First Integrals of Shear-Free Fluids and Complexity

A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function f(x). We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.     

High‐pressure rheology of polystyrene melts plasticized with CO2: Experimental measurement and predictive scaling relationships

A high‐pressure extrusion slit die rheometer was constructed to measure the viscosity of polymer melts plasticized by liquid and supercritical CO₂. A novel gas injection system was devised to accurately meter the follow of CO₂ into the extruder barrel. Measurements of pressure drop, within the die, confirm the presence of a one‐phase mixture and a fully developed flow during viscosity measurements. Experimental measurements of viscosity as a function of shear rate, pressure, temperature, and CO₂ concentration were conducted for three commercial polystyrene melts. The CO₂ was shown to be an effective plasticizer for polystyrene, lowering the viscosity of the polymer melt by as much as 80%, depending of the process conditions and CO₂ concentration. Existing theories for viscoelastic scaling of polymer melts and the prediction of T_g depression by a diluent were used to develop a free volume model for predicting the effects of CO₂ concentration and pressure on polymer melt rheology. The free volume model, dependent only on material parameters of the polymer melt and pure CO₂, was shown to accurately collapse the experimental data onto a single master curve independent of pressure and CO₂ concentration for each of the three polystyrene samples. This model constitutes a simple predictive set of equations to quantify the effects of gas‐induced plasticization on molten polymer systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3168–3180, 2000     

Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes

The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.     

二元混合工质的氧化分解机理研究

基于量子化学密度泛函理论对低全球变暖潜值工质R152a与R600a进行了氧化分解机理研究. 通过对它们的主要起始反应路径分析及能量变化情况计算,结果表明：R152a与R600a热分解的起始反应可以分为工质自身热分解和与氧气碰撞分解两类,其中工质自身热分解的反应能垒比工质与氧气反应的能垒高,并且R600a比R152a更容易发生氧化分解;在二者混合后的起始反应阶段,R600a更容易先发生分解,而链式反应中R152a与自由基的反应更占优势;两种工质与自由基的反应大部分为放热反应,可以向反应体系提供热量,促进链式反应的进行. 相关结果可为新型混合工质的氧化分解机理研究提供参考.     

相同模式内弧立波的强斜相互作用*

水文讨论分层流体中相同模式向孤立波的强斜相互作用,包括浅流体情形和深流体情形．采用Lazrange描述方法,发现在浅流体情形相互作用由KP方程描述;在深流体情形相互作用由二维的中等长波方程描述;在无限深情形相互作用由二维的BO方程描述．     

浸透限制固定相及其应用

讨论了浸透限制固定相的特性及其在药物分析中的应用。已发展起来的浸透限制固定相主要用于高效液相色谱法对生物体液中药物的直接进样分析。这种固定相填料是在疏水层上覆盖了一层亲水层,而亲水层允许小分子物质如药物自由出入于固定相的疏水部分,从而立体地阻止了大分子物质如蛋白质与固定相的疏水部分相互作用,使小分子物质得到分离。     

光纤智能化复合材料及其监控系统的研究

本文简要评述了一种新型功能材料——电流变体,和由它制造的超先进智能复合材料及其应用原理和前景。着重介绍了埋有光导纤维的复合材料——“敏感的皮肤”及纤维光学检测系统的原理、可行性及应用。提出了将光导纤维埋入含电流变体的超先进复合材料中而形成光纤智能化复合材料,并简述由其制成的监测系统的研究现状和展望。      

Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.     

Nonlinear dynamics of hydrostatic internal gravity waves

Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden–Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are important in designing the numerical scheme. A numerical method is designed with simplicity and minimal computational cost as the main design principles. Numerical tests demonstrate that no catastrophic effects are introduced when hyperbolicity is lost, and the scheme can represent propagating discontinuities without introducing spurious oscillations.