Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Free energy and confinement force of macromolecules in a slit at full equilibrium with a bulk solution

Nondilute athermal and theta solutions of nonadsorbing flexible macromolecules in equilibrium with repulsive slit-like pores were examined by the lattice Monte Carlo simulations. The free energy of confinement ΔA/kT and the force f/kT exerted by polymers on the slit were computed as a function of the slit width D in a wide range of bulk concentrations φ. The free energy and force profiles in nondilute solutions were found to deviate considerably from the ideal chain theory; the perturbation of chains by a presence of the slit walls were substantially reduced in nondilute solutions. The free energy and force functions appropriate for nondilute solutions were derived by fitting the simulation data. Further, the relative pressure p_I/p_E exerted by the nonadsorbing confined molecules on the slit walls was calculated. The depletion effect relevant to colloid stabilization was found in dilute solutions to be slightly weaker for excluded-volume chains than for ideal chains. The relative pressure equation was modified to cover semidilute solutions, by using the mean-field and scaling expressions of the osmotic pressure. Both the relative pressure p_I/p_E and the intra-slit concentration profiles φ_I(x) in tandem display a suppression of the depletion effect with increasing φ in simidilute solutions.     

Works of adhesion at the carbon fiber-liquid interface determined using a modified wetting technique

Works of adhesion W_SL between aqueous solutions with pH values in the range from 1 to 14 and carbon fibers from different sources, which were additionally treated in an inert atmosphere or in oxygen, were measured by use of a microbalance. These works of adhesion W_SL were found to show distinct stepwise dependencies on the pH value. The works of adhesion W_SL are attributed to dispersion interactions W_SL¹ and various acid-base interactions w_sl^ab—in the latter case between the acidic and basic surface groups of carbon and the various basic and acidic aqueous solutions.     

离心泵叶片边界层方程的解析解

给出了离心泵叶片表面的边界层动量积分方程的解的构造及其计算方法，并以计算实例说明了该解的唯一性和算法的稳定性、收敛性。它是分析离心泵流体在叶片表面边界层参数的基础。     

Growth and morphology of nanometer LiMn2O4 powder

The growth of Li_1+xMn₂O₄ via detonation reaction was investigated with respect to the presence of an energetic precursor, such as the metallic nitrate and the degree of confinement of the explosive charge. The detonation products were characterized by scanning electron microscopy. Powder X-ray diffraction and transmission electron microscopy were used to characterize the products. Li_1+xMn₂O₄ with 1-2 μm spherical morphology and more uniform secondary particles, but with smaller primary particles of diameters from 20 to 60 nm and a variety of morphologies were found. The oxides produced by this cheap method affirmed the validity of detonation synthesis of nano-size powders.     

Nonpathological Lyapunov functions and discontinuous Carathéodory systems

Differential equations with discontinuous right-hand side and solutions intended in Carathéodory sense are considered. For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.     

A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism

The Landau-Lifshitz (LL)equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions,are addressed. Author is supported by the Fund for Scientific Research - Flanders FWO (Belgium).     

神华乌海能源公司安全监控系统联网建设解读

神华乌海能源公司(以下简称"公司")在安全监控联网系统的开发过程中,针对可能出现的各种问题,提出了综合性的联网解决方案。同时又通过强有力的管理手段,保障了系统的稳定可靠运行,使系统达到了预期的应用效果,提升了公司的安全管理水平。     

Thermal conductivity of a dendritic ice layer

Measurements of the thermal conductivities of the frozen layer of aqueous binary solutions have been performed using the transient hot-wire method. Solutions of ethylene glycol and sodium chloride were utilized as the testing fluids, and they were frozen up in the test section in which the platinum wires 40 m in diameter and 170 mm in length were strung. Measurements were carried out under equilibrium at a variety of both the initial concentration of the solution and the temperature of the frozen layer. The expressions of the thermal conductivity of the frozen layer were determined. It was found that the thermal conductivity of the dendritic ice layer was favorably assessed with the Lichteneker's model by introducing the solid fraction under an assumption of the equililbrium within the range of parameters examined.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Transport properties of critical dilute solutions

On the basis of the isomorphism of critical phenomena, the behavior of transport properties of binary mixtures in the vicinity of the vapor-liquid critical line is considered. In particular, the renormalization of the singularity of the thermal conductivity in dilute critical solutions has been analyzed in detail. It is shown that the behavior of the thermal conductivity is determined by the critical background, i.e., the fluctuation-induced regular part, which diverges at the critical point of a solvent.