Structure of shock waves at re-entry speeds

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.

Unusual effects of anisotropic bonding in Cu(II) and Ni(II) oxides with K2NiF4 structure

Geometric constraints present in A2BO4 compounds with the tetragonal-T structure of K2NiF4 impose a strong pressure on the B---OII---B bonds and a stretching of the A---OI---A bonds in the basal planes if the tolerance factor is t congruent with RAO/√2 RBO < 1, where RAO and RBO are the sums of the A---O and B---O ionic radii. The tetragonal-T phase of La2NiO4 becomes monoclinic for Pr2NiO4, orthorhombic for La2CuO4, and tetragonal-T′ for Pr2CuO4. The atomic displacements in these distorted phases are discussed and rationalized in terms of the chemistry of the various compounds. The strong pressure on the B---OII---B bonds produces itinerant σ*x2−y2 bands and a relative stabilization of localized dz2 orbitals. Magnetic susceptibility and transport data reveal an intersection of the Fermi energy with the d2z2 levels for half the copper ions in La2CuO4; this intersection is responsible for an intrinsic localized moment associated with a configuration fluctuation; below 200 K the localized moment smoothly vanishes with decreasing temperature as the d2z2 level becomes filled. In La2NiO4, the localized moments for half-filled dz2 orbitals induce strong correlations among the σ*x2−y2 electrons above Td reverse similar, equals 200 K; at lower temperatures the σ*x2−y2 electrons appear to contribute nothing to the magnetic susceptibility, which obeys a Curie-Weiss law giving a μeff corresponding to S = 1/2, but shows no magnetic order to lowest temperatures. These surprising results are verified by comparison with the mixed systems La2Ni1−xCuxO4 and La2−2xSr2xNi1−xTixO4. The onset of a charge-density wave below 200 K is proposed for both La2CuO4 and La2NiO4, but the atomic displacements would be short-range cooperative in mixed systems. The semiconductor-metallic transitions observed in several systems are found in many cases to obey the relation Ea reverse similar, equals kTmin, where varrho = varrho0exp(−Ea/kT) and Tmin is the temperature of minimum resistivity varrho. This relation is interpreted in terms of a diffusive charge-carrier mobility with Ea reverse similar, equals ΔHm reverse similar, equals kT at T = Tmin.

Historical demography of Lantana camara L. reveals clues about the influence of land use and weather in the management of this widespread invasive species

Weather is a general stochastic influence on the life history of weeds. In contrast, anthropogenic disturbance (e.g. land use) is an important deterministic influence on weed demography. Our aim with this study was to investigate the relative contributions of land use and weather on the demography of Lantana camara (lantana), a weed of agricultural and natural habitats, based on the intensive monitoring of lantana populations under three land uses (viz. farm[pasture], and burnt and grazed forests) in subtropical Australia. Lantana populations were growing vigorously across all land uses (asymptotic population growth rate, lambda > 3). Examination of historical demography using retrospective perturbation analyses showed that weather was a strong influence on lantana demography with the transition from an El Nino (2008-09) to a La Nina (2009-10) year having a strong positive effect on population growth rate. This effect was most marked at the grazed site, and to a lesser extent at the burnt site, with seedling-to-juvenile and juvenile-to-adult transitions contributing most to these effects. This is likely the result of burning and grazing having eliminated/reduced interspecific competition at these sites. Prospective perturbation analyses revealed that lambda was most sensitive to proportionate changes in growth transitions, followed by fecundity and survival transitions. Examination of context-specific patterns in elasticity revealed that growth and fecundity transitions are likely to be the more critical vital rates to reduce lambda in wet years at the burnt and grazed forest sites, compared to the farm/pasture site. Management of lantana may need to limit the transition of juveniles into the adult stages, especially in sites where lantana is free from competition (e.g. in the presence of fire or grazing), and this particularly needs to be achieved in wet years. Collectively, these results shed light on aspects of spatial and temporal variation in the demography of lantana, and offer insights on its context-specific management.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Historical demography of Lantana camara L. reveals clues about the influence of land use and weather in the management of this widespread invasive species

Weather is a general stochastic influence on the life history of weeds. In contrast, anthropogenic disturbance (e.g. land use) is an important deterministic influence on weed demography. Our aim with this study was to investigate the relative contributions of land use and weather on the demography of Lantana camara (lantana), a weed of agricultural and natural habitats, based on the intensive monitoring of lantana populations under three land uses (viz. farm[pasture], and burnt and grazed forests) in subtropical Australia. Lantana populations were growing vigorously across all land uses (asymptotic population growth rate, λ > 3). Examination of historical demography using retrospective perturbation analyses showed that weather was a strong influence on lantana demography with the transition from an El Niño (2008–09) to a La Niña (2009–10) year having a strong positive effect on population growth rate. This effect was most marked at the grazed site, and to a lesser extent at the burnt site, with seedling-to-juvenile and juvenile-to-adult transitions contributing most to these effects. This is likely the result of burning and grazing having eliminated/reduced interspecific competition at these sites. Prospective perturbation analyses revealed that λ was most sensitive to proportionate changes in growth transitions, followed by fecundity and survival transitions. Examination of context-specific patterns in elasticity revealed that growth and fecundity transitions are likely to be the more critical vital rates to reduce λ in wet years at the burnt and grazed forest sites, compared to the farm/pasture site. Management of lantana may need to limit the transition of juveniles into the adult stages, especially in sites where lantana is free from competition (e.g. in the presence of fire or grazing), and this particularly needs to be achieved in wet years. Collectively, these results shed light on aspects of spatial and temporal variation in the demography of lantana, and offer insights on its context-specific management.

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

On the determination of energy eigenvalues and coupling strengths using duality

The Shifman-Vainshtein-Zakharov method of determining the eigenvalues and coupling strengths, from the operator product expansion, for the current correlation functions is studied in the nonrelativistic context, using the semiclassical expansion. The relationship between the low-lying eigenvalues, and the leading corrections to the imaginary-time Green function is elucidated by comparing systems which have almost identical spectra. In the case of an anharmonic oscillator it is found that with the procedure stated in the paper, that inclusion of more terms to the asymptotic expansion does not show any simple trend towards convergence to the exact values. Generalization to higher partial waves is given. In particular for the P-level of the oscillator, the procedure gives poorer results than for the S-level, although the ratio of the two comes out much better.

Theological Exegesis in the Canonical Context : Brevard S. Childs' Methodology of Biblical Theology

Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.

Structure of shock waves in partially ionized argon

The paper presents a unified picture of the structure of steady one-dimensional shock waves in partially ionized argon in the absence of external electric and magnetic fields. The study is based on a two-temperature three-fluid continuum approach using the Navier-Stokes equations as a model and taking account of nonequilibrium ionization. The analysis of the governing equations is based on the method of matched asymptotic expansions and leads to three layers: (1) a broad thermal layer dominated by electron thermal conduction; (2) an atom-ion shock structured by heavy-particle collisional dissipative mechanisms; and (3) an ionization relaxation layer in which electron-atom inelastic collisions dominate.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Low-frequency degenerate surface modes of an electron-hole plasma

The computations of Flahive and Quinn1 of the dispersion curves of low frequency degenerate surface (DS) modes propagating along the magnetic field in an electron-hole plasma are extended to higher values of the wavenumber. We find that beyond a certain value of the wavenumber the DS mode re-enters the allowed region of surface wave propagation and tends to an asymptotic frequency ωR (<ωLH). These low frequency resonances of an electron-hole plasma are discussed with reference to the experimental observations.

Effect of viscosity on internal waves from a source in a wall

The solution for a line source of oscillatory strength kept at the origin in a wall bounding a semi-infinite viscous imcompressible stratified fluid is presented in an integral form. The behaviour of the flow at far field and near field is studied by an asymptotic expansion procedure. The streamlines for different parameters are drawn and discussed. The real characteristic straight lines present in the inviscid problem are modified by the viscosity and the solutions obtained are valid even at the resonance frequency.