Dynamics near Unstable,Interfacial Fluids

We study three examples of unstable interfacial fluid motions: vortex sheets with surface tension, Hele-Shaw flows with surface tension, and vortex patches. In all three cases, the nonlinear dynamics of a large class of smooth perturbations is proven to be characterized by the corresponding fastest linear growing mode(s) up to the time scale of , where is the magnitude of the initial perturbation. In all three cases, the analysis is based on an unified analytical framework that includes precise bounds on the growth of the linearized operator, given by an explicit solution formula, as well as a special sharp nonlinear energy growth estimate. Our main contribution is establishing this nonlinear energy growth estimate for each interface problem in certain high energy norms. Y. G. was supported in part by NSF grants DMS-0305161, INT-9815432 and a Salomon award of Brown University. D. S. was supported in part by NSF grant DMS-0510121.     

复杂流体的聚集态结构,性质及应用

综合报道了油－水、油－油分散体系中中各种聚集体，如胶团，微乳状液、凝胶、Ｌｉｅｓｅｇａｎｇｒｉｎｇ及分形图形等的形成机理，结构和特性，以及流体中聚集结构的形成在实际生产中的意义。     

Steady Nonintegrable High-Dimensional Fluids

We consider the existence of steady incompressible fluids (solutions to the Euler equations) on Riemannian manifolds of dimensions three and higher. We demonstrate that, as in the case of the ABC fields in dimension three, there exist chaotic Beltrami fields – nonsingular eigenfields of the curl operator – in higher dimensions. We give an explicit set of analytic examples on a non-Euclidean five-torus T ⁵. We also detail a plug construction for inserting chaotic vortices into a Beltrami field. These constructions employ contact-topological techniques.     

Fluids of clusters in attractive colloids

We show that colloidal particles with attractive interactions induced by a nonadsorbing polymer exhibit a stable phase consisting of a fluid of clusters of particles. This phase persists even in the absence of any long-range repulsion due to charge, contrary to expectations based on simulation and theory. Cluster morphology depends strongly on the range of the interparticle attraction: With a shorter range, clusters are tenuous and branched; with a longer range, they are more compact.     

磁流变体的制备及性能

对以羰基铁粉、硅油和烃类油为悬浮相和悬浮介质,通过适当添加剂和工艺制备的磁流变体材料,制备方法、磁流变性能及影响因素进行了研究,认为是具有良好综合性能的磁流变体材料。制备的磁流变体具有较低的零场粘度（0．4－1．5Pas),较高的剪切应力（τ=50-75kPa)和良好的稳定性及阻尼性能。     

基于链化分析的磁流变液剪切屈服应力模型

基于磁性颗粒在磁场作用下的链化分析和统计分析方法,建立了磁流变液的宏观屈服剪应力的分析模型.模型考虑了磁感应强度、颗粒尺寸、体积分数、剪应变率以及饱和磁化强度等因素,能描述不同剪切应变率下剪切应力的变化及在高应变率下可能出现的剪切稀化效应.分析了不同因素对剪切屈服应力的影响,讨论了提高磁流变液剪切屈服应力的途径.分析表明,该模型的计算结果能较好地描述有关实验现象,并可用于高性能磁流变液的设计分析.     

Fluids of pseudo-hard bodies II. Reference models for water,methanol, and ammonia

Pseudo-hard body fluids resulting from extended primitive models of water, methanol, and ammonia have been investigated both by computer simulations and theory for a number of geometrical parameters. It is shown that none of the existing equations of state and integral equations for the site-site correlation functions is able to describe the properties of the pseudohard body fluids reasonably accurately. For the equation of state an accurate semi-empirical method is proposed and for the site-site correlation functions the reference average Mayer function perturbation theory has been found to perform at least qualitatively correctly, which is not the case with Ornstein-Zernike equation based theories.     

Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

Post-Newtonian Expansions for Perfect Fluids

We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations that have a first post-Newtonian expansion. The results here are based on the elliptic-hyperbolic formulation of the Einstein-Euler equations used in [15], which contains a singular parameter , where v _T is a characteristic velocity associated with the fluid and c is the speed of light. As in [15], energy estimates on weighted Sobolev spaces are used to analyze the behavior of solutions to the Einstein-Euler equations in the limit , and to demonstrate the validity of the first post-Newtonian expansion as an approximation.     

Inhomogeneous and Radiating Composite Fluids

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems.     

Lattice Boltzmann Simulation of Shear-Thinning Fluids

It is shown how shear-thinning flow can be simulated without the need for numerical differentiation by following a lattice Boltzmann approach. The basic idea of is to combine the Cross model of viscosity with a 3D multiple relaxation time lattice Boltzmann method and to extract the required velocity derivatives from intrinsic quantities of the lattice Boltzmann scheme. Computational results are presented for a simple benchmark and for the simulation of liquid composite moulding.     

电流变液中的电导率问题

直汉电场中电导率的微小变化会影响电流变效应是一个显见的事实，但长期以来，在电流变机理的研究中却被忽略。文章介绍近年来电流变液中的电导率问题研究的若干重要进展，包括经典点偶极子模型在直流电场中的改进、负电流变效应和电流变液的电导模型。     

Fluids absorbed in structured pores

A model of fluids absorbed in a pore with walls patterned with parallel channels is used to demonstrate some of the unity that can be proved to hold between the statistical mechanics of fluids absorbed in structured pores and of fluids adsorbed at unstructured walls and at edges/wedges where walls meet. In particular, the work done to reversibly shear a corrugated pore immersed in liquid is related to the difference in the density profile structure of liquid adsorbed near the edges of the channels. When the channel dimensions are mesoscopic or macroscopic but the minimum pore width is microscopic, statistical mechanics generates remarkable links between the surface tension of planar wall-fluid interfaces or, more generally, the solvation free energy of a planar pore, and the density profile at the sides of a channel wall in the vicinity of edges and wedges.     

Thermal Fields as Causal Fluids

In a previous paper we investigated a divergence-type theory (DDT) describing the dissipative interaction between a field and a fluid. In this paper we compare the macroscopic view of DDT with a microscopic special case, an O(N) scalar field to leading order in the large N approximation and its thermal fluctuations. Our aim is to compare within a simple model the two approaches.     

Experimental Critical-Exponent Values for Fluids

After a review of the history and an assessment of the current status of the subject, we present light-scattering data to determine the critical correlation-function exponents for an aqueous electrolyte solution yielding the experimental values γ=1.238±0.012, ν=0.629±0.003, η=0.032±0.013. We conclude the paper with some comments concerning the temperature dependence of non-asymptotic effective critical-exponent values of fluids.     

Solution Generating with Perfect Fluids

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect-fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a seed solution of the Einstein-perfect-fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P = or (ii) a timelike Killing vector and equation of state + 3P = 0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions.     

One-Dimensional Fluids with Positive Potentials

We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the thermodynamic limit of the given model.     

Molecular Fluids at High Dimensionality

We extend the analysis of orientational first-order phase transitions in anisotropic molecular fluids at high spatial dimensionality to hard-disk fluids, and then to mixture of hard disks and hard spheres. The effect of hard-sphere admixture depends sensitively on the relative sizes of the two geometrical objects, and large spheres completely quench the disk transition. An introductory study is made of spatially ordered states.