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.

Testing the beneficial acclimation hypothesis

Recent developments in evolutionary physiology have seen many of the long-held assumptions within comparative physiology receive rigorous experimental analysis. Studies of the adaptive significance of physiological acclimation exemplify this new evolutionary approach. The beneficial acclimation hypothesis (BAH) was proposed to describe the assumption that all acclimation changes enhance the physiological performance or fitness of an individual organism. To the surprise of most physiologists, all empirical examinations of the BAH have rejected its generality. However, we suggest that these examinations are neither direct nor complete tests of the functional benefit of acclimation. We consider them to be elegant analyses of the adaptive significance of developmental plasticity, a type of phenotypic plasticity that is very different from the traditional concept of acclimation that is used by comparative physiologists.

Electric-field-induced Mott insulating states in organic field-effect transistors

We consider the possibility that the electrons injected into organic field-effect transistors are strongly correlated. A single layer of acenes can be modeled by a Hubbard Hamiltonian similar to that used for the κ-(BEDT-TTF)2X family of organic superconductors. The injected electrons do not necessarily undergo a transition to a Mott insulator state as they would in bulk crystals when the system is half-filled. We calculate the fillings needed for obtaining insulating states in the framework of the slave-boson theory and in the limit of large Hubbard repulsion U. We also suggest that these Mott states are unstable above some critical interlayer coupling or long-range Coulomb interaction.

Separating the quantum sidebands of an optical field

In this paper we investigate the quantum optics of a double-ended optical cavity. We show that an impedance matched, far-detuned cavity can be used to separate the positive and negative sidebands of a field. The 'missing' sideband will be replaced by the equivalent sideband incident on the cavity from the other direction. This technique can be used to convert the quantum correlations between the sidebands of the incident fields into quantum correlations between the two spatially distinct output fields. We show that, under certain experimental conditions, the fields emerging from the cavity will display entanglement.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

l-(BETS)2FeCl4 undergoes transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe31 magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. We show how He can be extracted from the observed splitting of the Shubnikov–de Haas frequencies. We predict the field range for field-induced superconductivity in other materials.

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.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Mapping glider habitat in dry eucalypt forests for Montreal Process indicator 1.1: Fragmentation of forest types

Accurate habitat mapping is critical to landscape ecological studies such as required for developing and testing Montreal Process indicator 1.1e, fragmentation of forest types. This task poses a major challenge to remote sensing, especially in mixedspecies, variable-age forests such as dry eucalypt forests of subtropical eastern Australia. In this paper, we apply an innovative approach that uses a small section of one-metre resolution airborne data to calibrate a moderate spatial resolution model (30 m resolution; scale 1:50 000) based on Landsat Thematic Mapper data to estimate canopy structural properties in St Marys State Forest, near Maryborough, south-eastern Queensland. The approach applies an image-processing model that assumes each image pixel is significantly larger than individual tree crowns and gaps to estimate crown-cover percentage, stem density and mean crown diameter. These parameters were classified into three discrete habitat classes to match the ecology of four exudivorous arboreal species (yellowbellied glider Petaurus australis, sugar glider P. breviceps, squirrel glider P. norfolcensis , and feathertail glider Acrobates pygmaeus), and one folivorous arboreal marsupial, the greater glider Petauroides volans. These species were targeted due to the known ecological preference for old trees with hollows, and differences in their home range requirements. The overall mapping accuracy, visually assessed against transects (n = 93) interpreted from a digital orthophoto and validated in the field, was 79% (KHAT statistic = 0.72). The KHAT statistic serves as an indicator of the extent that the percentage correct values of the error matrix are due to ‘true’ agreement verses ‘chance’ agreement. This means that we are able to reliably report on the effect of habitat loss on target species, especially those with a large home range size (e.g. yellow-bellied glider). However, the classified habitat map failed to accurately capture the spatial patterning (e.g. patch size and shape) of stands with a trace or sub-dominance of senescent trees. This outcome makes the reporting of the effects of habitat fragmentation more problematic, especially for species with a small home range size (e.g. feathertail glider). With further model refinement and validation, however, this moderateresolution approach offers an important, cost eff e c t i v e advancement in mapping the age of dry eucalypt forests in the region.

Testing the relationship between morphological and molecular rates of change along phylogenies

Molecular evolution has been considered to be essentially a stochastic process, little influenced by the pace of phenotypic change. This assumption was challenged by a study that demonstrated an association between rates of morphological and molecular change estimated for total-evidence phylogenies, a finding that led some researchers to challenge molecular date estimates of major evolutionary radiations. Here we show that Omland's (1997) result is probably due to methodological bias, particularly phylogenetic nonindependence, rather than being indicative of an underlying evolutionary phenomenon. We apply three new methods specifically designed to overcome phylogenetic bias to 13 published phylogenetic datasets for vertebrate taxa, each of which includes both morphological characters and DNA sequence data. We find no evidence of an association between rates of molecular and morphological rates of change.

Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study. (C) 2002 Elsevier Science Ltd. All rights reserved.