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Wellposedness of some quasi-linear Schrdinger equations

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Science China Mathematics 2015年第5期58卷 891-914页

作者： cheMIN Jean-Yves SALORT Delphine Laboratoire J.-L. Lions UMR 7598 Universit'e Pierre et Marie Curie Laboratoire de Biologie Computationnelle et Quantitative UMR 7238Sorbonne Universit'es L'Institut jacques Monod UMR 7592 Universit'e Paris Diderot

This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.

关键词： quasilinear Schrodinger equation Strichartz estimates paradiffential calculus stationary phase method

KINETIC FUNCTIONS IN MAGNETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT

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Acta Mathematica Scientia 2009年第6期29卷 1684-1702页

作者： Philippe G. Le Siddhartha Mishra FlochLaboratoire jacques-Louis Lions Centre National de la Recherche ScientifiqueUniversit Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75258 Paris France Seminar for Applied Mathematics D-Math ETH HG Raemistrasse Zürich-8092 Switzerland

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we design a new class of ＂schemes with eontroled dissipation＂, following recent work by LeFloch and Mohammadian. It is now recognized that the equivalent equation associated with a scheme provides a guideline to design schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on high-order entropy conservative, finite differences for the hyperbolic flux, and high-order central differences for the resistivity and Hall terms. These schemes are tested for several regimes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in magnetohydrodynamics.

关键词： hyperbolic conservation law magnetohydrodynamics magnetic resistivity Hall effect undercompressive shock kinetic function

THE RANDOM BATCH METHOD FOR N-BODY QUANTUM DYNAMICS

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Journal of Computational Mathematics 2021年第6期39卷 897-922页

作者： Francois Golse Shi Jin Thierry Paul Ecole polytechnique CMLS91128 Palaiseau CedexFrance School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai 200240China Sorbonne Universite CNRSUniversite de ParisINRIALaboratoire Jacques-Louis Lions75005 ParisFrance

This paper discusses a numerical method for computing the evolution of large interacting system of quantum *** idea of the random batch method is to replace the total interaction of each particle with the N−1 other particles by the interaction with p≪N particles chosen at random at each time step,multiplied by(N−1)/*** reduces the computational cost of computing the interaction potential per time step from O(N^(2))to O(N).For simplicity,we consider only in this work the case p=1—in other words,we assume that N is even,and that at each time step,the N particles are organized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time *** obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N>1 and independent of the Planck constant h̵.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1(or Monge-Kantorovich-Rubinstein distance)on the set of Borel probability measures on Rd used in the context of optimal transport.

关键词： Time-dependent Schrodinger equations Random batch method Mean-field limit Wasserstein distance

X chromosome inactivation and active X upregulation in therian mammals: facts, questions, and hypotheses

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分子细胞生物学报:英文版 2015年第1期7卷 2-11页

作者： Reiner A.Veitia Frederic Veyrunes Samuel Bottani James A.Birchler Institut jacques Monod ParisFrance Universite Paris Diderot ParisFrance Institut des Sciences de l’Evolution de Montpellier CNRS/Universite Montpellier IIMontpellierFrance Matiere et Systemes Complexes ParisFrance Division of Biological Sciences University of MissouriColumbiaMOUSA

X chromosome inactivation is a mechanism that modulates the expression of X-linked genes in eutherian females(XX).Ohno proposed that to achieve a proper balance between X-linked and autosomal genes,those on the active X should also undergo a 2-fold *** some support for Ohno's hypothesis has been provided through the years,recent genomic studies testing this hypoth-esis have brought contradictory results and fueled *** far,there are as many results in favor as against Ohno's hypothesis,depending on the nature of the datasets and the various assumptions and thresholds involved in the ***,they have con-firmed the importance of dosage balance between X-linked and autosomal genes involved in stoichiometric *** facts as well as questions and hypotheses are discussed below.

关键词： X inactivation X chromosome upregulation monoallelic expression imprinting dosage balance

The Humanitarian Factors： An ICRC Perspective

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Contemporary International Relations 2012年第C期22卷 118-121页

作者： jacques de Maio jacques de Maio is the Head of Operations for South Asia International Committee of the Red Cross.

More than ten years have passed since the beginning of the Global War on Terror and the consequent launch of Operation Enduring Freedom in Afghanistan. Today, at the dawn of international forces＇ withdrawal, some substantive improvements are recorded in the field of infrastructure, power, communication, and education. The question is whether this relative progress is sustainable and whether the Afghan population will get the help it will actually need in an unpredictable, but a priori extremely difficult, future.

关键词：人道主义国际委员会反恐战争基础设施阿富汗自由

Perfusionist strategies for blood conservation in pediatric cardiac surgery

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World Journal of Cardiology 2010年第2期2卷 27-33页

作者： Yves Durandy Perfusion and Intensive Care Unit Pediatric Cardiac SurgeryInstitut Hospitalier Jacques CartierMassy 91300France

There is increasing concern about the safety of homologous blood transfusion during cardiac surgery,and a restrictive transfusion practice is associated with improved ***-free pediatric cardiac surgery is unrealistic for the vast majority of procedures in neonates or small infants;however,considerable progress has been made by using techniques that decrease the need for homologous blood products or even allow bloodless surgery in older infants and *** techniques involve a decrease in prime volume by downsizing the bypass circuit with the help of vacuumassisted venous drainage,microplegia,autologous blood predonation with or without infusion of recombinant(erythropoietin),cell salvaging,ultrafiltration and retrograde autologous *** three major techniques which are simple,safe,efficient,and cost-effective are:a prime volume as small as possible,cardioplegia with negligible hydric balance and circuit residual blood salvaged without any ***,these three techniques can be used for all the patients,including emergencies and small *** every pediatric surgical unit,a strategy to decrease or avoid blood bank transfusion must be implemented.A strategy to minimize transfusion requirement requires a combined effort involving the entire surgical team with pre-,peri-,and postoperative planning and management.

关键词： Autologous blood predonation Blood conservation Cardiopulmonary bypass Cell-salvage Microplegia Pediatric open-heart surgery Prime volume reduction Retrograde autologous priming Ultrafiltration Vacuum-assisted venous drainage

Scattering for the focusing energy-subcritical nonlinear Schrdinger equation

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Science China Mathematics 2011年第10期54卷 2037-2062页

作者： FANG DaoYuan XIE Jian CAZENAVE Thierry Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Hangzhou Normal University HangZhou 310036 China Universitd Pierre et Marie Curie & CNRS Laboratoire Jacques-Louis Lions B.C. 187 4 place Jussieu 75252 Paris Cedex 05 France

For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.

关键词： nonlinear SchrSdinger equation scattering mass-supercritical and energy-subcritical

Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation

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Chinese Annals of Mathematics,Series B 2013年第3期34卷 333-344页

作者： Jean-Michel CORON Jesǘs Ildefonso DIAZ Abdelmalek DRICI Tommaso MINGAZZINI Institut Universitaire de France and Universit Pierre et Marie Curie (Paris 6) UMR 7598 Laboratoire Jacques-Louis Lions 4 place Jussieu F-75252 Paris cedex 5 France Universidad Complutense de Madrid Instituto de Matemtica Interdisiplinar and Dpto. de Matemtica Aplicada Plaza de las Ciencias 3 28040 Madrid Espaa Universit Pierre et Marie Curie (Paris 6) UMR 7598 Laboratoire Jacques-Louis Lions 4 place Jussieu F-75252 Paris cedex 5 France Universidad Complutense de Madrid Dpto. de Matemtica Aplicada Plaza de las Ciencias 3 28040 Madrid Espaa

The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control. They assume that the internal control is only time dependent. The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.

关键词： Nonlinear control Nonlinear slow diffusion equation Porous mediumequation

Comparison between the SAPIEN S3 and the SAPIEN XT transcatheter heart valves:A single-center experience

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World Journal of Cardiology 2016年第12期8卷 735-745页

作者： Fadi J Sawaya Marco Spaziano Thierry Lefèvre Andrew Roy Phillippe Garot Thomas Hovasse Antoinette Neylon Hakim Benamer Mauro Romano Thierry Unterseeh Marie-Claude Morice Bernard chevalier Department of Cardiology Générale de SantéInstitut Cardiovasculaire Paris-Sud-Hopital Privé Jacques Cartier

AIM To investigate the clinical outcomes of transcatheter aortic valve implantation(TAVI) with the SAPIEN 3 transcatheter heart valve(S3-THV) vs the SAPIEN XT valve(XT-THV).METHODS We retrospectively analyzed 507 patients that underwent TAVI with the XT-THV and 283 patients that received the S3-THV at our institution between March 2010 and December *** Thirty-day mortality(3.5% vs 8.7%:OR=0.44,P=0.21) and 1-year mortality(25.7% vs 20.1%,P=0.55) were similar in the S3-THV and the XT-THV *** rates of both major vascular complication and paravalvular regurgitation(PVR)>1 were almost 4 times lower in the S3-THV group than the XT-THV group(major vascular complication: 2.8% vs 9.9%,P1: 2.4% vs 9.7%,P<0.0001).However,the rate of new pacemaker implantation was almost twice as high in the S3-THV group(17.3% vs 9.8%,P=0.03).In the S3 group,independent predictors of new permanent pacemaker were pre-procedural RBBB(OR=4.9:P=0.001),pre-procedural PR duration(OR=1.14,P=0.05) and device lack of coaxiality(OR=1.13:P=0.05) during *** The S3-THV is associated to lower rates of major vascular complications and PVR but higher rates of new pacemaker compared to the ***-optimal visualization of the S3-THV in relation to the aortic valvular complex during deployment is a predictor of new permanent pacemaker.

关键词： SAPIEN-3 valve Vascular complications Permanent pacemaker Lack of coaxiality Paravalvular regurgitation