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.

Capillary network models for transport in packed beds: Considerations of pore aspect ratio

The conventional analysis for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed for unconsolidated and grainy media.

Change in the rate of shell deposition and shell microstructure in response to shell borers in the abalone Haliotis rubra

Gastropod shells consist of two crystal types of calcium carbonate, an outer, prismatic calcite layer and an inner nacreous layer made of aragonite. In cross-section, the nacre of the nacreous layer appears to have a regular brick-like microstructure composed of thin laminae of aragonite crystals, separated by very thin sheets of protein (Lutz and Rhoads, 1980; Nakahara, 1983). In abalone (Genus, Haliotis) and other gastropods, thin layers of non-lamellar pigmented material occur within the nacre and have been termed alternatively, fine lines, growth rings or growth lines (Shepherd et al., 1995). It has been suggested that these pigmented layers are small, prismatic, calcite layers (Shepherd and Avalos-Borja, 1997; Zaremba et al., 1996) but investigations using a Raman laser in Haliotis rubra show that they contain aragonite rather than calcite (Hawkes et al, 1996). Day and Fleming (1992) suggest that the occurrence of pigmented layers is correlated with regular exogenous cues such as reproduction or temperature changes and indeed in some species, pigmented layers in the shell can be used to age abalone (review: Shepherd and Triantafillos, 1997). However, McShane and Smith (1992) suggest that pigmented layers can occur irregularly and therefore may be unreliable indicators of age.

The management of rice grown on raised beds with continuous furrow irrigation

A field experiment compared two rice (Oryza sativa L.) cropping systems: paddy or raised beds with continuous furrow irrigation; and trialled four cultivars: Starbonnet, Lemont, Amaroo and Ceysvoni, and one test line YRL39; that may vary in adaptation to growth on raised beds. The grain yield of rice ranged from 740 to 1250 g/m(2) and was slightly greater in paddy than on raised beds. Although there were early growth responses to fertilizer nitrogen on raised beds, the crop nitrogen content at maturity mostly exceeded 20 g/m(2) in both systems, so nitrogen was unlikely to have limited yield. Ceysvoni yielded best in both systems, a result of good post-anthesis growth and larger grain size, although its whole-grain mill-out percentage was poor relative to the other cultivars. Starbonnet and Lemont yielded poorly on raised beds, associated with too few tillers and too much leaf area. When grown on raised beds all cultivars experienced a delay in anthesis resulting in more tillers, leaf area and dry weight at anthesis, and probably a greater yield potential. The growth of rice after anthesis, however, was similar on raised beds and in paddy, so reductions in harvest index and grain size on raised beds were recorded. The data indicated that water supply was not a major limitation to rice growth on raised beds, but slower crop development was an issue that would affect the use of raised beds in a cropping system, especially in rice-growing areas where temperatures are too cool for optimal crop development. (C) 2001 Elsevier Science B.V. All rights reserved.

Ecology, shell morphology, anatomy and sperm ultrastructure of the caenogastropod Pyrgula annulata, with a discussion of the relationship between the 'Pyrgulidae' and Caspian and Baikalian rissooideans

The composition of the Pyrgulidae and its relationships to other member families of the caenogastropod superfamily Rissooidea are examined after a consideration of new anatomical (including gross anatomy, sperm ultrastructure), conchological (including protoconch features), ecological, biogeographical and palaeontological data and a re-evaluation of existing literature. Pyrgulidae can be distinguished from hydrobiids unequivocally only with the aid of the radula. Sperm ultrastructural features suggest a very close relationship between the Pyrgulidae, the Hydrobiidae and the Bithyniidae (in fact no family-diagnostic sperm characters can be found to separate these three taxa). Based upon neontological and fossil evidence it is likely that pyrgulids represent a Miocene offshoot from a paratethyal hydrobiid lineage. Pyrgulids may also represent the stock from which the baicaliids arose, in which case the Pyrgulidae must be considered a paraphyletic group. The huge biogeographic gap between the Caspian Sea and Lake Baikal is to some extent bridged by the finding of a Neogene pyrgulid from the Altai Mountains. An alternative scenario for the origin of baicaliids is presented.

Experimental investigation of liquid flow shift due to gas cross flow in non-wetted packed beds

An experimental study has been carried out for the gas-liquid two-phase flow in a packed bed simulating conditions of the gas and liquid flows in the lower part of blast furnace. The localised liquid flow phenomenon in presence of gas cross flow, which usually occurs around the cohesive zone and raceway in blast furnace, was investigated in detail. Such liquid flow is characterised in terms of liquid shift distance or liquid shift angle that can effectively be measured by the experiments involved in the current study. It is found that liquid shift angle does not significantly increase or decrease with different packing depth. This finding supports the hypothesis of the force balance model where a vectorial relationship among acting forces, i.e. gas drag force, gravitational force and solid-liquid friction force, and liquid shift angle does exist. Liquid shift angle is inversely proportional to particle size and liquid density, and proportional to square of gas superficial velocity, but is almost independent on liquid flowrate and liquid viscosity. The gas-liquid drag coefficient, an important aspect for quantifying the interaction between gas and liquid flows, was conceptually modified based on the discrete feature of liquid flow through a packed bed and evaluated by the combined theoretical and experimental investigation. Experimental measurements suggest that the gas-liquid drag coefficient is approximately a constant (C-DG(')=5.4+/-1.0) and is independent on liquid properties, gas velocity and packing structure. The result shows a good agreement with previous experimental data and prediction of the existing liquid flow model.

Drop penetration into porous powder beds

The kinetics of drop penetration were studied by filming single drops of several different fluids (water, PEG200, PEG600, and HPC solutions) as they penetrated into loosely packed beds of glass ballotini, lactose, zinc oxide, and titanium dioxide powders. Measured times ranged from 0.45 to 126 s and depended on the powder particle size,viscosity, surface tensions, and contact angle. The experimental drop penetration times were compared to existing theoretical predictions by M. Denesuk et al. (J. Colloid Interface Sci. 158, 114, 1993) and S. Middleman (Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops, Academic Press, San Diego, 1995) but did not agree. Loosely packed powder beds tend to have a heterogeneous bed structure containing large macrovoids which do not participate in liquid flow but are included implicitly in the existing approach to estimating powder pore size. A new two-phase model was proposed where the total volume of the macrovoids was assumed to be the difference between the bed porosity and the tap porosity. A new parameter, the effective porosity (epsilon)eff, was defined as the tap porosity multiplied by the fraction of pores that terminate at a macrovoid and are effectively blocked pores. The improved drop penetration model was much more successful at estimating the drop penetration time on all powders and the predicted times were generally within an order of magnitude of the experimental results. (C) 2002 Elsevier Science (USA).

Unsaturated liquid percolation flow through nonwetted packed beds

The unsaturated flow of liquid through packed beds of large particles was studied using six different liquids, all with contact angles greater than 90degrees on the bed packing (wax spheres of 9, 15 and 19.4 mm diameter). The liquid flow was discrete in nature, as drops for low flow rates and rivulets for high flow rates. For unsaturated liquid flows, the actual percolation velocity, not superficial velocity, should be used to characterize the flow. The percolation velocity did not vary with packed-bed depth, but was a strong function of liquid flow rate, liquid and particle properties. Effects of liquid and particle properties (but not flow rate) are well captured by a simple correlation between the liquid-particle friction factor and Reynolds number based on actual percolation velocities. Liquid dispersion, characterized by the maximum dispersion angle, varies significantly with liquid and particle properties. The tentative correlation suggested here needs further validation for a wider range of conditions.

Segregation in binary and ternary liquid fluidized beds

The mechanism underlying segregation in liquid fluidized beds is investigated in this paper, A binary fluidized bed system not at a stable equilibrium condition. is modelled in the literature as forming a mixed part-corresponding to stable mixture-at the bottom of the bed and a pure layer of excess components always floating on the mixed part. On the basis of this model: (0 comprehensive criteria for binary particles of any type to mix/segregate, and (ii) mixing, segregation regime map in terms of size ratio and density ratio of the particles for a given fluidizing medium, are established in this work. Therefore, knowing the properties of given particles, a second type of particles can be chosen in order to avoid or to promote segregation according to the particular process requirements. The model is then advanced for multicomponent fluidized beds and validated against experimental results observed for ternary fluidized beds. (C) 2002 Elsevier Science B.V. All rights reserved.