1,332 research outputs found
Summary biography of Violet K. de Cristoforo
No full textVariant of HMLSC_VKdC_007, Author's biography.Personal experiences of a Japanese-American internee during World War II, and her poetry published about her experiences later in life
Author's biography
No full textA brief autobiographical statement by Violet Kazue de Cristoforo.Personal experiences of a Japanese-American internee during World War II, and her poetry published about her experiences later in life
On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models
No full textInternational audienceIn this paper, the main objective is to generalize to the Navier-Stokes-Korteweg (with density dependent viscosities satisfying the BD relation) and Euler-Korteweg systems a recent relative entropy [proposed by D. Bresch, P. Noble and J.–P. Vila, (2016)] introduced for the compressible Navier-Stokes equations with a linear density dependent shear viscosity and a zero bulk viscosity. As a concrete application, this helps to justify mathematically the convergence between global weak solutions of the quantum Navier-Stokes system [recently obtained simultaneously by I. Lacroix-Violet and A. Vasseur (2017)] and dissipative solutions of the quantum Euler system when the viscosity coefficient tends to zero: This selects a dissipative solution as the limit of a viscous system. We also get weak-strong uniqueness for the Quantum-Euler and for the Quantum-Navier-Stokes equations. Our results are based on the fact that Euler-Korteweg systems and corresponding Navier–Stokes-Korteweg systems can be reformulated through an augmented system such as the compressible Navier-Stokes system with density dependent viscosities satisfying the BD algebraic relation. This was also observed recently [by D. Bresch, F. Couderc, P. Noble and J.–P. Vila, (2016)] for the Euler-Korteweg system for numerical purposes. As a by-product of our analysis, we show that this augmented formulation helps to define relative entropy estimates for the Euler Korteweg systems in a simplest way compared to recent works [See D. Donatelli, E. Feireisl, P. Marcati (2015) and J. Giesselmann, C. Lattanzio, A.-E. Tzavaras (2017)] with less hypothesis required on the capillary coefficient
Author-signed copy of Collected verses Violet Fane (1880)
No full textabstract: Author-signed copy of Collected verses Violet Fane (1880), gift copy inscribed to Lady Harringto
Numerical analysis of drift-diffusion models : convergence and asymptotic behaviors
No full textDans cette thèse, nous nous intéressons à un modèle simplifié de corrosion issu du modèle ''Diffusion Poisson Coupled Model'' (DPCM). Nous analysons de manière approfondie le schéma numérique qui a été implémenté dans le code CALIPSO utilisé par l'ANDRA. Il est de type Euler implicite en temps et volumes finis en espace, avec des flux de Scharfetter-Gummel. Nous étudions notamment la convergence de ce schéma ainsi que son comportement asymptotique en différentes limites de paramètres. Enfin, nous explorons différentes possibilités pour augmenter l'ordre en temps.In this PhD thesis, we are interested in a simplified corrosion model derived from the Diffusion Poisson Coupled Model (DPCM). We analyze the numerical scheme implemented in the CALIPSO code used by the French nuclear waste management agency ANDRA. It is a backward Euler scheme in time and a finite volume scheme in space, with Schafetter-Gummel approximation of the convection-diffusion fluxes. We study the convergence of this scheme and its asymptotic behavior for different limits of parameters. Finally, we compare several higher order schemes in time
Numerical simulation of Bose-Einstein condensates
No full textDans cette thèse, nous considérons une fonctionnelle d'énergie Gross--Pitaevskii (GP) comme modèle pour la rotation d'un espèce et de deux espèces de condensats de Bose--Einstein (BEC) en deux dimensions. Ce modèle peut être adimensionné pour mettre en évidence un régime de confinement fort avec une forte interaction entre les deux composants. Nous introduisons une nouvelle discrétisation de cette énergie, comportant à la fois des schémas de différence finie et de Fourier, dans un domaine borné dans R² en utilisant des conditions aux bords de Dirichlet. Nous développons un algorithme de méthode de gradient explicite avec pas adaptatif et projection (EPG) sur la variété de contraintes pour la minimisation de l'énergie. Cette méthode permet de dériver un critère d'arrêt. Nous proposons également deux algorithmes de post-traitement pour les minimiseurs numériques. L'un est destiné aux vortex simples tandis que l'autre est destiné aux nappes de vortex. Les deux algorithmes détectent ces structures et calculent leurs indices.Dans un article récent intitulé "Vortex patterns and sheets in segregated two component Bose-Einstein condensates", les auteurs étudient le comportement d'un BEC ségrégué à deux espèces mis en rotation. Ils ont pu prouver que pour une grande rotation, l'interface entre les deux composants s'allonge, conduisant éventuellement à des nappes de vortex. Ils ont également étudié les structures des vortex du BEC dans un régime ségrégué. Dans cette thèse, nous avons pu produire des simulations numériques à l'aide d'EPG, validant ces résultats théoriques récents, supportant des conjectures et couvrant différents cas physiques (les cas d'un espèce et de deux espèces en régime de coexistence qui existent déjà dans la littérature mathématique). Nous illustrons également l'efficacité d'EPG par rapport à la méthode bien connue de GPELab qui consiste à résoudre un système linéairement implicite à chaque pas de temps.Enfin, nous avons pu adapter quelques théorèmes trouvés dans la littérature à notre problème discret. Nous prouvons l'existence d'un minimiseur global de la fonctionnelle d'énergie Gross--Pitaevskii pour le schéma aux différences finies et étudions certaines de ses propriétés. Nous travaillons également sur des problèmes symétriques rencontrés dans certaines simulations numériques.In this thesis, we consider a Gross--Pitaevskii (GP) energy functional as a model for rotating one component and two components Bose--Einstein condensates (BEC) in two dimensions. This model can be non-dimensionalized to highlight a strong confinement regime with strong interaction between the two components. We introduce a new discretization of this energy, featuring both finite difference and fast Fourier schemes, in a bounded domain in R² using Dirichlet boundary conditions. We develop an explicit gradient method algorithm with adaptive step and projection (EPG) over the constraints manifold for the minimization of the energy. This method allows for the derivation of a stopping criterion. We propose as well two post processing algorithms for the numerical minimizers. One is aimed for single vortices while the other is aimed for vortex sheets. Both algorithms detect these structures and compute their indices.In a recent article titled "Vortex patterns and sheets in segregated two component Bose-Einstein condensates", the authors study the behaviour of a segregated two-component BEC set into rotation. They were able to prove that for large rotation, the interface between the components gets long, leading possibly towards vortex sheets. They also studied the vortex structures of BEC in a segregated regime. In this thesis, we were able to produce numerical simulations using EPG, validating these recent theoretical results, supporting conjectures and covering different physical cases (the cases of one component and two components in coexistence regime that alredy exists in the mathematical litterature). We also illustrate the efficiency of EPG compared to that well-known GPELab's method which consists on solving linearly implicit system at each time-step.Finally, we were able to adapt few theorems found in the literature to our discrete problem. We prove the existence of a global minimizer of the Gross--Pitaevskii energy functional for the finite difference scheme and study some of its properties. We also work on symmetrical problems we encountered in some of the numerical simulations
Lacroix and the calculus
No full textSilvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was adapted for teaching into a shorter, textbook version – the Traité élémentaire de calcul différentiel et de calcul intégral (1802; several later editions). This adaptation is also analysed. Lacroix and the Calculus should appeal to historians and mathematicians interested in the history of the calculus (and especially in the background to Cauchy and Bolzano) and in its teaching in the late 18th and early 19th centuries
Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit
No full textInternational audienceThis paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerate viscosity, together with the lack of integrability on the velocity. Our method is based on the construction of weak solutions that are renormalized in the velocity variable. The existence, and stability of these solutions do not need the Mellet-Vasseur inequality
High order linearly implicit methods for evolution equations: How to solve an ODE by inverting only linear systems
No full textInternational audienceThis paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs. The systematic design of these methods mixes the Runge-Kutta collocation formalism with collocation techniques, in such a way that the methods are linearly implicit and have high order. The fact that these methods are implicit allows to avoid CFL conditions when the large systems to integrate come from the space discretization of evolution PDEs. Moreover, these methods are expected to be efficient since they only require to solve one linear system of equations at each time step, and efficient techniques from the literature can be used to do so. After the introduction of the methods, we set suitable definitions of consistency and stability for these methods. This allows for a proof that arbitrarily high order linearly implicit methods exist and converge when applied to ODEs. Eventually, we perform numerical experiments on ODEs and PDEs that illustrate our theoretical results for ODEs, and compare our methods with standard methods for several evolution PDEs
Comportements asymptotiques, conditions aux limites et analyse numérique pour des modèles fluides
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