Ce travail de thèse se propose d’implémenter cette méthode de réduction de variance adaptative dans le code Monte-Carlo de transport de particules TRIPOLI-4,dédié entre autres aux études de radioprotection et d’instrumentation nucléaire. L’algorithme Adaptive Multilevel Splitting (AMS) a récemment fait son apparition dans la littérature de mathématiques appliquées, en tant que méthode de réduction de variance pour la simulation Monte Carlo de chaı̂nes de Markov. 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. The possible reasons for this disagreement are discussed. 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. These results are compared against the experimental results for the Lennard-Jones potential's closest physical analogue, the rare-gas solids. Lattice-switch Monte Carlo is then used to determine the fcc-hcp phase boundary of the Lennard-Jones solid in its entirety. 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. 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. The results in the literature for the structural phase behaviour of this relatively simple system are found to be completely inconsistent. 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. 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. 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. 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. The factors controlling the efficiency of the lattice-switch approach are explored, as is the character of the `gateway' microstates. The structural phase behaviour of the hard-sphere solid is determined at densities near melting and in the close-packed limit. 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. After compensating for this bias in the sampling, the free-energy difference between the two structures can be evaluated directly from their relative probabilities. To overcome this, extended-sampling techniques are used to encourage the simulation to visit `gateway' microstates where the switch will be successful. Generally, this `lattice switch' is found to be extremely unlikely to succeed in a normal Monte Carlo simulation. This new simulation technique uses a global coordinate transformation to switch between two different crystalline structures. This thesis builds on previous work (Physical Review Letters 79 p.3002), exploring a new Monte Carlo approach to this class of problem. 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. 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. This type of problem can only be dealt with fully via numerical simulation, as any less direct approach will involve making some uncontrolled approximation. 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 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. There are few reliable computational techniques applicable to the problem of structural phase behaviour.
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