Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Growth of a Bose-Einstein condensate: a detailed comparison of theory and experiment

We extend the earlier model of condensate growth of Davis et at (Davis M J, Gardiner C W and Ballagh R J 2000 Phys. Rev. A 62 063608) to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by Kohl et al (Kohl M, Davis M J, Gardiner C W, Hansch T and Esslinger T 2001 Preprint cond-mat/0106642) who study the formation of a rubidium Bose-Einstein condensate for a range of evaporative cooling parameters. We find that, in the regime where our model is valid, the theoretical curves agree with all the experimental data with no fitting parameters. However, for the slowest cooling of the gas the theoretical curve deviates significantly from the experimental curves. It is possible that this discrepancy may be related to the formation of a quasicondensate.

Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Limits to squeezing in the degenerate optical parametric oscillator

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Testing insect movement theory: empirical analysis of pest data routinely collected from agricultural crops

Observations of an insect's movement lead to theory on the insect's flight behaviour and the role of movement in the species' population dynamics. This theory leads to predictions of the way the population changes in time under different conditions. If a hypothesis on movement predicts a specific change in the population, then the hypothesis can be tested against observations of population change. Routine pest monitoring of agricultural crops provides a convenient source of data for studying movement into a region and among fields within a region. Examples of the use of statistical and computational methods for testing hypotheses with such data are presented. The types of questions that can be addressed with these methods and the limitations of pest monitoring data when used for this purpose are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Corporate stadium sponsorships, signaling theory, agency conflicts, and shareholder wealth

Contrary to the plethora of critical articles recently appearing in both the popular and business press, this carefully controlled investigation of 49 stadium- and arena-naming-rights agreement announcements provides striking evidence that such sponsorships can significantly enhance the stock prices of sponsoring companies. Indeed, the results of the study show that the average stadium sponsor's stock prices increased by 1.65 percent at the time of announcement of the programs-a result considerably in excess of the returns associated with other major marketing programs such as the signing of Olympic sponsorships and celebrity endorsers. A multiple regression analysis employing firm-specific changes in stock prices as the dependent variable and quantifiable corporate and sponsorship-related attributes as independent variables is also presented. Variables positively and significantly correlated with perceived sponsorship success include team-winning percentages, contract length, and high technology and locally based companies. Overall, the findings of the study are consistent with the novel hypothesis that, for some firms, the real value-added of a stadium sponsorship may lie in its ability to serve as an effective or honest signal of managerial confidence in the future of the company.

History of the events leading to the formulation of the apoptosis concept

Histological studies of ischaemic liver injury performed between 1962 and 1964 distinguished two types of cell death: classical necrosis, and a process involving conversion of scattered cells into small round masses of cytoplasm that often contained specks of condensed nuclear chromatin. Enzyme histochemistry demonstrated rupture of lysosomes in the former, but preservation of lysosomes in the latter. Similar small round masses were also observed sparsely in normal liver. Electron microscopy showed that the small round bodies resulted from cellular condensation and budding, that they were bounded by membranes and contained intact organelles, and that they were phagocytosed and digested by resident tissue cells, including epithelial cells. In work done in association with Jeffrey Searle, the process was found to occur spontaneously in a variety of malignant tumours and to be enhanced in squamous cell carcinomas of skin responding to radiotherapy. During 1971-1972, I collaborated with Andrew Wyllie and Alastair Currie while on sabbatical leave in Scotland. The newly defined type of cell death was shown to be regulated by hormones in the adrenal cortex and in breast carcinomas. Further, review of published electron micrographs of the cell death known to play an essential role in normal development revealed the same morphological pattern. We proposed that this distinctive phenomenon subserves a general homoeostatic function and suggested it be called apoptosis. © 2002 Elsevier Science Ireland Ltd. All rights reserved.

Bishadowing and hyperbolicity

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Child welfare workers' use of theory in working with physical child abuse: Implications for professional supervision

This article examines child welfare workers' understanding of physical child abuse and the Implications for those supervising these workers. The article Is based on the results of a study that involved In-depth Interviews and focus groups with statutory child welfare workers. Analysis revealed that workers' understanding of physical child abuse embodied a wide range of ideas that were generally consistent with existing literature. The study highlights the value and utility of a reflective approach In stimulating and making explicit the theoretical underpinnings of child welfare workers practice. Specific Implications for professional supervision are addressed.

Exact theory of sedimentation equilibrium made useful

The exact description of the thermodynamics of solutions has been used to describe, without approximation, the distribution of all the components of an incompressible solution in a centrifuge cell at sedimentation equilibrium. Thermodynamic parameters describing the interactions between solute components of known molar mass can be obtained by direct analysis of the experimental data. Interpretation of the measured thermodynamic parameters in terms of molecular interactions requires that an arbitrary distinction be made between nonassociative forces, like hard-sphere volume-exclusion and mean-field electrostatic repulsion or attraction, and specific short-range forces of association that give rise to the formation of molecular aggregates. Provided the former can be accounted for adequately, the effects of the latter can be elucidated in the form of good estimates of the equilibrium constants for the reactions of aggregation.

Theory of mind and peer acceptance in preschool children

Two studies tested the hypothesis that preschool children's theory of mind ability is related to their levels of peer acceptance. In Study 1, 78 children between the ages of 4 and 6 provided peer nominations that allowed determination of social preference and social impact scores, and classification in one of five peer status groups (following Coie & Dodge, 1983). Children were also tested on five different theory of mind tasks. The results showed that theory of mind scores were significantly related to social preference scores in a subsample of children who were over 5 years old. Further, popular children were found to score higher on theory of mind tasks than children classified as rejected. Study 2 replicated and extended the first study with a new sample of 87 4- to 6-year-old children. Study 2 included measures of peer acceptance, theory of mind ability and verbal intelligence, as well as teacher ratings of prosocial and aggressive behaviours. The results of Study 2 showed that for the total group of children, prosocial behaviour was the best predictor of social preference scores. When the Study 2 sample was split into older and younger children, theory of mind ability was found to be the best predictor of social preference scores for the older children (over age 5), while aggressive and prosocial behaviours were the best predictors of peer acceptance in the younger children. Overall, the pattern of results suggests that the impact of theory of mind ability on peer acceptance is modest but increases with children's age.

Usefulness of clinical risk markers and ischemic threshold to stratify risk in patients undergoing major noncardiac surgery

The risk of cardiac events in patients undergoing major noncardiac surgery is dependent on their clinical characteristics and the results of stress testing. The purpose of this study was to develop a composite approach to defining levels of risk and to examine whether different approaches to prophylaxis influenced this prediction of outcome. One hundred forty-five consecutive patients (aged 68 +/- 9 years, 79 men) with >1 clinical risk variable were studied with standard dobutamine-atropine stress echo before major noncardiac surgery. Risk levels were stratified according to the presence of ischemia (new or worsening wall motion abnormality), ischemic threshold (heart rate at development of ischemia), and number of clinical risk variables. Patients were followed for perioperative events (during hospital admission) and death or infarction over the subsequent 16 10 months. Ten perioperative events occurred in 105 patients who proceeded to surgery (10%, 95% confidence interval [CI] 5% to 17%), 40 being cancelled because of cardiac or other risk. No ischemia was identified in 56 patients, 1 of whom (1.8%) had a perioperative infarction. Of the 49 patients with ischemia, 22 (45%) had 1 or 2 clinical risk factors; 2 (9%, 95% CI 1% to 29%) had events. Another 15 patients had a high ischemic threshold and 3 or 4 risk factors; 3 (20%, 95% Cl 4% to 48%) had events. Twelve patients had a low ischemic threshold and 3 or 4 risk factors; 4 (33%, 95% CI 10% to 65%) had events. Preoperative myocardial revascularization was performed in only 3 patients, none of whom had events. Perioperative and long-term events occurred despite the use of beta blockers; 7 of 41 eta blocker-treated patients had a perioperative event (17%, 95% CI 7% to 32%); these treated patients were at higher anticipated risk than untreated patients (20 +/- 24% vs 10 +/- 19%, p = 0.02). The total event rate over late follow-up was 13%, and was predicted by dobutamine-atropine stress echo results and heart rate response. (C) 2002 by Excerpta Medica, Inc.