On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Using a cartographic modeling language to manipulate spectral satellite imagery

Land related information about the Earth's surface is commonIJ found in two forms: (1) map infornlation and (2) satellite image da ta. Satellite imagery provides a good visual picture of what is on the ground but complex image processing is required to interpret features in an image scene. Increasingly, methods are being sought to integrate the knowledge embodied in mop information into the interpretation task, or, alternatively, to bypass interpretation and perform biophysical modeling directly on derived data sources. A cartographic modeling language, as a generic map analysis package, is suggested as a means to integrate geographical knowledge and imagery in a process-oriented view of the Earth. Specialized cartographic models may be developed by users, which incorporate mapping information in performing land classification. In addition, a cartographic modeling language may be enhanced with operators suited to processing remotely sensed imagery. We demonstrate the usefulness of a cartographic modeling language for pre-processing satellite imagery, and define two nerv cartographic operators that evaluate image neighborhoods as post-processing operations to interpret thematic map values. The language and operators are demonstrated with an example image classification task.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

Specification, refinement and verification of concurrent systems - An integration of Object-Z and CSP

This paper presents a method of formally specifying, refining and verifying concurrent systems which uses the object-oriented state-based specification language Object-Z together with the process algebra CSP. Object-Z provides a convenient way of modelling complex data structures needed to define the component processes of such systems, and CSP enables the concise specification of process interactions. The basis of the integration is a semantics of Object-Z classes identical to that of CSP processes. This allows classes specified in Object-Z to he used directly within the CSP part of the specification. In addition to specification, we also discuss refinement and verification in this model. The common semantic basis enables a unified method of refinement to be used, based upon CSP refinement. To enable state-based techniques to be used fur the Object-Z components of a specification we develop state-based refinement relations which are sound and complete with respect to CSP refinement. In addition, a verification method for static and dynamic properties is presented. The method allows us to verify properties of the CSP system specification in terms of its component Object-Z classes by using the laws of the the CSP operators together with the logic for Object-Z.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Ethanol-related adaptive changes and physical dependence in rats after exposure to ethanol

Adaptive changes that occur after chronic exposure to ethanol are an important component in the development of physical dependence. We have focused our research on ethanol-induced changes in the expression of several genes that may be important in adaptation. In this article, we describe adaptive changes at the level of the N-methyl-D-aspartate receptor, in the protein expression and activity of the Egr transcription factors, and in the expression of a novel gene of unknown function. (C) 2001 Elsevier Science Inc. All rights reserved.

Panmixia in Pocillopora verrucosa from South Africa

The genetic structure of six local collections of Pocillopora verrrucosa from six coral reefs in KwaZulu-Natal, South Africa, was examined using allozyme electrophoresis. The six separate reefs lie within two different reef complexes. Twenty-two enzymes were screened on five buffer systems, but only five polymorphic loci (Gpi-1, Gdh-1, Lgg-2, Lpp-1, Est-1) could be consistently resolved. No significant differences in allelic frequencies were detected among the six sites. All local collections were genotypically diverse, with evidence of only very limited clonal replication at each site. Indeed, the ratio of observed to expected genotypic diversity (mean Go:Ge=0.64 +/-0.05 SD), the ratio of observed number of genotypes to the number of individuals (mean Ng:N = 0.65 +/-0.04 SE), and deviations from the Hardy-Weinberg equilibrium indicate that sexual reproduction plays a major role in the maintenance of the populations. No genetic differentiation was found either within (FSR = 0.026 +/-0.003 SE) or between (FRT = 0.000 +/-0.001 SE) reef complexes. The homogeneity of the gene frequencies across the six reefs strongly supports the assumption that the KwaZulu-Natal reef complexes are highly connected by gene flow (Nem=44). The reefs in the southern and central reef complexes along the northern Maputaland coastline can therefore be considered part of a single population.

Phylogenetic classification of Eudorylini (Diptera: Pipunculidae)

The phylogenetic relationships of members of Eudorylini (Diptera: Pipunculidae: Pipunculinae) were explored. Two hundred and fifty-seven species of Eudorylini from all biogeographical regions and all known genera were examined. Sixty species were included in an exemplar-based phylogeny for the tribe. Two new genera are described, Clistoabdominalis and Dasydorylas. The identity of Eudorylas Aczél, the type genus for Eudorylini, has been obscure since its inception. The genus is re-diagnosed and a proposal to stabilize the genus and tribal names is discussed. An illustrated key to the genera of Pipunculidae is presented and all Eudorylini genera are diagnosed. Numerous new generic synonyms are proposed. Moriparia nigripennis Kozánek & Kwon is preoccupied by Congomyia nigripennis Hardy when both are transferred to Claraeola, so Cla. koreana Skevington is proposed as a new name for Mo. nigripennis.

The effect of coal particle size on colorimetric analysis of roadway dust

Colorimetric analysis of roadway dust is currently a method for monitoring the incombustible content of mine roadways within Australian underground coal mines. To test the accuracy of this method, and to eliminate errors of judgement introduced by human operators in the analysis procedure, a number of samples were tested using scanning software to determine absolute greyscale values. High variability and unpredictability of results was noted during this testing, indicating that colorimetric testing is sensitive to parameters within the mine that are not currently reproduced in the preparation of reference samples. This was linked to the dependence of colour on particle surface area, and hence also to the size distribution of coal particles within the mine environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

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.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.