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Parameters of Heine and Abarenkov model potential (HAP) have been computed in this paper for sixteen body centered cubic (bcc) closed pack crystals. From the minimization of structure dependent energy of the pure crystal the inter-relation between the two parameters is first determined. Calculation uses pseudopotential technique with nine different exchange and correlation functions (ECF) and either only available experimental value of vacancy formation energy (VFE) or that obtained from an empirical relation based on other experimental parameters (Melting temperature, cohesive energy or activation energy) as tool. The variation of VFE with one parameter of HAP and different ECF show sharp fall in VFE near very small value of it after which it shows constancy for all bcc crystals. Comparison is made with parameter of Ashcroft model also. For increase in valency this parameter of HAP increases and show distinct different curves.

The global effort to rehabilitate and restore destroyed mangrove forests is unable to keep up with the high mangrove deforestation rates which exceed the average pace of global deforestation by three to five times. Our knowledge of the underlying processes of mangrove forest regeneration is too limited in order to find suitable techniques for the restoration of degraded mangrove areas. The general objective of my dissertation was to improve mangrove restoration by understanding regeneration processes and local plant-plant interaction in a regenerating Avicennia germinans forest. The study was conducted in a high-shore mangrove forest area on the Ajuruteua peninsula, State of Para, Northern Brazil. The dwarf forest consisting of shrub-like trees is recovering from a stand-replacing event caused by a road construction in 1974 which interrupted the tidal inundation of the study area. Consequently, infrequent inundation and high porewater salinity limit tree growth and canopy closure. All trees and seedlings were stem-mapped in six 20 m x 20 m plots which were located along a tree density gradient. Moreover, height, crown extent, basal stem diameter of trees were measured. The area of herbaceous ground vegetation and wood debris were mapped as well. The mapped spatial distribution of trees, seedlings and covariates was studied using point pattern analysis and point process models, such as Gibbs and Thomas point process, in order to infer underlying ecological processes, such as seed dispersal, seedling establishment, tree recruitment and tree interaction. In the first study (chapter 2), I analyzed the influence of abiotic and biotic factors on the seedling establishment and tree recruitment of A. germinans during the recolonization of severely degraded mangrove sites using point process modeling. Most seedlings established adjacent to adult trees especially under their crown cover. Moreover, seedling density was higher within patches of the herbaceous salt-marsh plants Blutaparon portulacoides and Sesuvium portulacastrum than in uncovered areas. The higher density of recruited A. germinans trees in herb patches indicated that ground vegetation did not negatively influence tree development of A. germinans. In addition, tree recruitment occurred in clusters. Coarse wood debris had no apparent effect on either life stage. These results confirm that salt-marsh vegetation acts as the starting point for mangrove recolonization and indicate that the positive interaction among trees accelerates forest regeneration. In the second study (chapter 3), I analyzed how intraspecific interaction among A. germinans trees determines their growth and size under harsh environmental conditions. Interaction among a higher number of neighboring trees was positively related to the development of a focal tree. However, tree height, internode length and basal stem diameter were only positively associated in low-density forest stands (1.2 trees m-2) and not in forest stands of higher tree density (2.7 trees m-2). These results indicated a shift from facilitation, i.e. a positive effect of tree interaction, towards a balance between facilitation and competition. In the third study (chapter 4), I used point process modeling and the individual-based model mesoFON to disentangle the impact of regeneration and interaction processes on the spatial distribution of seedlings and trees. In this infrequently inundated area, propagules of A. germinans are only dispersed at a maximum distance of 3 m from their parent tree. Furthermore, there is no evidence that the following seedling establishment is influenced by trees. I was able to differentiate positive and negative tree interactions simulated by the mangrove model mesoFON regardless of dispersal processes based on static tree size information using the mark-correlation function. The results of this dissertation suggest that mangrove forest regeneration in degraded areas is a result of facilitative and not competitive interactions among mangrove trees, seedling and herbaceous vegetation. This has important implications for the restoration of degraded mangrove forest. Degraded mangrove areas are usually restored by planting a high number of evenly spaced seedlings. However, high costs constrain this approach to small areas. Assisting natural regeneration could be a less costly alternative. Herbaceous vegetation plays a crucial role in forest recolonization by entrapping propagules and possibly ameliorating harsh environmental conditions. So far only competition among mangrove trees has been considered during restoration. However, facilitative tree interactions could be utilized by planting seedling clusters in order to assist natural regeneration instead of planting seedlings evenly-spaced over large areas. This dissertation also showed that point pattern analysis and point process modeling can enable forest ecologists to describe the spatial distribution of trees as well as to infer underlying ecological processes.

We consider the finite two-dimensional Ising model on a lattice with periodic boundaryconditions. Kaufman determined the spectrum of the transfer matrix on the finite,periodic lattice, and her derivation was a simplification of Onsager's famous result onsolving the two-dimensional Ising model. We derive and rework Kaufman's resultsby applying representation theory, which give us a more direct approach to computethe spectrum of the transfer matrix. We determine formulas for the spin correlationfunction that depend on the matrix elements of the induced rotation associated withthe spin operator. The representation of the spin matrix elements is obtained byconsidering the spin operator as an intertwining map. We wrap the lattice aroundthe cylinder taking the semi-infinite volume limit. We control the scaling limit of themulti-spin Ising correlations on the cylinder as the temperature approaches the criticaltemperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrixelements on the finite, periodic lattice. Finally, we compute the matrix representationof the spin operator for temperatures below the critical temperature in the infinite-volume limit in the pure state defined by plus boundary conditions.

This thesis deals with modeling of particle processes. In the first part we ex- amine Gibbs facet process on a bounded window with discrete orientation distri- bution and we derive central limit theorem (CLT) for U-statistics of facet process with increasing intensity. We calculate all asymptotic joint moments for interac- tion U-statistics and use the method of moments for deriving the CLT. Moreover we present an alternative proof which makes use of the CLT for U-statistics of a Poisson facet process. In the second part we model planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. Statistical methods are presented which first estimate scalar parameters by known approaches and then the reference distribution is estimated non-parametrically. We also introduce the Takacs-Fiksel estimate and demonstrate the use of estimators in a simulation study and also using data from actin fibres from stem cells images. In the third part we study a stationary Gibbs particle process with determin- istically bounded particles on Euclidean space defined in terms of a finite range potential and an activity parameter. For small activity parameters, we prove the CLT for certain statistics of this...

No presente trabalho descrevemos nossos resultados relativos à investigação da dinâmica de solvatação mecânica por meio de simulações por dinâmica molecular, respeitando o regime da resposta linear, em sistemas-modelo de argônio líquido com um soluto monoatômico ou diatômico dissolvido. Estudamos sistematicamente a influência dos parâmetros moleculares dos solutos (tamanho, polarizabilidade) e da densidade frente a vários modelos de solvatação. Funções de Correlação Temporal da Energia de Solvatação foram calculadas com relação à correlações de n-corpos (n = 2; 3) distinguindo interações repulsivas e atrativas para ambos os sistemas líquidos. Também obtivemos segundas derivadas temporais dessas funções referindo-se à parcelas translacionais, rotacionais e roto-translacionais na solução do diatômico. Encontramos que funções de correlação temporal coletivas podem ser razoavelmente bem aproximadas por correlações binárias a densidades baixas e, a densidades altas, correlações ternárias tornam-se mais importantes produzindo um descorrelacionamento mais rápido das funções coletivas devido a efeitos de cancelamento parciais. As funções de correlação para interações repulsivas e atrativas exibem comportamentos dinâmicos independentes do modelo de solvatação devido a fatores de escalonamento linear que afetam apenas as amplitudes das dessas funções de correlação temporal. Em geral, os sistemas com grau de liberdade rotacional apresentam tempos de correlação mais curtos para a dinâmica coletiva e tempos de correlação mais longos para as funções binárias e ternárias. Finalmente, esse estudo mostra que os sistemas contendo o diatômico relaxam-se predominantemente por mecanismos translacionais binários em modelos de solvatação envolvendo alterações apenas na polarizabilidade do soluto, e por mecanismos rotacionais atrativos binários em modelos envolvendo alterações no comprimento de ligação. / In the present work, we describe our results concerning our molecular dynamics investigation of the mechanical solvation dynamics within the linear response regime in model systems composed by liquid argon with a monoatomic or diatomic solute. The effect of molecular parameters (size, polarizability) and density has been elucidated for various solvation models. Time Correlation Functions for the solvation energy were calculated and separated into n-body (n = 2; 3) contributions distinguishing repulsive and attractive interactions in both liquid systems. In addition, we computed second time derivatives of these functions in order to describe translational, rotational, and roto-translational portions in the solutions containing the diatomics. We found that collective time correlation functions are well described by binary correlations at low liquid densities and, at high densities, ternary correlations become more important producing faster decaying collective time correlation functions due to partial cancellation effects. The repulsive and attractive time correlation functions exhibit a dynamic behavior that is independent on the solvation model due to linear scaling factors that only affect the absolute amplitudes of these functions. In general, the systems involving a rotational degree of freedom furnish smaller correlation times for the collective solvation dynamics, but stronger correlated two-body and three-body terms. Finally, this study shows that the solvation dynamics for the solution containing the diatomics relaxes predominatly by binary translational mechanisms when solvation models involving changes only in the polarizability parameter are considered. Binary attractive rotational mechanism become important in models with changes in the bond length.

FREIRE, Márcio de Melo. Funções de Green em Mecânica Estatística. 2014. 56 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-09-12T19:48:53Z No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-09-12T19:50:01Z (GMT) No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Made available in DSpace on 2014-09-12T19:50:01Z (GMT). No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) Previous issue date: 2014 / Neste trabalho estabeleceremos as definições das funções de Green em mecânica estatística e suas propriedades básicas. Estas funções dependem duplamente do tempo e da temperatura. Isto pode ser observado por meio de suas definições, onde aparecem os valores médios dos produtos de operadores. Neste caso a média é feita sobre o ensemble grão-canônico. Os operadores envolvidos nestas funções satisfazem a equação de movimento de Heisenberg, o que nos permite descrever as equações de evolução para as funções de Green. Por meio da representação espectral das funções de correlação temporal, que é feita através da introdução de uma transformada de Fourier para mudar o sistema do espaço dos tempos para o espaço das frequências, podemos obter as representações espectrais para as funções de Green retardada, avançada e causal. Por último, faremos o uso da função de Green retardada para descrever a condutividade elétrica de um sistema de elétrons submetido a um campo elétrico externo dependente de tempo, em outras palavras, descreveremos o tensor de condutividade elétrica em termos da função de Green retardada e, por último, calcularemos a condutividade elétrica de um sistema de elétrons e fônons.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos o espectro das massas de blindagem mais baixas em teorias do tipo Yang_Mills na rede.Utilizamos os grupos de calibre SU(2) e SU(3) em 2+1 e 3+1 dimensões. Os cálculos foram realizados perto da temperatura crítica da transição de fase confinamento-desconfinamento. Obtivemos valores para as razôes entre as massas consistentes com os valores previstos a partir de universidade. / In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the gauge groups SU(2) and SU(3) in 2 + 1 and 3 + 1 dimensions. Calculations were done near the critical temperature of the confinement-desconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments.

No presente trabalho descrevemos nossos resultados relativos à investigação da dinâmica de solvatação mecânica por meio de simulações por dinâmica molecular, respeitando o regime da resposta linear, em sistemas-modelo de argônio líquido com um soluto monoatômico ou diatômico dissolvido. Estudamos sistematicamente a influência dos parâmetros moleculares dos solutos (tamanho, polarizabilidade) e da densidade frente a vários modelos de solvatação. Funções de Correlação Temporal da Energia de Solvatação foram calculadas com relação à correlações de n-corpos (n = 2; 3) distinguindo interações repulsivas e atrativas para ambos os sistemas líquidos. Também obtivemos segundas derivadas temporais dessas funções referindo-se à parcelas translacionais, rotacionais e roto-translacionais na solução do diatômico. Encontramos que funções de correlação temporal coletivas podem ser razoavelmente bem aproximadas por correlações binárias a densidades baixas e, a densidades altas, correlações ternárias tornam-se mais importantes produzindo um descorrelacionamento mais rápido das funções coletivas devido a efeitos de cancelamento parciais. As funções de correlação para interações repulsivas e atrativas exibem comportamentos dinâmicos independentes do modelo de solvatação devido a fatores de escalonamento linear que afetam apenas as amplitudes das dessas funções de correlação temporal. Em geral, os sistemas com grau de liberdade rotacional apresentam tempos de correlação mais curtos para a dinâmica coletiva e tempos de correlação mais longos para as funções binárias e ternárias. Finalmente, esse estudo mostra que os sistemas contendo o diatômico relaxam-se predominantemente por mecanismos translacionais binários em modelos de solvatação envolvendo alterações apenas na polarizabilidade do soluto, e por mecanismos rotacionais atrativos binários em modelos envolvendo alterações no comprimento de ligação. / In the present work, we describe our results concerning our molecular dynamics investigation of the mechanical solvation dynamics within the linear response regime in model systems composed by liquid argon with a monoatomic or diatomic solute. The effect of molecular parameters (size, polarizability) and density has been elucidated for various solvation models. Time Correlation Functions for the solvation energy were calculated and separated into n-body (n = 2; 3) contributions distinguishing repulsive and attractive interactions in both liquid systems. In addition, we computed second time derivatives of these functions in order to describe translational, rotational, and roto-translational portions in the solutions containing the diatomics. We found that collective time correlation functions are well described by binary correlations at low liquid densities and, at high densities, ternary correlations become more important producing faster decaying collective time correlation functions due to partial cancellation effects. The repulsive and attractive time correlation functions exhibit a dynamic behavior that is independent on the solvation model due to linear scaling factors that only affect the absolute amplitudes of these functions. In general, the systems involving a rotational degree of freedom furnish smaller correlation times for the collective solvation dynamics, but stronger correlated two-body and three-body terms. Finally, this study shows that the solvation dynamics for the solution containing the diatomics relaxes predominatly by binary translational mechanisms when solvation models involving changes only in the polarizability parameter are considered. Binary attractive rotational mechanism become important in models with changes in the bond length.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos o espectro das massas de blindagem mais baixas em teorias do tipo Yang_Mills na rede.Utilizamos os grupos de calibre SU(2) e SU(3) em 2+1 e 3+1 dimensões. Os cálculos foram realizados perto da temperatura crítica da transição de fase confinamento-desconfinamento. Obtivemos valores para as razôes entre as massas consistentes com os valores previstos a partir de universidade. / In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the gauge groups SU(2) and SU(3) in 2 + 1 and 3 + 1 dimensions. Calculations were done near the critical temperature of the confinement-desconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments.