Numerical finite difference model for steady state cellular array growth

An improved finite difference analysis has been used to calculate self-consistent axisymmetric cellular shapes. The results obtained are compared with the analytical models which have been proposed to describe array growth. It is concluded that the analytical models should be used with extreme caution in the cellular region. A preliminary examination of the stability of the steady state shapes has been made numerically. The results are compared with experiment where it is found that neither the minimum undercooling condition nor marginal stability analysis as applied, correctly predicts the growth conditions. The model includes solute diffusion in the solid so that the extent of microsegregation is fully described for the first time.     

Application of the finite difference method for refining the model of the wear of work rolls in a broad-strip mill

A procedure is proposed to calculate the metal slip path and the friction work in the roll-strip contact. This procedure can predict the wear of the work rolls in continuous broad-strip mills and uses the finite difference method.     

A new finite element model for welding heat sources

A mathematical model for weld heat sources based on a Gaussian distribution of power density in space is presented. In particular a double ellipsoidal geometry is proposed so that the size and shape of the heat source can be easily changed to model both the shallow penetration arc welding processes and the deeper penetration laser and electron beam processes. In addition, it has the versatility and flexibility to handle non-axisymmetric cases such as strip electrodes or dissimilar metal joining. Previous models assumed circular or spherical symmetry. The computations are performed with ASGARD, a nonlinear transient finite element (FEM) heat flow program developed for the thermal stress analysis of welds.* Computed temperature distributions for submerged arc welds in thick workpieces are compared to the measured values reported by Christensen¹ and the FEM calculated values (surface heat source model) of Krutz and Segerlind.² In addition the computed thermal history of deep penetration electron beam welds are compared to measured values reported by Chong.³ The agreement between the computed and measured values is shown to be excellent.     

A mathematical model for analysis of pharmacologically induced changes in the kinetics of cardiac muscle

A mathematical model of the isometric contraction of cardiac muscle is developed and utilized to characterize the inotropic and lusitropic effects of cardioactive compounds in isolated guinea pig left atria. In contrast to metrics that are based on minima and maxima of an isometric twitch and its derivative function, the entire time course of the twitch is used to quantify the kinetics of the contraction-relaxation cycle. The model relates observed tension to a time-dependent activation function that describes generation of internal force and a coupling function that determines mechanical response to the activation function. The model is structured so that it is suitable for nonlinear curve fitting to observed data. Results obtained using the model for fitting experimental data from tissues treated with different classes of cardioactive compounds agree with more qualitative results presented by other authors. Experiments using the model to fit data over an extended (90 min) time course revealed differences in the kinetic profiles of milrinone and forskolin. Computer simulations that demonstrate the effect of each model parameter on twitch kinetics are presented, and the relationships between the model and other theoretical and empirical models of cardiac muscle are discussed. The mathematical model is useful to enable a more quantitative understanding of the kinetics of cardiac muscle contraction and relaxation and identify compounds that may be selective for inotropic or lusitropic effects.     

Stability of finite difference deconvolution II: simulation studies

Theoretical analysis of the stability of finite difference deconvolution (FDD) indicates that if the cumulative amount function is used to characterize the drug input the method is stable for any sampling schedule for an intravenous unit impulse response function. The analysis also indicates that the method is stable for an oral unit impulse response only for well designed sampling schedules. This article confirms these results through numerical simulation experiments. It is shown that the assumption that the unit impulse response is error-free has an influence on the performance of FDD which is generally of no practical significance, except possibly for the first few points estimated. It is also shown that there is no significant interaction between the statistical error due to data noise and the deterministic algorithm error. The major source of error in practice is likely to be the data noise in the input response function. The simulations confirm that, with the estimated cumulative amount function as the quantity estimated and, with a well designed sampling schedule for the case of an oral unit impulse response, FDD is in practice an accurate and stable method with acceptable precision under a typical error disturbance.     

有限差分改进算法及温度场求解实例验证

针对温度场实时仿真中，当节点数目众多，节点温度精度要求较高时求解速度缓慢的问题，本文在传统有限差分离散方程组的基础上，采用局部代数消元策略，导出了二维坐标下无步长条件△x=△y限制的13点差分改进算法。铜闪速炉反应塔炉壁温度场仿真实例表明，与传统5点差分算法相比，该算法具有收敛速度快、迭代次数少、求解速度显著提高的特点，为实时仿真系统中的温度场求解提供了一种新的快速求解算法。     

Two-dimensional finite difference analysis of shape instabilities in plates

A two-dimensional finite difference analysis is applied to surface diffusion-controlled instabilities of plates. Plates can evolve into “cylinders,” or if the plates have longitudinal internal boundaries, they may split into two segments. The evolution process of plates containing internal boundaries into equilibrium shapes depends on both the initial plate aspect ratio (plate width to thickness) and the ratio of the internal boundary energy to the plate-matrix interface energy. When the internal boundary energy is relatively low or the initial plate aspect ratio is relatively small, the transverse equilibrium cross-sectional area shape is composed of two circular segments, with an appropriate dihedral angle dictated by the ratio of the interface energy terms. As either the internal boundary energy or the initial aspect ratio increases, plate splitting, rather than cylinderization, becomes the dominant instability mode. The results of this work are compared to a recent theory of Courtney and Malzahn Kampe (CMK) on shape instability diagrams.^[1] The complicated interactive effects between cylinderization and boundary splitting were not considered in the analytical CMK approach; thus, when they are minimal, the results of this finite difference calculation are in reasonable accord with the CMK results, as far as predicting instability times are concerned. However, when the interaction is significant, cylinderization and/or splitting times are markedly changed. The present accurate calculations allow refinement of the CMK plate instability diagrams.     

The Orwellian difference model.

Comments on the assertion by E. Zigler and W. Berman (see record 1984-07983-001) that the deficit model has given way to the difference model in early childhood intervention. It is suggested that models in science are ordinarily abandoned when they no longer describe empirical observations and that such is not the case in light of the financial and sociocultural deficits experienced by many children. It is concluded that Blacks should spurn the difference model; developmental psychologists may have embraced it because it is a way of avoiding a difficult complex of problems. (1 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Developing a physically consistent model for gibbsite leaching kinetics

Leaching aluminium hydroxide from bauxite ores is the first step of the Bayer process which is widely used in the aluminium industry. This paper aims to develop a better understanding of the gibbsite leaching kinetics which can allow for subsequent process optimisation. Comparison of many conventional kinetic models developed for gibbsite leaching with experimental data showed poor agreement. Several new kinetic models have been developed and validated experimentally. The model equations were numerically integrated applying the fourth-order Runge-Kutta technique. Unknown model parameters were estimated by comparing numerical solutions with available experimental data using nonlinear regression analysis with the Levenberg-Marquardt algorithm. The new model for the gibbsite leaching controlled by diffusion through the surface ash/product layer did not compare well with the data. Taking into account the actual irregular surface morphology of the dissolving solids, the fractal geometry of this irregular surface was considered in the development of newer models. With the inclusion of the fractal dimension, the new models agreed better with the experimental data. Finally, the residual aluminium concentration remained in the solid phase after leaching was given consideration in the development of the new model which showed perfect agreement with the data. A physically consistent model for gibbsite leaching was thus obtained by considering these last two factors: fractal geometry of the shrinking gibbsite particles and residual aluminium concentration.