Academic literature on the topic 'Loi de Laplace'
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Journal articles on the topic "Loi de Laplace"
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Ingrand, P. "Loi normale de Laplace-Gauss." Journal d'imagerie diagnostique et interventionnelle 1 (October 2017): S4—S8. http://dx.doi.org/10.1016/s2543-3431(18)30066-6.
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Benjoudi, H., and P. Hubert. "À propos de la distribution statistique des cumuls pluviométriques annuels. Faut-il en finir avec la normalité?" Revue des sciences de l'eau 11, no. 4 (April 12, 2005): 617–30. http://dx.doi.org/10.7202/705324ar.
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Il est communément admis que la distribution statistique des précipitations cumulées annuelles suit une loi de Laplace-Gauss. Les écarts entre cette loi et les distributions empiriques sont cependant un fait d'expérience : au-delà d'une probabilité au non dépassement correspondant à une période de retour d'une vingtaine d'années et pour les valeurs les plus fortes de pluie, l'ajustement n'est plus acceptable. Ce décrochage par rapport à la loi normale est mieux mis en évidence par l'étude des longues séries pluviométriques, plus riches en événements extrêmes. Pour étudier le comportement statistique de ces derniers, il est fait appel à un formalisme multifractal qui permet de mettre en évidence que, contrairement à ce qui est généralement admis, la décroissance de la probabilité au dépassement est de nature hyperbolique plutôt qu'exponentielle. Les probabilités des événements catastrophiques sont donc plus importantes que l'on ne le croyait jusqu'ici, ce qui peut avoir des conséquences particulièrement importantes. Cette approche appliquée à un ensemble de séries pluviométriques de longue durée permet de cerner le paramètre caractérisant la décroissance de la probabilité au dépassement. Les résultats obtenus jusqu'ici laissent à penser que ce paramètre pourrait être universel.
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Wang, Xiongrui, Ruofeng Rao, and Shouming Zhong. "LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks withp-Laplace Diffusion." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/523812.
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The nonlinearp-Laplace diffusion (p>1) was considered in the Cohen-Grossberg neural network (CGNN), and a new linear matrix inequalities (LMI) criterion is obtained, which ensures the equilibrium of CGNN is stochastically exponentially stable. Note that, ifp=2,p-Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even ifp=2, the new criterion improves some recent ones due to computational efficiency. In addition, the resulting criterion has advantages over some previous ones in that both the impulsive assumption and diffusion simulation are more natural than those of some recent literatures.
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Rao, Ruofeng, Gaozhi Tang, Jiuqi Gong, Xiaoyan Wan, Guanghong Wu, Qiao Zhang, and Shouming Zhong. "Robust Stability of Nonlinear Diffusion Fuzzy Neural Networks with Parameter Uncertainties and Time Delays." Complexity 2018 (July 16, 2018): 1–19. http://dx.doi.org/10.1155/2018/6263931.
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In this paper, a class of nonlinear p-Laplace diffusion BAM Cohen-Grossberg neural networks (BAM CGNNs) with time delays is investigated. In the case of p>1 with p≠2, the authors construct novel Lyapunov functional to overcome the mathematical difficulties of nonlinear p-Laplace diffusion time-delay model with parameter uncertainties, deriving the LMI-based robust stability criterion applicable to computer MATLAB LMI toolbox and deleting the boundedness of the amplification functions. And in the case of p=2, LMI-based sufficient conditions are also inferred for robust input-to-state stability of reaction-diffusion Markovian jumping BAM CGNNs with the event-triggered control, which is different from those of many previous related literature. In particular, the role of diffusion can be reflected in newly acquired criteria. Finally, numerical examples verify the effectiveness of the proposed methods.
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Canino, Annamaria, Phuong Le, and Berardino Sciunzi. "Local $${W^{2,m(\cdot)}_{loc}}$$ regularity for p(.)-Laplace equations." Manuscripta Mathematica 140, no. 3-4 (April 12, 2012): 481–96. http://dx.doi.org/10.1007/s00229-012-0549-y.
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Ueda, Tetsuhiko. "Lifting surface calculations in the Laplace domain with application to root loci." AIAA Journal 25, no. 5 (May 1987): 698–704. http://dx.doi.org/10.2514/3.9685.
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Rao, Ruofeng, Xiongrui Wang, and Shouming Zhong. "LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/185854.
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Lyapunov stability theory, variational methods, Gronwall-Bellman-type inequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed to obtain the LMI-based global stochastic exponential stability criterion for a class of time-delays Laplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value, whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delays reaction-diffusion BAM neural networks. As far as the authors know, it is the first time to derive the LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily and efficiently computed by computer Matlab LMI toolbox. And the obtained criterion improves the allowable upper bounds of impulse against those of some previous related literature. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.
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Yu, Shi, Jiaxin Wu, Xianliang Meng, Ruizhi Chu, Xiao Li, and Guoguang Wu. "Mesoscale Simulation of Bacterial Chromosome and Cytoplasmic Nanoparticles in Confinement." Entropy 23, no. 5 (April 28, 2021): 542. http://dx.doi.org/10.3390/e23050542.
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In this study we investigated, using a simple polymer model of bacterial chromosome, the subdiffusive behaviors of both cytoplasmic particles and various loci in different cell wall confinements. Non-Gaussian subdiffusion of cytoplasmic particles as well as loci were obtained in our Langevin dynamic simulations, which agrees with fluorescence microscope observations. The effects of cytoplasmic particle size, locus position, confinement geometry, and density on motions of particles and loci were examined systematically. It is demonstrated that the cytoplasmic subdiffusion can largely be attributed to the mechanical properties of bacterial chromosomes rather than the viscoelasticity of cytoplasm. Due to the randomly positioned bacterial chromosome segments, the surrounding environment for both particle and loci is heterogeneous. Therefore, the exponent characterizing the subdiffusion of cytoplasmic particle/loci as well as Laplace displacement distributions of particle/loci can be reproduced by this simple model. Nevertheless, this bacterial chromosome model cannot explain the different responses of cytoplasmic particles and loci to external compression exerted on the bacterial cell wall, which suggests that the nonequilibrium activity, e.g., metabolic reactions, play an important role in cytoplasmic subdiffusion.
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Shen, I. Y. "Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments." Journal of Vibration and Acoustics 118, no. 1 (January 1, 1996): 70–77. http://dx.doi.org/10.1115/1.2889637.
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This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer function approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.
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Rao, Ruofeng, Xiongrui Wang, Shouming Zhong, and Zhilin Pu. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion." Journal of Applied Mathematics 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/396903.
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The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.
Dissertations / Theses on the topic "Loi de Laplace"
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Bernardoff, Philippe. "Lois multinomiales négatives indéfiniment divisibles et lois gamma multivariées indéfiniment divisibles." Toulouse 3, 2003. http://www.theses.fr/2003TOU30118.
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Manas, Arnaud. "Essais sur le club de Paris, la loi de Gibrat et l'histoire de la Banque de France." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM1136/document.
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Cette thèse sur travaux est la synthèse de publications réalisées entre 2005 et 2012 ainsi que de papiers de travail. Elle est organisée autour de trois axes : des questions relatives au Club de Paris, des articles au sujet de la loi de Gibrat et des travaux autour de l’Histoire de la Banque de France. Le premier axe comprend deux papiers publiés dans le bulletin de la Banque de France : l’un sur l’évaluation de l’initiative PPTE (Pays pauvres très endettés, mécanismes et éléments d’évaluation, Bulletin N°140, août 2005) et le second sur la modélisation des buybacks de créance au sein du club de Paris. Ce dernier papier a été sous deux formes (grand public : Modélisation et analyse des mécanismes du Club de Paris de rachat de créances par prépaiement, avec Laurent Daniel, Bulletin N° 152, août 2006, et recherche : Pricing the implicit contracts in the Paris Club debt buybacks avec Laurent Daniel, working paper, December 2007). Le second axe concerne la validation de la loi de Gibrat, avec la publication de trois articles (French butchers don't do Quantum Physics in Economics Letters, Vol. 103, May 2009, Pp. 101-106 ; The Paretian Ratio Distribution - An application to the volatility of GDP in Economics Letters, Vol. 111, May 2011, pp. 180-183 ; The Laplace Illusion in Physica A, Vol. 391, August 2012, pp. 3963–3970). Le dernier axe regroupe des travaux sur l’Histoire de la Banque de France. Certains sont publiés comme La Caisse de Réserve des Employés de la Banque de France 1800-1950, (Économies et Sociétés, série « Histoire Économique Quantitative », août 2007, n°37, pp. 1365-1383 ou en coursThis dissertation is made of several papers published between 2005 and 2012 and somme working papers. The first part deals with the Paris Club. Two papers published in the Bulletin of the Banque de France deal with the very indebted countries and debt buybacks ( Pricing the implicit contracts in the Paris Club debt buybacks). The second axis is oriented on the Gibrat's law (French butchers don't do Quantum Physics in Economics Letters, Vol. 103, May 2009, Pp. 101-106 ; The Paretian Ratio Distribution - An application to the volatility of GDP in Economics Letters, Vol. 111, May 2011, pp. 180-183 ; The Laplace Illusion in Physica A, Vol. 391, August 2012, pp. 3963–3970). The third axis deals with the history of the Banque de France
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Lévesque, Martin. "Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation." Paris, ENSAM, 2004. https://pastel.archives-ouvertes.fr/pastel-00001237.
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L’objectif principal de ce travail de thèse est d’établir un modèle, s’appuyant sur l’homogénéisation, permettant la prédiction du comportement mécanique de matériaux composites viscoélastiques non linéaires. L’approche est appliquée à un polypropylène renforcé de billes de verre réparties aléatoirement. La première partie du document est consacrée à l’écriture et l’identification d’une loi de comportement viscoélastique non linéaire pouvant être appliquée au polypropylène. La deuxième partie traite de l’établissement du modèle ainsi que de son implémentation numérique. Le modèle d’homogénéisation est développé au troisième chapitre. L’approche proposée permet de transposer certains modèles existants pour des matériaux ne dépendant pas de l’histoire de chargement à des comportements viscoélastiques non linéaires. La méthodologie permet donc de ramener le problème viscoélastique non linéaire à un problème viscoélastique linéaire à histoire de déformations libres. Ce nouveau problème est résolu à l’aide du principe de correspondance viscoélastique linéaire et des transformées de Laplace-Carson. Le quatrième chapitre est dédié à l’implémentation numérique du modèle. On insiste notamment sur le fait que le matériau viscoélastique linéaire de comparaison rencontre les exigences de la thermodynamique des milieux continus. De plus, nous proposons un algorithme conduisant à une inversion précise des transformées de Laplace-Carson. Finalement, la dernière partie de la thèse est consacrée à la validation des modèles proposés. Des modèles éléments finis de la microstructure et l’implémentation de la loi de comportement viscoélastique non linéaire sont réalisés au ch(…)The main objective of this thesis is to develop a model, based on homogenisation, for predicting the mechanical response of nonlinear viscoelastic composites. The model is applied to a glass beads reinforced polypropylene in which the beads are randomly distributed. The initial part of the thesis is concerned with the development of a three dimensional nonlinear viscoelastic constitutive law that can be applied to this polypropylene composite. The second stage of the thesis deals with the development and identification of the homogenisation model while this theoretical model is presented in Chapter Three. This approach allows material models, for which the response does not depend on the load history, to be applied to nonlinear viscoelastic materials. The approach involves transforming the initial nonlinear viscoelastic problem into one which is linear viscoelastic with a history of stress-free deformations. This problem is solved with the linear viscoelastic correspondence principle and Laplace-Carson transforms. Chapter Four deals with the numerical implementation of such a model. The implementation is achieved in such a way that the comparison materials, which represent the new linear viscoelastic problem, satisfy all thermodynamic requirements. Moreover, a new algorithm has been developed to numerically invert the Laplace-Carson transforms with good accuracy. The final part of the thesis validates the theoretical model through means of finite element models of typical microstructures and the numerical implementation of the nonlinear viscoelastic constitutive law. Comparisons are also presented between the predictions of the homogenisation model, the fi(…)
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Bonthonneau, Yannick. "Résonances du laplacien sur les variétés à pointes." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112141/document.
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Cette thèse à pour objet l’étude des résonances du laplacien sur les variétés à pointes. Ce sont des variétés dont les bouts sont des pointes hyperboliques réelles. Ces objets ont été introduits par Selberg pour les surfaces à pointes de courbure constante dans les années 50. Leur définition a ensuite été étendue en courbure variable par Lax et Phillips. Les résonances sont les poles d’une famille méromorphe de fonctions propres généralisées du laplacien. Elles sont associées au spectre continu du laplacien. Pour analyser ce spectre continu, plusieurs directions de recherche sont explorées ici. D’une part, on obtient des résultats sur la localisation de ces résonances. En particulier, si la courbure est négative, on montre que pour un ensemble générique de métriques, les résonances se séparent en deux ensembles. Le premier est contenu dans une bande près du spectre continu. L’autre partie est composé de résonances qui s’éloignent du spectre. Ceci laisse une zone de taille log sans résonance.D’autre part, on étudie les mesures microlocales associées à certaines suites de paramètre spectraux. En particulier, on montre que pour des suites de paramètres spectraux qui s’approche du spectre, mais pas trop vite, la mesure microlocale associée est nécessairement la mesure de Liouville. Cette propriété est valable quand la courbure de la variété est négativeIn this thesis, we study the resonances of the Laplace operator on cusp manifolds. They are manifolds whose ends are real hyperbolic cusps. The resonances were introduced by Selberg in the 50's for the constant curvature cusp surfaces. Their definition was later extended to the case of variable curvature by Lax and Phillips. The resonances are the poles of a meromorphic family of generalized eigenfunctions of the Laplace operator. They are associated to the continuous spectrum of the Laplace operator. To analyze this continuous spectrum, different directions of research are investigated.On the one hand, we obtain results on the localization of resonances. In particular, if the curvature is negative, for a generic set of metrics, they split into two sets. The first one is included in a band near the spectrum. The other is composed of resonances that are far from the spectrum. This leaves a log zone without resonances. On the other hand, we study the microlocal measures associated to certain sequences of spectral parameters. In particular we show that for some sequences of parameters that converge to the spectrum, but not too fast, the associated microlocal measure has to be the Liouville measure. This property holds when the curvature is negative
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Kouzayha, Salam. "Estimations géométriques de fonctionnelles spectrales pour le laplacien avec condition de Robin au bord." Electronic Thesis or Diss., Tours, 2019. http://www.theses.fr/2019TOUR4004.
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Le but de cette thèse est double : Donner des estimations pour les valeurs propres du laplacien sur un domaine borné d'une variété riemannienne avec la condition de Robin au bord. Nos premières estimations constituent une extension de la célèbre inégalité de Kröger sur les valeurs propres du laplacien euclidien avec condition de Neumann au bord, au cas plus gé- néral d'une variété riemannienne avec la condition de Robin au bord. De plus, ces estimations sont en accord avec la loi asymptotique de Weyl en ce qui concerne la dépendance en l'ordre de la valeur propre. Un deuxième type d'estimations géométriques pour les valeurs propres de Robin est obtenu dans le cas où la courbure de Ricci de la variété considérée est minorée. En utilisant la définition des valeurs propres par la formule de min-max, on est capable de les majorer en fonction de la dimension de la variété, du minorant de la courbure de Ricci, du volume du domaine et de son bord, et enfin de l'intégrale de la fonction de Robin sur le bord du domaine. Etudier le spectre du laplacien pondéré par la présence de deux densités sur un domaine borné d'une variété riemannienne avec les conditions de Neumann au bord dans le cas où l'une des densité est une puissance positive de l'autre. On démontre l'existence d'une valeur critique pour cette puissance : si la puissance est plus petite que cette valeur critique, la valeur propre correspondante est majorée. Cependant, si la puissance dépasse cette valeur, on démontre l'existence des domaines ayant une première valeur propre aussi grande que l'on veutThe aim of my thesis is to give some estimations for the eigenvalues of the Laplacian with Robin boundary conditions the principal results are divided in two categories. The first result is based on an algebric method and give an estimation of the eigenvalues in euclidean spaces and homogeneous manifolds. The second result is an estimation of the egenvalues in terms of the Ricci curvature of the manifold
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Li, Xiongya. "Robust multivariate mixture regression models." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38427.
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Doctor of PhilosophyDepartment of Statistics
Weixing Song
In this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest. A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure. As an illustration, the proposed method is also applied to a real data set.
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Marchand, Antonin. "Mouillage statique et dynamique : Influences géométriques aux échelles moléculaires." Phd thesis, Université Paris-Diderot - Paris VII, 2011. http://pastel.archives-ouvertes.fr/pastel-00656423.
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Cette thèse met en évidence différents effets géométriques intervenant dans des phénomènes de mouillage. La première partie est dédiée à l'élaboration d'un modèle d'interactions dans le liquide permettant de déterminer, à partir de la géométrie de l'interface, la distribution des forces capillaires à l'échelle moléculaire. Nous proposons dans ce cadre une interprétation de la construction d'Young en tant qu'équilibre des forces dans un coin de liquide. Ce modèle est ensuite appliqué dans la deuxième partie à diverses situations mettant en jeu la capillarité aux échelles moléculaires. La tension de ligne est étudiée grâce à des simulations de dynamique moléculaire et une interprétation géométrique du phénomène est présentée. L'existence d'un film de prémouillage est prédite lors de la saturation du phénomène d'électromouillage. Ce modèle fait en outre ressortir une distribution des forces tout à fait particulière dans un solide au voisinage de la ligne de contact, dont les effets ne sont visibles que lorsque le substrat est déformable. Ainsi, une confirmation expérimentale de l'existence d'une pression de Laplace supplémentaire lorsqu'un solide est immergé est apportée. Nous étudions ensuite l'influence de la mouillabilité du liquide sur le fléchissement et le flambage d'une plaque élastique sous l'effet de cette distribution de forces capillaires. Pour finir, la transition de démouillage dynamique par entraînement d'air est examinée, et nous mettons en évidence le rôle crucial de la dissipation dans l'écoulement de l'air lorsque celui-ci est entraîné et confiné sous le liquide.
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Coqueret, Guillaume. "Options exotiques, lois infiniment divisibles et processus de Lévy : aspects théoriques et pratiques." Thesis, Lille 1, 2012. http://www.theses.fr/2012LIL10146/document.
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Cette thèse comporte trois parties indépendantes. La première traite des formes fermées de la factorisation de Wiener-Hopf pour les processus de Lévy. Nous recensons la demie-douzaine de cas pour lesquels la factorisation peut être écrite explicitement, et mettons l'accent sur les fonctions méromorphes ayant des pôles d'ordre deux. La deuxième partie se focalise sur l'inversion de la transformée de Laplace. Son but est de présenter une nouvelle méthode approximative, dans un contexte probabiliste. Si la transformée de Laplace a un comportement facilement identifiable en zéro et si la densité associée est bornée, alors cette méthode permet d'obtenir une borne uniforme pour l'erreur commise sur la fonction de répartition. L'efficacité de cette méthode est testée sur deux exemples non triviaux. Enfin, la troisième et dernière partie est dédiée au pricing d'options exotiques dans le modèle log-stable aux moments finis de Carr et Wu. Dans certains cas, il est possible d'obtenir des formules fermées sous forme de séries convergentes pour les prix d’options lookback et barrières. Pour tous les autres cas, nous étudions divers techniques de simulation pour les trajectoires du processus sous-jacent, dans le but d'une évaluation par méthode de Monte-CarloThis thesis consists of three independent chapters.The first one deals with closed forms of the Wiener-hopf factorization for Lévy processes. We list the known cases for which this factorization can be explicitely written and provide a detailed account when the underlying functions are meromorphic of order two.The second chapter focuses on the inversion of the Laplace transform. We present an approximative method in a probabilistic setting. If the behavior of the Laplace transform near zero is known and if the underlying density is bounded, then this method yields a uniform bound for the error on the cumulative distribution function. We test this technique on two non-trivial examples.The final chapter of the thesis is dedicated to the pricing of exotic options in the Finite Moment Log-Stable model of Carr and Wu. In some cases, it is possible to obtain closed forms (converging series) for the prices of lookback and barrier options. In all other cases, we study several simulation techniques for the trajectories of the underlying for the purpose of Monte-Carlo valuation
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Bey, Mohamed Amine. "Modélisation mathématique et simulations numériques des écoulements sanguins dans des artères avec ou sans stents." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD027/document.
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Cette thèse est consacrée à la modélisation mathématique et simulations numériques des écoulements sanguins dans des artères en présence d’une endoprothèse vasculaire de type stent. La présence de stent peut être considérée comme une perturbation locale d’un bord lisse d’écoulement, plus précisément les parois de l’artère sont assimilées à une surface fortement rugueuse. Nous nous sommes principalement intéressés au contrôle de la régularité H² sur un modèle simplifié permettant de prendre en compte l’effet de ces stents lorsque le flux sanguin est gouverné par une équation de Laplace (en lien avec la composante axiale de la vitesse d’écoulement) avec une condition aux limites de type Dirichlet, dans un domaine à bord rugueux (en fonction d’un petit paramètre ε). Dans une première partie, nous soulevons la question d’existence et d’unicité de la solution de ce modèle d’écoulement sanguin et nous traitons la régularité H² par des techniques d’analyse variationnelle. Une étude minutieuse permet de contrôler la régularité H² en O(ε−1). Le deuxième axe est dédié à l’étude de la régularité H² par des analyse asymptotiques multiéchelles. Nous montrons que la norme H² de la solution de ce modèle d’écoulement sanguin est singulière en O(ε−½ ). D’autre part, nous améliorons les ordres de convergence des résultats existants concernant la construction des approximations multiéchelles. Dans un troisième temps, nous présentons des estimations d’erreur et des résultats numériques. Ces résultats illustrent le bien fondé des estimations d’erreur sur le plan pratique. Nous montrons bien l’importance des méthodes asymptotiques qui se révèlent plus efficaces qu’un calcul directThis thesis is devoted to mathematical modeling and numerical simulations of the blood-flows in arteries in the presence of a vascular prosthesis of type stent. The presence of stent can be considered as a local perturbation of a smooth edge of flow, more precisely the walls artery can be seen as a strongly rough surface.Weare mainly interested in controlling the H² regularity of a simplified model which takes into account the impact of these stents when the blood flow is controlled by a Laplace equation (in link with the axial component rateof flow) with a Dirichlet boundary condition, in a domain with a rough board (according to a small parameter ε). First, we raise the question of existence and unicity of the solution of this model of blood-flow and we study the H² regularity using variational analysis methods. By a detailed study, we control the H² regularity of order O(ε−1). The second part is devoted to the study of the regularity H² regularity using multi-scale analysis.We prove that the H² norm of the solution of this model is singular of order O(ε−½). Moreover, we improve the convergence rate of the existing results on the construction of the multi-scale approximation. Finally, we present an error estimation and numerical results. These numerical results illustrate the well-founded of the error estimates on a practical level. We show the importance of the asymptotic methods that seem to be more effective than a direct computation
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Cheruy, Pascale. "Étude de modèles de potentiels évoqués visuels en vue de la détection et de la classification des réponses en temps réel." Compiègne, 1990. http://www.theses.fr/1990COMPD256.
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Les potentiels évoqués visuels ont été étudiés avec pour objectif, de mettre au point une méthode permettant de discriminer les signaux élémentaires en termes de signal et de bruit, afin d'améliorer le rapport signal à bruit de la réponse moyenne et de diminuer la durée d'enregistrement. Une analyse bibliographique nous a permis de définir précisément les différents protocoles d'enregistrement. Nous avons également décrit les différentes méthodes classiques de traitement (moyennage, filtrage de WIENER, Latency Corrected Averaging et filtrage adapté). La partie essentielle de ce travail a consisté à tester et développer différentes méthodes de traitement du signal et de reconnaissance des formes (modèles autorégressifs, filtrage de Kalman, modèle basé à partir de courbes gaussiennes). Une analyse factorielle discriminante a été effectuée à partir de coefficients extraits des différents modèles pour séparer une classe de signaux de référence d'une classe de bruit (EEG). L'axe discriminant ainsi déterminé, permet d'effectuer la classification en temps réel et en termes de signal et de bruit, de signaux élémentaires pour différents sujets et ce, de façon indépendante du sujet. Le rapport signal à bruit de la réponse moyenne est considérablement augmenté pour tous les sujets que nous avons testés essentiellement pour la méthode basée sur les courbes gaussiennesA method is presented for single sweep analysis. It aims at increasing the average signal to noise ratio. A bibliographic study first describes different experimental protocols and classical signal processing including averaging, Wiener filter, and latency corrected averaging and adaptative filter. Three different models are tested : autoregressive model, kalman filtering and an original model based on Gaussian curves. A discriminant factor analysis is achieved using parameters derived from the three different models in order to separate a class of synthetic signals from a class of noise (EEG). A discriminant vector is calculated and used to classify single sweeps from different subjects. The selected averaging shows an increasing of the signal to noise ratio for every tested subject specially for the method based on Gaussian curves
Books on the topic "Loi de Laplace"
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service), SpringerLink (Online, ed. La loi de la gravitation universelle Newton, Euler et Laplace: Le cheminement d'une révolution scientifique vers une science normale. Paris: Springer-Verlag France, 2007.
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La loi de la gravitation universelle Newton, Euler et Laplace. Paris: Springer Paris, 2007. http://dx.doi.org/10.1007/978-2-287-72083-3.
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Mann, Peter. The (Not So?) Basics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0030.
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This chapter discusses matrices. Matrices appear in many instances across physics, and it is in this chapter that the background necessary for understanding how to use them in calculations is provided. Although matrices can be a little daunting upon first exposure, they are very handy for a lot of classical physics. This chapter reviews the basics of matrices and their operations. It discusses square matrices, adjoint matrices, cofactor matrices and skew-symmetric matrices. The concepts of matrix multiplication, transpose, inverse, diagonal, identity, Pfaffian and determinant are examined. The chapter also discusses the terms Hermitian, symmetric and antisymmetric, as well as the Levi-Civita symbol and Laplace expansion.
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Giordano, Claudia Marcela. Ecuaciones diferenciales parciales. Editorial de la Universidad Nacional de La Plata (EDULP), 2016. http://dx.doi.org/10.35537/10915/60310.
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El texto reúne los contenidos del curso semestral Ecuaciones Diferenciales Parciales que se dicta desde agosto de 2002 en la Facultad de Ciencias Astronómicas y Geofísicas de la UNLP para alumnos avanzados. Se requiere por parte del lector de una formación básica sobre Análisis Matemático en una y varias variables reales y en variable compleja, así como sobre Álgebra y Álgebra Lineal. Se halla organizado en ocho capítulos, y seis apéndices que incluyen material complementario. En estas notas desarrollaremos parte de lo que es una teoría general y clásica de EDP. El capítulo 1 desarrolla la teoría de integración de las ecuaciones generales de primer orden, presentando el método de las características para la obtención de soluciones generales, introduce los distintos tipos de soluciones o superficies integrales y trata la resolución de un problema de valor inicial o problema de Cauchy, discutiendo las condiciones necesarias y suficientes para la existencia de una solución única. El capítulo 2 aborda la clasificación y reducción a sus formas normales de las EDP de segundo orden. El capítulo 3 se dedica al estudio con cierto detalle de la ecuación de ondas en una dimensión espacial, paradigma de las ecuaciones lineales hiperbólicas. El estudio de procesos de conductividad térmica o difusión en una dimensión espacial descriptos por el arquetipo de las ecuaciones lineales parabólicas se incluye en el capítulo 4. La teoría relativa a la ecuación de Laplace y los problemas de contorno a ella asociados se aborda en el capítulo 5, brindando una detallada descripción de las condiciones necesarias para que los problemas sean ”bien planteados"; también se presentan interesantes propiedades de las funciones armónicas de frecuente aparición en el planteo matemático de problemas de la física. Las ecuaciones hiperbólicas y parabólicas en más de una dimensión espacial se estudian en los capítulos 6 y 7. El capítulo 8 presenta la teoría de los potenciales de volumen y de superficie, de doble y simple capa, y su aplicación al tratamiento de problemas de contorno para las ecuaciones de Laplace, Poisson y la ecuación de Helmholtz mediante la resolución de ecuaciones integrales. Los apéndices A, B y D cubren tópicos que resultan auxiliares para el abordaje de los problemas de contorno objeto de estudio de modo que el texto sea autocontenido. El método de separación de variables tratado en C constituye un tema importante que nos conducirá a los problemas de Sturm-Liouville y sus autovalores, resultados que se aplican en varios de los problemas resueltos y se describen en el apéndice E. Finalmente, el apéndice F brinda una introducción a los métodos de resolución de ecuaciones integrales. El libro contiene numerosos ejemplos resueltos, con el propósito de consolidar la comprensión de los tópicos abordados, y también un buen número de problemas propuestos, con sus soluciones respectivas, destinados a desarrollar en el lector la habilidad de resolverlos y el dominio de las estructuras matemáticas a ellos asociados.
Book chapters on the topic "Loi de Laplace"
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"Stochastic Log-Laplace Equation." In Three Classes of Nonlinear Stochastic Partial Differential Equations, 83–104. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814452366_0005.
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Trinidad Guillen Bonilla, José, Alex Guillen Bonilla, Mario Alberto García Ramírez, Gustavo Adolfo Vega Gómez, Héctor Guillen Bonilla, María Susana Ruiz Palacio, Martín Javier Martínez Silva, and Verónica María Bettancourt Rodriguez. "Interference Pattern Representation on the Complex s-Plane." In Advances in Complex Analysis and Applications. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.89491.
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In this work, the normalized interference pattern produced by a coherence interferometer system was represented as a complex function. The Laplace transform was applied for the transformation. Poles and zeros were determined from this complex function, and then, its pole-zero map and its Bode diagram were proposed. Both graphical representations were implemented numerically. From our numerical results, pole location and zero location depend on the optical path difference (OPD), while the Bode diagram gives us information about the OPD parameter. Based on the results obtained from the graphical representations, the coherence interferometer systems, the low-coherence interferometer systems, the interferometric sensing systems, and the fiber optic sensors can be analyze on the complex s-plane.
Conference papers on the topic "Loi de Laplace"
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Fang, Sidong, Linsong Cheng, Shijun Huang, and Cao Renyi. "Laplace Domain Coupled Dual Continuum and Embedded Discrete Fracture Model for Rate Transient Analysis in Low Permeability Reservoirs." In SPE Low Perm Symposium. Society of Petroleum Engineers, 2016. http://dx.doi.org/10.2118/180265-ms.
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Mallick, Arijit, Sourya Roy, Sheli Sinha Chaudhuri, and Sangita Roy. "Optimization of Laplace of Gaussian (LoG) filter for enhanced edge detection: A new approach." In 2014 International Conference on Control, Instrumentation, Energy and Communication (CIEC). IEEE, 2014. http://dx.doi.org/10.1109/ciec.2014.6959172.
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UEDA, T. "A calculation method for unsteady aerodynamic forces in the Laplace domain and its application to root loci." In 27th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1986. http://dx.doi.org/10.2514/6.1986-866.
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Guo, Xin, Boyuan Pan, Deng Cai, and Xiaofei He. "Robust Asymmetric Bayesian Adaptive Matrix Factorization." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/244.
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Low rank matrix factorizations(LRMF) have attracted much attention due to its wide range of applications in computer vision, such as image impainting and video denoising. Most of the existing methods assume that the loss between an observed measurement matrix and its bilinear factorization follows symmetric distribution, like gaussian or gamma families. However, in real-world situations, this assumption is often found too idealized, because pictures under various illumination and angles may suffer from multi-peaks, asymmetric and irregular noises. To address these problems, this paper assumes that the loss follows a mixture of Asymmetric Laplace distributions and proposes robust Asymmetric Laplace Adaptive Matrix Factorization model(ALAMF) under bayesian matrix factorization framework. The assumption of Laplace distribution makes our model more robust and the asymmetric attribute makes our model more flexible and adaptable to real-world noise. A variational method is then devised for model inference. We compare ALAMF with other state-of-the-art matrix factorization methods both on data sets ranging from synthetic and real-world application. The experimental results demonstrate the effectiveness of our proposed approach.
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Wang, Pingfeng, Adebayo O. Adewunmi, and Zequn Wang. "Evolving Design Model Synchronization for System Health Management Using Laplace Approximation." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34552.
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Lifecycle health management plays an increasingly important role in realizing resilience of aging complex engineered systems since it detects, diagnoses, and predicts system-wide effects of adverse events, therefore enables a proactive approach to deal with system failures. To address an increasing demand to develop high-reliability low-cost systems, this paper presents a new platform for operational stage system health management, referred to as Evolving Design Model Synchronization (EDMS), which enables health management of aging engineered systems by efficiently synchronizing system design models with degrading health conditions of actual physical system in operation. A Laplace approximation approach is employed for the design model updating, which can incorporate heterogeneous operating stage information from multiple sources to update the system design model based on the information theory, thereby increases the updating accuracy compared with traditionally used Bayesian updating methodology. The design models synchronized over time using sensory data acquired from the system in operation can thus reflect system health degradation with evolvingly updated design model parameters, which enables the application of failure prognosis for system health management. One case study is used to demonstrate the efficacy of the proposed approach for system health management.
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Akbarzadeh, A. H., and Z. T. Chen. "Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78617.
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In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.
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Henninger, Stefan, Peter Jeschke, Graham Ashcroft, and Edmund Kügeler. "Time-Domain Implementation of Higher-Order Non-Reflecting Boundary Conditions for Turbomachinery Applications." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42362.
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The present paper demonstrates the time-domain implementation of arbitrary-order non-reflecting boundary conditions for a 3d non-linear time-accurate RANS solver for turbomachinery applications. The conditions are based on the 2d circumferential mode decomposition of the linearized Euler equations. The exact linearized conditions are non-local since they involve space-time Fourier/Laplace transforms. Time-local conditions of arbitrary order are obtained by approximation of the inverse Laplace transform Bessel function convolution kernel by sums of exponential functions. Likewise, this corresponds to a rational function approximation of the exact non-reflecting boundary kernel in the frequency-domain. The boundary conditions are validated against two numerical test cases. The first test case mimics Tyler-Sofrin modes present in turbomachinery applications by prescribing 2d acoustic modes in a uniform flow. The second test case is concerned with the potential contamination of blade flutter analyses by spurious reflections on artificial boundaries. For the benchmark problem Standard Configuration 10, blade flutter with non-zero inter-blade phase angle, acoustic resonance generates spinning waves susceptible to reflection. Contrasting the results of non-reflecting boundary conditions of varying order of accuracy shows that low order conditions can fail for challenging cases, which emphasizes the need for an accurate non-reflecting boundary treatment.
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Chu, Hongyang, Xinwei Liao, Cao Wei, and John Lee. "Rate/Pressure Transient Analysis of a Variable Bottom Hole Pressure Multi-Well Horizontal Pad with Well Interference." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/206046-ms.
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Abstract Multi-well horizontal pads are common in unconventional reservoirs. With addition of infill wells and hydraulic fracturing, interference between multiple multi-fractured-horizontal wells (MFHWs) has become a serious issue. Current RTA workflows assume a single MFHW in the unconventional formation. This paper presents a new multi-MFHW solution and related analysis methodology to analyze targeted well rate performance in a multi-MFHW system. In this work, a semi-analytical equation describing multi-well pad in the Laplace domain with well interference is proposed. The proposed semi-analytical model can simulate the rate performance of a multi-well horizontal pad with variable BHP for a targeted well in the pad and different initial production durations for the offset well. From the constant BHP condition and Laplace transforms, we obtained multi-MFHW solutions for transient flow. We used superposition of various constant BHP solutions to study interference among various fractures and MFHWs. The variable BHP of the targeted well is achieved by a variable dimensionless BHP function in the Laplace domain without any convolution or deconvolution calculations. A systematic validation for the proposed method is conducted using a commercial numerical simulator for cases of different initial production times for offset MFHWs, multi-MFHWs with variable BHP. Through the total material balance of the multi-MFHW system, we can analyze a target well in the pad with this multi-MFHW analysis. Interference by offset wells often appears after pseudo-radial flow in the target well's hydraulic fracture. It causes the pressure derivative curve during elliptical and infinite-acting radial flow (IARF) to rise, as does the RNP derivative. The inverse semi-log derivative has the opposite trend. Well interference also makes the rate/pressure drop functions to deviate from initial straight lines in later stages. Sensitivity analysis of well spacing shows that "transition flow" will change from elliptical to formation linear flow between wells as well spacing increases and it can show the transitional flow characteristics in more common cases.
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Wang, Hao, Suresh V. Garimella, and Jayathi Y. Murthy. "Analysis of the Total Heat Transfer in an Evaporating Thin Film." In ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer. ASMEDC, 2008. http://dx.doi.org/10.1115/mnht2008-52386.
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When a liquid wets a solid wall, the extended meniscus may be divided into three regions: a non-evaporating region where liquid is adsorbed on the wall; a thin-film region where effects of long-range molecular forces (disjoining pressure) are felt; and an intrinsic meniscus region where capillary forces dominate. In this work, a simplified model based on the augmented Young-Laplace equation is developed and an analytical solution is obtained to more easily evaluate the total heat transfer in the thin-film region. The results are consistent with previously published numerical solutions. The present work is valid for a much wider range of fluid thermal conductivity than a previous analytical solution by Schonberg et al, which is only applicable for fluids with very low conductivity.
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Wan, Zhiliang, Alan Feinerman, Gary Friedman, and Hongjun Zeng. "Electrocapillary Piston Motion and a Prototype of Phase-Manipulating Micromirror." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41288.
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In this paper we study the piston motion of a mercury droplet that is confined in a metal-plated micro-hole. This droplet is actuated by the electrocapillary effect and large displacements of up to 250μm are achieved with very low voltages (2V). We use a high-speed camera (10,000frames/s) to capture the piston motion and we find the resonance frequency is ~45Hz. The mercury droplet geometry in equilibrium state is analyzed based on Laplace equation and volume conservation. A mathematical model is developed and predicts a resonant frequency of mercury droplet and the value is found to be 119Hz. A prototype of piston-motion micromirror is also demonstrated in the experiment, with frequency of 400Hz and amplitude of ~8μm at 2V.
Reports on the topic "Loi de Laplace"
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Zhang, Yongping, Wen Cheng, and Xudong Jia. Enhancement of Multimodal Traffic Safety in High-Quality Transit Areas. Mineta Transportation Institute, February 2021. http://dx.doi.org/10.31979/mti.2021.1920.
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Numerous extant studies are dedicated to enhancing the safety of active transportation modes, but very few studies are devoted to safety analysis surrounding transit stations, which serve as an important modal interface for pedestrians and bicyclists. This study bridges the gap by developing joint models based on the multivariate conditionally autoregressive (MCAR) priors with a distance-oriented neighboring weight matrix. For this purpose, transit-station-centered data in Los Angeles County were used for model development. Feature selection relying on both random forest and correlation analyses was employed, which leads to different covariate inputs to each of the two jointed models, resulting in increased model flexibility. Utilizing an Integrated Nested Laplace Approximation (INLA) algorithm and various evaluation criteria, the results demonstrate that models with a correlation effect between pedestrians and bicyclists perform much better than the models without such an effect. The joint models also aid in identifying significant covariates contributing to the safety of each of the two active transportation modes. The research results can furnish transportation professionals with additional insights to create safer access to transit and thus promote active transportation.