An implicit enthalpy scheme for one-phase Stefan problems

A compact finite-difference scheme to solve one-phase Stefan problems in one dimension is described. Numerical experiments indicate that the moving interface is obtained withO(t) accuracy when 3–4 iterations per time step are used to solve the nonlinear implicit scheme. The scheme can be adapted to ADI methods in higher dimensions.     

Differential Evolution Algorithm Based Self-adaptive Control Strategy for Fed-batch Cultivation of Yeast

In the fed-batch cultivation of Saccharomyces cerevisiae, excessive glucose addition leads to increased ethanol accumulation, which will reduce the efficiency of glucose utilization and inhibit product synthesis. Insufficient glucose addition limits cell growth. To properly regulate glucose feed, a different evolution algorithm based on self-adaptive control strategy was proposed, consisting of three modules (PID, system identification and parameter optimization). Performance of the proposed and conventional PID controllers was validated and compared in simulated and experimental cultivations. In the simulation, cultivation with the self-adaptive control strategy had a more stable glucose feed rate and concentration, more stable ethanol concentration around the set-point (1.0 g•L^-1), and final biomass concentration of 34.5 g-DCW•L^-1, 29.2% higher than that with a conventional PID control strategy. In the experiment, the cultivation with the self-adaptive control strategy also had more stable glucose and ethanol concentrations, as well as a final biomass concentration that was 37.4% higher than that using the conventional strategy.     

Discretized LKF method for stability of coupled differential‐difference equations with multiple discrete and distributed delays

Time‐delay systems described by coupled differential‐functional equations include as special cases many types of time‐delay systems and coupled differential‐difference systems with time delays. This article discusses the discretized Lyapunov–Krasovskii functional (LKF) method for the stability problem of coupled differential‐difference equations with multiple discrete and distributed delays. Through independently dividing every delay region that the plane regions consists in two delays to discretize LKF, the exponential stability conditions for coupled systems with multiple discrete and distributed delays are established based on a linear matrix inequality (LMI). The numerical examples show that the analysis limit of delay bound in which the systems are stable may be approached by our result. Copyright © 2011 John Wiley & Sons, Ltd.     

A new model of job design: Initial evidence and implications for future research

Clegg and Spencer's (2007) model of job design synthesizes and extends recent conceptions of the job design process by incorporating variables such as knowledge, motivation, and trust into a cyclical and dynamic system. The objective of this study was to examine the sequential organization of variables that comprise the model, as a basis from which to justify further investigations of the model's dynamic properties. Data were collected via questionnaires from 432 participants in two work organizations. Results obtained from structural equation modeling are broadly supportive of the proposed relationships between the variables. Implications of this initial study for future research and practice are discussed. © 2011 Wiley Periodicals, Inc.     

Stability of Impulsive Stochastic Neutral Partial Differential Equations With Infinite Delays

In this paper, we study the existence and asymptotic stability in the pth moment of the mild solutions to impulsive stochastic neutral partial differential equations with infinite delays. Sufficient conditions ensuring the stability of the impulsive stochastic system are established. The results are obtained via the Banach fixed point theorem.     

DTA measurements of normal-incommensurate phase transition in (NH4)2ZnCl4 and K2ZnCl4 crystals

Differential thermal analysis (DTA) was applied to determine the changes in enthalpy and entropy of (NH₄)₂ZnCl₄ and K₂ZnCl₄ crystals at their phase transition from the orthorhombic normal phase to the incommensurate phase. The temperature of this transition, T _i , is 406 K for (NH₄)₂ZnCl₄ and 555 K for K₂ZnCl₄ and the entropy changes (S/R) are 0.053 and 0.035, respectively. The low value obtained for S/R is characteristic of incommensurate phase transitions. The results were compared with the data reported for other crystals of the A₂BX₄ family. Thermal properties of the crystals of the A₂ZnCl₄ subgroup were found to the correlated with the length of A-Cl bonds.     

Equations of state for hard-sphere fluids

Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus— Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficient() is, in general, a function of the volume fraction. In mixtures the coefficient( _i ,d _i ), in general, depends upon the volume fraction _i , and diameterd _i , of each species,i andj. For the contact valuesY _ij of the rdf's, the mixing coefficients _ij ( _k ) also depend on speciesi andj. Density expansions for the exact for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in our own work, as well as with simulations. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expressions forY _ij unless one allows _ij to depend on mole fractionsx _i even at the zeroth order of its density expansion. We also find that _ij must depend on particle speciesi andj in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits we have considered is suggested.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Probability densities for conditional statistics in the cubic sensor problem

This paper applies the techniques of Malliavin’s stochastic calculus of variations to Zakai’s equation for the one-dimensional cubic sensor problem in order to study the existence of densities of conditional statistics. Let {X _t} be a Brownian motion observed by a cubic sensor corrupted by white noise, and let denote the unnormalized conditional estimate of φ(X _i ). If φ₁,...,φ _n are linearly independent, and if , it is shown that the probability distribution of admits a density with respect to Lebesgue measure for anyn. This implies that, at any fixed time, the unnormalized conditional density cannot be characterized by a finite set of sufficient statistics. Research supported in part by NSF Grant No. MCS-8301880 and by the Institute for Mathematics and It Applications, Minneapolis, Minnesota.     

Two new characteristic parameters for runoff computation

A method capable of estimating the hydrograph from a prescribed storm for a practical mild slope upstream catchment is proposed. This method makes use of two new characteristic parameters, andS, in conjunction with the kinematic wave equation to compute lateral inflows of the main stream of the catchment. The depth profile of overland flow at any instant within the catchment and hydrograph at any location can be easily found. Lag times for individual lateral inflows are then considered and are linearly combined to obtain the hydrograph at the outlet of the catchment or depth profile of the main stream at any instant. The validity of the excess rainfall-surface runoff linear relationship in this study has also been verified with Tatsunokuchiyama catchment, and it shows good results for this computed runoff.     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。