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. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken 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. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - II. Testing simulation capabilities of wheat growth

To simulate cropping systems, crop models must not only give reliable predictions of yield across a wide range of environmental conditions, they must also quantify water and nutrient use well, so that the status of the soil at maturity is a good representation of the starting conditions for the next cropping sequence. To assess the suitability for this task a range of crop models, currently used in Australia, were tested. The models differed in their design objectives, complexity and structure and were (i) tested on diverse, independent data sets from a wide range of environments and (ii) model components were further evaluated with one detailed data set from a semi-arid environment. All models were coded into the cropping systems shell APSIM, which provides a common soil water and nitrogen balance. Crop development was input, thus differences between simulations were caused entirely by difference in simulating crop growth. Under nitrogen non-limiting conditions between 73 and 85% of the observed kernel yield variation across environments was explained by the models. This ranged from 51 to 77% under varying nitrogen supply. Water and nitrogen effects on leaf area index were predicted poorly by all models resulting in erroneous predictions of dry matter accumulation and water use. When measured light interception was used as input, most models improved in their prediction of dry matter and yield. This test highlighted a range of compensating errors in all modelling approaches. Time course and final amount of water extraction was simulated well by two models, while others left up to 25% of potentially available soil water in the profile. Kernel nitrogen percentage was predicted poorly by all models due to its sensitivity to small dry matter changes. Yield and dry matter could be estimated adequately for a range of environmental conditions using the general concepts of radiation use efficiency and transpiration efficiency. However, leaf area and kernel nitrogen dynamics need to be improved to achieve better estimates of water and nitrogen use if such models are to be use to evaluate cropping systems. (C) 1998 Elsevier Science B.V.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - III. The integrated wheat model (I_WHEAT)

Previous work has identified several short-comings in the ability of four spring wheat and one barley model to simulate crop processes and resource utilization. This can have important implications when such models are used within systems models where final soil water and nitrogen conditions of one crop define the starting conditions of the following crop. In an attempt to overcome these limitations and to reconcile a range of modelling approaches, existing model components that worked demonstrably well were combined with new components for aspects where existing capabilities were inadequate. This resulted in the Integrated Wheat Model (I_WHEAT), which was developed as a module of the cropping systems model APSIM. To increase predictive capability of the model, process detail was reduced, where possible, by replacing groups of processes with conservative, biologically meaningful parameters. I_WHEAT does not contain a soil water or soil nitrogen balance. These are present as other modules of APSIM. In I_WHEAT, yield is simulated using a linear increase in harvest index whereby nitrogen or water limitations can lead to early termination of grainfilling and hence cessation of harvest index increase. Dry matter increase is calculated either from the amount of intercepted radiation and radiation conversion efficiency or from the amount of water transpired and transpiration efficiency, depending on the most limiting resource. Leaf area and tiller formation are calculated from thermal time and a cultivar specific phyllochron interval. Nitrogen limitation first reduces leaf area and then affects radiation conversion efficiency as it becomes more severe. Water or nitrogen limitations result in reduced leaf expansion, accelerated leaf senescence or tiller death. This reduces the radiation load on the crop canopy (i.e. demand for water) and can make nitrogen available for translocation to other organs. Sensitive feedbacks between light interception and dry matter accumulation are avoided by having environmental effects acting directly on leaf area development, rather than via biomass production. This makes the model more stable across environments without losing the interactions between the different external influences. When comparing model output with models tested previously using data from a wide range of agro-climatic conditions, yield and biomass predictions were equal to the best of those models, but improvements could be demonstrated for simulating leaf area dynamics in response to water and nitrogen supply, kernel nitrogen content, and total water and nitrogen use. I_WHEAT does not require calibration for any of the environments tested. Further model improvement should concentrate on improving phenology simulations, a more thorough derivation of coefficients to describe leaf area development and a better quantification of some processes related to nitrogen dynamics. (C) 1998 Elsevier Science B.V.

Squeezing-induced complete transparency in two-level systems

The modification of the statistical properties of vacuum fluctuations, via quadrature squeezing, can dramatically reduce the absorptive and dispersive properties of two-level atoms. We show that for some range of parameter values the system exhibits zero absorption accompanied by zero dispersion of the probe field. This complete transparency is attributed to the coherent population oscillations induced by the squeezed vacuum.

Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

Classical and quantum noise in electronic systems

We review the description of noise in electronic circuits in terms of electron transport. The Poisson process is used as a unifying principle. In recent years, much attention has been given to current noise in light-emitting diodes and laser diodes. In these devices, random events associated with electron transport are correlated with photon emission times, thus modifying both the current statistics and the statistics of the emitted light. We give a review of experiments in this area with special emphasis on the ability of such devices to produce subshot-noise currents and light beams. Finally we consider the noise properties of a class of mesoscopic devices based on the quantum tunnelling of an electron into and out of a bound state. We present a simple quantum model of this process which confirms that the current noise in such a device should be subshot-noise.

Shift of the subharmonic resonances and suppression of fluorescence in a two-level atom driven by a bichromatic field

We study the behavior of a two-level atom that is driven by a bichromatic field consisting of a strong resonant component and a weaker tunable component. In addition to the splitting of the energy levels (the multiphoton AC Stark effect), we find that the weaker component also shifts the subharmonic resonances, an effect we attribute to a dynamic Stark shift. When the weaker component is tuned to a shifted resonance, no fluorescence occurs at either the frequency of the strong component or the three-photon mixing frequency. Results are obtained with numerical techniques and explained in terms of the dressed-atom model of the system. (C) 1998 Optical Society of America [S0740-3224(98)01508-2] OCIS codes: 270.4180, 270.6620, 270.0270.

Analysis of pore-fluid pressure gradient and effective vertical-stress gradient distribution in layered hydrodynamic systems

A theoretical analysis is carried out to investigate the pore-fluid pressure gradient and effective vertical-stress gradient distribution in fluid saturated porous rock masses in layered hydrodynamic systems. Three important concepts, namely the critical porosity of a porous medium, the intrinsic Fore-fluid pressure and the intrinsic effective vertical stress of the solid matrix, are presented and discussed. Using some basic scientific principles, we derive analytical solutions and explore the conditions under which either the intrinsic pore-fluid pressure gradient or the intrinsic effective vertical-stress gradient can be maintained at the value of the lithostatic pressure gradient. Even though the intrinsic pore-fluid pressure gradient can be maintained at the value of the lithostatic pressure gradient in a single layer, it is impossible to maintain it at this value in all layers in a layered hydrodynamic system, unless all layers have the same permeability and porosity simultaneously. However, the intrinsic effective vertical-stress gradient of the solid matrix can be maintained at a value close to the lithostatic pressure gradient in all layers in any layered hydrodynamic system within the scope of this study.

5-cycle systems of K-v-F with a hole

Recently the problem of the existence of a 5-cycle system of K-v with a hole of size u was completely solved. In this paper we prove necessary and sufficient conditions on v and u for the existence of a 5-cycle system of K-v - F, with a hole of size u.

(m,n)-cycle systems

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.

Effects of coping strategies, social support and work-nonwork conflict on shift worker's health

Objectives This study examines the direct and mediated effects of shift workers' coping strategies and social support on structural work-nonwork conflict and subjective health. Methods The participants were 172 registered female nurses, aged 21 to 40 years. They all worked full-time, on rapidly rotating, 8-hour shifts in metropolitan general hospitals. All the respondents completed a self-administered questionnaire requesting demographic information and data on sources of social support, work-nonwork conflict, and coping strategies. Results A path model with good fit (chi(2)=28.88, df=23, P>.23, CFI=0.97) demonstrated complex effects of social support and coping on structural work-nonwork conflict and health. Conclusions Structural work-nonwork conflict mediated the effects of social support from supervisors and emotionally expressive coping on psychological symptoms. Control of shifts mediated the effect of social support from supervisors on structural work-nonwork conflict. Disengagement coping had direct and mediated effects on psychological and physical health. However, it also had mediated effects, with the effect on psychological health being mediated by support from co-workers and the effect on physical symptoms being mediated by family support. Go-worker support mediated the effect of social support from supervisors on psychological symptoms. Overall, these findings support previous research and clarify the process by which coping strategies and social support affect structural work-nonwork conflict and health in shift work.

Quantum open-systems approach to current noise in resonant tunneling junctions

A quantum Markovian master equation is derived to describe the current noise in resonant tunneling devices. This equation includes both incoherent and coherent quantum tunneling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict subshot noise statistics for strong tunneling between the wells. The method is an alternative to Green's function methods and population master equations for very small coherently coupled quantum dots.