation. Computations were carried out for various adsorption energies. Results showed that with decreasing energy of adsorption the character and rate of nucleation and subsequent condensation vary. With decreasing energy of adsorption the probability of nucleation of islets on substrate reduces, the filling of the next atomic layers on islets occurs earlier than the filling of the substrate, the growth rate of islets in height increases as compared to condensation of a continuous film, and the growth rate of area of islets decreases. There is a typical energy of adsorption at which the growth rate of islets in height reaches its maximum. At a further drop of adsorption energy, there is a growth of islets only in height, the growth rate, however, reduces. The phenomena revealed in computations illustrate the mechanism of origin of columnar and filamentary crystals.     

Statistical properties for a class of nonlinear squeezed states

Theoretical investigations of dynamical behavior in optical parametric oscillators (OPO) have generally assumed that the cavity detunings of the interacting fields are controllable parameters. However, OPOs are known to experience mode hops, where the system jumps to the mode of lowest cavity detuning. We note that this phenomenon significantly limits the range of accessible detunings and thus may prevent instabilities predicted to occur above a minimum detuning from being evidenced experimentally. As a simple example among a number of instability mechanisms possibly affected by this limitation, we discuss the Hopf bifurcation leading to periodic behavior in the monomode mean-field model of a triply resonant OPO and show that it probably can be observed only in very specific setups.     

Elucidation of the crystallization kinetics for sodium-alumino-silicate glasses containing different amounts of manganese oxide

The glass samples [40SiO₂?+?5Al₂O₃?+?{55???x}Na₂O?+?xMnO₂] where x?=?0.05, 0.2, 0.4, 0.6, 0.8, and 1?mol% MnO₂ before and after being heat treated were subjected to X-ray diffraction. The diffraction lines provided clear evidence of the nucleation and growth, which are characteristic of sodium silicate phase. Crystallization studies were conducted using differential thermal analysis. Crystallization peak temperatures were identified and the transformed fractions were determined. Both the rate of growth, K ₀, and the activation energy, E, depend on the influence of manganese ions in the glass network as a modifier or as a former and the manganese content. The values of the Avrami parameter, n, were calculated using two methods and were in excellent agreement. The process of nucleation and growth rate depends on the manganese content.     

Stability of Crystal Growth Face and Dissolution Face in Crystallization from Solution under Microgravity

The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied.It is proved that the stable shapes of crystal growth face and dissolution face do exist,which are suitably shaped curves with their upper parts inclined backward properly.The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters,Ra,Pr and Sc.It is shown that the stronger the convection relative to the diffusion in solution is,the more backward the upper parts of the stable crystal growth face and dissolution face are inclined.The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.     

Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.