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.

Development of composite adsorbents of carbon and intercalated clay for N2 and O2 adsorption: A preliminary study

Composite adsorbents of carbon and alumina intercalated montmorillonite were prepared and characterized by adsorption of N-2 and O-2 at various temperatures. The effects of pyrolysis, temperature, heating rate, subsequent degassing, and doping of cations and anions were investigated. The adsorption capacities of the composite adsorbents developed at higher temperatures (0 and -79 degrees C) are found to be larger than those of normal alumina pillared clays. The experimental results showed that the framework of these adsorbents is made of alumina particles and clay sheets while the pyrolyzed carbon distributes in the space of interlayers and interpillars. The pores between the carbon particles, clay sheets, and alumina pillars are very narrow with very strong adsorption forces, leading to enhanced adsorption capacities at 0 and -79 degrees C. The composite adsorbents exhibit features similar to those of carbonaceous adsorbents. Their pore structures, adsorption capacities, and selectivities to oxygen can be tailored by a controlled degassing procedure. Meanwhile, ions can be doped into the adsorbents to modify their adsorption properties, as usually observed for oxide adsorbents like zeolite and pillared clays. Such flexibility in pore structure tailoring is a potential advantage of the composite adsorbents developed for their adsorption and separation applications. (C) 1999 Academic Press.

Novel composite membranes for gas separation: Preparation and performance

High performance composite membranes based on molecular sieving silica (MSS) were synthesized using sols containing silicon co-polymers (methyltriethoxysilane and tetraethylorthosilicate). Alpha alumina supports were treated with hydrochloric acid prior to sol deposition. Permselectivity of CO2 over CH4 as high as 16.68 was achieved whilst permeability of CO2 up to 36.7 GPU (10(-6) cm(3) (STP) cm(-2) . s(-1) . cm Hg-1) was measured. The best membrane's permeability was finger printed during various stages of the synthesis process showing an increase in CO2/CH4 permselectivity by over 25 times from initial support condition (no membrane film) to the completion of pore structure tailoring. Transport measurement results indicate that the membrane pretreated with HCl has highest permselectivity and permeation rate. In particular, there is a definite cut-off pore size between 3.3 and 3.4 angstroms which is just below the kinetic diameters of Ar and CH4. This demonstrates that the mechanism for the separation in the prepared composite membrane is molecular sieving (activated diffusion), rather than Knudsen diffusion.

Long-term quantification of the release of monomers from dental resin composites and a resin-modified glass ionomer cement

This study quantified the release of monomers from polymerized specimens of four commercially available resin composites and one glass ionomer cement immersed in water:ethanol solutions. Individual standard curves were prepared from five monomers: (1) triethylene glycol dimethacrylate (TEGDMA), (2) 2-hydroxy-ethyl methacrylate (HEMA), (3) urethane dimethacrylate (UDMA), (4) bisphenol A glycidyl dimethacrylate (BISGMA), and (5) bisphenol A. The concentration of the monomers was determined at Days 1, 7, 30, and 90 with the use of electrospray ionization/mass spectrometry. Data were expressed in mean mumol per mm(2) surface area of specimen and analyzed with Scheffe's test (P < 0.05). The following monomers were found in water: monomers (1) and (2) from Delton sealant, monomer (5) from ScotchBond Multipurpose Adhesive and Delton sealant, monomer (3) from Definite and monomer (4) from Fuji II LC, ScotchBond Multipurpose Adhesive, Synergy and Definite. All these monomers increased in concentration over time, with the exception of monomer (1) from Delton sealant. Monomers (3) and (5) were found in extracts of materials despite their absence from the manufacturer's published composition. All monomers were released in significantly higher concentrations in water:ethanol solutions than in water. The greatest release of monomers occurred in the first day. The effect of the measured concentrations of monomers (1-5) on human genes, cells, or tissues needs to be considered with the use of a biological model. (C) 2002 Wiley Periodicals, Inc.

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Modelling cement grinding circuits

Modelling and simulation studies were carried out at 26 cement clinker grinding circuits including tube mills, air separators and high pressure grinding rolls in 8 plants. The results reported earlier have shown that tube mills can be modelled as several mills in series, and the internal partition in tube mills can be modelled as a screen which must retain coarse particles in the first compartment but not impede the flow of drying air. In this work the modelling has been extended to show that the Tromp curve which describes separator (classifier) performance can be modelled in terms of d(50)(corr), by-pass, the fish hook, and the sharpness of the curve. Also the high pressure grinding rolls model developed at the Julius Kruttschnitt Mineral Research Centre gives satisfactory predictions using a breakage function derived from impact and compressed bed tests. Simulation studies of a full plant incorporating a tube mill, HPGR and separators showed that the models could successfully predict the performance of the another mill working under different conditions. The simulation capability can therefore be used for process optimization and design. (C) 2001 Elsevier Science Ltd. All rights reserved.

Analysis of acousto-ultrasonic characteristics for contact-type transducers coupled to composite laminated plates

The acousto-ultrasonic (AU) input-output characteristics for contact-type transmitting and receiving transducers coupled to composite laminated plates are considered in this paper. Combining a multiple integral transform method, an ordinary discrete layer theory for the laminates and some simplifying assumptions for the electro-mechanical transduction behaviour of the transducers, an analytical solution is developed which can deal with all the wave processes involved in the AU measurement system, i.e, wave generation, wave propagation and wave reception. The spectral response of the normal contact pressure sensed by the receiving transducer due to an arbitrary input pulse excited by the transmitting transducer is obtained. To validate the new analytical-numerical spectral technique in the low-frequency regime, the results are compared with Mindlin plate theory solutions. Based on the analytical results, numerical calculations are carried out to investigate the influence of various external parameters such as frequency content of the input pulse, transmitter/receiver spacing and transducer aperture on the output of the measurement system. The results show that the presented analytical-numerical procedure is an effective tool for understanding the input-output characteristics of the AU technique for laminated plates. (C) 2001 Elsevier Science Ltd. All rights reserved.

Precipitation hardening of Cu-Fe-Cr alloys - Part I - Mechanical and electrical properties

This research is part of a project whose scope was to investigate the engineering properties of new non-commercial alloy formulations based on the Cu rich corner of the Cu-Fe-Cr ternary system with the primary aim of exploring the development of a new cost-effective high-strength, high-conductivity copper alloy. The literature indicated that Cu rich Cu-Cr and Cu-Fe alloys have been thoroughly investigated. A number of commercial alloys have been developed and these are used for a variety of applications requiring combinations of high-strength, high-conductivity and resistance to softening. Little evidence was found in the literature that the Cu rich corner of the Cu-Fe-Cr system had previously been investigated for the purpose of developing high-strength, high-conductivity copper alloys resistant to softening. The aim of these present investigations was to explore the possibility that new alloys could be developed that combined the properties of both sets of alloys, ie large precipitation hardening response combined with the ability to stabilise cold worked microstructures to high temperatures while at the same maintain high electrical conductivity. To assess the feasibility of this goal the following alloys were chosen for investigation: Cu-0.7wt%Cr-0.3wt%Fe, Cu-0.7wt%Cr-0.8wt%Fe, Cu-0.7wt%Cr-2.0wt%Fe. This paper reports on the mechanical property investigation which indicated that the Cu-0.7wt%Cr-0.3wt%Fe, and Cu-0.7wt%Cr-2.0wt%Fe alloys were worthy of further investigation. (C) 2001 Kluwer Academic Publishers.

Precipitation hardening of Cu-Fe-Cr alloys - Part II - Microstructural characterisation

This research is part of a project whose scope was to investigate the engineering properties of new non-commercial alloy formulations based on the Cu rich corner of the Cu-Fe-Cr ternary system with the primary aim of exploring the development of a new cost-effective high-strength, high-conductivity copper alloy. Promising properties have been measured for the following alloys: Cu-0.7wt%Cr-0.3wt%Fe and Cu-0.7wt%Cr-2.0wt%Fe. This paper reports on the microstructural characterisation of these alloys and discusses the mechanical and electrical properties of these alloys in terms of their microstructure, particularly the formation of precipitates. These alloys have evinced properties that warrant further investigation. Cost modelling has shown that Cu-0.7wt%Cr-0.3wt%Fe is approximately 25% cheaper to produce than commercial Cu-1%Cr. It has also been shown to be more cost efficient on a yield stress and % IACS per dollar basis. The reason for the cost saving is that the Cu-0.7%Cr-0.3%Fe alloy can be made with low carbon ferro-chrome additions as the source of chromium rather than the more expensive Cu-Cr master-alloy. For applications in which cost is one of the primary materials selection criteria, it is envisaged that there would be numerous applications in both cast and wrought form, where the Cu-0.7%Cr-0.3%Fe alloy would be more suitable than Cu-1%Cr. (C) 2001 Kluwer Academic Publishers.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

An age hardening model for Al-7Si-Mg casting alloys

Yield strength (YS) ageing curves have been modelled for A356 and A357 aluminium casting alloys below the solvus temperature of the main hardening precipitate. Predictions are based on the Shercliff and Ashby methodology (Acta MetaH. Mater. 38 (1990) 1789) for wrought alloys. Differences between strengthening in wrought and cast Al-Si-Mg alloys are considered. A Brinell hardness to YS conversion incorporating strain hardening has been established to enable YS ageing curves to be predicted with reduced experimental effort. (C) 2002 Elsevier Science B.V. All rights reserved.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.