Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.

Microstates of a neutral black hole in M theory

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T6). From a type-IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a simple D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Interhemispheric visual integration in humans explored by multimodal brain imaging

Résumé: Les récents progrès techniques de l'imagerie cérébrale non invasives ont permis d'améliorer la compréhension des différents systèmes fonctionnels cérébraux. Les approches multimodales sont devenues indispensables en recherche, afin d'étudier dans sa globalité les différentes caractéristiques de l'activité neuronale qui sont à la base du fonctionnement cérébral. Dans cette étude combinée d'imagerie par résonance magnétique fonctionnelle (IRMf) et d'électroencéphalographie (EEG), nous avons exploité le potentiel de chacune d'elles, soit respectivement la résolution spatiale et temporelle élevée. Les processus cognitifs, de perception et de mouvement nécessitent le recrutement d'ensembles neuronaux. Dans la première partie de cette thèse nous étudions, grâce à la combinaison des techniques IRMf et EEG, la réponse des aires visuelles lors d'une stimulation qui demande le regroupement d'éléments cohérents appartenant aux deux hémi-champs visuels pour en faire une seule image. Nous utilisons une mesure de synchronisation (EEG de cohérence) comme quantification de l'intégration spatiale inter-hémisphérique et la réponse BOLD (Blood Oxygenation Level Dependent) pour évaluer l'activité cérébrale qui en résulte. L'augmentation de la cohérence de l'EEG dans la bande beta-gamma mesurée au niveau des électrodes occipitales et sa corrélation linéaire avec la réponse BOLD dans les aires de VP/V4, reflète et visualise un ensemble neuronal synchronisé qui est vraisemblablement impliqué dans le regroupement spatial visuel. Ces résultats nous ont permis d'étendre la recherche à l'étude de l'impact que le contenu en fréquence des stimuli a sur la synchronisation. Avec la même approche, nous avons donc identifié les réseaux qui montrent une sensibilité différente à l'intégration des caractéristiques globales ou détaillées des images. En particulier, les données montrent que l'implication des réseaux visuels ventral et dorsal est modulée par le contenu en fréquence des stimuli. Dans la deuxième partie nous avons a testé l'hypothèse que l'augmentation de l'activité cérébrale pendant le processus de regroupement inter-hémisphérique dépend de l'activité des axones calleux qui relient les aires visuelles. Comme le Corps Calleux présente une maturation progressive pendant les deux premières décennies, nous avons analysé le développement de la fonction d'intégration spatiale chez des enfants âgés de 7 à 13 ans et le rôle de la myelinisation des fibres calleuses dans la maturation de l'activité visuelle. Nous avons combiné l'IRMf et la technique de MTI (Magnetization Transfer Imaging) afin de suivre les signes de maturation cérébrale respectivement sous l'aspect fonctionnel et morphologique (myelinisation). Chez lés enfants, les activations associées au processus d'intégration entre les hémi-champs visuels sont, comme chez l'adulte, localisées dans le réseau ventral mais se limitent à une zone plus restreinte. La forte corrélation que le signal BOLD montre avec la myelinisation des fibres du splenium est le signe de la dépendance entre la maturation des fonctions visuelles de haut niveau et celle des connections cortico-corticales. Abstract: Recent advances in non-invasive brain imaging allow the visualization of the different aspects of complex brain dynamics. The approaches based on a combination of imaging techniques facilitate the investigation and the link of multiple aspects of information processing. They are getting a leading tool for understanding the neural basis of various brain functions. Perception, motion, and cognition involve the formation of cooperative neuronal assemblies distributed over the cerebral cortex. In this research, we explore the characteristics of interhemispheric assemblies in the visual brain by taking advantage of the complementary characteristics provided by EEG (electroencephalography) and fMRI (Functional Magnetic Resonance Imaging) techniques. These are the high temporal resolution for EEG and high spatial resolution for fMRI. In the first part of this thesis we investigate the response of the visual areas to the interhemispheric perceptual grouping task. We use EEG coherence as a measure of synchronization and BOLD (Blood Oxygenar tion Level Dependent) response as a measure of the related brain activation. The increase of the interhemispheric EEG coherence restricted to the occipital electrodes and to the EEG beta band and its linear relation to the BOLD responses in VP/V4 area points to a trans-hemispheric synchronous neuronal assembly involved in early perceptual grouping. This result encouraged us to explore the formation of synchronous trans-hemispheric networks induced by the stimuli of various spatial frequencies with this multimodal approach. We have found the involvement of ventral and medio-dorsal visual networks modulated by the spatial frequency content of the stimulus. Thus, based on the combination of EEG coherence and fMRI BOLD data, we have identified visual networks with different sensitivity to integrating low vs. high spatial frequencies. In the second part of this work we test the hypothesis that the increase of brain activity during perceptual grouping depends on the activity of callosal axons interconnecting the visual areas that are involved. To this end, in children of 7-13 years, we investigated functional (functional activation with fMRI) and morphological (myelination of the corpus callosum with Magnetization Transfer Imaging (MTI)) aspects of spatial integration. In children, the activation associated with the spatial integration across visual fields was localized in visual ventral stream and limited to a part of the area activated in adults. The strong correlation between individual BOLD responses in .this area and the myelination of the splenial system of fibers points to myelination as a significant factor in the development of the spatial integration ability.

Quantitative Assessment of Soil Physical Quality in Northern China Based on S-theory

ABSTRACT Quantitative assessment of soil physical quality is of great importance for eco-environmental pollution and soil quality studies. In this paper, based on the S-theory, data from 16 collection sites in the Haihe River Basin in northern China were used, and the effects of soil particle size distribution and bulk density on three important indices of theS-theory were investigated on a regional scale. The relationships between unsaturated hydraulic conductivityKi at the inflection point and S values (S/hi) were also studied using two different types of fitting equations. The results showed that the polynomial equation was better than the linear equation for describing the relationships between -log Ki and -logS, and -log Kiand -log (S/hi)2; and clay content was the most important factor affecting the soil physical quality index (S). The variation in the S index according to soil clay content was able to be fitted using a double-linear-line approach, with decrease in the S index being much faster for clay content less than 20 %. In contrast, the bulk density index was found to be less important than clay content. The average S index was 0.077, indicating that soil physical quality in the Haihe River Basin was good.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.