967 resultados para Numerical methods
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En simulant lcoulement du sang dans un rseau de capillaires (en labsence de contrle biologique), il est possible dobserver la prsence doscillations de certains paramtres comme le dbit volumique, la pression et lhmatocrite (volume des globules rouges par rapport au volume du sang total). Ce comportement semble tre en concordance avec certaines expriences in vivo. Malgr cet accord, il faut se demander si les fluctuations observes lors des simulations de lcoulement sont physiques, numriques ou un artefact de modles irralistes puisquil existe toujours des diffrences entre des modlisations et des expriences in vivo. Pour rpondre cette question de faon satisfaisante, nous tudierons et analyserons lcoulement du sang ainsi que la nature des oscillations observes dans quelques rseaux de capillaires utilisant un modle convectif et un modle moyenn pour dcrire les quations de conservation de masse des globules rouges. Ces modles tiennent compte de deux effets rhologiques importants : leffet Fhraeus-Lindqvist dcrivant la viscosit apparente dans un vaisseau et leffet de sparation de phase schmatisant la distribution des globules rouges aux points de bifurcation. Pour dcrire ce dernier effet, deux lois de sparation de phase (les lois de Pries et al. et de Fenton et al.) seront tudies et compares. Dans ce mmoire, nous prsenterons une description du problme physiologique (rhologie du sang). Nous montrerons les modles mathmatiques employs (moyenn et convectif) ainsi que les lois de sparation de phase (Pries et al. et Fenton et al.) accompagns dune analyse des schmas numriques implments. Pour le modle moyenn, nous employons le schma numrique explicite traditionnel dEuler ainsi quun nouveau schma implicite qui permet de rsoudre ce problme dune manire efficace. Ceci est fait en utilisant une mthode de Newton- Krylov avec gradient conjugu prconditionn et la mthode de GMRES pour les itrations intrieures ainsi quune mthode quasi-Newton (la mthode de Broyden). Cette mthode inclura le schma implicite dEuler et la mthode des trapzes. Pour le schma convectif, la mthode explicite de Kiani et al. sera implmente ainsi quune nouvelle approche implicite. La stabilit des deux modles sera galement explore. laide de trois diffrentes topologies, nous comparerons les rsultats de ces deux modles mathmatiques ainsi que les lois de sparation de phase afin de dterminer dans quelle mesure les oscillations observes peuvent tre attribuables au choix des modles mathmatiques ou au choix des mthodes numriques.
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Ralis en majeure partie sous la tutelle de feu le Professeur Paul Arminjon. Aprs sa disparition, le Docteur Aziz Madrane a pris la relve de la direction de mes travaux.
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Cette thse, compose de quatre articles scientifiques, porte sur les mthodes numriques atomistiques et leur application des systmes semi-conducteurs nanostructurs. Nous introduisons les mthodes acclres conues pour traiter les vnements activs, faisant un survol des dveloppements du domaine. Suit notre premier article, qui traite en dtail de la technique d'activation-relaxation cintique (ART-cintique), un algorithme Monte Carlo cintique hors-rseau autodidacte bas sur la technique de l'activation-relaxation nouveau (ARTn), dont le dveloppement ouvre la voie au traitement exact des interactions lastiques tout en permettant la simulation de matriaux sur des plages de temps pouvant atteindre la seconde. Ce dveloppement algorithmique, combin des donnes exprimentales rcentes, ouvre la voie au second article. On y explique le relchement de chaleur par le silicium cristallin suite son implantation ionique avec des ions de Si 3 keV. Grce nos simulations par ART-cintique et l'analyse de donnes obtenues par nanocalorimtrie, nous montrons que la relaxation est dcrite par un nouveau modle en deux temps: "rinitialiser et relaxer" ("Replenish-and-Relax"). Ce modle, assez gnral, peut potentiellement expliquer la relaxation dans d'autres matriaux dsordonns. Par la suite, nous poussons l'analyse plus loin. Le troisime article offre une analyse pousse des mcanismes atomistiques responsables de la relaxation lors du recuit. Nous montrons que les interactions lastiques entre des dfauts ponctuels et des petits complexes de dfauts contrlent la relaxation, en net contraste avec la littrature qui postule que des "poches amorphes" jouent ce rle. Nous tudions aussi certains sous-aspects de la croissance de botes quantiques de Ge sur Si (001). En effet, aprs une courte mise en contexte et une introduction mthodologique supplmentaire, le quatrime article dcrit la structure de la couche de mouillage lors du dpt de Ge sur Si (001) l'aide d'une implmentation QM/MM du code BigDFT-ART. Nous caractrisons la structure de la reconstruction 2xN de la surface et abaissons le seuil de la temprature ncessaire pour la diffusion du Ge en sous-couche prdit thoriquement par plus de 100 K.
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Dans ce rapport de mmoire, nous avons utilis les mthodes numriques telles que la dynamique molculaire (code de Lammps) et ART-cintique. Ce dernier est un algorithme de Monte Carlo cintique hors rseau avec construction du catalogue d'vnements la vole qui incorpore exactement tous les effets lastiques. Dans la premire partie, nous avons compar et valu des divers algorithmes de la recherche du minimum global sur une surface d'nergie potentielle des matriaux complexes. Ces divers algorithmes choisis sont essentiellement ceux qui utilisent le principe Bell-Evans-Polanyi pour explorer la surface d'nergie potentielle. Cette tude nous a permis de comprendre d'une part, les tapes ncessaires pour un matriau complexe d'chapper d'un minimum local vers un autre et d'autre part de contrler les recherches pour vite trouver le minimum global. En plus, ces travaux nous ont amen comprendre la force de ces mthodes sur la cintique de l'volution structurale de ces matriaux complexes. Dans la deuxime partie, nous avons mis en place un outil de simulation (le potentiel ReaxFF coupl avec ART-cintique) capable d'tudier les tapes et les processus d'oxydation du silicium pendant des temps long comparable exprimentalement. Pour valider le systme mis en place, nous avons effectu des tests sur les premires tapes d'oxydation du silicium. Les rsultats obtenus sont en accord avec la littrature. Cet outil va tre utilis pour comprendre les vrais processus de l'oxydation et les transitions possibles des atomes d'oxygne la surface du silicium associe avec les nergies de barrire, des questions qui sont des dfis pour l'industrie micro-lectronique.
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There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright 2015John Wiley & Sons, Ltd.
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This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.
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This thesis lays importance in the preparation and characterization of a few selected representatives of the ferrite family in the nanoregime. The candidates being manganese zinc ferrite and cobalt ferrite prepared by coprecipitation and sol-gel combustion techniques respectively. The thesis not only stresses importance on the preparation techniques and optimization of the reaction conditions, but emphasizes in investigating the various properties namely structural, magnetic and electrical. Passivated nickel nanocomposites are synthesized using polystyrene beads and adopting a novel route of ion exchange reduction. The structural and magnetic properties of these magnetic nanocomposites are correlated. The magnetocaloric effect (MCE) exhibited by these materials are also investigated with a view to finding out the potential of these materials as magnetic refrigerants. Calculations using numerical methods are employed to evaluate the entropy change on selected samples.
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There are basically two methods for prediction of shallow water waves, viz. the graphical method and the numerical method. The numerical methods are being widely used, nowadays, because they are fast, accurate and are especially useful when the prediction over a large spatial frame is required. Practically little has been done on the development of numerical models for the prediction of height and spectral transformation of waves as applicable to our coasts. Synchronized deep and shallow water wave measurements which are essential for study of wave transformation are very much lacking for our coasts. Under these circumstances, a comprehensive study of the wave transformation in the shallow waters of our coast was felt very important and is undertaken in the present investigation.
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Mesh generation is an important step inmany numerical methods.We present the HierarchicalGraphMeshing (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.
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The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.
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Lecture slides and notes for a PhD level course on linear algebra for electrical engineers and computer scientists. This course is given in in the framework of the School of Electronics and Computer Science Mathematics Training Courses https://secure.ecs.soton.ac.uk/notes/pg_maths/ (ECS password required)
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Dynamic optimization methods have become increasingly important over the last years in economics. Within the dynamic optimization techniques employed, optimal control has emerged as the most powerful tool for the theoretical economic analysis. However, there is the need to advance further and take account that many dynamic economic processes are, in addition, dependent on some other parameter different than time. One can think of relaxing the assumption of a representative (homogeneous) agent in macro- and micro-economic applications allowing for heterogeneity among the agents. For instance, the optimal adaptation and diffusion of a new technology over time, may depend on the age of the person that adopted the new technology. Therefore, the economic models must take account of heterogeneity conditions within the dynamic framework. This thesis intends to accomplish two goals. The first goal is to analyze and revise existing environmental policies that focus on defining the optimal management of natural resources over time, by taking account of the heterogeneity of environmental conditions. Thus, the thesis makes a policy orientated contribution in the field of environmental policy by defining the necessary changes to transform an environmental policy based on the assumption of homogeneity into an environmental policy which takes account of heterogeneity. As a result the newly defined environmental policy will be more efficient and likely also politically more acceptable since it is tailored more specifically to the heterogeneous environmental conditions. Additionally to its policy orientated contribution, this thesis aims making a methodological contribution by applying a new optimization technique for solving problems where the control variables depend on two or more arguments --- the so-called two-stage solution approach ---, and by applying a numerical method --- the Escalator Boxcar Train Method --- for solving distributed optimal control problems, i.e., problems where the state variables, in addition to the control variables, depend on two or more arguments. Chapter 2 presents a theoretical framework to determine optimal resource allocation over time for the production of a good by heterogeneous producers, who generate a stock externalit and derives government policies to modify the behavior of competitive producers in order to achieve optimality. Chapter 3 illustrates the method in a more specific context, and integrates the aspects of quality and time, presenting a theoretical model that allows to determine the socially optimal outcome over time and space for the problem of waterlogging in irrigated agricultural production. Chapter 4 of this thesis concentrates on forestry resources and analyses the optimal selective-logging regime of a size-distributed forest.
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La present tesi proposa una metodologa per a la simulaci probabilstica de la fallada de la matriu en materials compsits reforats amb fibres de carboni, basant-se en l'anlisi de la distribuci aleatria de les fibres. En els primers captols es revisa l'estat de l'art sobre modelitzaci matemtica de materials aleatoris, clcul de propietats efectives i criteris de fallada transversal en materials compsits. El primer pas en la metodologia proposada s la definici de la determinaci del tamany mnim d'un Element de Volum Representatiu Estadstic (SRVE) . Aquesta determinaci es du a terme analitzant el volum de fibra, les propietats elstiques efectives, la condici de Hill, els estadstics de les components de tensi i defromaci, la funci de densitat de probabilitat i les funcions estadstiques de distncia entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mnim, es comparen un model peridic i un model aleatori, per constatar la magnitud de les diferncies que s'hi observen. Es defineix, tamb, una metodologia per a l'anlisi estadstic de la distribuci de la fibra en el compsit, a partir d'imatges digitals de la secci transversal. Aquest anlisi s'aplica a quatre materials diferents. Finalment, es proposa un mtode computacional de dues escales per a simular la fallada transversal de lmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecniques. Es descriuen algunes aplicacions i possibilitats d'aquest mtode i es comparen els resultats obtinguts de la simulaci amb valors experimentals.
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La feina feta en aquest treball de tesis s'ha desenvolupat a partir de tres objectius vertebradors, que fonamentalment sn: El primer dels objectius d'aquest treball de tesis s presentar un recull dels factors que intervenen en l'acstica urbanstica: soroll produt pels diferents vehicles, frmules de predicci de soroll, geometria dels edificis... , tot estudiant els seus efectes en la ciutat de Girona. Un altre objectiu ha estat desenvolupar uns mtodes numrics propis, contrastats experimentalment i extrapolables a qualsevol entorn urbanstic, que permetin predir els valors de les pertorbacions acstiques produdes pels diferents vehicles en diferents situacions, entre els que es destaquen: -Frmula de predicci del soroll en un entorn urb i la seva aplicaci a Girona. -Clcul de l'increment de soroll en un carrer provocat per les reflexions de les ones sonores en les faanes dels edificis. -Estudi del nivell de soroll en la boca de la cavitat d'un tnel produt pel pas del ferrocarril. -Determinaci del soroll provocat pel pas d'un tren sobre un viaducte. -Mtode de distribuci i planificaci del trnsit urb per disminuir l'impacte acstic sobre la zona. El darrer objectiu consisteix en fer una descripci analtica de les principals fonts de soroll que afecten a la ciutat: el trnsit viari i el ferrocarril. Per realitzar aquests objectius s'ha disposat d'un banc de dades amb ms de 2.000 mesures sonores de Girona (nivells equivalents de 10 minuts de durada). La metodologia seguida i els principis en que es fonamenta es detallen a l'inici de cada apartat. La finalitat de tots aquests estudis, no s altre que millorar el confort acstic, i la qualitat de vida, de les ciutats. Gaireb tots els grans nuclis de poblaci del planeta es veuen afectats per una gravssima problemtica mediambiental, doncs a l'anomenada contaminaci acstica cal afegir uns alts ndexs de polluci atmosfrica (altes concentracions de bixid de carboni, generaci d'illes de calor...). Aquesta situaci, generalitzada arreu del planeta, ha propiciat l'aparici de mesures drstiques consistents fonamentalment en restringir l'accs dels vehicles motoritzats als nuclis i zones centrals de les rees urbanes. Precisament aquesta opci s'ha proposat per les zones interiors de Girona on l'elevada densitat de les edificacions deixa un escs marge per plantejar la construcci de noves rutes o vies alternatives. Cal esmentar que tots els clculs i teories que es desenvolupen en aquest treball de tesis reflecteixen la realitat acstica actual provocada pels diferents mitjans de transport. Molt possiblement, en un futur no massa lluny, els nivells de soroll (dB) enregistrats en situacions de trfic similar seran fora menors. Sn molts els factors que poden contribuir a aquesta disminuci de la intensitat de les emissions sonores: reducci del fregament mecnic, augment del coeficient aerodinmic, nous materials pels pneumtics i l'asfalt ... Sense cap mena de dubte, per, una millora transcendental, i no noms pel que fa al confort acstic sin per l'ecosistema en general, seria potenciar la construcci de motors elctrics o d'hidrogen. Aquests ltims per exemple, a diferncia dels motors de combusti, funcionen mitjanant piles de combustible que converteixen, amb molta netedat, el gas hidrogen en electricitat i possibiliten l'existncia de vehicles no contaminants propulsats per motors elctrics menys sorollosos. Aix, al haver-hi menys fregament entre les parts mbils del motor (no hi ha pistons ni cilindres) el soroll generat es reduiria considerablement.
