Universiẗat, Diss., 2003--Mainz.

Current researchers have looked to nature to learn how self-assembly processes occur. By understanding the self-assembly process, designers can begin to build strong structural materials that are extremely light weight. The discrete element modeling method was used to gain a better understanding of the directed self-assembly of M13 bacteriophage. This model was parameterized from molecular dynamics simulations at the nanometer scale. Three types of functionalized bacteriophage were studied: Wild-type, 4E, and CLP8. Results showed that Wild-type phage are attracted in a head-to-tail orientation, but repelled in head-to-head orientation. The 4E bacteriophage behaved similarly with a stronger bond in the head-to-tail orientation, and CLP8 showed to physically repel in either orientation. The overall finding was that the electrostatic physics dominated as the controlling forces of the phage interactions.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Chemnitz, Techn. Univ., Masterarb., 2008.

Made available in DSpace on 2014-06-11T19:22:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-10-25Bitstream added on 2014-06-13T19:08:28Z : No. of bitstreams: 1 araujo_jcb_me_sjrp.pdf: 676720 bytes, checksum: ec12d48a0e70f3225d98b32f48a1f86d (MD5) / Neste trabalho é apresentado o formalismo supersimétrico que consiste em uma generalização do método de fatorização para se encontrar a solução da equação de Schrödinger. O oscilador harmônico e o átomo de hidrogênio são resolvidos através deste formalismo. Para o potencial de Lennard-Jones (12,6) é utilizado o método variacional, onde utilizamos a supersimetria para encontrar uma função de onda que se assemelhe com a função real, este procedimento é feito através da escolha de um superpotencial que gere um potencial efetivo que se aproxima do potencial original. Com isto as autofunções e os autovalores para o estado fundamental e o primeiro estado excitado são encontrados. Alguns resultados numéricos obtidos são comparados com outros encontrados na literatura. / In this work it is presented the supersymmetrical formalism that consists of a generalization of the factorization method to find the solution of Schrödinger equation. The harmonic oscillator and the hydrogen atom are decided through this formalism. For the potential of Lennard-Jones (12,6) the variational method is used, where we use the supersymmetry to find a wave function that is similar to the real function, this procedure is made through the choice of a superpotential that generates an effective potential that approaches to the original potential. With this the autofunctions and the autovalues for the fundamental state and the first state excited are found. Some gotten numerical results are compared with others found in the literature.

Three models for surface stress loading effect on a micromechanical cantilever are proposed as concentrated moment acting at the free end (Model I), concentrated moment plus axial force acting at the free end (Model II), and uniformly distributed surface force acting along the microcantilever (Model III). Solution to Model I loading is based on the Stoney formula, assuming that the microcantilever is subjected to pure bending and deformed with a constant curvature. Model II takes into account the clamping effect in such a way that an additional axial force is introduced. The deflections resulting from Models I and II surface stress loading effect are solved by Euler-Bernoulli beam theory. In Model III, the effect of surface stress is modeled as uniformly distributed surface force that causes both uniformly distributed bending moment and axial force acting along the axis of the microcantilever. The energy method is then used to obtain the governing equation and boundary conditions for Model III displacement. Comparison of the results obtained by the three models with those by the finite element method and experiment indicates that Model III is the most realistic model for surface stress loading effect to obtain the deflection of a microcantilever. Model III for surface stress loading effect is then used to demonstrate the applications of a microcantilever in sensor technology through the measurement of tip deflection under an atomic adsorption as the source of surface stress. Dual attractive or repulsive characteristics of interactions between a pair of mercury atoms are described in terms of Lennard-Jones potential. The force per unit atomic spacing induced by the adjacent free surface atoms of a monolayer is then computed using the potential. The sensitivities of atomic spacing and monolayer thickness to the tip-deflection of a microcantilever are studied in this research. / Master of Science

Die Charakterisierung hochdimensionaler Systeme mit Lyapunov-Instabilität wird durch das Lyapunov-Spektrum und die zugehörigen Lyapunov-Vektoren ermöglicht. Für eine Vielzahl von derartigen Systemen (Coupled-Map-Lattices, Hartkugel-Systeme, Systeme mit ausgedehnten Potentialen ...) konnte durch die Untersuchung der Lyapunov-Vektoren die Existenz von hydrodynamischen Lyapunov-Moden nachgewiesen werden. Diese kollektiven Anregungen zeigen sich in Lyapunov-Vektoren, deren Lyapunov-Exponenten dem Betrage nach am kleinsten sind. Da Lyapunov-Exponenten charakteristische Zeitskalen innerhalb der Systeme repräsentieren, ist durch die Lyapunov-Moden eine Untersuchung des Langzeitverhaltens möglich. In dieser Arbeit werden die hydrodynamischen Lyapunov-Moden durch Molekulardynamiksimulationen von mehrkomponentigen Lennard-Jones-Flüssigkeiten untersucht. Die Charakterisierung der Lyapunov-Moden zeigt im weiteren eine Ähnlichkeit zu Dispersionsrelationen von Phononen.

L'objectif ultime de ce travail est de fournir des méthodologies robustes et efficaces sur le plan des calculs pour la modélisation et la résolution des problèmes de contact adhésifs basés sur le potentiel de Lennard-Jones (LJ). Pour pallier les pièges théoriques et numériques du modèle LJ liés à ses caractéristiques nondéfinies et non-bornées, une méthode d'adaptativité en modèle est proposée pour résoudre le problème purement-LJ comme limite d'une séquence de problèmes multiniveaux construits de manière adaptative. Chaque membre de la séquence consiste en une partition modèle entre le modèle microscopique LJ et le modèle macroscopique de Signorini. La convergence de la méthode d'adaptativité est prouvée mathématiquement sous certaines hypothèses physiques et réalistes. D'un autre côté, la méthode asymptotique numérique (MAN) est adaptée et utilisée pour suivre avec précision les instabilités des problèmes de contact à grande échelle et souples. Les deux méthodes sont incorporées dans le cadre multiéchelle Arlequin pour obtenir une résolution précise, tout en réduisant les coûts de calcul. Dans la méthode d'adaptativité en modèle, pour capturer avec précision la localisation des zones d'intérêt (ZDI), une stratégie en deux résolutions est suggérée : une résolution macroscopique est utilisée comme une première estimation de la localisation de la ZDI. La méthode Arlequin est alors utilisée pour obtenir une résolution microscopique en superposant des modèles locaux aux modèles globaux. En outre, dans la stratégie MAN, la méthode Arlequin est utilisée pour supprimer les oscillations numériques, améliorer la précision et réduire le coût de calcul. / The ultimate goal of this work is to provide computationally efficient and robust methodologies for the modelling and solution of a class of Lennard-Jones (LJ) potential-based adhesive contact problems. To alleviate theoretical and numerical pitfalls of the LJ model related to its non-defined and nonbounded characteristics, a model-adaptivity method is proposed to solve the pure-LJ problem as the limit of a sequence of adaptively constructed multilevel problems. Each member of the sequence consists of a model partition between the microscopic LJ model and the macroscopic Signorini model. The convergence of the model-adaptivity method is proved mathematically under some physical and realistic assumptions. On the other hand, the asymptotic numerical method (ANM) is adapted to track accurately instabilities for soft contact problems. Both methods are incorporated in the Arlequin multiscale framework to achieve an accurate resolution at a reasonable computational cost. In the model-adaptivity method, to capture accurately the localization of the zones of interest (ZOI), a two-step strategy is suggested: a macroscopic resolution is used as the first guess of the ZOI localization, then the Arlequin method is used there to achieve a fine scale resolution. In the ANM strategy, the Arlequin method is also used to suppress numerical oscillations and improve accuracy.

Made available in DSpace on 2016-12-12T20:15:52Z (GMT). No. of bitstreams: 1 Graziele Bortolini.pdf: 3189488 bytes, checksum: 6e8f5c11b189fb8f0ee4624270ebcee3 (MD5) Previous issue date: 2015-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Nosé-Hoover dynamics is deterministic and time-reversible and performs a statistical sampling of the canonical ensemble of a many-body system directly from the system dynamics. This system is coupled to one extra degree of freedom (extended system) acting as a heat reservoir. In this work, we study the dynamical of the prototype system: the harmonic oscillator thermalized in the Nosé-Hoover dynamics. We observe periodic and quasi periodic regular trajectories in the phase space for different initial conditions. However, the oscillator is non-ergodic and non-canonical in the Nosé-Hoover dynamics, when we add one reservoir degree of freedom (thermostats chain), the momentum distribution tends to the canonical one. The second system studied is an Argonne gas with 4000 particles which interact by means of a Lennard-Jones potential. For this system, we observe phase transitions, momentum distributions in agreement of canonical ensemble, as well, the thermostat efficiency to keep constant the average temperature. / A dinâmica de Nosé-Hoover é determinística e reversível no tempo e realiza uma amostragem estatística de um sistema de muitos corpos no ensemble canônico diretamente a partir da dinâmica do sistema. Esse sistema é acoplado a um grau de liberdade extra (sistema estendido) que desempenha o papel de um reservatório térmico. Neste trabalho, estudamos a dinâmica do sistema protótipo mínimo: o oscilador harmônico na dinâmica de Nosé-Hoover. Observamos trajetórias regulares periódicas e quase periódicas no espaço de fase para diferentes condições iniciais. Embora, o oscilador não seja ergódico e não reproduza as médias do ensemble canônico na dinâmica de Nosé-Hoover, ao adicionarmos mais um grau de liberdade ao reservatório (cadeia de termostatos), a distribuição de momentos tende a canônica. O segundo sistema estudado é um gás de Argônio constituído de 4000 partículas que interagem segundo um potencial de Lennard-Jones. Para esse sistema, observamos transições de fase, distribuições de momento em concordância com o ensemble canônico, assim como a eficiência do termostato de Nosé-Hoover em manter a temperatura média constante.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Devido à sua importância, o chamado problema de Lennard-Jones tem atraído pesquisadores de diversos campos da ciência pura e aplicada. Tal problema resume-se em achar as coordenadas de um sistema no espaço Euclidiano tridimensional, as quais correspondem a um mínimo de um potencial de energia. Esse problema desempenha um papel de fundamental importância na determinação da estabilidade de moléculas em arranjos altamente ramificados, como das proteínas. A principal dificuldade para resolver o problema de Lennard-Jones decorre do fato de que a função objetivo é não-convexa e altamente não-linear com várias variáveis, apresentando, dessa forma, um grande número de mínimos locais. Neste trabalho, foram utilizados alguns métodos de otimização global estocástica, onde procurou-se comparar os resultados numéricos dos algoritmos, com o objetivo de verificar quais se adaptam melhor à minimização do referido potencial. No presente estudo, abordou-se somente micro agrupamentos possuindo de 3 a 10 átomos. Os resultados obtidos foram comparados também com o melhores resultados conhecidos atualmente na literatura. Os algoritmos de otimização utilizados foram todos implementados em linguagem C++. / Because of its importance, the so-called Lennard-Jones problem has attracted researchers from various fields of pure and applied science. This problem boils down to find the coordinates of a system with three-dimensional Euclidean space, which correspond to minimum potential energy. This problem plays a fundamental role in determining the stability of molecules in highly branched arrangement, such as proteins. The main difficulty in solving the problem of Lennard-Jones from the fact that the objective function is non-convex and highly nonlinear with several variables, thus presenting a large number of local minima. Here, we used some methods of stochastic global optimization, where we seek to compare the results of the numerical algorithm, in order to see which are better suited to the minimization of the potential. In this study, we addressed only micro groups having 3-10 atoms. The results were also compared with the currently best known results in literature. The optimization algorithms were all implemented in C + +.