Toxicant distributions and impact models in environmental risk analysis of waste sites

Myrkyllisten aineiden jakaumat ja vaikutusmallit jätealueiden ympäristöriskien analyysissä.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds. We apply our results to give a distributed (2 + ε)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

A new model for the breakage frequency of drops in turbulent stirred dispersions

A model of drop breakage in turbulent stirred dispersions based on interaction of a drop with eddies of a length scale smaller than the drop diameter has been developed. It predicts that, unlike the equal breakage assumed by earlier models, a large drop reduces in size due to stripping of smaller segments off it through unequal breakage. It is only when the drop nears the value of the maximum stable drop diameter that it breaks into equal parts. This new model of drop breakage, coupled with the pattern of interaction of drops with eddies of different sizes existing in the vessel, has been used to evaluate not only the breakage frequency, but also the size distribution of the daughter droplets(which was hitherto assumed). The model has been incorporated in the population balance equation and the resulting cumulative size distributions compared with those availble in the literature.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Vesicle and Stable Monolayer Formation from Simple ``Click'' Chemistry Adducts in Water

Click chemistry has been successfully extended into the field of molecular design of novel amphiphatic adducts. After their syntheses and characterizations, we have studied their aggregation properties in aqueous medium. Each of these adducts forms stable suspensions in water. These suspensions have been characterized by dynamic light scattering (DLS) studies and transmission electron microscopy (TEM). The presence of inner aqueous compartments in such aggregates has been demonstrated using dye (methylene blue) entrapment studies. These aggregates have been further characterized using X-ray diffraction (XRD), which indicates the existence of bilayer structures in them. Therefore, the resulting aggregates could be described as vesicles. The temperature-induced order-to-disorder transitions of the vesicular aggregates and the accompanying changes in their packing and hydration have been examined using high-sensitivity differential scanning calorimetry, fluorescence anisotropy, and generalized polarization measurements using appropriate membrane-soluble probe, 1,6-diphenylhexatriene, and Paldan, respectively. The findings of these studies are consistent with each other in terms of the apparent phase transition temperatures. Langmuir monolayer studies confirmed that these click adducts also form stable monolayers on buffered aqueous subphase at the air-water interface.

An Approach Toward Homocalystegines and Silyl-homocalystegines. Acid-Mediated Migrations of Acetates in Seven-Membered Ring Systems

A short access to homocalystegine analogues silylated at C7 is described. The synthesis involves the desymmetrization of a (phenyldimethylsilyl)methylcycloheptatriene using osmium-mediated dihydroxylation, followed by the diol protection and a cycloaddition involving the remaining diene moiety and an acylnitroso reagent. Additions of the osmium and acylnitroso reagents were shown, through X-ray diffraction studies of the resulting major isomers, to occur anti and syn, respectively, relative to the SiCH2 substituent. N-O bond cleavage on the resulting cycloadduct then produces the aminopolyol having a silylmethyl substituent. Oxidation of the C-Si bond also afforded an access to unusual amino-heptitols having five contiguous stereogenic centers. In the course of this work, we finally observed a unusual rearrangement taking place on cycloheptanone 18 substituted by two acetyl groups and a neighboring Boc-protected amine. A profound reorganization of the substituents on the seven-membered ring effectively took place under acidic conditions (TFA) leading to the thermodynamically more stable homocalystegine-type compound., DFT calculations of the conformational energy of isomeric silyl homocalystegines indicated that the product observed upon the acid-mediated rearrangement was the most stable of a series of analogues with various distributions of substituents along the seven-membered ring backbone. A tentative mechanism is proposed to rationalize the acetate migrations and inversions of the stereochemistry at various stereocenters.

A β,β,β-trialkoxyethyllithium stable towards fragmentation: a carboxyl protected acetic acid dianion equivalent

The novel alkyllithium 1b is not only intriguingly stable towards fragmentation, but also a synthetically useful reagent, complementing current carboxylic ester enolate methodology. Its design is based on interesting mechanistic principles, and harnesses the known stability of the 2,4,10-trioxaadamantane framework.

Geographical Distribution Patterns of Amphibians in the Western Ghats, India

The Western Ghats of India are very rich in amphibian species with 117 species of frogs, toads and caecilians. Eighty-nine species are endemic to this biogeographical region. Analysis of ranges and patterns of geographical distribution of amphibians on the Western Ghats suggest that the southern half of the Western Ghats and the low-medium elevation hills are more diverse in species than the northern half and higher hills. This is attributed to the more widespread rainfall and the less variable climatic conditions in the south. About half the species are apparently localized. Of those species with wider ranges, a majority show patchy distribution. Species preferring the moist evergreen forests as habitats tend to have patchy distributions. This appears to be a result of habitat destruction and fragmentation. The overall patterns of species richness and local endemism are rather different from those of the angiosperms and birds. In birds and angiosperms, a significant proportion of endemics are found on the higher hills. On the contrary, endemic amphibian species are found in the lower altitudinal range of 0-1000 m, with a majority between 800 and 1000 m.

High level stable expression of rat brain type IIA sodium channel ?-subunit in CHO cells

The neuronal sodium channels are responsible for the rising phase of action potential and are composed of three subunits, of which the alpha-subunit has been shown to be adequate for most of its functional properties. We have stably expressed the rat brain type IIA sodium channel alpha-subunit in CHO cell tine using a CMV promoter-based vector. The expression was confirmed by detecting a 6.5 kb RNA corresponding to sodium channel alpha-subunit using Northern hybridization. The cells stably expressing the alpha-subunit, yield isolated sodium currents of amplitudes greater than 4nA when studied in whole-cell configuration of the patch-clamp technique. The sodium currents are characterized by activation and inactivation properties similar to neuronal sodium channels, and are blocked by the voltage gated sodium channel blocker tetrodotoxin (TTX).

Adaptive optimal tuning of a general class of stable LTI systems with restricted inputs

The problem addressed is one of model reference adaptive control (MRAC) of asymptotically stable plants of unknown order with zeros located anywhere in the s-plane except at the origin. The reference model is also asymptotically stable and lacking zero(s) at s = 0. The control law is to be specified only in terms of the inputs to and outputs of the plant and the reference model. For inputs from a class of functions that approach a non-zero constant, the problem is formulated in an optimal control framework. By successive refinements of the sub-optimal laws proposed here, two schemes are finally design-ed. These schemes are characterized by boundedness, convergence and optimality. Simplicity and total time-domain implementation are the additional striking features. Simulations to demonstrate the efficacy of the control schemes are presented.

Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid

Natural convection from an isothermal vertical surface to a thermally stratified fluid is studied numerically. A wide range of stratification levels is considered. It is shown that at high levels of ambient thermal stratification, a portion at the top of the plate absorbs heat, while a horizontal plume forms around a location where the plate temperature equals the ambient temperature. The plume is shown to be inherently unsteady, and its transient nature is investigated in detail. The effect of the temperature defect in striating the plume is discussed. Average Nusselt number data are presented for Pr = 6.0 and 0.7.

Stable carbon isotope ratios in Asian elephant collagen: implications for dietary studies

Stable carbon isotope ratios in bone collagen have been used in a variety of dietary studies in modern and fossil animals, including humans. Inherent in the stable isotope technique is the assumption that the isotopic signature is a reflection of the diet and is persistent in collagen because this is a relatively inert protein. Carbon isotope analyses of bones from a southern Indian population of Asian elephant (Elephas maximus), a long-lived mammal that alternates seasonally between a predominantly C3 (browse) and C4 (grass) plant diet, showed two patterns that have important implications for dietary interpretation based on isotopic studies. Relative to the quantity of the two plant types consumed on average, the ?13C signal in collagen indicated that more carbon was incorporated from C3 plants, possibly due to their higher protein contribution. There was a much greater variance in ?13C values of collagen in sub-adult (range -10.5� to-22.7�, variance=14.51) compared to adult animals (range -16.0� to -20.3�, variance=1.85) pointing to high collagen turnover rates and non-persistent isotopic signatures in younger, growing animals. It thus seems important to correct for any significant relative differences in nutritive value of food types and also consider the age of an animal before drawing definite conclusions about its diet from isotope ratios.

The fatigue crack growth rate in L-72 Al-alloy plate specimens with cold worked holes

A fatigue crack growth rate study has been carried out on L-72 aluminium alloy plate specimens with and without cold worked holes. The cold worked specimens showed significantly increased fatigue life compared to unworked specimens. Computer software is developed to evaluate the stress intensity factor for non-uniform stress distributions using Green's function approach. The exponents for the Paris equation in the stable crack growth region for cold worked and unworked specimens are 1.26 and 3.15 respectively. The reduction in exponent value indicates the retardation in crack growth rate. An SEM study indicates more plastic deformation at the edge of the hole for unworked samples as compared to the worked samples during the crack initiation period.