Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.

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.

Willingness to pay for conservation of the Asian elephant in Sri Lanka: A contingent valuation study

Results from a CVM survey of willingness to pay for the conservation of the Asian elephant of a sample of urban residents in three selected housing schemes in Colombo, the capital of Sri Lanka, are reported. Face– to–face surveys were conducted using an interview schedule. A non-linear logit regression model was constructed to analyse the respondents’ responses for the payment principle questions and to identify the factors that influence their responses. We investigate whether urban residents’ WTP for the conservation of elephants is sufficient to compensate farmers for the damage caused by elephants, and consequently to raise farmers’ tolerance of the presence of elephants on the farming fields. We find that beneficiaries (the urban residents) could compensate losers (the farmers in the HEC affected areas) and be better off than in the absence of elephants in Sri Lanka. This suggests that there is a strong economic case for the conservation of the wild elephant population in Sri Lanka. However, we have insufficient data to determine Sri Lanka’s optimal elephant population in the Kaldor-Hicks sense.

The net benefit of saving the Asian Elephant: A policy and contingent valuation Study

Reports results from a contingent valuation survey of willingness to pay for the conservation of the Asian elephant of a sample of urban residents living in three selected housing schemes in Colombo, the capital of Sri Lanka. Face–to–face surveys were conducted using an interview schedule. A non-linear logit regression model is used to analyse the respondents’ responses for the payment principle questions and to identify the factors that influence their responses. We investigate whether urban residents’ willingness to pay for the conservation of elephants is sufficient to compensate farmers for the damage caused by elephants. We find that the beneficiaries (the urban residents) could compensate losers (the farmers in the areas affected by human–elephant conflict) and be better off than in the absence of elephants in Sri Lanka. Therefore, there is a strong economic case for the conservation of the wild elephant population in Sri Lanka. However, we have insufficient data to determine the optimal level of this elephant population in the Kaldor-Hicks sense. Nevertheless, the current population of elephant in Sri Lanka is Kaldor-Hicks preferable to having none.

Parametric signal regeneration

We present an ultra-high bandwidth all-optical digital signal regeneration device concept utilising non-degenerate parametric interaction in a one-dimensional waveguide. Performance is analysed in terms of re-amplification, re-timing, and re-shaping (including centre frequency correction) of time domain multiplexed signals. Bandwidths of 10-100 THz are achievable. (C) 2001 Published by Elsevier Science B.V.

Compact clinical MRI magnet design using a multilayer current density approach

In this work, a new method of optimization is successfully applied to the theoretical design of compact, actively shielded, clinical MRI magnets. The problem is formulated as a two-step process in which the desired current densities on multiple, cc-axial surface layers are first calculated by solving Fredholm equations of the first kind. Non-linear optimization methods with inequality constraints are then invoked to fit practical magnet coils to the desired current densities. The current density approach allows rapid prototyping of unusual magnet designs. The emphasis of this work is on the optimal design of short, actively-shielded MRI magnets for whole-body imaging. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric, and asymmetric MRI magnets. Magnet designs are presented for actively-shielded, symmetric magnets of coil length 1.0 m, which is considerably shorter than currently available designs of comparable dsv size. Novel, actively-shielded, asymmetric magnet designs are also presented in which the beginning of a 50-cm dsv is positioned just 11 cm from the end of the coil structure, allowing much improved access to the patient and reduced patient claustrophobia. Magn Reson Med 45:331540, 2001. (C) 2001 Wiley-Liss, Inc.

On the relation between ownership structure and capital structure

The agency relationship between managers and shareholders has the potential to influence decision-making in the firm which in turn potentially impacts on firm characteristics such as value and leverage. Prior evidence has demonstrated an association between ownership structure and firm value. This paper extends the literature by examining a further link between ownership structure and capital structure. Using an agency framework, it is argued that the distribution of equity ownership among corporate managers and external blockholders may have a significant relation with leverage. The empirical results provide support for a positive relation between external blockholders and leverage, and non-linear relation between the level of managerial share ownership and leverage. The results also suggest that the relation between external block ownership and leverage varies across the level of managerial share ownership. These results are consistent with active monitoring by blockholders, and the effects of convergence-of-interests and management entrenchment.

Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

Interactive expectations

In modeling expectation formation, economic agents are usually viewed as forming expectations adaptively or in accordance with some rationality postulate. We offer an alternative nonlinear model where agents exchange their opinions and information with each other. Such a model yields multiple equilibria, or attracting distributions, that are persistent but subject to sudden large jumps. Using German Federal Statistical Office economic indicators and German IFO Poll expectational data, we show that this kind of model performs well in simulation experiments. Focusing upon producers' expectations in the consumption goods sector, we also discover evidence that structural change in the interactive process occurred over the period of investigation (1970-1998). Specifically, interactions in expectation formation seem to have become less important over time.

The copolymerization of N-vinyl-2-pyrrolidone with 2-hydroxyethyl methacrylate

The bulk free radical copolymerization of 2-hydroxyethyl methacrylate (HEMA) with N-vinyl-2-pyrrolidone (VP) was carried out to low conversions at 50 degreesC, using benzoyl peroxide (BPO) as initiator. The compositions of the copolymers; were determined using C-13 NMR spectroscopy. The conversion of monomers to polymers was studied using FT-NIR spectroscopy in order to predict the extent of conversion of monomer to polymer. From model fits to the composition data, a statistical F-test revealed that die penultimate model describes die copolymerization better than die terminal model. Reactivity ratios were calculated by using a non-linear least squares analysis (NLLS) and r(H) = 8.18 and r(V) = 0.097 were found to be the best fit values of the reactivity ratios for the terminal model and r(HH) = 12.0, r(VH) = 2.20, r(VV) = 0.12 and r(HV) = 0.03 for the penultimate model. Predictions were made for changes in compositions as a function of conversion based upon the terminal and penultimate models.

Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys

The rheological behaviour of nine unprocessed Australian honeys was investigated for the applicability of the Williams-Landel-Ferry (WLF) model. The viscosity of the honeys was obtained over a range of shear rates (0.01-40 s(-1)) from 2degrees to 40 degreesC, and all the honeys exhibited Newtonian behaviour with viscosity reducing as the temperature was increased. The honeys with high moisture were of lower viscosity, The glass transition temperatures of the honeys, as measured with a differential scanning calorimeter (DSC), ranged from -40degrees to -46 degreesC, and four models (WLF. Arrhenius, Vogel-Tammann-Fulcher (VTF), and power-law) were investigated to describe the temperature dependence of the viscosity. The WLF was the most suitable and the correlation coefficient averaged 0.999 +/- 0.0013 as against 0.996 +/- 0.0042 for the Arrhenius model while the mean relative deviation modulus was 0-12% for the WLF model and 10-40% for the Arrhenius one. With the universal values for the WLF constants, the temperature dependence of the viscosity was badly predicted. From non-linear regression analysis, the constants of the WLF models for the honeys were obtained (C-1 = 13.7-21.1: C-2 = 55.9-118.7) and are different from the universal values. These WLF constants will be valuable for adequate modeling of the rheology of the honeys, and they can be used to assess the temperature sensitivity of the honeys. (C) 2002 Elsevier Science Ltd. All rights reserved.

Are wing size, wing shape and asymmetry related to field fitness of Trichogramma egg parasitoids?

The effects of wing shape, wing size, and fluctuating asymmetry in these measures oil the field fitness of T. nr. brassicae and T. pretiosum were investigated. Trichogramma wasps mass-reared on eggs of the factitious host Sitotroga cerealella were released in tomato paddocks and those females ovipositing on Helicoverpo spp. eggs were recaptured. Comparisons of the recaptured group with a sample from the release population were used to assess fitness. Wing data were obtained by positioning landmarks on mounted forewings. Size was then measured as the centroid size computed from landmark distances, while Procrustes analysis followed by principal component analysis was used to assess wing shape. Similar findings were obtained for both Trichogramma species: fitness of wasps was strongly related to wing size and some shape dimensions, but not to the asymmetries of these measures. Wasps which performed well in the field had larger wings and a different wing shape compared to wasps from the mass reared population. Both size and the shape dimensions were linearly associated with fitness although there was also some evidence for non-linear selection on shape. The results suggest that wing shape and wing size are reliable predictors of field fitness for these Trichogramma wasps.

Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.