No description available.

There are few reliable computational techniques applicable to the problem of structural phase behaviour. This is starkly emphasised by the fact that there are still a number of unanswered questions concerning the solid state of some of the simplest models of matter. To determine the phase behaviour of a given system we invoke the machinery of statistical physics, which identifies the equilibrium phase as that which minimises the free-energy. This type of problem can only be dealt with fully via numerical simulation, as any less direct approach will involve making some uncontrolled approximation. In particular, a numerical simulation can be used to evaluate the free-energy difference between two phases if the simulation is free to visit them both. However, it has proven very difficult to find an algorithm which is capable of efficiently exploring two different phases, particularly when one or both of them is a crystalline solid. This thesis builds on previous work (Physical Review Letters 79 p.3002), exploring a new Monte Carlo approach to this class of problem. This new simulation technique uses a global coordinate transformation to switch between two different crystalline structures. Generally, this `lattice switch' is found to be extremely unlikely to succeed in a normal Monte Carlo simulation. To overcome this, extended-sampling techniques are used to encourage the simulation to visit `gateway' microstates where the switch will be successful. After compensating for this bias in the sampling, the free-energy difference between the two structures can be evaluated directly from their relative probabilities. As concrete examples on which to base the research, the lattice-switch Monte Carlo method is used to determine the free-energy difference between the face-centred cubic (fcc) and hexagonal close-packed (hcp) phases of two generic model systems --- the hard-sphere and Lennard-Jones potentials. The structural phase behaviour of the hard-sphere solid is determined at densities near melting and in the close-packed limit. The factors controlling the efficiency of the lattice-switch approach are explored, as is the character of the `gateway' microstates. The face-centred cubic structure is identified as the thermodynamically stable phase, and the free-energy difference between the two structures is determined with high precision. These results are shown to be in complete agreement with the results of other authors in the field (published during the course of this work), some of whom adopted the lattice-switch method for their calculations. Also, the results are favourably compared against the experimentally observed structural phase behaviour of sterically-stabilised colloidal dispersions, which are believed to behave like systems of hard spheres. The logical extension of the hard sphere work is to generalise the lattice-switch technique to deal with `softer' systems, such as the Lennard-Jones solid. The results in the literature for the structural phase behaviour of this relatively simple system are found to be completely inconsistent. A number of different approaches to this problem are explored, leading to the conclusion that these inconsistencies arise from the way in which the potential is truncated. Using results for the ground-state energies and from the harmonic approximation, we develop a new truncation scheme which allows this system to be simulated accurately and efficiently. Lattice-switch Monte Carlo is then used to determine the fcc-hcp phase boundary of the Lennard-Jones solid in its entirety. These results are compared against the experimental results for the Lennard-Jones potential's closest physical analogue, the rare-gas solids. While some of the published rare-gas observations are in approximate agreement with the lattice-switch results, these findings contradict the widely held belief that fcc is the equilibrium structure of the heavier rare-gas solids for all pressures and temperatures. The possible reasons for this disagreement are discussed. Finally, we examine the pros and cons of the lattice-switch technique, and explore ways in which it can be extended to cover an even wider range of structures and interactions.

No description available.

Zugl.: Ulm, University, Diss.

University, Diss., 2007--Bonn.

Submitted by GABRIEL DIAZ ITURRY null (gabriel.diaz.iturry@gmail.com) on 2017-05-04T14:59:10Z No. of bitstreams: 1 dissertacao_GDI.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-05-05T14:41:22Z (GMT) No. of bitstreams: 1 diaziturry_g_me_rcla.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) / Made available in DSpace on 2017-05-05T14:41:22Z (GMT). No. of bitstreams: 1 diaziturry_g_me_rcla.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) Previous issue date: 2017-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Estudamos nessa dissertação algumas propriedades estatísticas no regime de equilibrio pós transitório para o modelo bouncer unidimensional considerando ambas versões completa e simplificada. O modelo consiste de uma partícula clássica movendo-se sob ação de uma força gravitacional constante e sofrendo colisões com uma plataforma móvel de massa muito maior que a massa da partícula. A versão completa leva em conta o movimento real da fronteira e o instante da colisão entre partícula e plataforma é obtido a partir da solução numérica de uma equação transcendental. Já o modelo simplificado, também conhecido como modelo de aproximação de fronteira fixa, assume que para o cálculo do instante da colisão a fronteira está parada, porém a partícula troca energia após a colisão ocorre como se a fonteira estivesse em movimento. Os comportamentos da velocidade média, velocidade quadrática média e desvio da velocidade quadrática média foram obtidos em função dos parâmetros de controle. Desenvolvemos um método semi-analítico permitindo-nos deduzir equações dos valores médios sem fazer simulações de larga escala. Em seguida, elaboramos uma simulação do tipo Monte-Carlo que nos permite obter os valores médios no estado estacionário sem resolver equações transcendentais, acelerando assim as simulações numéricas. O método de Monte-Carlo apresentado pode ser útil na investigação de sistemas mais complexos incluindo bilhares clássicos dependentes do tempo. / We studied some statistical properties in the stationary and post transitory state for the one-dimensional bouncer model considering wither complete and simplified versions. The model consists of a classical particle moving under the effect of a constant gravitational force and collides with a periodic moving platform whose mass is heavier as compared to the particle. The complete version takes into account the real motion of the moving wall. The instant of collision is obtained from the numerical solution of a transcendental equation. The simplified version, also called as a static wall approximation, takes into account to calculate the instant of the collisions as if the wall was fixed. However, the particle experiences an exchange of energy and momentum at the collision as if the wall were moving. The behavior for the average velocity, average squared velocity and deviation of the average squared velocity were obtained as a function of the control parameters. We developed a semi-analytic method allowing us to deduce equations for the average values without the need of doing large scale simulations. Using a Monte-Carlo-like simulation we obtained the average values for the stationary state without solving the transcendental equations. The Monte-Carlo method may have applications in the investigation of more complex systems including time dependent billiard systems.

No description available.

There are many tools to simulate physical phenomena. Generally, the simulation technique is defined by the size of the simulation area. Two well know techniques for simulating atom dynamics are kinetic Monte Carlo (kMC) and molecular dynamics (MD). In this work we simulate physical vapor deposition of binary metallic systems using the kMC technique. A sufficient quantity of atoms are deposited so that morphological features can be observed. Where kMC has fallen short we have used MD to supplement our results.

<p>Algorithmica Research AB develops software application for the financial markets. One of their products is Quantlab that is a tool for quantitative analyses. An effective method to value several financial instruments is Monte Carlo simulation. Since it is a common method Algorithmica is interesting in investigating if it is possible to create a Monte Carlo framework.</p><p>A requirement from Algorithmica is that the framework is general and this is the main problem to solve. It is difficult to generate a generalized framework because financial derivatives have very different appearances. To simplify the framework the thesis will be delimitated to European style derivatives where the underlying asset is following a Geometric Brownian Motion.</p><p>The definition of the problem and delimitation were defined gradually, in parallel with the review of literature, this to be able to decide what purpose, and delimitations that is reasonable to treat. Standard Monte Carlo requires a large number of trials and is therefore slow. To speed up the process there exist different variance reduction techniques and also Quasi Monte Carlo simulation, where deterministic numbers (low discrepancy sequences) is used instead of random. The thesis investigated the variance reduction techniques; control variate technique, antithetic variate technique, and the low discrepancy sequences; Sobol, Faure and Halton.</p><p>Three test instruments were chosen to test the framework, an Asian option and a Barrier option where the purpose is to conclude which Monte Carle method that performs best, and also a structured product; Smart Start, that is more complex and the purpose is to test that the framework can handle it.</p><p>To increase the understanding of the theory the Halton, Faure and Sobol sequence were implemented in Quantlab in parallel with the review of literature. The Halton and Faure sequences also seemed to perform worse than Sobol so they were not further analyzed.</p><p>The developing of the framework was an iterative process. The chosen solution is to design a general framework by using five function pointers; the path generator, the payoff function, the stop criterion function and the volatility and interest rates. The user specifies these functions by him/her given some obligatory input and output values. It is not a problem-free solution to use function pointers and several conflicts and issues are defined, therefore it is not recommended to implement the framework as it is designed today.</p><p>In parallel with the developing of the framework several experiments on the Asian and Barrier options were performed with varying result and it is not possible to draw a conclusion on which method that is best. Often Sobol seems to converge better and fluctuates less than standard Monte Carlo. The literature indicates that it is important that the user has an understanding of the instrument that should be valued, the stochastic process it follows and the advantages and disadvantages of different Monte Carlo methods. It is recommended to evaluate the different method with experiments, before deciding which method to use when valuing a new derivative.</p>

Algorithmica Research AB develops software application for the financial markets. One of their products is Quantlab that is a tool for quantitative analyses. An effective method to value several financial instruments is Monte Carlo simulation. Since it is a common method Algorithmica is interesting in investigating if it is possible to create a Monte Carlo framework. A requirement from Algorithmica is that the framework is general and this is the main problem to solve. It is difficult to generate a generalized framework because financial derivatives have very different appearances. To simplify the framework the thesis will be delimitated to European style derivatives where the underlying asset is following a Geometric Brownian Motion. The definition of the problem and delimitation were defined gradually, in parallel with the review of literature, this to be able to decide what purpose, and delimitations that is reasonable to treat. Standard Monte Carlo requires a large number of trials and is therefore slow. To speed up the process there exist different variance reduction techniques and also Quasi Monte Carlo simulation, where deterministic numbers (low discrepancy sequences) is used instead of random. The thesis investigated the variance reduction techniques; control variate technique, antithetic variate technique, and the low discrepancy sequences; Sobol, Faure and Halton. Three test instruments were chosen to test the framework, an Asian option and a Barrier option where the purpose is to conclude which Monte Carle method that performs best, and also a structured product; Smart Start, that is more complex and the purpose is to test that the framework can handle it. To increase the understanding of the theory the Halton, Faure and Sobol sequence were implemented in Quantlab in parallel with the review of literature. The Halton and Faure sequences also seemed to perform worse than Sobol so they were not further analyzed. The developing of the framework was an iterative process. The chosen solution is to design a general framework by using five function pointers; the path generator, the payoff function, the stop criterion function and the volatility and interest rates. The user specifies these functions by him/her given some obligatory input and output values. It is not a problem-free solution to use function pointers and several conflicts and issues are defined, therefore it is not recommended to implement the framework as it is designed today. In parallel with the developing of the framework several experiments on the Asian and Barrier options were performed with varying result and it is not possible to draw a conclusion on which method that is best. Often Sobol seems to converge better and fluctuates less than standard Monte Carlo. The literature indicates that it is important that the user has an understanding of the instrument that should be valued, the stochastic process it follows and the advantages and disadvantages of different Monte Carlo methods. It is recommended to evaluate the different method with experiments, before deciding which method to use when valuing a new derivative.