Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. It is based on the population balance equations for the two-sided molecular distributions of pendant chains associated with every chemically distinguishable kind of bonds. An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. Examples of its use are presented with polycondensation systems leading to hyperbranched polymers, the anionic polymerization of mono- and divinyl monomers and a radical polymerization with terminal branching and transfer to polymer.     

基于模态Petri网的行为有效区间寻找最优路径的方法

为满足客户需求,在行为约束下的业务流程中寻找行为执行的最优路径具有一定的实际意义。已有的研究是建立在静态分析基础上,通过优化算法或是行为分析来寻找最优执行路径,忽略了行为约束条件对执行行为有效性的影响,所得结果具有一定的局限性。文中在已有方法的基础上,利用Petri网行为轮廓序关系描述约束条件并确定行为有效区间,提出了基于模态Petri网分支有效区间的业务流程最优路径选择方法。该方法以行为有效区间替代已有的固定值方法,以便更好地描述业务流程的行为约束以及约束下的有效行为。通过一个具体的业务流程分析实例分析了该方法的有效性。     

Small-angle neutron scattering from branched epoxide resins

Small-angle neutron scattering experiments in the range of q² from 0.01 to 25 nm⁻² have been carried out on branched epoxide resins based on bisphenol-A at the Institute Laue—Langevin (I.L.L) in Grenoble (q=(4π/λ) sin(θ/2)). Measurements were made with six samples in the range of M_W from 1500 to 19 000 and four concentrations between 1.3 and 10% (w/w) in deuterated diglyme. The results are as follows: (i) The mean square radius of gyration follows a relationship S²_z=4.69×10⁻⁴M^1.20_W (nm²). (ii) In all cases fairly large second virial coefficients A₂ are obtained which, however, decrease strongly with molecular weight. Above M_W=2500, the virial coefficient follows the relationship A₂=1.6M^−0.85_W (mol cm³g⁻²). (ii) The reciprocal particle scattering factor as a function of q² exhibits only a slight upturn and otherwise shows the behaviour of a randomly branched polycondensate. The slight upturn is discussed as being caused by the finite volume of the monomeric unit. Possible reasons for the high exponent in the S²_z versus M_W dependence are briefly discussed.     

The influence of branch length on the deformation and microstructure of polyethylene

The length and number of side chain branches have a profound influence on the microstructure and physical properties of polyethylene (PE). For a series of linear PE copolymers: environmental stress cracking resistance (ESCR), melting points, creep resistance and modulus, and equilibrium spherulite size were all found to increase with increasing branch length (methyl to hexyl) at a given density and molecular weight. It is proposed that (at a fixed molecular weight) branch length and branch concentration determine spherulite size and, consequently, spherulitic boundary areas, in which the dry crazing/voiding occurs during the incubation period of environmental stress cracking (ESC). At a fixed density, decreased spherulite size contributes to greater spherulite boundary slip and increased creep at low (less than 2 MPa) stresses.     

熔体过热对Ag-Cu合金生长取向的影响

通过对Ag-Cu合金熔体的过热处理，研究了不同生长速率时的平界面的结晶位向，发现高的熔体温度使平面单晶的位向产生分支现象。应用Leonard-Jones势能和团簇概念分析了位向分支的形成原因，表明团簇状态在母相中的分布对结晶取向具有重要作用。     

The manpower allocation problem with time windows and job-teaming constraints: A branch-and-price approach

In this paper, we consider the manpower allocation problem with time windows, job-teaming constraints and a limited number of teams (m-MAPTWTC). Given a set of teams and a set of tasks, the problem is to assign to each team a sequential order of tasks to maximize the total number of assigned tasks. Both teams and tasks may be restricted by time windows outside which operation is not possible. Some tasks require cooperation between teams, and all teams cooperating must initiate execution simultaneously. We present an integer programming model for the problem, which is decomposed using Dantzig–Wolfe decomposition. The problem is solved by column generation in a branch-and-price framework. Simultaneous execution of tasks is enforced by the branching scheme. To test the efficiency of the proposed algorithm, 12 realistic test instances are introduced. The algorithm is able to find the optimal solution in 11 of the test instances. The main contribution of this article is the addition of synchronization between teams in an exact optimization context.     

Semi-linear Stochastic Difference Equations

We consider in this paper a class of vector valued processes that have the form Y _n + 1 = A _n ( Y _n ) + B _n . B _n is assumed to be stationary ergodic and A _n is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability distribution as well as for the two first moments of state vectors at the stationary regime. We then apply this approach to derive two formalisms to describe the infinite server queue. The first is based on a branching process approach adapted to phase type service time distributions. The second is based on a linear stochastic difference equation and is adapted to independent and generally distributed service times with bounded support. In both cases we allow for generally distributed arrival process (not necessarily i.i.d. nor Markovian).

Dynamic consistency in process algebra: From Paradigm to ACP

The coordination modelling language Paradigm addresses collaboration between components in terms of dynamic constraints. Within a Paradigm model, component dynamics are consistently specified at various levels of abstraction. The operational semantics of Paradigm is given. For a large, general subclass of Paradigm models a translation into process algebra is provided. Once expressed in process algebra, relying on a correctness result, Paradigm models are amenable to process algebraic reasoning and to verification via the mCRL2 toolset. Examples of a scheduling problem illustrate the approach.     

Branched aliphatic polyesters by ring-opening (co)polymerization

The rapid development of biodegradable and biocompatible materials for biomedical applications is reflected in the search for new methods for aliphatic polyester modification applicable in this field. One possible approach is modification by changes to the polymer topology.This review covers the main methods of synthesis of branched aliphatic biodegradable and biocompatible (co)polyesters, where the ring-opening polymerization (ROP) of cyclic esters or cyclic carbonates is the leading process. First, literature examples of ring-opening multibranching polymerization (ROMBP) of AB₂-type hydroxyl-substituted cyclic lactones, lactides and carbonates are cited followed by the presentation of the application of AB-type cyclic esters and additionally AB₂ cyclic ethers or esters as “branching monomers” for the synthesis of branched polyesters based on polycaprolactone (PCL), polylactide (PLA) and polyglycolide (PGA). In the following part, methods involving the combination of the ROP of AB-type cyclic esters and condensation processes leading to branched structures are summarized. Other related strategies leading to “dendri-star” or “core–shell” copolyesters are also discussed. Several examples of approaches to PCL and PLA graft copolymer syntheses are also shown. The advantages and disadvantages of the presented methodologies of branched polyester synthesis are highlighted. Finally, the influence of the branched structure on the properties of the presented class of polyesters, important from the application point of view, is considered.