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.     

Vapor-liquid equilibrium and volumetric properties calculations for solutions in the supercritical carbon dioxide

The calculations of gas solubilities in supercritical solvents require equations of state remaining accurate in the critical range, which are difficult to obtain with classical models. In this work, the Helmholtz energy of a mixture is considered as the sum of the Helmholtz energies of pure components taken at a constant packing fraction and of a residual term which may have the form of a RedlichKister, Van Laar, NRTL, UNIQUAC, or UNIFAC function. Thus it is possible to assign to a given component an equation of state whose form is different from that of the others. This model has been applied to binary systems containing supercritical carbon dioxide. The results are improved with respect to those obtained with the classical model for vapor-liquid equilibria and for volumetric properties.     

Pulsed field gradient n.m.r. measurements and theoretical interpretation of the self-diffusion of polystyrene in solution

The self-diffusion coefficients of polystyrene dissolved in C₆D₆ were measured by means of pulsed field gradient n.m.r.. The dependence on the molecular weight was of the power of -2 in accordance with the reptation model. The concentration dependence was theoretically calculated within the blob concept which shows that in the crossover region the self-diffusion coefficient is determined only by the blob dimensions and the monomeric friction coefficient is constant. The calculated concentration dependence agrees well with that observed by the authors.     

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.     

An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.     

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.     

Oxidation of oleuropein studied by EPR and spectrophotometry

The autoxidation at alkaline pH and enzymatic oxidation by mushroom tyrosinase of oleuropein, the dominant biophenol present in the fruits and leaves of Olea europea, was followed by both electron paramagnetic resonance (EPR) and absorption spectroscopy. For comparison, the same oxidation processes were applied to 4‐methylcatechol, a simple polyphenol present in olive mill wastewaters. EPR spectra of stable o‐semiquinone radicals produced during autoxidation at pH 12 and short‐lived o‐semiquinone free radicals produced during autoxidation at pH 9.0 or tyrosinase action and stabilized by chelation with a diamagnetic metal ion (Mg²⁺) were recorded for both polyphenols, and the corresponding hyperfine splitting constants were determined. The UV‐Vis spectral characteristics of the oxidation of polyphenols were highly dependent on the type of polyphenol, oxidant type and the pH of the reaction. The kinetic behavior of tyrosinase in the presence of oleuropein and 4‐methylcatechol was followed by recording spectral changes at 400 nm (absorption maximum) over time. The tysosinase activity with oleuropein showed a pronounced pH optimum at pH 6.5 and a minor one around pH 8. From the data analysis of the initial rate at pH 6.5, the kinetic parameters K_m = 0.34 ± 0.03 mM and V_max = 0.029 ± 0.002 ΔA₄₀₀ min^–1 were determined for oleuropein.