Dinàmica de sistemes mesoscòpics amb correlacions quàntiques mitjançant la formulació de de Broglie-Bohm

Per a determinar la dinàmica espai-temporal completa d’un sistema quàntic tridimensional de N partícules cal integrar l’equació d’Schrödinger en 3N dimensions. La capacitat dels ordinadors actuals permet fer-ho com a molt en 3 dimensions. Amb l’objectiu de disminuir el temps de càlcul necessari per a integrar l’equació d’Schrödinger multidimensional, es realitzen usualment una sèrie d’aproximacions, com l’aproximació de Born–Oppenheimer o la de camp mig. En general, el preu que es paga en realitzar aquestes aproximacions és la pèrdua de les correlacions quàntiques (o entrellaçament). Per tant, és necessari desenvolupar mètodes numèrics que permetin integrar i estudiar la dinàmica de sistemes mesoscòpics (sistemes d’entre tres i unes deu partícules) i en els que es tinguin en compte, encara que sigui de forma aproximada, les correlacions quàntiques entre partícules. Recentment, en el context de la propagació d’electrons per efecte túnel en materials semiconductors, X. Oriols ha desenvolupat un nou mètode [Phys. Rev. Lett. 98, 066803 (2007)] per al tractament de les correlacions quàntiques en sistemes mesoscòpics. Aquesta nova proposta es fonamenta en la formulació de la mecànica quàntica de de Broglie– Bohm. Així, volem fer notar que l’enfoc del problema que realitza X. Oriols i que pretenem aquí seguir no es realitza a fi de comptar amb una eina interpretativa, sinó per a obtenir una eina de càlcul numèric amb la que integrar de manera més eficient l’equació d’Schrödinger corresponent a sistemes quàntics de poques partícules. En el marc del present projecte de tesi doctoral es pretén estendre els algorismes desenvolupats per X. Oriols a sistemes quàntics constituïts tant per fermions com per bosons, i aplicar aquests algorismes a diferents sistemes quàntics mesoscòpics on les correlacions quàntiques juguen un paper important. De forma específica, els problemes a estudiar són els següents: (i) Fotoionització de l’àtom d’heli i de l’àtom de liti mitjançant un làser intens. (ii) Estudi de la relació entre la formulació de X. Oriols amb la aproximació de Born–Oppenheimer. (iii) Estudi de les correlacions quàntiques en sistemes bi- i tripartits en l’espai de configuració de les partícules mitjançant la formulació de de Broglie–Bohm.

High-resolution numerical modelling of flow-vegetation interactions

In this paper, we present and apply a new three-dimensional model for the prediction of canopy-flow and turbulence dynamics in open-channel flow. The approach uses a dynamic immersed boundary technique that is coupled in a sequentially staggered manner to a large eddy simulation. Two different biomechanical models are developed depending on whether the vegetation is dominated by bending or tensile forces. For bending plants, a model structured on the Euler-Bernoulli beam equation has been developed, whilst for tensile plants, an N-pendula model has been developed. Validation against flume data shows good agreement and demonstrates that for a given stem density, the models are able to simulate the extraction of energy from the mean flow at the stem-scale which leads to the drag discontinuity and associated mixing layer.

Numerical Taxonomy of Old World Phlebotominae (Diptera: Psychodidae): 1. Considerations of Morphological Characters in the Genus Phlebotomus Rondani & Berté 1840

Numerical analyses (correspondence analysis, ascending hierarchical classification, cladistic approach) were applied to the morphological characters of the adults of the genus Phlebotomus Rondani & Berté 1840. They confirm the reliability of the classic classifications, and also redefine the taxonomic and phylogenetic position of certain taxa. Thus, Spelaeophlebotomus Theodor 1948, Idiophlebotomus Quate & Fairchild 1961 and Australophlebotomus Theodor 1948 deserve generic rank. Among the vectors of leishmaniasis, the subgenus Phlebotomus Rondani & Berté 1840 is probably ancient. The results attribute an intermediate taxonomic and phylogenetic position to the taxa Euphlebotomus Theodor 1948 and Anaphlebotomus Theodor 1948, and reveal the probable artificial nature of the latter. The comparatively large numbers of species of subgenera Paraphlebotomus Theodor 1948, Synphlebotomus Theodor 1948 and, above all, Larroussius Nitzulescu 1931 and Adlerius Nitzulescu 1931, suggest that they are relatively recent. The development of adult morphological characters, the validity of their use in taxonomy and proposals for further studies are discussed.

Numerical Taxonomy of Old World Phlebotominae (Diptera: Psychodidae): 2. Restatement of Classification upon Subgeneric Morphological Characters

Numerical analyses (correspondence analysis, ascending hierarchical classification, and cladistics) were done with morphological characters of adult phlebotomine sand flies. The resulting classification largely confirms that of classical taxonomy for supra-specific groups from the Old World, though the positions of some groups are adjusted. The taxa Spelaeophlebotomus Theodor 1948, Idiophlebotomus Quate & Fairchild 1961, Australophlebotomus Theodor 1948 and Chinius Leng 1987 are notably distinct from other Old World groups, particularly from the genus Phlebotomus Rondani & Berté 1840. Spelaeomyia Theodor 1948 and, in particular, Parvidens Theodor & Mesghali 1964 are clearly separate from Sergentomyia França & Parrot 1920.

Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers

Recent technological advances in remote sensing have enabled investigation of the morphodynamics and hydrodynamics of large rivers. However, measuring topography and flow in these very large rivers is time consuming and thus often constrains the spatial resolution and reach-length scales that can be monitored. Similar constraints exist for computational fluid dynamics (CFD) studies of large rivers, requiring maximization of mesh-or grid-cell dimensions and implying a reduction in the representation of bedform-roughness elements that are of the order of a model grid cell or less, even if they are represented in available topographic data. These ``subgrid'' elements must be parameterized, and this paper applies and considers the impact of roughness-length treatments that include the effect of bed roughness due to ``unmeasured'' topography. CFD predictions were found to be sensitive to the roughness-length specification. Model optimization was based on acoustic Doppler current profiler measurements and estimates of the water surface slope for a variety of roughness lengths. This proved difficult as the metrics used to assess optimal model performance diverged due to the effects of large bedforms that are not well parameterized in roughness-length treatments. However, the general spatial flow patterns are effectively predicted by the model. Changes in roughness length were shown to have a major impact upon flow routing at the channel scale. The results also indicate an absence of secondary flow circulation cells in the reached studied, and suggest simpler two-dimensional models may have great utility in the investigation of flow within large rivers. Citation: Sandbach, S. D. et al. (2012), Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers, Water Resour. Res., 48, W12501, doi: 10.1029/2011WR011284.

Decomposable approximations of nuclear C*-algebras

We show that nuclear C*-algebras have a re ned version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B.

Analyzing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling

The unstable rock slope, Stampa, above the village of Flåm, Norway, shows signs of both active and postglacial gravitational deformation over an area of 11 km2. Detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, as well as geomorphic analysis of high-resolution digital elevation models based on airborne and terrestrial laser scanning indicate that slope deformation is complex and spatially variable. Numerical modeling was used to investigate the influence of former rockslide activity and to better understand the failure mechanism. Field observations, kinematic analysis and numerical modeling indicate a strong structural control of the unstable area. Based on the integration of the above analyses, we propose that the failure mechanism is dominated by (1) a toppling component, (2) subsiding bilinear wedge failure and (3) planar sliding along the foliation at the toe of the unstable slope. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points have an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks with volumes smaller than 300,000 m3. Large fractures indicate deep-seated gravitational deformation of volumes reaching several 100 million m3, but the movement rates in these areas are below 2 mm/year. Two different lobes of prehistoric rock slope failures were dated with terrestrial cosmogenic nuclides. While the northern lobe gave an average age of 4,300 years BP, the southern one resulted in two different ages (2,400 and 12,000 years BP), which represent most likely multiple rockfall events. This reflects the currently observable deformation style with unstable blocks in the northern part in between Joasete and Furekamben and no distinct blocks but a high rockfall activity around Ramnanosi in the south. With a relative susceptibility analysis it is concluded that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes > 100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A larger collapse involving several million m3 is presently considered of very low likelihood.

Numerical simulation of left ventricular assist device implantations: comparing the ascending and the descending aorta cannulations.

In this work we present numerical simulations of continuous flow left ventricle assist device implantation with the aim of comparing difference in flow rates and pressure patterns depending on the location of the anastomosis and the rotational speed of the device. Despite the fact that the descending aorta anastomosis approach is less invasive, since it does not require a sternotomy and a cardiopulmonary bypass, its benefits are still controversial. Moreover, the device rotational speed should be correctly chosen to avoid anomalous flow rates and pressure distribution in specific location of the cardiovascular tree. With the aim of assessing the differences between these two approaches and device rotational speed in terms of flow rate and pressure waveforms, we set up numerical simulations of network of one-dimensional models where we account for the presence of an outflow cannula anastomosed to different locations of the aorta. Then, we use the resulting network to compare the results of the two different cannulations for several stages of heart failure and different rotational speed of the device. The inflow boundary data for the heart and the cannulas are obtained from a lumped parameters model of the entire circulatory system with an assist device, which is validated with clinical data. The results show that ascending and descending aorta cannulations lead to similar waveforms and mean flow rate in all the considered cases. Moreover, regardless of the anastomosis region, the rotational speed of the device has an important impact on wave profiles; this effect is more pronounced at high RPM.

Steady-state expression of self-regulated genes.

MOTIVATION: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of appropriate behavior. The lack of precise knowledge on the steady-state distribution of gene expression requires the use of Gillespie algorithms and Monte-Carlo approximations. METHODOLOGY: In this study, we provide new exact formulas and efficient numerical algorithms for computing/modeling the steady-state of a class of self-regulated genes, and we use it to model/compute the stochastic expression of a gene of interest in an engineered network introduced in mammalian cells. The behavior of the genetic network is then analyzed experimentally in living cells. RESULTS: Stochastic models often reveal counter-intuitive experimental behaviors, and we find that this genetic architecture displays a unimodal behavior in mammalian cells, which was unexpected given its known bimodal response in unicellular organisms. We provide a molecular rationale for this behavior, and we implement it in the mathematical picture to explain the experimental results obtained from this network.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Imputation in data fusion of heterogeneous data sets a model-based numerical experiment

Given the very large amount of data obtained everyday through population surveys, much of the new research again could use this information instead of collecting new samples. Unfortunately, relevant data are often disseminated into different files obtained through different sampling designs. Data fusion is a set of methods used to combine information from different sources into a single dataset. In this article, we are interested in a specific problem: the fusion of two data files, one of which being quite small. We propose a model-based procedure combining a logistic regression with an Expectation-Maximization algorithm. Results show that despite the lack of data, this procedure can perform better than standard matching procedures.

Segmentation and grid generation for numerical simulations of vad connections with patient-specific data

Objectives: We are interested in the numerical simulation of the anastomotic region comprised between outflow canula of LVAD and the aorta. Segmenta¬tion, geometry reconstruction and grid generation from patient-specific data remain an issue because of the variable quality of DICOM images, in particular CT-scan (e.g. metallic noise of the device, non-aortic contrast phase). We pro¬pose a general framework to overcome this problem and create suitable grids for numerical simulations.Methods: Preliminary treatment of images is performed by reducing the level window and enhancing the contrast of the greyscale image using contrast-limited adaptive histogram equalization. A gradient anisotropic diffusion filter is applied to reduce the noise. Then, watershed segmentation algorithms and mathematical morphology filters allow reconstructing the patient geometry. This is done using the InsightToolKit library (www.itk.org). Finally the Vascular Model¬ing ToolKit (www.vmtk.org) and gmsh (www.geuz.org/gmsh) are used to create the meshes for the fluid (blood) and structure (arterial wall, outflow canula) and to a priori identify the boundary layers. The method is tested on five different patients with left ventricular assistance and who underwent a CT-scan exam.Results: This method produced good results in four patients. The anastomosis area is recovered and the generated grids are suitable for numerical simulations. In one patient the method failed to produce a good segmentation because of the small dimension of the aortic arch with respect to the image resolution.Conclusions: The described framework allows the use of data that could not be otherwise segmented by standard automatic segmentation tools. In particular the computational grids that have been generated are suitable for simulations that take into account fluid-structure interactions. Finally the presented method features a good reproducibility and fast application.

Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica

En el marc del projecte "Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica" s'han desenvolupat un conjunt d'eines numèriques que permeten avançar en l'ús de l'espectroscòpia òptica per a l'obtenció d'informació morfològica de materials compostos consistents en partícules metàl•liques en matriu dielèctrica. S'han implementat esquemes numèrics per a calcular les propietats òptiques de materials compostos on les partícules poden presentar una distribució de mides i formes i diferent graus d'ordenament espacial. Les simulacions s'han realitzat a dos nivells: i) amb l’aproximació quasi-estàtica, que permet descriure el comportament d'aquests materials en termes de constants òptiques efectives i ii) amb càlculs electrodinàmics exactes, que han servit per avaluar la validesa de l’aproximació anterior i que han permès d'estudiar la interacció de partícules amb feixos de llum focalitzats o amb polarització no homogènia. A través de l’anàlisi d'aquestes simulacions, s'han desenvolupat models senzills que permeten parametritzar la influència de diferents quantitats físiques en el comportament òptic del material. Aquests models s'han implementat en un programari de càlcul que permeten trobar el valor òptim dels paràmetres físics d'interès mitjançant l'ajust d'espectres òptics. Els models s'han avaluat amb l'anàlisi de dades experimentals subministrades per altres laboratoris.