Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Bandpass filters using periodically loaded combline resonators

A novel combline filter is proposed for cellular‐radio base stations. The Q‐factor is significantly improved. The eigenvalue equation is expressed with the single‐team approximation in the gap region of the combline resonator. A two‐pole combline filter is designed. The calculation, simulation, and experiment results are presented and are in good agreement. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Theory of propagating deformation bands

A model for propagating deformation bands is developed, based on a mechanical equation of state and on evolution equations for the structure parameters. It is shown that, contrary to normal deformation, it is necessary to discriminate between global parameters which depend solely on time elapsed and local parameters which are functions of the strain history. Correspondingly, two sets of equations are presented, one describing the development of the global parameters in the course of time, the other giving the evolution of the local state parameters in the course of deformation, i.e. as a function of strain. Measurable quantities derived from the first set are the load serrations and the band velocity, while the second set yields the flow stress and the strain profile of the propagating band.     

热平衡流量计研究与应用

依据热平衡方法测流量原理研制的热平衡流量计没有任何可动部件，可靠性大大加强，可以代替常用的浮子流量计和涡轮流量计。该仪器的应用为油水井及注聚合物井的流量测试提供了更为有效的手段和方法。     

Salt-water up-coning during extraction of fresh water from a tropical island

Rainwater can collect in a lens-shaped region within the rock of a tropical island, and may be separated from the underlying salt water by a sharp interface. This paper presents a nonlinear theory for determining the shape of this interface. The island is assumed to be saturated with rain, and provision is made for the outflow of rain-water through the sides of the island. The effect of a bore well on the shape of the interface is investigated, and the problem is solved using a spectral method. An integral-equation method is also presented for the case when the island has infinite width.     

Comparative Study of Different Adaptive Window Protocols

We study an Adaptive Window Protocol (AWP) with general increase and decrease profiles in the presence of window dependent random losses. We derive a steady-state Kolmogorov equation, and then obtain its solution in analytic form for particular TCP versions proposed for high speed networks, such as Scalable TCP and HighSpeed TCP. We also relate window evolution under an AWP to workload process in queueing systems; this observation gives us a way to compare various AWP protocols.     

A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm

The estimation of the differences among groups in observational studies is frequently inaccurate owing to a bias caused by differences in the distributions of covariates. In order to estimate the average treatment effects when the treatment variable is binary, Rosenbaum and Rubin [1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41-55] proposed an adjustment method for pre-treatment variables using propensity scores. Imbens [2000. The role of the propensity score in estimating dose-response functions. Biometrika 87, 706-710] extended the propensity score methodology for estimation of average treatment effects with multivalued treatments.However, these studies focused only on estimating the marginal mean structure. In many substantive sciences such as the biological and social sciences, a general estimation method is required to deal with more complex analyses other than regression, such as testing group differences on latent variables. For latent variable models, the EM algorithm or the traditional Monte Carlo methods are necessary. However, in propensity score adjustment, these methods cannot be used because the full distribution is not specified.In this paper, we propose a quasi-Bayesian estimation method for general parametric models that integrate out the distributions of covariates using propensity scores. Although the proposed Bayes estimates are shown to be consistent, they can be calculated by existing Markov chain Monte Carlo methods such as Gibbs sampler. The proposed method is useful to estimate parameters in latent variable models, while the previous methods were unable to provide valid estimates for complex models such as latent variable models.We also illustrated the procedure using the data obtained from the US National Longitudinal Survey of Children and Youth (NLSY1979-2002) for estimating the effect of maternal smoking during pregnancy on the development of the child's cognitive functioning.     

Anti-Dissipative Schemes for Advection and Application to Hamilton–Jacobi–Bellmann Equations

We propose two new antidiffusive schemes for advection (or linear transport), one of them being a mixture of Roe’s Super-Bee scheme and of the “Ultra-Bee” scheme. We show how to apply these schemes to treat time-dependent first order Hamilton–Jacobi–Bellman equations with discontinuous initial data, possibly infinitely-valued. Numerical tests are proposed, in one and two space dimensions, in order to validate the methods AMS subject classifications. Primary 65M12, Secondary 58J47     

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.