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Two numerical procedures, the regularization method and the maximum entropy method, have been investigated and developed to solve some basic inverse problems in theoretical physics. Both of them are applied to the inverse black body radiation problem and the inverse phonon density of states problem. The inverse black body radiation problem is concerned with the determination of the area temperature distribution of a black body source from spectral measurements of its radiation. The phonon density of states problem is defined to be the determination of the phonon density of states function from the measured lattice specific heat function at constant volume. Those problems are ill-posed and can be expressed as a Fredholm integral equation of the first kind. It appears that both the regularization method and the maximum entropy method are successful in solving the two ill-posed problems. Generally the two procedures can be applied to any inverse problem which belongs to the class of the Fredholm integral equation of the first kind.

An apparatus for measuring energy and angular distributions of keV ions forward scattered from atomically clean silicon surfaces was designed and assembled. A consistent procedure for cleaning Si(100) single crystal surfaces under ultra-high vacuum was established. Experimentally, oxygen ions were surface scattered from a clean Si(100) sample and the ratios of outgoing negative to positive ions were measured. By using a positive oxygen beam and then a negative oxygen beam we obtained strong evidence that ions retain no memory of their initial charge state after it undergoes a violent collision with a single atom. The ratios of negative to positive scattered oxygen ions for both an incident O$\sp-$ ion beam and O$\sp+$ ion beam (under identical scattering conditions) were found to be the same (within statistical uncertainty) for incident energies between 6 keV and 20 keV.

Models written in terms of stochastic delay differential equations (SDDE's) have recently appeared in a number of fields, such as physiology, optics, and climatology. Unfortunately, the development of a Fokker-Planck approach for these equations is being hampered by their non-Markovian nature. In this thesis, an exact Fokker-Planck equation (FPE) is formulated for univariate SDDE's involving Gaussian white noise. Although this FPE is not self-sufficient, it is found to be helpful in at least two different contexts: with a short delay approximation and under an appropriate separation of time scales. In the short delay approximation, a Taylor expansion is applied to an SDDE with nondelayed diffusion and yields a nondelayed stochastic differential equation. The aforementioned FPE then allows the derivation of an alternate and complementary approximation of the original SDDE. This method is illustrated with linear and logistic SDDE's. Under the separation of time scales assumption, the FPE of a bistable system is reduced to a form that is uniquely determined by the steady-state probability density when the diffusion term of the SDDE is nondelayed. In the context of an overdamped particle with delayed coupling to a symmetrical and stochastically driven potential, the resulting FPE is used with standard techniques to express the transition rate between wells in terms of the noise amplitude and of the steady-state probability density. The same is also accomplished for the mean first passage time from one point to another. This whole approach is then applied to the case of a quartic potential, for which all realisations eventually stabilise on an oscillatory trajectory with an ever increasing amplitude. Although this latter phenomenon prevents the existence of a steady-state limit, a pseudo-steady-state probability density can be defined and used instead of the non-existent steady-state one when the transition rate to these unbounded oscillatory trajectories is sufficiently small. The transition to this peculiar attractor is investigated in more detail for a family of single-well potentials, and interestingly, the transition rate follows Arrhenius' law when the noise amplitude is small. Overall, it is found that the Fokker-Planck approach can play a significant role in the analysis of SDDE's.

Experimental results are presented on excitonic effects related to the Bose-Einstein condensation (BEC) of excitons in Cu2O. Such effects include resonant light polarization dependent absorption, exciton creation and diffusion by absorption of scattered light, and resonant high density exciton packet induced absorption. These results are then utilized, in conjunction with similar results on excitonic BEC, to develop a plausible model for condensate amplification. Condensates are initially created at T = 1.8K with high intensity ND:YAG pulses (lambda = 532 nm) and then stimulated by a secondary source tuned around the 1S orthoexciton resonance (lambda = 609.51 nm); the latter induces the observed condensate amplification. By careful analysis of the various interactions between the secondary light source, the crystal, and the condensate itself, an improved understanding of how the secondary pulse excitations interact with the passage of a high density exciton packet is obtained.

On etudie l'evolution stochastique d'un systeme multivarie et deterministiquement multistable soumis a un bruit dichotomique markovien additif. A cette fin, on definit un support, duquel le systeme ne peut s'echapper, pour la densite de probabilite stationnaire. Une condition frontiere est alors imposee afin d'evaluer numeriquement cette distribution sur le support. Lorsque l'amplitude du bruit est suffisamment grande, le systeme peut evoluer dun attracteur stochastique a un autre. Un critere de definition permettant de separer le support en especes disjointes est ici suggere. Il est alors possible d'etudier la cinetique des transitions se produisant entre ces especes et menant vers l'etat stationnaire. La methode des projecteurs permet d'obtenir une loi phenomenologique qui est valide lorsque l'echelle de temps sur laquelle se deroulent les transitions inter-especes est beaucoup plus longue que toutes les autres echelles de temps caracterisant le systeme. On obtient egalement une equation permettant d'evaluer a l'aide d'une simulation directe les taux de transition de la loi phenomenologique. Comme cas particulier, on considere un systeme bivarie possedant de facon deterministe deux points fixes stables et un point de selle. Les resultats confirment la validite de l'expression obtenue pour les taux de transition dans la mesure ou le temps de correlation du bruit est suffisamment petit.

The drift and diffusion motions of biased particles are commonly studied using random walks on lattices. We present a novel theoretical approach that makes it possible to calculate exact mobilities in the presence of lattice obstacles. Several two-dimensional examples are studied and a particular attention is given to separation techniques and how our model can be used to study such devices. We also broach the problems related to the field-dependence of the diffusion coefficient during random walks, and we present new algorithms that remove these difficulties. We develop new Monte Carlo algorithms that make it possible to study both drift and diffusion processes simultaneously, even in presence of very strong fields. Finally, we present two brief discussions about the addition of curved field lines and viscosity gradients to our lattice models. This work opens the door to a wide range of applications, especially for the study of electrophoretic technologies.

Un modèle en réseau pour la formation de pores alignés de peptides dans une bi-couche lipidique est construit à partir du modèle établi par Fournier et Joos. Ce modèle est tout d'abord étendu pour supporter des rampes de tension. Nous reproduisons les résultats obtenus par Evans et al. Lorsque le taux d'application de la tension sur une membrane est augmenté, la tension à laquelle elle se brise augmente et la densité de probabilité de rupture s'élargit. Notre modèle prédit aussi qu'avec une augmentation de la concentration de peptides, la tension à la rupture diminue et la largeur de la distribution de tension à la rupture augmente. Il prédit aussi qu'a tension zéro, une certaine concentration de peptides causera la formation de pores peptides et ainsi la perte de contenu vesiculaire. La demi-vie du processus de perte de contenu dépend linéairement du module de compressibilité et de la longueur des chaînes hydrophobes. Nous montrons que la tension de rupture d'une membrane contient une composante qui varie avec l'inverse du nombre de lipides composant la membrane.

This work presents results on the permeability of a lipid bilayer to water molecules. We look at the change in bilayer permeability as a function of lipid structure and area per lipid molecule. A molecular dynamic simulation (MDS) of a solvent surfactant system was used in the canonical ensemble to simulate the membranes. Permeability was obtained by calculating the permeative resistance. This method, developed by Marrink and Berendsen, allows the sampling of very long time scale events on short time scale simulations. The structural properties of the simulated bilayer are studied and compared both to atomistic MDS and experiments. The elasticity of the simulated membranes are shown to be in good agreement with experimental results. The permeation is found to increase only slightly for a relative stretch of up to 20%, a result which is qualitatively similar to recent experiments. The increase is described by a linear relation between the permeability and the relative extension. Most of the changes in the lipid bilayer are found to occur in the central part near the ends of the tails. The effect of lipid packing on bilayer permeability are also discussed.