Asymptotic estimation of errors and derivatives for the numerical solution of ordinary differential equations,

"Supported in part by contract US AEC AT(11-1)2383."

Numerical solution of flood prediction and river regulation problems; report.

Reports 2 and 3 by E. Isaacson, J. J. Stoker, and A. Troesch.

Methods in Monte Carlo solution of the radiation transport equation /

"UNC-5014 (Volume A) Final Report covering the period 20 March 1961 - 31 May 1962."

Investigations on microscopic foams and on protoplasm : experiments & observations directed towards a solution of the question of the physical conditions of the phenomena of life /

"Literature": p. [331]-340.

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Non-additivity of attractive potentials in modeling of N-2 and Ar adsorption isotherms on graphitized carbon black and porous carbon by means of density functional theory

We present a new approach accounting for the nonadditivity of attractive parts of solid-fluid and fluidfluid potentials to improve the quality of the description of nitrogen and argon adsorption isotherms on graphitized carbon black in the framework of non-local density functional theory. We show that the strong solid-fluid interaction in the first monolayer decreases the fluid-fluid interaction, which prevents the twodimensional phase transition to occur. This results in smoother isotherm, which agrees much better with experimental data. In the region of multi-layer coverage the conventional non-local density functional theory and grand canonical Monte Carlo simulations are known to over-predict the amount adsorbed against experimental isotherms. Accounting for the non-additivity factor decreases the solid-fluid interaction with the increase of intermolecular interactions in the dense adsorbed fluid, preventing the over-prediction of loading in the region of multi-layer adsorption. Such an improvement of the non-local density functional theory allows us to describe experimental nitrogen and argon isotherms on carbon black quite accurately with mean error of 2.5 to 5.8% instead of 17 to 26% in the conventional technique. With this approach, the local isotherms of model pores can be derived, and consequently a more reliab * le pore size distribution can be obtained. We illustrate this by applying our theory against nitrogen and argon isotherms on a number of activated carbons. The fitting between our model and the data is much better than the conventional NLDFT, suggesting the more reliable PSD obtained with our approach.

Adsorption of N-2, Ar, acetone, chloroform and acetone-chloroform mixture on carbon black in the framework of molecular layer structure theory (MLST)

Adsorption of pure nitrogen, argon, acetone, chloroform and acetone-chloroform mixture on graphitized thermal carbon black is considered at sub-critical conditions by means of molecular layer structure theory (MLST). In the present version of the MLST an adsorbed fluid is considered as a sequence of 2D molecular layers, whose Helmholtz free energies are obtained directly from the analysis of experimental adsorption isotherm of pure components. The interaction of the nearest layers is accounted for in the framework of mean field approximation. This approach allows quantitative correlating of experimental nitrogen and argon adsorption isotherm both in the monolayer region and in the range of multi-layer coverage up to 10 molecular layers. In the case of acetone and chloroform the approach also leads to excellent quantitative correlation of adsorption isotherms, while molecular approaches such as the non-local density functional theory (NLDFT) fail to describe those isotherms. We extend our new method to calculate the Helmholtz free energy of an adsorbed mixture using a simple mixing rule, and this allows us to predict mixture adsorption isotherms from pure component adsorption isotherms. The approach, which accounts for the difference in composition in different molecular layers, is tested against the experimental data of acetone-chloroform mixture (non-ideal mixture) adsorption on graphitized thermal carbon black at 50 degrees C. (C) 2005 Elsevier Ltd. All rights reserved.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.

T-Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j -> infinity limit of the corresponding transfer matrix with spin-j (i.e., (2j + I)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian. (c) 2006 Elsevier B.V. All rights reserved.

XPS and bioactivity study of the bisphosphonate pamidronate adsorbed onto plasma sprayed hydroxyapatite coatings

This paper reports the use of X-ray photoelectron spectroscopy (XPS) to investigate bisphosphonate (BP) adsorption onto plasma sprayed hydroxyapatite (HA) coatings commonly used for orthopaedic implants. BPs exhibit high binding affinity for the calcium present in HA and hence can be adsorbed onto HA-coated implants to exploit their beneficial properties for improved bone growth at the implant interface. A rigorous XPS analysis of pamidronate, a commonly used nitrogenous BP, adsorbed onto plasma sprayed HA-coated cobalt-chromium substrates has been carried out, aimed at: (a) confirming the adsorption of this BP onto HA; (b) studying the BP diffusion profile in the HA coating by employing the technique of XPS depth profiling; (c) confirming the bioactivity of the adsorbed BR XPS spectra of plasma sprayed HA-coated discs exposed to a 10 mM aqueous BP solution (pamidronate) for periods of 1, 2 and 24 h showed nitrogen and phosphorous photoelectron signals corresponding to the BP confirming its adsorption onto the HA substrate. XPS depth profiling of the 2 h BP-exposed HA discs showed penetration of the BP into the HA matrix to depths of at least 260 nm. The bioactivity of the adsorbed BP was confirmed by the observed inhibition of osteoclast (bone resorbing) cell activity. In comparison to the HA sample, the HA sample with adsorbed BP exhibited a 25-fold decrease in primary osteoclast cells. (c) 2006 Elsevier B.V. All rights reserved.

Synapses, quantum theory and panpsychism

The introduction situates the ‘hard problem’ in its historical context and argues that the problem has two sides: the output side (the Kant-Eccles problem of the freedom of the Will) and the input side (the problem of qualia). The output side ultimately reduces to whether quantum mechanics can affect the operation of synapses. A discussion of the detailed molecular biology of synaptic transmission as presently understood suggests that such affects are unlikely. Instead an evolutionary argument is presented which suggests that our conviction of free agency is an evolutionarily induced illusion and hence that the Kant-Eccles problem is itself illusory. This conclusion is supported by well-known neurophysiology. The input side, the problem of qualia, of subjectivity, is not so easily outflanked. After a brief review of the neurophysiological correlates of consciousness (NCC) and of the Penrose-Hameroff microtubular neuroquantology it is again concluded that the molecular neurobiology makes quantum wave-mechanics an unlikely explanation. Instead recourse is made to an evolutionarily- and neurobiologically-informed panpsychism. The notion of an ‘emergent’ property is carefully distinguished from that of the more usual ‘system’ property used by most dual-aspect theorists (and the majority of neuroscientists) and used to support Llinas’ concept of an ‘oneiric’ consciousness continuously modified by sensory input. I conclude that a panpsychist theory, such as this, coupled with the non-classical understanding of matter flowing from quantum physics (both epistemological and scientific) may be the default and only solution to the problem posed by the presence of mind in a world of things.

Steric stabilization and dissolution characteristics of aqueous suspensions of pharmaceutical interest

The adsorption of two qroups of nonionic surface active agents and a series of hiqh molecular weiqht hydrophilic polymer fractions onto a polystyrene latex and a drug substance diloxanide furoate B.P. has been investigated. The presence of pores within the drug surface has been demonstrated and this is shown to increase the adsorption of low molecular weight polymer species. Differences in the maximum amount of polymer adsorbed at both solid-solution interfaces have been ascribed to the different hydrophobicities of the surface as determined by contact angle measurements. Adsorbed layer thicknesses of polymer on polystyrene latex have been determined by three techniques: microelectrophoresis, intensity fluctuation spectroscopy and by viscometric means. These results, in combination with adsorption data, were used to interpret the configuration of the adsorbed polymer molecules at the interface. The type of druq suspension produced on adsorbing the different polymers in the absence of electrostatic stabilization was correlated with theoretical prediuctions of suspension characteristics deduced from potential energy diagrams, The agreement was good for the adsorption of short chain length surfactants, but for the polyvinylalcohols, discrepancies were found between experiment and theory. This was attributed to the inappropriate use of a mean segment density approximation within the adsorbed layer to calculate attractive potentials between particles. A maximum in the redispersibility values for suspensions coated with adsorbed nonylphenylethoxylates was attributed to "partial static stabilization" of the particles in conjunction with the attractive forces operating in the sediment between bare surface patches on neighbouring particles. No significant change in the dissolution of the drug was observed when nonylphenylethoxylates were adsorbed due to desorption upon contact with the dissolution medium. Pluronic F68 and all the polyvinylalcohol fractions caused a reduction in the dissolution rate which is explained by the decreased diffusion of drug' through the adsorbed polymer layer.

Aircraft rotable inventory optimisation: development of a new solution

Analysis of the use of ICT in the aerospace industry has prompted the detailed investigation of an inventory-planning problem. There is a special class of inventory, consisting of expensive repairable spares for use in support of aircraft operations. These items, called rotables, are not well served by conventional theory and systems for inventory management. The context of the problem, the aircraft maintenance industry sector, is described in order to convey some of its special characteristics in the context of operations management. A literature review is carried out to seek existing theory that can be applied to rotable inventory and to identify a potential gap into which newly developed theory could contribute. Current techniques for rotable planning are identified in industry and the literature: these methods are modelled and tested using inventory and operational data obtained in the field. In the expectation that current practice leaves much scope for improvement, several new models are proposed. These are developed and tested on the field data for comparison with current practice. The new models are revised following testing to give improved versions. The best model developed and tested here comprises a linear programming optimisation, which finds an optimal level of inventory for multiple test cases, reflecting changing operating conditions. The new model offers an inventory plan that is up to 40% less expensive than that determined by current practice, while maintaining required performance.