Titanium nanocarbides: Synthesis and modeling

The present state of research on the production and modeling of nanostructures based on titanium carbide-a typical representative of an extensive class of carbides of d-and f-metals-is reviewed. Methods for the synthesis of various Ti-C nanostructures (molecular clusters, nanocrystallites, nanospheres, nanofibers, nanowires) are examined, and their morphology, atomic structure, and known physicochemical characteristics are described. Theoretical models of the atomic structure and properties of new types of nanostructures in the titanium-carbon system (endo-and exohedral titanofullerenes, “hybrid” structures based on carbon nanotubes, the so-called peapods, nanocables, and a number of others) and the prospects for their application as components of nanoceramics, hydrogen accumulators, materials for spintronics, etc. are discussed. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 1, pp. 1–23, January–February, 2007.     

Degradative chain transfer in vinyl acetate polymerizations using toluene as solvent

In this work, we propose that retardation in vinyl acetate polymerization rate in the presence of toluene is due to degradative chain transfer. The transfer constant to toluene (C_trs) determined using the Mayo method is equal to 3.8 × 10^?3, which is remarkably similar to the value calculated from the rate data, assuming degradative chain transfer (2.7 × 10^?3). Simulations, including chain‐length‐dependent termination, were carried out to compare our degradative chain transfer model with experimental results. The conversion–time profiles showed excellent agreement between experiment and simulation. Good agreement was found for the M_n data as a function of conversion. The experimental and simulation data strongly support the postulate that degradative chain transfer is the dominant kinetic mechanism. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3620–3625, 2007     

抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

Residual currents and corridor of flow in the Rio de la Plata

The Rio de la Plata is a large and shallow water body that discharges onto the Atlantic Ocean. The main driving forces for the river flow are the bathymetry, tides, the outflow from the Paraná and Uruguay rivers and the winds. A numerical model covering the entire river was set up with the objective of increasing our understanding of the hydrographical features and morphological dynamics in the Estuary. The simulations revealed a counter-clockwise residual circulation in the Samborombón Bay and an eastward net flow near the Uruguayan coast. The residual flow is forced by both the tides and the bathymetry. The residence time for the entire river ranges from 40 to 80 days. However, residence times above 120 days was found in the Samborombón Bay. Three corridors of flow have been identified.     

加权微分建模的初步研究

加权建模是必要的,微分建模是重要的,把二者结合起来,进行加权微分建模既必要也重要.给出了常用模型的微分建模结果,讨论了加权建模中的计算和权重选择问题,探讨了加权微分建模的思路和方法,并结合典型数据验证了该方法的有效性和稳定性.象加权建模一样,加权微分建模的精度、实用价值等,是和权重确定得合理与否紧密相联;应先进行模拟,以与近期实际值或典型样本相差最小的参数所对应的模型为准.     

Modeling hyperelastic behavior of rubber: A novel invariant‐based and a review of constitutive models

A constitutive phenomenological model completing the Gent‐Thomas concept is carried out to formulate laws governing the hyperelastic behavior of incompressible rubber materials. It is shown that the phenomenological Gent‐Thomas model (1958) and the constrained chain model (1992) give similar precise results at small to moderate deformation. On the other hand, comparisons of the outcome of the proposed model with that of the molecular model from the combined concepts of Flory‐Erman and Boyce‐Arruda (2000), and with those of the phenomenological models of Ogden (1982), Yeoh‐Fleming (1997), Pucci‐Saccomandi (2002) and Beda (2005) are made. Residual inconveniences raised by attractive continuum models in rubber elasticity literature have been successfully overcome. Results from both the statistical and phenomenological mechanics concepts are compared with the data of some useful classical materials (rubbers of Treloar, Rivlin‐Saunders, Pak‐Flory and Yeoh‐Fleming). The results permit one to see salient equivalence of the two theories for a more reliable prediction of stress‐stretch response for all states of any mode of deformation. A complete and exhaustive analysis of the Mooney plot that combines small and very large extension‐compression has been quite essential in assessing the validity of models. A method of identification of material parameters is presented and data of the simple tension suffice for the determination of the parameter values. It is shown that the ordinary identification procedures, such as the usual least squares, a very much used numerical method in materials investigation, can be unsuitable in some cases of hyperelastic modeling. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1713–1732, 2007     

Speed of adaptation in structured populations

Adaptation of populations takes place with the occurrence and subsequent fixation of mutations that confer some selective advantage to the individuals which acquire it. For this reason, the study of the process of fixation of advantageous mutations has a long history in the population genetics literature. Particularly, the previous investigations aimed to find out the main evolutionary forces affecting the strength of natural selection in the populations. In the current work, we investigate the dynamics of fixation of beneficial mutations in a subdivided population. The subpopulations (demes) can exchange migrants among their neighbors, in a migration network which is assumed to have either a random graph or a scale-free topology. We have observed that the migration rate drastically affects the dynamics of mutation fixation, despite of the fact that the probability of fixation is invariant on the migration rate, accordingly to Maruyama's conjecture. In addition, we have noticed a topological dependence of the adaptive evolution of the population when clonal interference becomes effective.     

Modeling of RF plasma torch with a metallic tube inserted for reactant injection

Flow, temperature, and electromagnetic (EM) fields in a radio-frequency thermal plasma torch designed for the preparation of superconducting powders or films have been analysed by using a new two-dimensional modeling approach with the electric field intensity as the fundamental EM field variable. The insertion of a stainless steel injection tube into the torch leads to large induction currents in this tube. Although such large induction currents cause pronounced changes of the EM fields near the injection tube, flow and temperature fields are little affected. There exists only one large toroidal vortex in the upper part of the present torch, while the maximum temperature appears at an off-axis location within the coil region.     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

Quantitative theory of living free‐radical polymerization. III. Calculation of copolymerization products' spinodal

The problem of finding conditions of the loss of thermodynamic stability by the reaction system was solved on the basis of the developed theory of living free‐radical copolymerization. The spinodal's calculations were carried out for a significant number of systems differing in the values of kinetic, stoichiometric, and thermodynamic parameters. Analysis of the results of such calculations revealed some regularities in the spinodal curves' behavior and permitted us to classify their possible topological types. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 892–902, 2003