A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

L-Fuzzy Structured Query Language

Lattice valued fuzziness is more general than crispness or fuzziness based on the unit interval. In this work, we present a query language for a lattice based fuzzy database. We define a Lattice Fuzzy Structured Query Language (LFSQL) taking its membership values from an arbitrary lattice L. LFSQL can handle, manage and represent crisp values, linear ordered membership degrees and also allows membership degrees from lattices with non-comparable values. This gives richer membership degrees, and hence makes LFSQL more flexible than FSQL or SQL. In order to handle vagueness or imprecise information, every entry into an L-fuzzy database is an L-fuzzy set instead of crisp values. All of this makes LFSQL an ideal query language to handle imprecise data where some factors are non-comparable. After defining the syntax of the language formally, we provide its semantics using L-fuzzy sets and relations. The semantics can be used in future work to investigate concepts such as functional dependencies. Last but not least, we present a parser for LFSQL implemented in Haskell.

The Effects of Magnetic Dilution and Applied Pressure on Several Frustrated Spinels

The effects of magnetic dilution and applied pressure on frustrated spinels GeNi2O4, GeCo2O4, and NiAl2O4 are reported. Dilution was achieved by substitution of Mg2+ in place of magnetically active Co2+ and Ni2+ ions. Large values of the percolation thresholds were found in GeNi(2-x)MgxO4. Specifically, pc1 = 0.74 and pc2 = 0.65 in the sub-networks associated with the triangular and kagome planes, respectively. This anomalous behaviour may be explained by the kagome and triangular planes behaving as coupled networks, also know as a network of networks. In simulations of coupled lattices that form a network of networks, similar anomalous percolation threshold values have been found. In addition, at dilution levels above x=0.30, there is a T^2 dependency in the magnetic heat capacity which may indicate two dimensional spin glass behaviour. Applied pressures in the range of 0 GPa to 1.2 GPa yield a slight decrease in ordering temperature for both the kagome and triangular planes. In GeCo(2-x)MgxO4, the long range magnetic order is more robust with a percolation threshold of pc=0.448. Similar to diluted nickel germanate, at low temperatures, a T^2 magnetic heat capacity contribution is present which indicates a shift from a 3D ordered state to a 2D spin glass state in the presence of increased dilution. Dynamic magnetic susceptibility data indicate a change from canonical spin glass to a cluster glass behaviour. In addition, there is a non-linear increase in ordering temperature with applied pressure in the range P = 0 to 1.0 GPa. A spin glass ground state was observed in Ni(1-x)MgxAl2O4 for (x=0 to 0.375). Analysis of dynamic magnetic susceptibility data yield a characteristic time of tau* = 1.0x10^(-13) s, which is indicative of canonical spin glass behaviour. This is further corroborated by the linear behaviour of the magnetic specific heat contribution. However, the increasing frequency dependence of the freezing temperature suggests a trend towards spin cluster glass formation.

Étude de la formation d'une communauté épistémique : l'influence réciproque d'acteurs sociaux et de conceptualisations en santé publique

L'étude de la formation d'une communauté épistémique québécoise en santé publique en ayant recours à l'interactionnisme-structural permet d'appréhender ce phénomène social sous l'angle d'une influence réciproque entre d'une part des acteurs sociaux interagissant entre-eux et d'autre part, des conceptualisations variées des objets de santé publique; ces éléments sociaux et sémantiques subissent des transformations simultanées. Notre étude démontre et illustre qu'au même moment où un réseau social de chercheurs prend forme, une thématique nouvelle prend place et rallie ces mêmes chercheurs, non pas seulement dans leurs relations sociales, mais dans les idées qu'ils manipulent lors de leur travail de production et de diffusion de connaissances; les identités sociales se lient, mais pas au hasard, parce qu'elles partagent des éléments sémantiques communs. C'est notamment en explorant 20 ans de collaborations scientifiques à l'aide d'outils d'analyse de réseaux, d'analyse en composantes discrètes et par l'exporation de treillis de Galois que cette étude a été menée. Notre approche est principalement exploratoire et une attention toute particulière est portée sur les aspects méthodologiques et théoriques du travail de recherche scientifique.

Identification d’une architecture à base de composants dans une application orientée objets à l’aide d’une analyse dynamique

Un système, décrit avec un grand nombre d'éléments fortement interdépendants, est complexe, difficile à comprendre et à maintenir. Ainsi, une application orientée objet est souvent complexe, car elle contient des centaines de classes avec de nombreuses dépendances plus ou moins explicites. Une même application, utilisant le paradigme composant, contiendrait un plus petit nombre d'éléments, faiblement couplés entre eux et avec des interdépendances clairement définies. Ceci est dû au fait que le paradigme composant fournit une bonne représentation de haut niveau des systèmes complexes. Ainsi, ce paradigme peut être utilisé comme "espace de projection" des systèmes orientés objets. Une telle projection peut faciliter l'étape de compréhension d'un système, un pré-requis nécessaire avant toute activité de maintenance et/ou d'évolution. De plus, il est possible d'utiliser cette représentation, comme un modèle pour effectuer une restructuration complète d'une application orientée objets opérationnelle vers une application équivalente à base de composants tout aussi opérationnelle. Ainsi, La nouvelle application bénéficiant ainsi, de toutes les bonnes propriétés associées au paradigme composants. L'objectif de ma thèse est de proposer une méthode semi-automatique pour identifier une architecture à base de composants dans une application orientée objets. Cette architecture doit, non seulement aider à la compréhension de l'application originale, mais aussi simplifier la projection de cette dernière dans un modèle concret de composant. L'identification d'une architecture à base de composants est réalisée en trois grandes étapes: i) obtention des données nécessaires au processus d'identification. Elles correspondent aux dépendances entre les classes et sont obtenues avec une analyse dynamique de l'application cible. ii) identification des composants. Trois méthodes ont été explorées. La première utilise un treillis de Galois, la seconde deux méta-heuristiques et la dernière une méta-heuristique multi-objective. iii) identification de l'architecture à base de composants de l'application cible. Cela est fait en identifiant les interfaces requises et fournis pour chaque composant. Afin de valider ce processus d'identification, ainsi que les différents choix faits durant son développement, j'ai réalisé différentes études de cas. Enfin, je montre la faisabilité de la projection de l'architecture à base de composants identifiée vers un modèle concret de composants.

On Space-Time Trade-Off for Montgomery Multipliers over Finite Fields

La multiplication dans le corps de Galois à 2^m éléments (i.e. GF(2^m)) est une opérations très importante pour les applications de la théorie des correcteurs et de la cryptographie. Dans ce mémoire, nous nous intéressons aux réalisations parallèles de multiplicateurs dans GF(2^m) lorsque ce dernier est généré par des trinômes irréductibles. Notre point de départ est le multiplicateur de Montgomery qui calcule A(x)B(x)x^(-u) efficacement, étant donné A(x), B(x) in GF(2^m) pour u choisi judicieusement. Nous étudions ensuite l'algorithme diviser pour régner PCHS qui permet de partitionner les multiplicandes d'un produit dans GF(2^m) lorsque m est impair. Nous l'appliquons pour la partitionnement de A(x) et de B(x) dans la multiplication de Montgomery A(x)B(x)x^(-u) pour GF(2^m) même si m est pair. Basé sur cette nouvelle approche, nous construisons un multiplicateur dans GF(2^m) généré par des trinôme irréductibles. Une nouvelle astuce de réutilisation des résultats intermédiaires nous permet d'éliminer plusieurs portes XOR redondantes. Les complexités de temps (i.e. le délais) et d'espace (i.e. le nombre de portes logiques) du nouveau multiplicateur sont ensuite analysées: 1. Le nouveau multiplicateur demande environ 25% moins de portes logiques que les multiplicateurs de Montgomery et de Mastrovito lorsque GF(2^m) est généré par des trinômes irréductible et m est suffisamment grand. Le nombre de portes du nouveau multiplicateur est presque identique à celui du multiplicateur de Karatsuba proposé par Elia. 2. Le délai de calcul du nouveau multiplicateur excède celui des meilleurs multiplicateurs d'au plus deux évaluations de portes XOR. 3. Nous determinons le délai et le nombre de portes logiques du nouveau multiplicateur sur les deux corps de Galois recommandés par le National Institute of Standards and Technology (NIST). Nous montrons que notre multiplicateurs contient 15% moins de portes logiques que les multiplicateurs de Montgomery et de Mastrovito au coût d'un délai d'au plus une porte XOR supplémentaire. De plus, notre multiplicateur a un délai d'une porte XOR moindre que celui du multiplicateur d'Elia au coût d'une augmentation de moins de 1% du nombre total de portes logiques.

Evaluation of electrical conductivity and thermal diffusivity of vanadyl naphthalocyanine

The electrical conductivity and thermal diffusivity of pristine and iodine doped vanadyl naphthalocyanine (VONc) were studied. In the pristine sample, the temperature dependence was very weak below 300 K. The increase in conductivity at higher temperature must be due to an enhancement in carrier density with increase in thermal energy. The electrical conductivity of VONc increased when doped with iodine. The behavior of VONcI indicated that considerable changes have occurred in the electronic environment of the molecule as a result of doping. Iodine doping enhanced the thermal diffusivity of VONc. The increase in thermal diffusivity of the iodine doped sample may be due to the disorder of iodine atoms occupying the channels in one dimensional lattices.

Development of novel surface coatings based on acrylic copolymers

The present study describes the preparation of Vinyl acetate-Butyl acrylate copolymer lattices of varying compositions and solid contents by semicontinuous emulsion polymerization method. This copolymer lattices were used as binder to develop a new surface coating formulation. The properties of this surface coating were improved by using nano TiO2 colloidal sol as a pigment. Antimicrobial activity of surface coatings was improved by the addition of carboxymethyl chitosan as biocide. Uniformly dispersed tyre crumb was used to give a mat finish to the coating. The mechanical properties adhesive properties, thermal properties etc. of the coatings are presented in thesis.

Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study

ic first-order transition line ending in a critical point. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling. In particular, the premartensitic transition occurs when such coupling is strong enough to freeze the involved mode phonon. The implication of the results in relation to the available experimental data is discussed.