Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Titanium Complexes for the Polymerisation of Ethene and Caprolactone

The literature part of the thesis mainly reviews the results of the use of titanium catalysts for ethene and caprolactone polymerisation. The behaviour of titanium catalysts bearing phenoxy-imino ligands has been the focus of more detailed investigations in ethene polymerisation. Reasons for the production of multimodal polyethene for a range of catalysts are also given. The experimental part of the thesis is divided into two sections based on the monomers used in the polymerisations: Part A (ethene) and part B (caprolactone). Part A: Titanium(IV) complexes bearing phenoxy-imino ligands are known to possess high ethene polymerisation activities after MAO activation. Depending on the ligand, the activities of the catalysts in polymerisation can vary between 1 and 44000 kgPE/(mol*cat*h*bar). Depending on the polymerisation temperature and the electronic and steric properties of the catalyst ligands, low to high molar mass values and uni- and multimodal polydispersity values can been observed. In order to discover the reasons for these differences, 22 titanium(IV) complexes containing differently substituted phenoxy-imino derivatives as di- and tetradentate ligands were synthesised with high yields and used as homogeneous catalysts in ethene polymerisations. Computational methods were used to predict the geometry of the synthesised complexes and their configuration after activation. Based on the results obtained, the geometry of the catalyst together with the ligand substituents seem to play a major role in defining the catalytic activity. Novel titanium(IV) complexes bearing malonate ligands were also synthesised. Malonates are considered to be suitable ligand pre-cursors since they can be produced by the simple reaction of any primary or secondary alcohol with malonylchloride, and thus they are easily modifiable. After treatment with MAO these complexes had polymerisation activities between 10 and 50 kgPE/(mol*cat*h*bar) and surprisingly low polydispersity values when compared with similar types of catalysts bearing the O?O chelate ligand. Part B: One of the synthesis routes in the preparation of the above mentioned phenoxy-imino titanium dichloride complexes involved the use of Ti(NMe2)4 with a range of salicylaldimine type compounds. On reaction, these two compounds formed an intermediate product selectively and quantitatively which was active in the ring-opening polymerisation of caprolactone. Several mono-anionic alcoholates were also combined with Ti(NMe2)4 in different molar ratios and used as catalysts. Full conversion of the monomer was achieved within 15 minutes with catalysts having a co-ordination number of 4 while after 22 hours full conversion was achieved with catalysts having a co-ordination number of 6.

Mechanoformation of ammonium perchlorate-potassium perchlorate solid solutions

Ammonium perchlorate-potassium perchlorate mixtures, upon pelletization, form a series of homogeneous solid solutions as manifested by X-ray powder diffractograms. Scanning electron microscopic studies throw light on the mechanism of the solid-solution formation. Solid solutions of ammonium perchlorate-potassium perchlorate have also been obtained by a modified cocrystallization technique. The thermal and combustion behavior of the solid solutions have also been studied, using the DTA technique and the Crawford strand burner.

Studies on Plant Aspartate Transcarbamylase Purification and Properties of the Enzyme from Mung-Bean (Phaseolus aureus) Seedlings

Aspartate transcarbamylase is purified from mung bean seedlings by a series of steps involving manganous sulphate treatment, ammonium sulphate fractionation, DEAE-cellulose chromatography, followed by a second ammonium sulphate fractionation and finally gel filtration on Sephadex-G 100. The enzyme is homogeneous on ultracentrifugation and on polyacrylamide gel electrophoresis. It functions optimally at 55°C. It has two pH optima, one at 8.0 and the other at 10.2. The enzyme follows Michaelis-Menten kinetics with l-aspartate as the variable substrate. However, it exhibits sigmoid saturation curves at both the pH optima when the concentration of carbamyl phosphate is varied. The enzyme is allosterically inhibited by UMP at both the pH optima. Increasing phosphorylation of the uridine nucleotide decreases the inhibitory effect. The enzyme is desensitized to inhibition by UMP on treatment with p-hydroxymercuribenzoate, gel electrophoresis indicating that the enzyme is dissociated by this treatment; the dissociated enzyme can be reassociated by treatment with 2-mercaptoethanol. The properties of the mung bean enzyme are compared with the enzyme from other sources.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Measuring Physiological Stress in Australian Flying-Fox Populations

Flying-foxes (pteropid bats) are the natural host of Hendra virus, a recently emerged zoonotic virus responsible for mortality or morbidity in horses and humans in Australia since 1994. Previous studies have suggested physiological and ecological risk factors for infection in flying-foxes, including physiological stress. However, little work has been done measuring and interpreting stress hormones in flying-foxes. Over a 12-month period, we collected pooled urine samples from underneath roosting flying-foxes, and urine and blood samples from captured individuals. Urine and plasma samples were assayed for cortisol using a commercially available enzyme immunoassay. We demonstrated a typical post-capture stress response in flying-foxes, established urine specific gravity as an attractive alternative to creatinine to correct urine concentration, and established population-level urinary cortisol ranges (and geometric means) for the four Australian species: Pteropus alecto 0.5–305.1 ng/mL (20.1 ng/mL); Pteropus conspicillatus 0.3–370.9 ng/mL (18.9 ng/mL); Pteropus poliocephalus 0.3–311.3 ng/mL (10.1 ng/mL); Pteropus scapulatus 5.2–205.4 ng/mL (40.7 ng/mL). Geometric means differed significantly except for P. alecto and P. conspicillatus. Our approach is methodologically robust, and has application both as a research or clinical tool for flying-foxes, and for other free-living colonial wildlife species

Allosteric serine hydroxymethyltransferase from monkey liver: temperature induced conformational transitions

The homogeneous serine hydroxymethyltransferase from monkey liver was optimally activate at 60°C and the Arrhenius plot for the enzyme was nonlinear with a break at 15°C. The monkey liver enzyme showed high thermal stability of 62°C, as monitored by circular dichroism at 222 nm, absorbance at 280 nm and enzyme activity. The enzyme exhibited a sharp co-operative thermal transition in the range of 50°-70° (Tm= 65°C), as monitored by circular dichroism. L-Serine protected the enzyme against both thermal inactivation and thermal disruption of the secondary structure. The homotropic interactions of tetrahydrofolate with the enzyme was abolished at high temperatures (at 70°C, the Hill coefficient value was 1.0). A plot of h values vs. assay temperature of tetrahydrofolate saturation experiments, showed the presence of an intermediate conformer with an h value of 1.7 in the temperature range of 45°-60°C. Inclusion of a heat denaturation step in the scheme employed for the purification of serine hydroxymethyltransferase resulted in the loss of cooperative interactions with tetrahydrofolate. The temperature effects on the serine hydroxylmethyltransferase, reported for the first time, lead to a better understanding of the heat induced alterations in conformation and activity for this oligomeric protein.

Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

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.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Optical and Physical Properties of Atmospheric Aerosols over the Bay of Bengal during ICARB

Simultaneous and collocated measurements of total and hemispherical backscattering coefficients (σ and β, respectively) at three wavelengths, mass size distributions, and columnar spectral aerosol optical depth (AOD) were made onboard an extensive cruise experiment covering, for the first time, the entire Bay of Bengal (BoB) and northern Indian Ocean. The results are synthesized to understand the optical properties of aerosols in the marine atmospheric boundary layer and their dependence on the size distribution. The observations revealed distinct spatial and spectral variations of all the aerosol parameters over the BoB and the presence of strong latitudinal gradients. The size distributions varied spatially, with the majority of accumulation modes decreasing from north to south. The scattering coefficient decreased from very high values (resembling those reported for continental/urban locations) in the northern BoB to very low values seen over near-pristine environments in the southeastern BoB. The average mass scattering efficiency of BoB aerosols was found to be 2.66 ± 0.1 m2 g−1 at 550 nm. The spectral dependence of columnar AOD deviated significantly from that of the scattering coefficients in the northern BoB, implying vertical heterogeneity in the aerosol type in that region. However, a more homogeneous scenario was observed in the southern BoB. Simultaneous lidar and in situ measurements onboard an aircraft over the ocean revealed the presence of elevated aerosol layers of enhanced extinction at altitudes of 1 to 3 km with an offshore extent of a few hundred kilometers. Back-trajectory analyses showed these layers to be associated with advection from west Asia and western India. The large spatial variations and vertical heterogeneity in aerosol properties, revealed by the present study, need to be included in the regional radiative forcing over the Bay of Bengal.

Distribution and characterization of Poleroviruses affecting food legumes in Central/West Asia and North Africa (CWANA) region and Australia

During the past 15 years, surveys to identify virus diseases affecting cool-season food legume crops in Australia and 11 CWANA countries (Algeria, China, Egypt, Ethiopia, Lebanon, Morocco, Sudan, Syria, Tunisia, Uzbekistan and Yemen) were conducted. More than 20,000 samples were collected and tested for the presence of 14 legume viruses by the tissue-blot immunoassay (TBIA) using a battery of antibodies, including the following Luteovirus monoclonal antibodies (McAbs): a broad-spectrum legume Luteovirus (5G4), BLRV, BWYV, SbDV and CpCSV. A total of 195 Luteovirus samples were selected for further testing by RT-PCR using 7 primers (one is degenerate, and can detect a wide range of Luteoviridae virus species and the other six are species-specific primers) at the Virology Laboratory, QDAF, Australia, during 2014. A total of 145 DNA fragments (represented 105 isolates) were sequenced. The following viruses were characterized based on molecular analysis: BLRV from Lebanon, Morocco, Tunisia and Uzbekistan; SbDV from Australia, Syria and Uzbekistan; BWYV from Algeria, China, Ethiopia, Lebanon, Morocco, Sudan, Tunisia and Uzbekistan; CABYV from Algeria, Lebanon, Syria, Sudan and Uzbekistan; CpCSV from Algeria, Ethiopia, Lebanon, Morocco, Syria and Tunisia, and unknown Luteoviridae species from Algeria, Ethiopia, Morocco, Sudan, Uzbekistan and Yemen. This study has clearly shown that there are a number of Polerovirus species, in addition to BWYV, all can produce yellowing/stunting symptoms in pulses (e.g. CABYV, CpCSV, and other unknown Polerovirus species). Based on our knowledge this is the first report of CABYV affecting food legumes. Moreover, there was about 95% agreement between results obtained from serological analysis (TBIA) and molecular analysis for the detection of BLRV and SbDV. Whereas, TBIA results were not accurate when using CpCSV and BWYV McAbs . It seems that the McAbs for CpCSV and BWYV used in this study and those available worldwide, are not virus species specific. Both antibodies, reacted with other Polerovirus species (e.g. CABYV, and unknown Polerovirus). This highlights the need for more accurate characterization of existing antibodies and where necessary the development of better, virus-specific antibodies to enable their use for accurate diagnosis of Poleroviruses.

Middleware for Mobile Sensing Applications in Urban Environments

Sensor networks represent an attractive tool to observe the physical world. Networks of tiny sensors can be used to detect a fire in a forest, to monitor the level of pollution in a river, or to check on the structural integrity of a bridge. Application-specific deployments of static-sensor networks have been widely investigated. Commonly, these networks involve a centralized data-collection point and no sharing of data outside the organization that owns it. Although this approach can accommodate many application scenarios, it significantly deviates from the pervasive computing vision of ubiquitous sensing where user applications seamlessly access anytime, anywhere data produced by sensors embedded in the surroundings. With the ubiquity and ever-increasing capabilities of mobile devices, urban environments can help give substance to the ubiquitous sensing vision through Urbanets, spontaneously created urban networks. Urbanets consist of mobile multi-sensor devices, such as smart phones and vehicular systems, public sensor networks deployed by municipalities, and individual sensors incorporated in buildings, roads, or daily artifacts. My thesis is that "multi-sensor mobile devices can be successfully programmed to become the underpinning elements of an open, infrastructure-less, distributed sensing platform that can bring sensor data out of their traditional close-loop networks into everyday urban applications". Urbanets can support a variety of services ranging from emergency and surveillance to tourist guidance and entertainment. For instance, cars can be used to provide traffic information services to alert drivers to upcoming traffic jams, and phones to provide shopping recommender services to inform users of special offers at the mall. Urbanets cannot be programmed using traditional distributed computing models, which assume underlying networks with functionally homogeneous nodes, stable configurations, and known delays. Conversely, Urbanets have functionally heterogeneous nodes, volatile configurations, and unknown delays. Instead, solutions developed for sensor networks and mobile ad hoc networks can be leveraged to provide novel architectures that address Urbanet-specific requirements, while providing useful abstractions that hide the network complexity from the programmer. This dissertation presents two middleware architectures that can support mobile sensing applications in Urbanets. Contory offers a declarative programming model that views Urbanets as a distributed sensor database and exposes an SQL-like interface to developers. Context-aware Migratory Services provides a client-server paradigm, where services are capable of migrating to different nodes in the network in order to maintain a continuous and semantically correct interaction with clients. Compared to previous approaches to supporting mobile sensing urban applications, our architectures are entirely distributed and do not assume constant availability of Internet connectivity. In addition, they allow on-demand collection of sensor data with the accuracy and at the frequency required by every application. These architectures have been implemented in Java and tested on smart phones. They have proved successful in supporting several prototype applications and experimental results obtained in ad hoc networks of phones have demonstrated their feasibility with reasonable performance in terms of latency, memory, and energy consumption.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.