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International Journal of Modeling, Simulation, and Scientific Computing 2019年第6期10卷 107-128页

作者： Salem Ahmedou Bamba Abdellatif Ellabib Universite Cadi Ayyad Laboratoire de mathematiques Appliquees et Informatique Faculte des Sciences et Techniques Marrakech Avenue Abdelkrim El Khttabi B.P.549 Morocco

In this paper,a bioheat model of temperature distribution in the human eye is studied,the mathematical formulation of this model is described using adequate mathematical *** existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in *** validation of all algorithm is done using a numerical application for an example where the analytical solution is *** properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition *** obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

关键词： Nonoverlapping domain decomposition human eye bioheat transfer finite element computation

First-principles study of the electronic structure of a superstoichiometric rare earth dihydride GdH2.25

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Journal of Rare Earths 2016年第1期34卷 66-70页

作者： z.ayat a.boukraa b.daoudi Univ Ouargla Fac. Des Mathematiques et des Sciences de la Matidre Lab. Developpement des energies nouvelles et renouvelables dans les zones arides et sahariennes Ouargla 30000 Algeria

We performed ab initio calculations of electronic structure and equilibrium properties for the rare earth superstoichiometric dihydride GdH2.25 （with the space group Pm-3m （No. 221）） using the full-potential linearized augmented plane wave method （FP-LAPW） approach within the density functional theory （DFT） in the generalized gradient approximation （GGA） and local density approximation （LDA） as implemented in the WIEN2k simulation code at 0 K. The equilibrium properties were determined, the density of states, electronic density and the energy band structures were studied in details. It was concluded that the GGA optimized lattice parameter agreed much better with the experimental findings than the LDA one, The non negligible electronic density of states at the Fermi level confirmed that the GdH2.25 had a metallic character. The Fermi energy EF fell at a level where most of the states were rare-earth 5d-eg conduction states while negligible contributions of both interstitial （tetrahedral and octahedral） H s-states were observed near EF, From electronic density, the bonding between Gd and tetrahedral H atoms was of prominent covalency, while was ionic between Gd and octahedral H atoms.

关键词： rare-earth dihydrides GdU2.25 density functional theory ab initio calculations WIEN2k

Nonstandard finite-difference schemes for the two-level Bloch model

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International Journal of Modeling, Simulation, and Scientific Computing 2018年第4期9卷 186-208页

作者： Marc E.Songolo Brigitte Bidegaray-Fesquet Departement de mathematiques et Informatique Universit´e de Lubumbashi 1825 Lubumbashi Republique Democratique du Congo Univ.Grenoble Alpes Grenoble INP LJK38000 GrenobleFrance

In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.

关键词： Bloch equation exponential of a matrix exact finite-difference schemes nonstandard finite-difference schemes splitting method.

A Comparison Theorem and Uniqueness Theorem of Backward Doubly Stochastic Differential Equations

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 223-232页

作者： Qian Lin Zhen Wu School of Mathematics Shandong University Jinan 250100 China Laboratoire de mathematiques CNRS UMR 6205 Universite de Bretagne Occidentale 6 avenue Victor Le Gorgeu CS 93837 29238 Brest cedex 3 France

In this paper, we deal with one dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.

关键词： backward doubly stochastic differential equations comparison theorem backward stochastic integral uniqueness theorem

On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations

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Communications in Computational Physics 2023年第8期34卷 613-671页

作者： Francois Dubois Pierre Lallemand Laboratoire de mathematiques d’Orsay Faculte des Sciences d’OrsayUniversite Paris-SaclayFrance Conservatoire National des Arts et Metiers LMSSC laboratoryParisFrance International Research Laboratory 3457 Centre National de la Recherche ScientifiqueCentre de Recherches MathematiquesUniversite de MontrealMontrealQCCanada Beijing Computational Science Research Center Haidian DistrictBeijing 100094China

In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle *** precisely,we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved and nonconserved *** question is to determine the algebraic expressions of the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each *** compare the fluid equations and the result of the Taylor expansion method at second order accuracy for bidimensional examples with a maximum of 17 velocities and three-dimensional schemes with at most 33 *** some cases,it is not possible to fit exactly the physical *** several examples,we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.

关键词： Partial differential equations asymptotic analysis

High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

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Communications in Computational Physics 2017年第1期21卷 271-312页

作者： Walter Boscheri Raphael Loubere Laboratory of AppliedMathematics Department of CivilEnvironmental and Mechanical EngineeringUniversity of TrentoI-38123 TrentoItaly CNRS and Institut de mathematiques de Toulouse(IMT)Universite Paul-Sabatier ToulouseFrance

In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source *** scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)*** this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become *** new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence *** Riemann problems and explosion problems with exact solutions are simulated in 2D and *** overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

关键词： Direct Arbitrary-Lagrangian-Eulerian a posteriori MOOD stabilization Baer-Nunziato model stiff source terms non-conservative products unstructured mesh ADER high order of accuracy in space and time high performance computing(HPC) hyperbolic conservation laws

Numerical Study of Solutions of the 3D Generalized Kadomtsev-Petviashvili Equations for Long Times

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Communications in Computational Physics 2009年第10期6卷 1022-1062页

作者： F.Hamidouche Y.Mammeri S.M.Mefire Laboratoire de mathematiques CNRS UMR 8628Universite Paris-Sud 1191405 Orsay CedexFrance Laboratoire de mathematiques–Paul Painleve CNRS UMR 8524Universite des Sciences et Technologies de Lille59655 Villeneuve d’Ascq CedexFrance Laboratoire Amienois de Mathematique Fondamentale et Appliquee CNRS UMR 6140Universite de Picardie33 r.Saint-Leu80039 Amiens Cedex 1France

From a spectral method combined with a predictor-corrector scheme,we numerically study the behavior in time of solutions of the three-dimensional generalized Kadomtsev-Petviashvili *** a systematic way,the dispersion,... 详细信息

关键词： 3D-KP equations spectral method predictor-corrector method dispersion blow-up soliton transverse instability

On a fractional stochastic Hodgkin-Huxley model

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International Journal of Biomathematics 2018年第5期11卷 1-16页

作者： Laure Coutin Jean-Marc Guglielmi Nicolas Marie Institut de mathematiques de Toulouse Toulouse France American Hospital of Paris NeuiUy-sur-Seine France Laboratoire Modal'X Universite Paris 10 Nanterre France ESME Sudria Paris France

The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for R× [0, 1]3. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.

关键词： Hodgkin-Huxley model stochastic differential equations fractional Brownian motion viability theorem.

SUR LES FAMILLES NORMALES DE FONCTIONS MEROMORPHES

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Science in China,Ser.A 1978年第4期 431-445页

作者：顾永兴 Departement de mathematiques Ecole Normale de Nan-Tchong

Prineipalement est etabli te theoreme:Theareme 1. Soit {f（z）} une famille de fonctions meromrphes dans un domaine （D） ou chaque fonction f（z） admet ∞ et p （≥1） nombres finis distincts ai （i=1, …, p） comme valeurs multiples d’ordre≥s （≥1） et≥mi（≥2） respectivement, et sa derivse d’ordre k fk（z） admet q （≥1） hombres finis non nuls et distincts bi （j=1,…, q） comme valeurs multiples d’ordre ≥ni （≥2）. Si les inegalitessum from i=1 to p （kq+q）/mi+sum from j=1 to q 1/nj+l/S（l+k sum from j=I to q l/nj）（kq+l）/mi, （i=l,…, p）,sont verifiees, alors {f（z）} est une famille normale dans le domaine （D）.Puis, nous donnons une generalisation de ce theoreme.

关键词： DE SUR LES FAMILLES NORMALES DE FONCTIONS MEROMORPHES

Estimate of an Hypoelliptic Heat-Kernel outside the Cut-Locus in Semi-Group Theory

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Applied Mathematics 2012年第12期3卷 2063-2070页

作者： Remi Leandre Laboratoire de mathematiques Universite de Franche-ComteBesanconFrance

We give a proof in semi-group theory based on the Malliavin Calculus of Bismut type in semi-group theory and Wentzel-Freidlin estimates in semi-group of our result giving an expansion of an hypoelliptic heat-kernel ou... 详细信息

关键词： Subriemannian Geometry Heat-Kernels