Typical, potential-driven force fields have been usefully applied to small molecules for decades. However, complex effects such as polarisation, π systems and hydrogen bonding remain difficult to model while these effects become increasingly relevant. In fact, these complex electronic effects become crucial when considering larger biological molecules in solution. Instead, machine learning can be used to recognise patterns in chemical behaviour and predict them, sacrificing computational efficiency for accuracy and completeness of the force field. The kriging machine learning method is capable of taking the geometric features of a molecule and predicting its electrostatic properties after being trained using ab initio data of the same system. We present significant improvements in functionality, application and understanding of the kriging machine learning as part of an electrostatic force field. These improvements are presented alongside an up-scaling of the problems the force field is applied to. The force field predicts electrostatic energies for all common amino acids with a mean error of 4.2 kJmol-1 (1 kcal mol-1), cholesterol with a mean error of 3.9 kJmol-1 and a 10-alanine helix with a mean error of 6.4 kJmol-1. The kriging machine learning has been shown to work identically with charged systems, π systems and hydrogen bonded systems. This work details how different chemical environments and parameters affect the kriging model quality and assesses optimal methods for computationally-efficient kriging of multipole moments. In addition to this, the kriging models have been used to predict moments for atoms they have had no training data for with little loss in accuracy. Thus, the kriging machine learning has been shown to produce transferable models.

La résolution des équations intégrales liées aux problèmes de propagation des ondes est confrontée aux limitations des moyens informatiques pour la considération des problèmes à hautes fréquences. Nous proposons dans ce mémoire de thèse, un couplage de deux types de méthodes ayant pour but de réduire les couts de calcul et la place mémoire consommée lors de la résolution de ces équations intégrales par méthode itérative. La méthode de discrétisation microlocale introduite par T. Abboud, J.-C. Nédélec et B. Zhou, permet de réduire considérablement la taille du système par approximation de la phase de l'inconnue. Cependant, elle nécessite un précalcul très couteux. Nous utilisons alors le principe des méthodes multipoles rapides introduites par V. Rokhlin, pour accélérer ce précalcul. Cette application originale des méthodes multipoles dans le cadre d'une discrétisation microlocale aboutit à une méthode dont l'application à la formulation intégrale de B. Després pour l'équation de Helmholtz est très efficace. Son application à la résolution des équations de Maxwell bien que moins spectaculaire est tout de meme intéressante.

This work presents new development and applications of ab-initio simulation tools for material science. Focus lies on materials with strong electronic correlation and strong spin-orbit coupling. Improvements on methods for solving the impurity problem in LDA+DMFT is presented, as well as a reliant method for charge self-consistency in a LMTO based electronic structure code. A new adaptive scheme for Brillouin zone integration is developed, where we show a strong reduction of numerical noise compared to standard techniques. A reformulation of the standard LDA+U method aiming to reduce the number of free parameters is introduced. Fast and realistic reduction of the number of free parameters provides the possibility of high throughput calculations and enabled us to study a large number of compounds. An analysis method for polarization in terms of coupled multipoles, and their corresponding energy contributions is developed and applied. This led to the formulation of Katt's rules, a set of rules complementary to Hund's rules. Katt's rules applies for occupying the orbitals of an electronic shell with strong spin-orbit coupling. The analysis is also used to investigate the unconventional Uranium based superconductors URu2Si2, UPt3, UPd2Al3 and UNi2Al3, as well as the high temperature superconductor LaOFeAs. We also investigate the non-magnetic delta-phase of Plutonium, providing insight to the electronic structure and the branching ratios of 4d to 5f transitions seen in photo emission spectra.The influence of surface reconstruction on the magneto crystalline anisotropy is investigated in multilayer Fe/ZnSe, showing that Fe deposited on an unreconstructed interface strongly reduces the uniaxial component of the MAE. We provide a detailed understanding of the magnetic properties of Fe2P, opening possible routes for enhancing the MAE in this system. A general route to strong MAE in nano-laminates is presented, we apply this to propose a candidate with extremely strong anisotropy energy density, 5Fe/2W1-xReX for x=[0.6-0.8].

Thesis (Ph.D.); Submitted to Massachusetts Inst. of Tech., Cambridge, MA (US); 1 Aug 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-174" "DOE/ER/40150-2747" Zhengwei Chai. 08/01/2003. Report is also available in paper and microfiche from NTIS.

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The subject of the thesis is creation and description of mathematical model of three-phase asymmetric power line and proposal for three-phase operation calculating of the power network by variet aspects. Another component is the creation of a program in PHP, which would use this mathematical model for the calculation of the three-phase operation of the power network. Part of this work deals with derivation of matrices of elementary multipoles and their serial ordering derive complex multipoles that can be use for concentrated parameters compensation of the power lines.

La première partie de la thèse concerne le calcul numérique des ondes de gravité en 3D. Le modèle résout les équations d'Euler incompressibles avec surface libre pour un écoulement potentiel. L'association de l'Algorithme des Multipôles Rapides avec la Méthode des Eléments aux Frontières permet d'améliorer significativement l'efficacité du modèle. Deux applications sont alors considérées : le déferlement d'une onde solitaire sur un fond tridimensionnel et la focalisation spatiale générée par un batteur à houle. Dans la seconde partie, une étude plus en amont est effectuée dans le contexte des ondes internes en deux dimensions. A l'aide d'un système de type Korteweg de Vries, des ondes solitaires généralisées sont discutées dans le cas où la vitesse approche la valeur critique correspondant à l'apparition des fronts. Ces solutions résultent de la résonance entre une onde solitaire large ayant une amplitude limite et une onde courte, qui se propagent à la même vitesse de phase.

A large aspect ratio leads to higher ion capacity in miniaturized ion trap mass spectrometers. The aspect ratio (AR) of an ion trap represents the ratio between an extended trapping dimension and the characteristic trapping dimension. In contrast to linear and rectilinear traps, changing the AR of a toroidal ion trap (TorIT) results in changes to the degree of curvature and shape of the trapping potential, and hence, on performance as a mass analyzer. SIMION simulations show that higher-order terms in the trapping potential vary strongly for small and moderate AR values (below ~10), with the effects asymptotically flattening for larger AR values. Because of the asymmetry in electrode geometry, the trapping center does not coincide with the geometric center of the trap, and this displacement also varies with AR. For instance, in the asymmetric TorIT, the saddle point in the trapping potential and the geometric trap center differ from +0.6 to -0.4 mm depending on AR. Ion secular frequencies also change with the AR. Whereas ions in the simplified TorIT have stable trajectories for any value of AR, ions in the asymmetric TorIT become unstable at large AR values. Variations in high-order terms, the trapping center, and secular frequencies with AR are a unique feature of toroidal traps, and require significant changes in trap design and operation as the aspect ratio is changed.