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     

Bohr-Mottelson转动谱公式参数之间的新关系式

在利用Harris两参数公式研究Bohr-Mottelson转动谱公式参数之间的关系的基础上,改用Harris三参数公式,并由此提出了Bohr-Mottelson转动谱公式参数之间的新关系式,进而用I(I+1)四参数展开式计算了A～60,80,130,140,150,190区超形变偶偶核的基带和锕系和稀土区正常形变核基带,讨论了参数之间的关系,发现新关系式与实验较好地符合.     

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     

A computational study into the reactivity of epichlorohydrin and epibromohydrin under basic conditions in the gas phase and solution

Ab initio molecular orbital calculations were carried out on epibromohydrin (EBH) and epichlorohydrin (ECH) in an attempt to elucidate their reactivity with respect to a hard nucleophile, hydroxide. These systems were modeled in both the gas phase and a polar solvent under basic conditions. In the gas phase, it was determined that a direct displacement mechanism (nucleophilic attack at the C1 position) was operative for EBH, while an indirect pathway (nucleophilic attack at the C3 position and subsequent intramolecular displacement) was followed for ECH. In an acetone solution, only the indirect displacement mechanism was found to occur. An electrostatic argument is advanced to account for this behavior in polar solution. Copyright © 2007 John Wiley & Sons, Ltd.     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

对期望理论的两个重要推进——损失厌恶系数λ及参考点研究

行为金融学是近20年来最为重要的新兴金融理论,期望理论更是其中的亮点,其运用领域之广超乎人们的想象,所以对它的完善改进具有非常重要的意义。本文对期望理论中的损失厌恶系数和参考点问题进行了深入研究,并且得出了创新性的结果:损失厌恶系数不是常数而是动态变量;得出了内生且纳入更多投资者行为特征的参考点。这些结果是对期望理论的重要改善和推进,对其在大量金融领域和涉及到财富偏好的问题的解决中都大有裨益。     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007