An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

Freeform fabrication of aluminum metal-matrix composites

A series of metal-matrix composites were formed by extrusion freeform, fabrication of a sinterable aluminum alloy in combination with silicon carbide particles and whiskers, carbon fibers, alumina particles, and hollow flyash cenospheres. Silicon carbide particles were most successful in that the composites retained high density with up to 20 vol% of reinforcement and the strength approximately doubles over the strength of the metal matrix alone. Comparison with simple models suggests that this unexpectedly high degree of reinforcement can be attributed to the concentration of small silicon carbide particles around the larger metal powder. This fabrication method also allows composites to be formed with hollow spheres that cannot be formed by other powder or melt methods.

A practical method for identifying intermetallic phase particles in aluminium alloys by electron probe microanalysis

Aluminium alloys that contain Si, Mg, Fe, Mn and/or Cu usually contain one or more types of intermetallic phases that are not readily distinguishable in the microstructure by conventional microscopy methods. It has thus been a challenge to develop a method that will unambiguously identify them. A practical approach has been developed that is based on an inherent linear relationship revealed for the overall distribution of any two elements in a precipitate/matrix geometry and the first-order approximation of electron probe microanalysis (EPMA) results. Application of this approach to a direct chill cast 6082 alloy is demonstrated, and its major limitations are discussed.

A comparative study of iterative Chebyshev and Lanczos implementations of the boundary inhomogeneity method for quantum scattering

We have recently developed a scaleable Artificial Boundary Inhomogeneity (ABI) method [Chem. Phys. Lett.366, 390–397 (2002)] based on the utilization of the Lanczos algorithm, and in this work explore an alternative iterative implementation based on the Chebyshev algorithm. Detailed comparisons between the two iterative methods have been made in terms of efficiency as well as convergence behavior. The Lanczos subspace ABI method was also further improved by the use of a simpler three-term backward recursion algorithm to solve the subspace linear system. The two different iterative methods are tested on the model collinear H+H2 reactive state-to-state scattering.

An advanced method for eliminating impacts from frequency deviations in power system signal processing

Frequency deviation is a common problem for power system signal processing. Many power system measurements are carried out in a fixed sampling rate assuming the system operates in its nominal frequency (50 or 60 Hz). However, the actual frequency may deviate from the normal value from time to time due to various reasons such as disturbances and subsequent system transients. Measurement of signals based on a fixed sampling rate may introduce errors under such situations. In order to achieve high precision signal measurement appropriate algorithms need to be employed to reduce the impact from frequency deviation in the power system data acquisition process. This paper proposes an advanced algorithm to enhance Fourier transform for power system signal processing. The algorithm is able to effectively correct frequency deviation under fixed sampling rate. Accurate measurement of power system signals is essential for the secure and reliable operation of power systems. The algorithm is readily applicable to such occasions where signal processing is affected by frequency deviation. Both mathematical proof and numerical simulation are given in this paper to illustrate robustness and effectiveness of the proposed algorithm. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

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.

Method for generation of homogeneous multicellular tumor spheroids applicable to a wide variety of cell types

Multicellular tumor spheroids (MCTS) are used as organotypic models of normal and solid tumor tissue. Traditional techniques for generating MCTS, such as growth on nonadherent surfaces, in suspension, or on scaffolds, have a number of drawbacks, including the need for manual selection to achieve a homogeneous population and the use of nonphysiological matrix compounds. In this study we describe a mild method for the generation of MCTS, in which individual spheroids form in hanging drops suspended from a microtiter plate. The method has been successfully applied to a broad range of cell lines and shows nearly 100% efficiency (i.e., one spheroid per drop). Using the hepatoma cell line, HepG2, the hanging drop method generated well-rounded MCTS with a narrow size distribution (coefficient of variation [CV] 10% to 15%, compared with 40% to 60% for growth on nonadherent surfaces). Structural analysis of HepG2 and a mammary gland adenocarcinoma cell line, MCF-7, composed spheroids, revealed highly organized, three-dimensional, tissue-like structures with an extensive extracellular matrix. The hanging drop method represents an attractive alternative for MCTS production, because it is mild, can be applied to a wide variety of cell lines, and can produce spheroids of a homogeneous size without the need for sieving or manual selection. The method has applications for basic studies of physiology and metabolism, tumor biology, toxicology, cellular organization, and the development of bioartificial tissue. (C) 2003 Wiley Periodicals, Inc.

Pseudo-ternary phase diagrams of aqueous mixtures of Quil A, cholesterol and phospholipid prepared by the lipid-film hydration method

Pseudo-ternary phase diagrams of the polar lipids Quil A, cholesterol (Chol) and phosphatidylcholine (PC) in aqueous mixtures prepared by the lipid film hydration method (where dried lipid film of phospholipids and cholesterol are hydrated by an aqueous solution of Quil A) were investigated in terms of the types of particulate structures formed therein. Negative staining transmission electron microscopy and polarized light microscopy were used to characterize the colloidal and coarse dispersed particles present in the systems. Pseudo-ternary phase diagrams were established for lipid mixtures hydrated in water and in Tris buffer (pH 7.4). The effect of equilibration time was also studied with respect to systems hydrated in water where the samples were stored for 2 months at 4degreesC. Depending on the mass ratio of Quil A, Chol and PC in the systems, various colloidal particles including ISCOM matrices, liposomes, ring-like micelles and worm-like micelles were observed. Other colloidal particles were also observed as minor structures in the presence of these predominant colloids including helices, layered structures and lamellae (hexagonal pattern of ring-like micelles). In terms of the conditions which appeared to promote the formation of ISCOM matrices, the area of the phase diagrams associated with systems containing these structures increased in the order: hydrated in water/short equilibration period < hydrated in buffer/short equilibration period < hydrated in water/prolonged equilibration period. ISCOM matrices appeared to form over time from samples, which initially contained a high concentration of ring-like micelles suggesting that these colloidal structures may be precursors to ISCOM matrix formation. Helices were also frequently found in samples containing ISCOM matrices as a minor colloidal structure. Equilibration time and presence of buffer salts also promoted the formation of liposomes in systems not containing Quil A. These parameters however, did not appear to significantly affect the occurrence and predominance of other structures present in the pseudo-binary systems containing Quil A. Pseudo-ternary phase diagrams of PC, Chol and Quil A are important to identify combinations which will produce different colloidal structures, particularly ISCOM matrices, by the method of lipid film hydration. Colloidal structures comprising these three components are readily prepared by hydration of dried lipid films and may have application in vaccine delivery where the functionality of ISCOMs has clearly been demonstrated. (C) 2003 Elsevier B.V. All rights reserved.

Peptide quantification by matrix-assisted laser desorption ionisation time-of-flight mass spectrometry: Investigations of the cyclotide kalata B1 in biological fluids

A rapid method has been developed for the quantification of the prototypic cyclotide kalata B I in water and plasma utilizing matrix-assisted laser desorption ionisation time-of-flight (MALDI-TOF) mass spectrometry. The unusual structure of the cyclotides means that they do not ionise as readily as linear peptides and as a result of their low ionisation efficiency, traditional LC/MS analyses were not able to reach the levels of detection required for the quantification of cyclotides in plasma for pharmacokinetic studies. MALDI-TOF-MS analysis showed linearity (R-2 > 0.99) in the concentration range 0.05-10 mu g/mL with a limit of detection of 0.05 mu g/mL (9 fmol) in plasma. This paper highlights the applicability of MALDI-TOF mass spectrometry for the rapid and sensitive quantification of peptides in biological samples without the need for extensive extraction procedures. (c) 2005 Elsevier B.V. All rights reserved.

Encapsulation of lipopeptides within liposomes: Effect of number of lipid chains, chain length and method of liposome preparation

The purpose of this study was to systematically investigate the effect of lipid chain length and number of lipid chains present on lipopeptides on their ability to be incorporated within liposomes. The peptide KAVYNFATM was synthesized and conjugated to lipoamino acids having acyl chain lengths of C-8, C-12 and C-16. The C-12 construct was also prepared in the monomeric, dimeric and trimeric form. Liposomes were prepared by two techniques: hydration of dried lipid films (Bangham method) and hydration of freeze-dried monophase systems. Encapsulation of lipopeptide within liposomes prepared by hydration of dried lipid films was incomplete in all cases ranging from an entrapment efficiency of 70% for monomeric lipoamino acids at a 5% (w/w) loading to less than 20% for di- and trimeric forms at loadings of 20% (w/w). The incomplete entrapment of lipopeptides within liposomes appeared to be a result of the different solubilities of the lipopeptide and the phospholipids in the solvent used for the preparation of the lipid film. In contrast, encapsulation of lipopeptide within liposomes prepared by hydration of freeze-dried monophase systems was high, even up to a loading of 20% (w/w) and was much less affected by the acyl chain length and number than when liposomes were prepared by hydration of dried lipid films. Freeze drying of monophase systems is better at maintaining a molecular dispersion of the lipopeptide within the solid phospholipid matrix compared to preparation of lipid film by evaporation, particularly if the solubility of the lipopeptide in solvents is markedly different from that of the polar lipids used for liposome preparation. Consequently, upon hydration, the lipopeptide is more efficiently intercalated within the phospholipid bilayers. (C) 2005 Elsevier B.V. All rights reserved.