Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

It is shown that quasigroups constructed using the standard construction from 2-perfect directed m-cycle systems are precisely the finite members of a variety if and only if m=3, 4 or 5.

New gene technologies and their potential value for sugarcane

An efficient system is now in place for improving diverse sugarcane cultivars by genetic transformation, that is, the insertion of useful new genes into single cells followed by the regeneration of genetically modified (transgenic) plants. The method has already been used to introduce genes for resistance to several major diseases, insect pests and a herbicide, Field testing has begun, and research is underway to identify other genes for increased environmental stress resistance, agronomic efficiency and yield of sucrose or other valuable products. Experience in other crops has shown that genetically improved varieties which provide genuine environmental and consumer benefits are welcomed by producers and consumers. Substantial research is still needed, but these new gene technologies will reshape the sugar industry and determine the international competitive efficiency of producers.

Lambda-fold 3-perfect 9-cycle systems

The spectrum for the decomposition of lambda K-v into 3-perfect 9-cycles is found for all lambda > 1. (The case lambda = 1 was dealt with in an earlier paper by the authors and Lindner.) The necessary conditions for the existence of a suitable decomposition turn out to be sufficient.

Squeezing in anomalous resonance fluorescence

The squeezing properties of the fluorescence field emitted by a two-level atom driven by a coherent laser field in a squeezed vacuum are calculated. We show that in the region of the anomalous resonance fluorescence the emitted field exhibits squeezing that is much larger than that in the input squeezed vacuum. The squeezing spectrum attains a minimum value that corresponds to 75% squeezing. We also find that, in the total fluorescence field, squeezing attains an optimum achievable value in the fluorescence field emitted by a two-level atom. The optimum squeezing is associated with the collapse of the system into a pure state. (C) 1997 Optical Society of America.

Modelling of cold-formed purlin-sheeting systems .1. Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold-formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper. (C) 1997 Elsevier Science Ltd.

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

Muscle-specific regulation of tropomyosin gene expression and myofibrillogenesis differs among muscle systems examined at metamorphosis of the gastropod Haliotis rufescens

The spatial and temporal association of muscle-specific tropomyosin gene expression, and myofibril assembly and degradation during metamorphosis is analyzed in the gastropod mollusc. Haliotis rufescens. Metamorphosis of tile planktonic larva to the benthic juvenile includes rearrangement and atrophy of specific larval muscles, and biogenesis of the new juvenile muscle system. The major muscle of the larva - the larval retractor muscle - reorganizes at metamorphosis, with two suites of cells having different fates. The ventral cells degenerate, while the dorsal cells become part of the developing juvenile mantle musculature. Prior to these changes in myofibrillar structure, tropomyosin mRNA prevalence declines until undetectable in the ventral cells, while increasing markedly in the dorsal cells. In the foot muscle and right shell muscle, tropomyosin mRNA levels remain relatively stable, even trough myofibril content increases. In a population of median mesoderm cells destined to form de novo the major muscle of the juvenile and adult (the columellar muscle), tropomyosin expression is initiated at 45 h after induction of metamorphosis. Myofibrillar filamentous actin is not detected in these cells until about 7 days later. Given that patterns of tropomyosin mRNA accumulation in relation to myofibril assembly and disassembly differ significantly among the four major muscle systems examined, we suggest that different regulatory mechanisms, probably operating at both transcriptional and post-transcriptional levels, control the biogenesis and atrophy of different larval and postlarval muscles at metamorphosis.

Strongly 2-perfect cycle systems and their quasigroups

A recent result of Bryant and Lindner shows that the quasigroups arising from 2-perfect m-cycle systems form a variety only when m = 3, 5 and 7. Here we investigate the situation in the case where the distance two cycles are required to be in the original system.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Synchronization of mutually coupled chaotic systems

We report on the experimental observation of both basic frequency locking synchronization and chaos synchronization between two mutually coupled chaotic subsystems. We show that these two kinds of synchronization are two stages of interaction between coupled chaotic systems. in particular the chaos synchronization could be understood as a state of phase locking between coupled chaotic oscillations.