考虑细胞外基质黏弹性行为的细胞黏附力学模型

细胞外基质由大量胶原蛋白和纤维蛋白组成,这些基质蛋白形成复杂的交联网络状结构,具有黏弹性力学特性.研究表明,黏弹性基质能显著影响细胞迁移、增殖和分化等生理行为,还能影响癌症转移和组织纤维化等疾病的发生与发展.然而,细胞感知细胞外基质黏弹性力学特性的分子机制仍不清楚.该文通过建立细胞黏附力学模型,从分子层次揭示细胞黏附在细胞响应外界黏弹性力学微环境中的作用.结果表明,细胞能通过调控细胞黏附动力学（包括黏附周期和黏附形成时间）响应细胞外基质的黏弹性力学特性.通过将模型计算结果与实验现象相比较,验证了模型的正确性.细胞黏附力学模型将为组织工程中细胞力学微环境的构建奠定理论基础.     

复杂介质中扩散和耗散行为的分数阶导数唯象建模

复杂介质一般是多相混合物.与普通固体、液体和气体相比,其力学行为具有明显的记忆、路径依赖性特征,难以用一般的经典力学模型来描述,因而显得反常.从数学力学建模上看,整数阶导数的局部极限定义不适合描述这样的非局部力学行为.分数阶导数实质上是微分-积分算子,能精确地刻画力学行为的全局相关特征.而且分数阶模型具有明确的统计物理解释.20世纪末至今,复杂介质反常力学行为的分数阶导数模型由于具有参数少,且参数的物理意义明确等突出优点,开始引起广泛关注.该文从唯象建模的角度,综述了分数阶导数和分形导数在复杂介质的反常扩散和频率依赖能量耗散建模中的应用与发展.     

均聚物玻璃化转变的非平衡统计理论——I.玻璃化转变的统计动力学理论 *

提出了非晶态和半晶态均聚物的网络结构模型 ,认为高聚物是由玻璃化微区 高分子链组网、微晶 高分子链组网、交联 高分子链组网络和缠结链组网络构成 .以链组作为形变和统计单元 ,用统计力学和动力学相结合的方法计算出 4种网络的链组数、链组末端距的几率分布函数 ,建立了均聚物玻璃化转变的统计动力学理论 ,得到了等温和非等温玻璃化动力学方程及其DSC曲线的理论表征式 ;计算出了 4种网络玻璃化转变粘弹性形变自由能和微区的玻璃化自由能以及均聚物网络玻璃化转变的总自由能 ;求得了均聚物玻璃化转变的静态模量、记忆函数、松弛谱和动态力学性能 (动态粘度、动态模量和损耗角正切 )等表征式 .     

三叉树上分支马氏链的等价性质

在二叉树上分支马氏链的等价性质研究的基础上,给出了三叉树上分支马氏链定义的离散形式,除了把二叉树上分支马氏链的两个等价性质平移到三叉树上分支马氏链以外,又给出了三叉树上分支马氏链的两个等价性质及两个性质.得出结论的关键方法是在概率乘积公式及条件概率公式的计算中正确处理其中所涉及到的许多繁杂的必然事件.     

层次模型Markov链的观测与统计

对于连续时间的层次模型M arkov链,所有的转移速率都可以由最底层状态的逗留时间和击中时间分布惟一决定,因而整个M arkov链的统计性质由它们的统计所决定.并给出了相应的算法和数例.     

细胞骨架与细胞外基质的力学建模与分析

细胞和生物组织需要适应人体内复杂的力学生物学环境,一方面要被动地承受外部环境中的机械力,另一方面在组织生长、修复等生理过程中要积极主动地产生机械力调整自身的结构和形态.细胞和生物组织的力学性质主要由细胞骨架和细胞外基质决定,它们在微观上都是生物聚合物交联形成的复杂的、各向异性的三维网络结构.这方面早期的力学研究主要集中在通过各种网络模型,理解其普遍存在的非线性响应和硬化行为.近年来随着实验方法、理论建模和计算机模拟技术的大幅进步,这些生命介质的力学性质及其潜在的力学机理得到了更深入的理解.该文回顾了近些年细胞骨架和细胞外基质研究方面取得的部分进展,主要侧重动态交联属性、生物聚合物力学化学耦合赋予的主动材料属性、交联网络塑性和断裂,以及力学训练引发的自适应网络重构.发展细胞骨架与细胞外基质的力学模型与计算方法,分析该类生命介质的复杂力学行为,理解这些力学行为的潜在机制,可以加深我们对细胞和组织的力学生物学认识,并为人造生物材料和细胞组织工程提供基础和参考.     

二叉树上分支马氏链的等价性质

本文给出了二叉树上分支马氏链定义的离散形式,然后研究了它的两个等价性质.最后,我们指出在二叉树情况下,树指标马氏链就是一类特殊的分支马氏链.     

树指标马氏链的若干性质

主要研究了树指标马氏链的若干性质,它与一般直线上的马氏链有类似的性质.     

缠结高分子链的Brown运动模型及其解缠弛豫时间的计算机模拟

以缠结高分子链的质心在约束管子中作Brown运动为基本假定,在忽略有效管长的涨落下,得到解缠弛豫时间τ链长N的渐近依赖关系τ^_N3。在有限链长及约束管长涨落的条件下,采用计算机模拟得到关系式τ^_N3.40±0.16。这一结论合理地解释了缠结高分子链动力学的实验结果。     

大型射电望远镜馈源体轨迹跟踪系统的力学分析

给出了悬挂重物的悬索系统悬链线的曲线方程及其受力分析,在此基础上,运用作复合运动的刚体的运动学和动力学的方法,对大型射电望远镜的馈源系统进行了力学分析及馈源体轨迹跟踪运动的控制研究,给出了控制馈源体轨迹跟踪运动的方法及步骤．算例验证了理论及方法的正确性、可行性．     

The statistical mechanics of a class of dissipative systems

The statistical mechanics of dynamical systems on which only isotropic viscous friction forces act is developed. A non-stationary analogue of the Gibbs canonical distribution, which enables each such system to be made to correspond to a certain thermodynamic system that satisfies the first and second laws of thermodynamics, is introduced. The evolution of non-Gibbs probability distributions with time is also considered.     

Review of recent scientific publications in the field of polymer mechanics

The results of research in polymer mechanics carried out by the authors or with their direct participation during the last 5 years are briefly reviewed. The following questions are covered: theory and methods of solution of problems of polymer mechanics, statistical methods in polymer mechanics, the experimental investigation of the properties of polymeric materials, and the reflection of the theory and methods of polymer mechanics in the textbooks.     

Constraint Selection and Deterministic Annealing

The deterministic annealing optimization method is related to homotopy methods of optimization, but is oriented towards global optimization: specifically, it tries to tune a penalty parameter, thought of as ``temperature', in such a way as to reach a global optimum. Optimization by deterministic annealing is based on thermodynamics, in the same sense that simulated annealing is based on statistical mechanics. It is claimed to be very fast and effective, and is popular in significant engineering applications. The language used to describe it is usually that of statistical physics and there has been relatively little attention paid by the optimization community; this paper in part attempts to overcome this barrier by describing deterministic annealing in more familiar terms.The main contribution of this paper is to show explicitly that that constraints can be handled in the context of deterministic annealing by using constraint selection functions, a generalization of penalty and barrier functions. Constraint selection allows embedding of discrete problems into (non-convex) continuous problems.We also show how an idealized version of deterministic annealing can be understood in terms of bifurcation theory, which clarifies limitations of its convergence properties.     

The thermodynamic irreversibility of a mechanical system possessing the property of recurrence

The transition from one thermodynamic state to another by a mechanical system possessing the property of recurrence is investigated. It is established that the concept of a state in phenomenological thermodynamics corresponds to the concept of an attainability set in mechanics. It is shown that the presence of states that are reversible within the framework of classical mechanics, does not contradict the irreversibility of thermodynamic states.     

Nonextensive distribution and factorization of the joint probability

The problem of factorization of Tsallis' nonextensive probability distribution is discussed in a general way. It is shown that the correlation energy between the correlated subsystems in the canonical composite system cannot be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established without factorization approximation in the framework of the incomplete statistical mechanics.     

Newtonian viscosity of polymer solutions over a wide range of compositions as a function of certain parameters determining it

Using solutions of various polymers in a large number of solvents as an example, the possibility of constructing a generalized characteristic for their viscosity, which is invariant relative to the molecular weight of the polymer and the nature of the solvent, is indicated. It is shown that the parameters characterizing the properties of individual macromolecular chains are the dimensions of the coils [], and the rheological effectiveness of interaction of the segments K_M retain their importance and quantities determining the viscous properties of the polymer solution over the whole range of compositions. A connection is established between the datum parameter K_M and the thermodynamic properties of dilute solutions of polymers, the flexibility of the polymer chain, and the energy of its intermolecular interaction.A. M. Gor'kii, Ural State University, Sverdlovsk. A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1110–1117, November–December, 1972.     

Statistical Irreversible Thermodynamics in the Framework of Zubarev’s Nonequilibrium Statistical Operator Method

We describe the formalism of statistical irreversible thermodynamics constructed based on Zubarev’s nonequilibrium statistical operator (NSO) method, which is a powerful and universal tool for investigating the most varied physical phenomena. We present brief overviews of the statistical ensemble formalism and statistical irreversible thermodynamics. The first can be constructed either based on a heuristic approach or in the framework of information theory in the Jeffreys-Jaynes scheme of scientific inference; Zubarev and his school used both approaches in formulating the NSO method. We describe the main characteristics of statistical irreversible thermodynamics and discuss some particular considerations of several authors. We briefly describe how Rosenfeld, Bohr, and Prigogine proposed to derive a thermodynamic uncertainty principle.     

Entangled Markov chains

Motivated by the problem of finding a satisfactory quantum generalization of the classical random walks, we construct a new class of quantum Markov chains which are at the same time purely generated and uniquely determined by a corresponding classical Markov chain. We argue that this construction yields as a corollary, a solution to the problem of constructing quantum analogues of classical random walks which are “entangled” in a sense specified in the paper.The formula giving the joint correlations of these quantum chains is obtained from the corresponding classical formula by replacing the usual matrix multiplication by Schur multiplication.The connection between Schur multiplication and entanglement is clarified by showing that these quantum chains are the limits of vector states whose amplitudes, in a given basis (e.g. the computational basis of quantum information), are complex square roots of the joint probabilities of the corresponding classical chains. In particular, when restricted to the projectors on this basis, the quantum chain reduces to the classical one. In this sense we speak of entangled lifting, to the quantum case, of a classical Markov chain. Since random walks are particular Markov chains, our general construction also gives a solution to the problem that motivated our study.In view of possible applications to quantum statistical mechanics too, we prove that the ergodic type of an entangled Markov chain with finite state space (thus excluding random walks) is completely determined by the corresponding ergodic type of the underlying classical chain. Mathematics Subject Classification (2000) Primary 46L53, 60J99; Secondary 46L60, 60G50, 62B10     

资金约束下三层供应链的融资和定价决策研究

实际生活中,供应链的资金管理是极其复杂多变的,现有学者关于供应链定价问题研究多以简单的二层供应链为基础,脱离了实际可用性。本文将二层供应链拓展成三层供应链,以单一供应商、单一生产商和单一零售商组成的三层供应链为研究对象,在市场风险中性的假设条件下,探究在供应商拥有不同初始资金约束情形下的供应链融资与最优定价决策,弥补了原先模型使用范围的狭隘性。通过模型的建立与数值分析显示,当供应商存在资金约束时,供应链融资能够使整条供应链上参与者的最优利润增加,从而创造价值。