Generic finite-size enhancement of pairing in mesoscopic Fermi systems

The finite-size-dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two-body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well as atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Interaccion among systems of finite size in predictive relativistic mechanics I. General framework

We derive a Hamiltonian formulation for the three-dimensional formalism of predictive relativistic mechanics. This Hamiltonian structure is used to derive a set of dynamical equations describing the interaction among systems in perturbation theory.

Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Interactions among systems of finite size en predictive relativistic mechanics III. Short-range interaction and second-order terms

We compute up to and including all the c-2 terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.

Fluctuations in finite systems: fluctuations in fluids in thermocapillary motion

We compute nonequilibrium correlation functions about the stationary state in which the fluid moves as a consequence of tangential stresses on the liquid surface, related to a varying surface tension (thermocapillary motion). The nature of the stationary state makes it necessary to take into account that the system is finite. We then extend a previous analysis on fluctuations about simple stationary states to include some effects related to the finite size of the sample.

Budgeting rockfall and modeling sedimentary delivery in torrent systems

This thesis is a compilation of projects to study sediment processes recharging debris flow channels. These works, conducted during my stay at the University of Lausanne, focus in the geological and morphological implications of torrent catchments to characterize debris supply, a fundamental element to predict debris flows. Other aspects of sediment dynamics are considered, e.g. the coupling headwaters - torrent, as well as the development of a modeling software that simulates sediment transfer in torrent systems. The sediment activity at Manival, an active torrent system of the northern French Alps, was investigated using terrestrial laser scanning and supplemented with geostructural investigations and a survey of sediment transferred in the main torrent. A full year of sediment flux could be observed, which coincided with two debris flows and several bedload transport events. This study revealed that both debris flows generated in the torrent and were preceded in time by recharge of material from the headwaters. Debris production occurred mostly during winter - early spring time and was caused by large slope failures. Sediment transfers were more puzzling, occurring almost exclusively in early spring subordinated to runoffconditions and in autumn during long rainfall. Intense rainstorms in summer did not affect debris storage that seems to rely on the stability of debris deposits. The morpho-geological implication in debris supply was evaluated using DEM and field surveys. A slope angle-based classification of topography could characterize the mode of debris production and transfer. A slope stability analysis derived from the structures in rock mass could assess susceptibility to failure. The modeled rockfall source areas included more than 97% of the recorded events and the sediment budgets appeared to be correlated to the density of potential slope failure. This work showed that the analysis of process-related terrain morphology and of susceptibility to slope failure document the sediment dynamics to quantitatively assess erosion zones leading to debris flow activity. The development of erosional landforms was evaluated by analyzing their geometry with the orientations of potential rock slope failure and with the direction of the maximum joint frequency. Structure in rock mass, but in particular wedge failure and the dominant discontinuities, appear as a first-order control of erosional mechanisms affecting bedrock- dominated catchment. They represent some weaknesses that are exploited primarily by mass wasting processes and erosion, promoting not only the initiation of rock couloirs and gullies, but also their propagation. Incorporating the geological control in geomorphic processes contributes to better understand the landscape evolution of active catchments. A sediment flux algorithm was implemented in a sediment cascade model that discretizes the torrent catchment in channel reaches and individual process-response systems. Each conceptual element includes in simple manner geomorphological and sediment flux information derived from GIS complemented with field mapping. This tool enables to simulate sediment transfers in channels considering evolving debris supply and conveyance, and helps reducing the uncertainty inherent to sediment budget prediction in torrent systems. Cette thèse est un recueil de projets d'études des processus de recharges sédimentaires des chenaux torrentiels. Ces travaux, réalisés lorsque j'étais employé à l'Université de Lausanne, se concentrent sur les implications géologiques et morphologiques des bassins dans l'apport de sédiments, élément fondamental dans la prédiction de laves torrentielles. D'autres aspects de dynamique sédimentaire ont été abordés, p. ex. le couplage torrent - bassin, ainsi qu'un modèle de simulation du transfert sédimentaire en milieu torrentiel. L'activité sédimentaire du Manival, un système torrentiel actif des Alpes françaises, a été étudiée par relevés au laser scanner terrestre et complétée par une étude géostructurale ainsi qu'un suivi du transfert en sédiments du torrent. Une année de flux sédimentaire a pu être observée, coïncidant avec deux laves torrentielles et plusieurs phénomènes de charriages. Cette étude a révélé que les laves s'étaient générées dans le torrent et étaient précédées par une recharge de débris depuis les versants. La production de débris s'est passée principalement en l'hiver - début du printemps, causée par de grandes ruptures de pentes. Le transfert était plus étrange, se produisant presque exclusivement au début du printemps subordonné aux conditions d'écoulement et en automne lors de longues pluies. Les orages d'été n'affectèrent guère les dépôts, qui semblent dépendre de leur stabilité. Les implications morpho-géologiques dans l'apport sédimentaire ont été évaluées à l'aide de MNT et études de terrain. Une classification de la topographie basée sur la pente a permis de charactériser le mode de production et transfert. Une analyse de stabilité de pente à partir des structures de roches a permis d'estimer la susceptibilité à la rupture. Les zones sources modélisées comprennent plus de 97% des chutes de blocs observées et les bilans sédimentaires sont corrélés à la densité de ruptures potentielles. Ce travail d'analyses des morphologies du terrain et de susceptibilité à la rupture documente la dynamique sédimentaire pour l'estimation quantitative des zones érosives induisant l'activité torrentielle. Le développement des formes d'érosion a été évalué par l'analyse de leur géométrie avec celle des ruptures potentielles et avec la direction de la fréquence maximale des joints. Les structures de roches, mais en particulier les dièdres et les discontinuités dominantes, semblent être très influents dans les mécanismes d'érosion affectant les bassins rocheux. Ils représentent des zones de faiblesse exploitées en priorité par les processus de démantèlement et d'érosion, encourageant l'initiation de ravines et couloirs, mais aussi leur propagation. L'incorporation du control géologique dans les processus de surface contribue à une meilleure compréhension de l'évolution topographique de bassins actifs. Un algorithme de flux sédimentaire a été implémenté dans un modèle en cascade, lequel divise le bassin en biefs et en systèmes individuels répondant aux processus. Chaque unité inclut de façon simple les informations géomorpologiques et celles du flux sédimentaire dérivées à partir de SIG et de cartographie de terrain. Cet outil permet la simulation des transferts de masse dans les chenaux, considérants la variabilité de l'apport et son transport, et aide à réduire l'incertitude liée à la prédiction de bilans sédimentaires torrentiels. Ce travail vise très humblement d'éclairer quelques aspects de la dynamique sédimentaire en milieu torrentiel.

Mobile robot experimental modeling and control strategies using sensor fusion

This research work deals with the problem of modeling and design of low level speed controller for the mobile robot PRIM. The main objective is to develop an effective educational, and research tool. On one hand, the interests in using the open mobile platform PRIM consist in integrating several highly related subjects to the automatic control theory in an educational context, by embracing the subjects of communications, signal processing, sensor fusion and hardware design, amongst others. On the other hand, the idea is to implement useful navigation strategies such that the robot can be served as a mobile multimedia information point. It is in this context, when navigation strategies are oriented to goal achievement, that a local model predictive control is attained. Hence, such studies are presented as a very interesting control strategy in order to develop the future capabilities of the system. In this context the research developed includes the visual information as a meaningful source that allows detecting the obstacle position coordinates as well as planning the free obstacle trajectory that should be reached by the robot

Statistical modeling of bowing control applied to violin sound synthesis

Excitation-continuous music instrument control patterns are often not explicitly represented in current sound synthesis techniques when applied to automatic performance. Both physical model-based and sample-based synthesis paradigmswould benefit from a flexible and accurate instrument control model, enabling the improvement of naturalness and realism. Wepresent a framework for modeling bowing control parameters inviolin performance. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing control parameter signals.We model the temporal contour of bow velocity, bow pressing force, and bow-bridge distance as sequences of short Bézier cubic curve segments. Considering different articulations, dynamics, and performance contexts, a number of note classes are defined. Contours of bowing parameters in a performance database are analyzed at note-level by following a predefined grammar that dictates characteristics of curve segment sequences for each of the classes in consideration. As a result, contour analysis of bowing parameters of each note yields an optimal representation vector that is sufficient for reconstructing original contours with significant fidelity. From the resulting representation vectors, we construct a statistical model based on Gaussian mixtures suitable for both the analysis and synthesis of bowing parameter contours. By using the estimated models, synthetic contours can be generated through a bow planning algorithm able to reproduce possible constraints caused by the finite length of the bow. Rendered contours are successfully used in two preliminary synthesis frameworks: digital waveguide-based bowed stringphysical modeling and sample-based spectral-domain synthesis.

Modeling and control of electromechanical systems

The material presented in the these notes covers the sessions Modelling of electromechanical systems, Passive control theory I and Passive control theory II of the II EURON/GEOPLEX Summer School on Modelling and Control of Complex Dynamical Systems.We start with a general description of what an electromechanical system is from a network modelling point of view. Next, a general formulation in terms of PHDS is introduced, and some of the previous electromechanical systems are rewritten in this formalism. Power converters, which are variable structure systems (VSS), can also be given a PHDS form.We conclude the modelling part of these lectures with a rather complex example, showing the interconnection of subsystems from several domains, namely an arrangement to temporally store the surplus energy in a section of a metropolitan transportation system based on dc motor vehicles, using either arrays of supercapacitors or an electric poweredflywheel. The second part of the lectures addresses control of PHD systems. We first present the idea of control as power connection of a plant and a controller. Next we discuss how to circumvent this obstacle and present the basic ideas of Interconnection and Damping Assignment (IDA) passivity-based control of PHD systems.

Use of Remote Sensing for Collection of Data Elements for Linear Referencing Systems, 2001

This report evaluates the use of remotely sensed images in implementing the Iowa DOT LRS that is currently in the stages of system architecture. The Iowa Department of Transportation is investing a significant amount of time and resources into creation of a linear referencing system (LRS). A significant portion of the effort in implementing the system will be creation of a datum, which includes geographically locating anchor points and then measuring anchor section distances between those anchor points. Currently, system architecture and evaluation of different data collection methods to establish the LRS datum is being performed for the DOT by an outside consulting team.

Modeling morphogen gradient formation from arbitrary realistically shaped sources.

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.