A new wavelet-based adaptive method for solving population balance equations

A new wavelet-based adaptive framework for solving population balance equations (PBEs) is proposed in this work. The technique is general, powerful and efficient without the need for prior assumptions about the characteristics of the processes. Because there are steeply varying number densities across a size range, a new strategy is developed to select the optimal order of resolution and the collocation points based on an interpolating wavelet transform (IWT). The proposed technique has been tested for size-independent agglomeration, agglomeration with a linear summation kernel and agglomeration with a nonlinear kernel. In all cases, the predicted and analytical particle size distributions (PSDs) are in excellent agreement. Further work on the solution of the general population balance equations with nucleation, growth and agglomeration and the solution of steady-state population balance equations will be presented in this framework. (C) 2002 Elsevier Science B.V. All rights reserved.

Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Self-assembly of a charge-neutral molecular square

Complexation of cadmium(II) by the ditopic (bis-tridentate) thiocarbazone ligand 1,5-bis(6-methyl-2-pyridylmethylene) thiocarbonohydrazide, H2L1, results in the self-assembly of a charge-neutral 2 x 2 molecular grid, [Cd-4(L-1)(4)], comprising four metals and four ligands in an interlocked cyclic array. The solid-state structure of this tetramer has been established by X-ray crystallography and in solution by H-1 NMR spectroscopy. The presence of lower molecular weight oligomers was identified by both NMR and ESI-MS.

Existence of solutions to some equilibrium problems

The concept of a monotone family of functions, which need not be countable, and the solution of an equilibrium problem associated with the family are introduced. A fixed-point theorem is applied to prove the existence of solutions to the problem.

Kierkegaard as a paradoxical therapist

The essential problem that Soren Kierkegaard is concerned with in his authorship is that of becoming a Christian. It is argued that Kierkegaard's authorial strategy reflects the principles of paradoxical psychotherapy. These principles indicate that both the psychological problem and its solution involve an ironic process. In the Kierkegaardian frame of reference, the situation of the immature self is paradoxical, and so is the pathway to full selfhood. The philistine and the aesthete attempt to secure autonomy and personal freedom through an external orientation. But the way to the self is inwards. Consequently, these personalities get caught in an ironic process. The further they push outwards, the further they move away from the locus of genuine selfhood and freedom. This immature form of life can only lead to a loss of self and the associated experience of despair. Paradoxically, Kierkegaard advocates the choice of despair as the way to find oneself in God.

An evaluation of different models of water recovery in flotation

Water recovery is one of the key parameters in flotation modelling for the purposes of plant design and process control, as it determines the circulating flow and residence time in the individual process units in the plant and has a significant effect on entrainment and froth recovery. This paper reviews some of the water recovery models available in the literature, including both empirical and fundamental models. The selected models are tested using the data obtained from the experimental work conducted in an Outokumpu 3 m(3) tank cell at the Xstrata Mt Isa copper concentrator. It is found that all the models fit the experimental data reasonably well for a given flotation system. However, the empirical models are either unable to distinguish the effect of different cell operating conditions or required to determine the empirical model parameters to be derived in an existing flotation system. The model developed by [Neethling, SJ., Lee, H.T., Cilliers, J.J., 2003, Simple relationships for predicting the recovery of liquid from flowing foams and froths. Minerals Engineering 16, 1123-1130] is based on fundamental understanding of the froth structure and transfer of the water in the froth. It describes the water recovery as a function of the cell operating conditions and the froth properties which can all be determined on-line. Hence, the fundamental model can be used for process control purposes in practice. By incorporating additional models to relate the air recovery and surface bubble size directly to the cell operating conditions, the fundamental model can also be used for prediction purposes. (C) 2005 Elsevier Ltd. All rights reserved.

Factor analysis of the self-report Dysexecutive (DEX-S) Questionnaire

The self-rating Dysexecutive Questionnaire (DEX-S) is a recently developed standardized self-report measure of behavioral difficulties associated with executive functioning such as impulsivity, inhibition, control, monitoring, and planning. Few studies have examined its construct validity, particularly for its potential wider use across a variety of clinical and nonclinical populations. This study examines the factor structure of the DEX-S questionnaire using a sample of nonclinical (N = 293) and clinical (N = 49) participants. A series of factor analyses were evaluated to determine the best factor solution for this scale. This was found to be a 4-factor solution with factors best described as inhibition, intention, social regulation, and abstract problem solving. The first 2 factors replicate factors from the 5-factor solutions found in previous studies that examined specific subpopulations. Although further research is needed to evaluate the factor structure within a range of subpopulations, this study supports the view that the DEX has the factor structure sufficient for its use in a wider context than only with neurological or head-injured patients. Overall, a 4-factor solution is recommended as the most stable and parsimonious solution in the wider context.

A comparison of different choices for the regularization parameter in inverse electrocardiography models

Calculating the potentials on the heart’s epicardial surface from the body surface potentials constitutes one form of inverse problems in electrocardiography (ECG). Since these problems are ill-posed, one approach is to use zero-order Tikhonov regularization, where the squared norms of both the residual and the solution are minimized, with a relative weight determined by the regularization parameter. In this paper, we used three different methods to choose the regularization parameter in the inverse solutions of ECG. The three methods include the L-curve, the generalized cross validation (GCV) and the discrepancy principle (DP). Among them, the GCV method has received less attention in solutions to ECG inverse problems than the other methods. Since the DP approach needs knowledge of norm of noises, we used a model function to estimate the noise. The performance of various methods was compared using a concentric sphere model and a real geometry heart-torso model with a distribution of current dipoles placed inside the heart model as the source. Gaussian measurement noises were added to the body surface potentials. The results show that the three methods all produce good inverse solutions with little noise; but, as the noise increases, the DP approach produces better results than the L-curve and GCV methods, particularly in the real geometry model. Both the GCV and L-curve methods perform well in low to medium noise situations.