Effects of Polymer Bridging and Electrostatics on the Rheological Behavior of Aqueous Colloidal Dispersions†

Effects of a low molecular weight physically adsorbed polyethylene oxide (PEO) and the range of the electrostatic repulsion on the rheological behavior of silica dispersions (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing the polymer concentration in the system and also effectiveness of the polymer as a dispersant under extreme conditions (high ionic strength). Results indicate that at small separation distances and low polymer coverage, the polymer chains are long enough to adsorb on the surface of two particles simultaneously causing bridging flocculation in the system and hence increasing the viscosity and linear viscoelastic functions of the dispersion. A significant increase was observed in the viscosity of the dispersion at salt concentrations high enough to eliminate electrostatics between the particles. Under these conditions,the viscosity of the system increased significantly when PEO was added to the dispersion showing that at high electrolyte concentrations, a neutral polymer such as PEO is not able to stabilize the system.     

Dynamics of Single-Pulse Echo Signals under the Conditions of Zeeman Switching

The signals of a single-pulse echo (SE) generated on nonresonant excitation of an inhomogeneously broadened two-level system by a radio-frequency pulse (RFP), against the background of which a magnetic video pulse (MVP) of certain length has been switched on, have been described analytically. It is established that under the conditions of such excitation several SE signals are formed whose generation moments are determined by the duration and amplitudes of the RFP and MVP. The amplitudes of some of these signals depend on the Rabi frequency according to a quadratic law, and the amplitudes of others depend on this frequency according to a biquadratic law. It has been established that the mechanism underlying the appearance of these signals is associated with zero beats arising as a result of superposition of the magnetization fluctuations at variable frequencies and at a frequency of detuning from resonance. It is shown that in the limiting case, where the RFP duration considerably exceeds the duration of the MVP or is comparable with it, the number of SE signals decreases to two. Theoretical results on the formation of SE and the dependence of the amplitude of these signals on the MVP amplitude agree with the experimental data on NMR pulsed signals in ferromagnetic materials.     

高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

集中荷载下叠合梁抗剪强度

本文对低叠合面钢筋破简支在合梁二阶段受力的斜截面抗剪性能进行了试验研究，并运用非线性有限元分析和试验实测数据，得出了一个适合于集中荷载下高低叠合面叠合梁的抗剪强度计算公式．     

Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.     

A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

Separation of screw-sensed particles in a homogeneous shear field

The Stokes motions of three-dimensional screw-sensed slender particles in a homogeneous shear field are investigated, including the effects of buoyancy. Conclusions are drawn about the possibility of achieving a separation of mixtures of right- and left-handed particles. The linearity of the Stokes equations allows complex flows to be solved by adding the effects of the several terms which describe the flow in which the particle is immersed. The homogeneous shear flow considered here consists of three such terms; solutions for a series of 12 unit motions are sufficient to determine the hydrodynamic resistance tensors. The forces and torques experienced by screw-sensed particles are calculated from these 51 resistance tensors, using slender-filament theory. The results allow an estimate of the range of buoyancy parameters for which gravitational sedimentation can be neglected. The fundamental component of the particle motion is a rotation, at approximately the same angular velocity as that of the fluid. Superimposed on this are variations, of large period, in the particle orientation. A phase plane analysis is used to find the terminal orientations. Very long calculation times are required for the phase portrait. An approximate method based on azimuthally-averaged equations is developed to avoid the requirements for long time integration.     

An algorithm for decomposing a polynomial system into normal ascending sets

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.     

ℙmax variations related to slaloms

We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π₂-statements in the structure 〈H (ω ₂), ∈, NS_{ω 1}, R 〉 for some set R of reals in L (ℝ), for the following statements: (1) The cofinality of the null ideal is ℵ₁. (2) There exists a good basis of the strong measure zero ideal. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.