Proposal for underwater structural analysis using the techniques of ESPI and digital holography

The purpose of this article is to study the application of the holographic interferometry techniques in the structural analysis of submarine environment. These techniques are widely used today, with applications in many areas. Nevertheless, its application in submarine environments presents some challenges. The application of two techniques, electronic speckle pattern interferometry (ESPI) and digital holography, comparison of advantages and disadvantages of each of them is presented. A brief study is done on the influence of water properties and the optical effects due to suspended particles as well as possible solutions to minimize these problems. (C) 2009 Elsevier Ltd. All rights reserved.

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects. (c) 2007 Elsevier B.V. All rights reserved.

Digitale Einstrahl-Holographie atmosphärischer Eiskristalle

Es wurde ein für bodengebundene Feldmessungen geeignetes System zur digital-holographischen Abbildung luftgetragener Objekte entwickelt und konstruiert. Es ist, abhängig von der Tiefenposition, geeignet zur direkten Bestimmung der Größe luftgetragener Objekte oberhalb von ca. 20 µm, sowie ihrer Form bei Größen oberhalb von ca. 100µm bis in den Millimeterbereich. Die Entwicklung umfaßte zusätzlich einen Algorithmus zur automatisierten Verbesserung der Hologrammqualität und zur semiautomatischen Entfernungsbestimmung großer Objekte entwickelt. Eine Möglichkeit zur intrinsischen Effizienzsteigerung der Bestimmung der Tiefenposition durch die Berechnung winkelgemittelter Profile wurde vorgestellt. Es wurde weiterhin ein Verfahren entwickelt, das mithilfe eines iterativen Ansatzes für isolierte Objekte die Rückgewinnung der Phaseninformation und damit die Beseitigung des Zwillingsbildes erlaubt. Weiterhin wurden mithilfe von Simulationen die Auswirkungen verschiedener Beschränkungen der digitalen Holographie wie der endlichen Pixelgröße untersucht und diskutiert. Die geeignete Darstellung der dreidimensionalen Ortsinformation stellt in der digitalen Holographie ein besonderes Problem dar, da das dreidimensionale Lichtfeld nicht physikalisch rekonstruiert wird. Es wurde ein Verfahren entwickelt und implementiert, das durch Konstruktion einer stereoskopischen Repräsentation des numerisch rekonstruierten Meßvolumens eine quasi-dreidimensionale, vergrößerte Betrachtung erlaubt. Es wurden ausgewählte, während Feldversuchen auf dem Jungfraujoch aufgenommene digitale Hologramme rekonstruiert. Dabei ergab sich teilweise ein sehr hoher Anteil an irregulären Kristallformen, insbesondere infolge massiver Bereifung. Es wurden auch in Zeiträumen mit formal eisuntersättigten Bedingungen Objekte bis hinunter in den Bereich ≤20µm beobachtet. Weiterhin konnte in Anwendung der hier entwickelten Theorie des ”Phasenrandeffektes“ ein Objekt von nur ca. 40µm Größe als Eisplättchen identifiziert werden. Größter Nachteil digitaler Holographie gegenüber herkömmlichen photographisch abbildenden Verfahren ist die Notwendigkeit der aufwendigen numerischen Rekonstruktion. Es ergibt sich ein hoher rechnerischer Aufwand zum Erreichen eines einer Photographie vergleichbaren Ergebnisses. Andererseits weist die digitale Holographie Alleinstellungsmerkmale auf. Der Zugang zur dreidimensionalen Ortsinformation kann der lokalen Untersuchung der relativen Objektabstände dienen. Allerdings zeigte sich, dass die Gegebenheiten der digitalen Holographie die Beobachtung hinreichend großer Mengen von Objekten auf der Grundlage einzelner Hologramm gegenwärtig erschweren. Es wurde demonstriert, dass vollständige Objektgrenzen auch dann rekonstruiert werden konnten, wenn ein Objekt sich teilweise oder ganz außerhalb des geometrischen Meßvolumens befand. Weiterhin wurde die zunächst in Simulationen demonstrierte Sub-Bildelementrekonstruktion auf reale Hologramme angewandt. Dabei konnte gezeigt werden, dass z.T. quasi-punktförmige Objekte mit Sub-Pixelgenauigkeit lokalisiert, aber auch bei ausgedehnten Objekten zusätzliche Informationen gewonnen werden konnten. Schließlich wurden auf rekonstruierten Eiskristallen Interferenzmuster beobachtet und teilweise zeitlich verfolgt. Gegenwärtig erscheinen sowohl kristallinterne Reflexion als auch die Existenz einer (quasi-)flüssigen Schicht als Erklärung möglich, wobei teilweise in Richtung der letztgenannten Möglichkeit argumentiert werden konnte. Als Ergebnis der Arbeit steht jetzt ein System zur Verfügung, das ein neues Meßinstrument und umfangreiche Algorithmen umfaßt. S. M. F. Raupach, H.-J. Vössing, J. Curtius und S. Borrmann: Digital crossed-beam holography for in-situ imaging of atmospheric particles, J. Opt. A: Pure Appl. Opt. 8, 796-806 (2006) S. M. F. Raupach: A cascaded adaptive mask algorithm for twin image removal and its application to digital holograms of ice crystals, Appl. Opt. 48, 287-301 (2009) S. M. F. Raupach: Stereoscopic 3D visualization of particle fields reconstructed from digital inline holograms, (zur Veröffentlichung angenommen, Optik - Int. J. Light El. Optics, 2009)

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.

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.

Genome reconstruction and comparative genomics of pneumocystis jirovecii

Pneumocystis jirovecii is a fungus belonging to a basal lineage of the Ascomycotina, the Taphrinomycotina subphylum. It is a parasite specific to humans that dwells primarily in the lung and can cause severe pneumonia in individuals with debilitated immune system. Despite its clinical importance, many aspects of its biology remain poorly understood, at least in part because of the lack of a continuous in vitro cultivation system. The present thesis consists in the genome reconstruction and comparative genomics of P. jirovecii. It is made of three parts: (i) the de novo sequencing of P. jirovecii genome starting from a single broncho- alveolar lavage fluid of a single patient (ii) the de novo sequencing of the genome of the plant pathogen Taphrina deformans, a fungus closely related to P. jirovecii, and (iii) the genome scale comparison of P. jirovecii to other Taphrinomycotina members. Enrichment in P. jirovecii cells by immuno-precipitation, whole DNA random amplification, two complementary high throughput DNA sequencing methods, and in silico sorting and assembly of sequences were used for the de novo reconstruction of P. jirovecii genome from the microbiota of a single clinical specimen. An iterative ad hoc pipeline as well as numerical simulations was used to recover P. jirovecii sequences while purging out contaminants and assembly or amplification chimeras. This strategy produced a 8.1 Mb assembly, which encodes 3,898 genes. Homology searches, mapping on biochemical pathways atlases, and manual validations revealed that this genome lacks (i) most of the enzymes dedicated to the amino acids biosyntheses, and (ii) most virulence factors observed in other fungi, e.g. the glyoxylate shunt pathway and specific peptidases involved in the degradation of the host cell membrane. The same analyses applied to the available genomic sequences from Pneumocystis carinii the species infecting rats and Pneumocystis murina the species infecting mice revealed the same deficiencies. The genome sequencing of T. deformans yielded a 13 Mb assembly, which encodes 5,735 genes. T. deformans possesses enzymes involved plant cell wall degradation, secondary metabolism, the glyoxylate cycle, detoxification, sterol biosynthesis, as well as the biosyntheses of plant hormones such as abscisic acid or indole-3-acetic acid. T. deformans also harbors gene subsets that have counterparts in plant saprophytes or pathogens, which is consistent with its alternate saprophytic and pathogenic lifestyles. Mating genes were also identified. The homothallism of this fungus suggests a mating-type switching mechanism. Comparative analyses indicated that 81% of P. jirovecii genes are shared with eight other Taphrinomycotina members, including T. deformans, P. carinii and P. murina. These genes are mostly involved in housekeeping activities. The genes specific to the Pneumocystis genus represent 8%, and are involved in RNA metabolism and signaling. The signaling is known to be crucial for interaction of Pneumocystis spp with their environment. Eleven percent are unique to P. jirovecii and encode mostly proteins of unknown function. These genes in conjunction with other ones (e.g. the major surface glycoproteins) might govern the interaction of P. jirovecii with its human host cells, and potentially be responsible of the host specificity. P. jirovecii exhibits a reduced genome in size with a low GC content, and most probably scavenges vital compounds such as amino acids and cholesterol from human lungs. Consistently, its genome encodes a large set of transporters (ca. 22% of its genes), which may play a pivotal role in the acquisition of these compounds. All these features are generally observed in obligate parasite of various kingdoms (bacteria, protozoa, fungi). Moreover, epidemiological studies failed to evidence a free-living form of the fungus and Pneumocystis spp were shown to co-evolved with their hosts. Given also the lack of virulence factors, our observations strongly suggest that P. jirovecii is an obligate parasite specialized in the colonization of human lungs, and which causes disease only in individuals with compromised immune system. The same conclusion is most likely true for all other Pneumocystis spp in their respective mammalian host. - Pneumocystis jirovecii est un champignon appartenant à ine branche basale des Ascomycotina, le sous-embranchement des Taphrinomycotina. C'est un parasite spécifique aux humains qui réside principalement dans les poumons, et qui peut causer des pneumonies sévères chez des individus ayant un système immunitaire déficient. En dépit de son importance clinique, de nombreux aspects de sa biologie demeurent,largement méconnus, au moins en partie à cause de l'absence d'un système de culture in vitro continu. Cette thèse traite de la reconstruction du génome et de la génomique comparative de P. jirovecii. Elle comporte trois parties: (i) le séquençage de novo du génome de P. jirovecii à partir d'un lavage broncho-alvéolaire provenant d'un seul patient, (ii) le séquençage de novo du génome d'un champignon pathogène de plante Taphrina deformans qui est phylogénétiquement proche de P. jirovecii, et (iii) la comparaison du génome de P. jirovecii à celui d'autres membres du sous-embranchement des Taphrinomycotina. Un enrichissement en cellules de P. jirovecii par immuno-précipitation, une amplification aléatoire des molécules d'ADN, deux méthodes complémentaires de séquençage à haut débit, un tri in silico et un assemblage des séquences ont été utilisés pour reconstruire de novo le génome de P. jirovecii à partir du microbiote d'un seul échantillon clinique. Un pipeline spécifique ainsi que des simulations numériques ont été utilisés pour récupérer les séquences de P. jirovecii tout en éliminant les séquences contaminants et les chimères d'amplification ou d'assemblage. Cette stratégie a produit un assemblage de 8.1 Mb, qui contient 3898 gènes. Les recherches d'homologies, de cartographie des voies métaboliques et des validations manuelles ont révélé que ce génome est dépourvu (i) de la plupart des enzymes dédiées à la biosynthèse des acides aminés, et (ii) de la plupart des facteurs de virulence observés chez d'autres champignons, par exemple, le cycle du glyoxylate ainsi que des peptidases spécifiques impliquées dans la dégradation de la membrane de la cellule hôte. Les analyses appliquées aux données génomiques disponibles de Pneumocystis carinii, l'espèce infectant les rats, et de Pneumocystis murina, l'espèce infectant les souris, ont révélé les mêmes déficiences. Le séquençage du génome de T. deformans a généré un assemblage de 13.3 Mb qui contient 5735 gènes. T. deformans possède les gènes codant pour les enzymes impliquées dans la dégradation des parois cellulaires des plantes, le métabolisme secondaire, le cycle du glyoxylate, la détoxification, la biosynthèse des stérols ainsi que la biosynthèse d'hormones de plantes telles que l'acide abscissique ou l'acide indole 3-acétique. T. deformans possède également des sous-ensembles de gènes présents exclusivement chez des saprophytes ou des pathogènes de plantes, ce qui est consistent avec son mode de vie alternatif saprophyte et pathogène. Des gènes impliqués dans la conjugaison ont été identifiés. L'homothallisme de ce champignon suggère mécanisme de permutation du type conjuguant. Les analyses comparatives ont démontré que 81% des gènes de P. jirovecii sont présent chez les autres membres du sous-embranchement des Taphrinomycotina. Ces gènes sont essentiellement impliqués dans le métabolisme basai. Les gènes spécifiques au genre Pneumocystis représentent 8%, et sont impliqués dans le métabolisme de l'ARN et la signalisation. La signalisation est connue pour être cruciale pour l'interaction des espèces de Pneumocystis avec leur environnement. Les gènes propres à P. jirovecii représentent 11% et codent en majorité pour des protéines dont la fonction est inconnue. Ces gènes en conjonction avec d'autres (par exemple, les glycoprotéines de surface), pourraient être déterminants dans l'interaction de P. jirovecii avec les cellules de l'hôte humain, et être potentiellement responsable de la spécificité d'hôte. P. jirovecii possède un génome de taille réduite à faible pourcentage en GC et récupère très probablement des composés vitaux comme les acides aminés et le cholestérol à partir des poumons humains. De manière consistante, son génome code pour de nombreux transporteurs (22% de ses gènes), qui pourraient jouer un rôle essentiel dans l'acquisition de ces composés. Ces caractéristiques sont généralement observées chez les parasites obligatoires de plusieurs règnes (bactéries, protozoaires, champignons). De plus, les études épidémiologiques n'ont pas réussi à prouver l'existence d'ime forme vivant librement du champignon. Etant donné également l'absence de facteurs de virulence, nos observations suggèrent que P. jirovecii est un parasite obligatoire spécialisé dans la colonisation des poumons humains, ne causant une maladie que chez des individus ayant un système immunitaire compromis. La même conclusion est très probablement applicable à toutes les autres espèces de Pneumocystis dans leur hôte mammifère respectif.

Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography.

Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

Reconstruction des structures magnéto-convectives solaires sous une région active, par l’utilisation conjointe d’un modèle de convection anélastique et d’une méthode d’assimilation de données.

L’utilisation d’une méthode d’assimilation de données, associée à un modèle de convection anélastique, nous permet la reconstruction des structures physiques d’une partie de la zone convective située en dessous d’une région solaire active. Les résultats obtenus nous informent sur les processus d’émergence des tubes de champ magnétique au travers de la zone convective ainsi que sur les mécanismes de formation des régions actives. Les données solaires utilisées proviennent de l’instrument MDI à bord de l’observatoire spatial SOHO et concernent principalement la région active AR9077 lors de l’ ́évènement du “jour de la Bastille”, le 14 juillet 2000. Cet évènement a conduit à l’avènement d’une éruption solaire, suivie par une importante éjection de masse coronale. Les données assimilées (magnétogrammes, cartes de températures et de vitesses verticales) couvrent une surface de 175 méga-mètres de coté acquises au niveau photosphérique. La méthode d’assimilation de données employée est le “coup de coude direct et rétrograde”, une méthode de relaxation Newtonienne similaire à la méthode “quasi-linéaire inverse 3D”. Elle présente l’originalité de ne pas nécessiter le calcul des équations adjointes au modèle physique. Aussi, la simplicité de la méthode est un avantage numérique conséquent. Notre étude montre au travers d’un test simple l’applicabilité de cette méthode à un modèle de convection utilisé dans le cadre de l’approximation anélastique. Nous montrons ainsi l’efficacité de cette méthode et révélons son potentiel pour l’assimilation de données solaires. Afin d’assurer l’unicité mathématique de la solution obtenue nous imposons une régularisation dans tout le domaine simulé. Nous montrons enfin que l’intérêt de la méthode employée ne se limite pas à la reconstruction des structures convectives, mais qu’elle permet également l’interpolation optimale des magnétogrammes photosphériques, voir même la prédiction de leur évolution temporelle.

Reconstruction des mouvements du plasma dans une région active solaire à l'aide de données d'observation et d'une minimisation Lagrangienne

À ce jour, les différentes méthodes de reconstruction des mouvements du plasma à la surface du Soleil qui ont été proposées présupposent une MHD idéale (Welsch et al., 2007). Cependant, Chae & Sakurai (2008) ont montré l’existence d’une diffusivité magnétique turbulente à la photosphère. Nous introduisons une généralisation de la méthode du Minimum Energy Fit (MEF ; Longcope, 2004) pour les plasmas résistifs. Le Resistive Minimum Energy Fit (MEF-R ; Tremblay & Vincent, 2014) reconstruit les champs de vitesse du plasma et la diffusivité magnétique turbulente qui satisfont à l’équation d’induction magnétique résistive et qui minimisent une fonctionnelle analogue à l’énergie cinétique totale. Une séquence de magnétogrammes et de Dopplergrammes sur les régions actives AR 9077 et AR 12158 ayant chacune produit une éruption de classe X a été utilisée dans MEF-R pour reconstruire les mouvements du plasma à la surface du Soleil. Les séquences temporelles des vitesses et des diffusivités magnétiques turbulentes calculées par MEF-R sont comparées au flux en rayons X mous enregistré par le satellite GOES-15 avant, pendant et après l’éruption. Pour AR 12158, nous observons une corrélation entre les valeurs significatives de la diffusivité magnétique turbulente et de la vitesse microturbulente pour les champs magnétiques faibles.

Numerical simulation of tephra transport and deposition of the 1982 El Chichón eruption and implications for hazard assessment

El Chichón volcano, Chiapas, Mexico, erupted explosively on March 29th, 1982, after a repose period of about 550 years. Amongst ten eruptive episodes documented between March 29th and April 4th, only the three that occurred on March 29th and April 4th produced significant pyroclastic tephra deposits. Here we use analytical (HAZMAP) and numerical (FALL3D) tephra transport models to reconstruct the deposits and the atmospheric plume dispersal associated with the three main fallout units of the 1982 eruption. On the basis of such a reconstruction, we produce hazard maps of tephra fallout associated to a Plinian eruption and discuss the implications of such a severe eruption scenario.

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction. To cite this article: A. Ern et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.