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Zaynab Ahmad Salloum

Associate professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: EDP/ Mécanique de fluide
Interests: Voyage, Lecture.

Positions
2008 - 2013 : Enseignante-Chercheuse

Université Libanaise-Faculté des Sciences 5-LIBAN
Nabatieh

2008 - present : Enseignante-Chercheuse

Université Libanaise-Faculté des Sciences 1-LIBAN
Beyrouth

2009 - 2009 : Post Doc

Université Lille 1-FRANCE
Lille-France

2008 - 2009 : Enseignante

Université Saint Joseph-LIBAN
Beyrouth

2008 - 2014 : Enseignante

Université Islamique du Liban-LIBAN
Beyrouth

2006 - 2008 : ATER

Université Paris-Est-FRANCE
France

2002 - 2006 : Enseignante

Institut Technique Supérieur-LIBAN
Beyrouth

Teaching 5 Taught Courses
Conferences 15 participations
Journée en l'honneur de Colette Guillopé-FRANCE:Mathématiciennes et mathématiciens, mécanique des fluides, aspects déterministes et stochastiques

Colloquium
2013-09-13 to 2013-09-13

International conference on discrete mathematics and computer science-LIBAN

Conference
2012-11-13 to 2012-11-17

Séminaire sur Penelope Maddy à Université Lille 3-FRANCE

Seminar
2012-10-01 to 2012-10-23

Workshop on fluid mechanics and dynamics of populations-LIBAN

Conference
2012-09-10 to 2012-09-14

Workshop on geometric control for PDE's-LIBAN

Seminar
2012-01-31 to 2012-02-02

CFM2011, Congrés Français de Mécanique-FRANCE

Congress
2011-08-28 to 2011-09-02

9ème Forum des jeunes mathématiciennes, Institut Henri Poincaré-FRANCE

Conference
2009-11-06 to 2009-11-07

Ecole d'été de Universitat Autònoma de Barcelona-ESPAGNE: Advanced Course on Optimization: Theory, Methods and Applications

Summer School
2009-07-20 to 2009-07-24

Conférence de Scuola Normale Superiore, ITALIE: Geometric Flows in Mathematics and Theoretical Physics

Conference
2009-06-22 to 2009-06-25

Conférence de l'Institut Henri Poincaré-FRANCE: Control of Physical Systems and Partial Differential Equations

Conference
2008-06-16 to 2008-06-20

Colloque en l'honneur de Jean-Claude Saut-FRANCE: Modèles dispersifs et dynamique des fluides

Colloquium
2007-09-06 to 2007-09-07

Congrès en l'honneur de Luc Tatar-FRANCE: Des Equations aux dérivées partielles au calcul scientifique

Congress
2007-07-02 to 2007-07-06

CAMS, AUB-LIBAN: Mathematical Theory of Nonlinear Dispersive Waves

Summer School
2005-09-12 to 2005-09-16

CIMPA-LIBAN: Géométrie et Arithmétique des courbes

Summer School
2004-07-05 to 2004-07-16

CIMPA-SYRIE: Aspects théoriques et appliquées de quelques EDP issus de la géométrie ou de la physique

Summer School
2004-05-15 to 2004-05-27

Publications 17 publications
en collaboration avec S.Rahman et J.G.Grasnrtom Ibn Sina's approach to equality and unity Arabic Sciences and Philosophy, Cambridge University Press, Vol. 24, pp. 297-307 2014

Aristotle did not develop the quantification of the predicate, but, as shown in a recent paper by Hasnawi, Ibn Sīnā did. In fact, assuming the Aristotelian subject-predicate structure, Ibn Sīnā qualifies those propositions that carry a quantified predicate as deviating (muḥarrafa) propositions. A consequence of Ibn Sīnā’s approach is that the second quantification is absorbed by the predicate term. The clear differentiation between a quantified subject, that settles the domain of quantification, and a predicative part, that builds a proposition over this domain, corresponds structurally to the distinction, made in constructive type theory, between the type of sets and the type of propositions. Neither did Aristotle combine his logical analysis of quantification with his ontological theory of relations or equality. But Ibn Sīnā makes use of syllogisms that require a logic of equality, and considered cases where quantification combines via equality with singular terms. Moreover these reflections provide the basis for his theory of numbers that is based on the interplay between the One and the Many. If we combine Ibn Sīnā’s metaphysical theory of equality with his work on the quantification of the predicate, a logic of equality comes out naturally. Indeed, the interaction between quantification of the predicate and equality can be applied to Ibn Sīnā’s own examples of syllogisms involving these notions. By using the formal instruments provided Martin-Löf's constructive type theory, the present paper establishes links between Ibn Sīnā’s metaphysics and his logical work: links that have been discussed in relation to other topics by Thom and Street. Ibn Sīnā did not develop a logic of identity, but he did develop the conceptual means to do so.

en collaboration avec G.Mompean et T.Zambrano Development of secondary flows in viscoelastic curved ducts and the influence of outlet region C. R. Mecanique, Vol. 342, pp. 478-484 2014

This paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan–Thien–Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150) and for three Deborah numbers (0.1,0.2,0.3). The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region.

en collaboration avec Honoré Gnanga, Zita H. Moussambi Membetsi, Roger Ondo Ndong, Hugues M. Omanda CFD of a Cubic Eddy-Viscosity Turbulence Model in the Square Duct International Journal of Dynamics of Fluids, Vol. 10, No. 1, pp. 21-35 2014

The aim of this work is to predict numerically the turbulent flow through a straight square duct. The numerical simulations using Reynolds Averaged Navier-Stokes equations with a cubic eddy-viscosity turbulence model. This model has been devised by Craft, Launder and Suga (1996). In order to handle wall proximity effects, damping functions are introduced by H. Gnanga (2008). Using a priori procedure, we show the capacity of this model to predict such flows. The Reynolds number of 4600 is based on the bulk velocity and hydraulic diameter of the duct. A grid refinement study is carried out using 61×61grid points, regularly spaced in the cross-section and 11 grid points in the streamwise direction. The mean flow field and the turbulent statistics are compared with existing numerical and experimental data for square and rectangular duct flow. The model performance is shown to be satisfactory. In particular, the mean secondary velocity vectors and streamwise vorticity are well predicted.

en collaboration avec Honoré Gnanga, Zita H. Moussambi Membetsi, Roger Ondo Ndong, Hugues M. Omanda Predictive Capabilities of Cubic Turbulence Model in the Square Duct International Journal of Electrical Engineering, Vol. 7, No. 2, pp. 185-195. 2014

The aim of this work is to predict numerically the turbulent flow through a straight square duct. The numerical simulations using Reynolds Averaged Navier-Stokes equations with a cubic eddy-viscosity turbulence model. This model has been devised by Craft, Launder and Suga (1996). The paper deals with a priori evaluation and improvement of the Explicit Algebraic Renolds Stress model (EARSM) in order to assess its predictive capabilities in the simulation of a fully turbulent flow through a straight square duct. In order to handle wall proximity effects, damping functions are introduced. The comparison of the numerical results with available DNS shows good agreements.

Local existence and uniqueness of solutions for non stationary compressible viscoelastic fluid of Oldroyd type IJOPCM, Vol. 6, No. 1, pp. 12-30. 2013

This work is devoted to the study of a compressible viscoelastic fluids satisfying the Oldroyd-B model in a regular bounded domain. We prove the local existence of solutions and uniqueness of flows by a classical fi xed point argument.

en collaboration avec S.Rahman Quantification, unité et identité dans la philosophie d'Ibn Sina La périodisation en histoire des sciences et de la philosophie: la fin d'un mythe, éd. Hassan Tahiri, pp.51-61 2013

Nous allons montrer que l'étude d'Ibn Sina sur l'interaction entre identité et la quantification du sujet et du prédicat peut être exprimée dans un cadre formel moderne à l'aide de la notion de quantification restreinte; Ibn Sina étudie la constitution des classes d'équivalences.

en collaboration avec G.Mompean et T.Zambrano Numerical study of a viscoelastic fluid in the output region of curved duct using a finite volume method AIP Conference Proceedings, Vol. 1558, pp. 1414-1416. 2013

A Finite volume method using generalized orthogonal coordinates is presented and applied to solve viscoelastic flows in a curved duct. The influence of the length of the output region of the duct, on the vortex development, is analyzed for different Dean and Deborah numbers. In this work it is showed the evolution of the Dean four-cell vortex pattern for the exit part of the curved duct.

en collaboration avec S.Rahman et J.G.Grasnrtom Egalité et Quantification des prédicats Al-Mukhatabat. Trilingual Journal for Logic, Epistemology and Analytic Philosophy, Vol. 8 , pp. 102-111, 2013

Aristote n’a pas développé une théorie de la quantification de prédicat, mais une étude récente de Hasnawi a montré qu’Ibn Sīnā l’a consacré une étude rigoureuse. En supposant la structure aristotélicienne sujet-prédicat, Ibn Sīnā qualifie les propositions, qui portent un prédicat quantifié, comme étant une proposition déviante (muḥarrafah محرفة). Une conséquence de cette approche avicennienne est que la seconde quantification est absorbée par le prédicat. La distinction claire entre un sujet quantifié, qui se trouve dans le domaine de la quantification, et une partie prédicative, qui construit une proposition sur ce domaine, correspond structurellement à la distinction, faite dans la théorie constructive des types, entre le type des ensembles et le type de propositions

en collaboration avec C.Guillopé et R.Talhouk Existence result for flows of slightly compressible viscoelastic fluid in a bounded domain with corners Analysis and Applications (AA), Vol. 10, No. 4, pp. 381-411 2012

Steady flows of slightly compressible viscoelastic fluids of Oldroyd's type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces , where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇φ.

en collaboration avec G.Mompean et T.Zambrano Etude numérique de l'effet de la portance inverse pour un fluide de Bingham autour d'un obstacle article no. 715, Actes du XXème Congrès Français de Mécanique, Presses universitaires de Franche-Comté (Presses-ufc) 2011

Ce travail porte sur la simulation numérique d'un écoulement de fluide non-Newtonien (Bingham) autour d'un obstacle en forme de profil hydrodynamique. La méthode des volumes finis avec un maillage orthogonale généralisée est utilisée. Les résultats du calcul montrent une portance inverse pour l'écoulement du fluide de Bingham en régime laminaire. Ceci est en accord avec des résultats expérimentaux concernant la portance inverse obtenus par B. Dollet et al. (Physical Review Letters, 2005) pour une solution mousseuse.

en collaboration avec G.Mompean et T.Zambrano Simulation numérique des écoulements newtonien et viscoélastique dans une conduite courbe de 180 degrés avec section carrée article no. 625, Actes du XXème Congrès Français de Mécanique, Presses universitaires de Franche-Comté (Presses-ufc) 2011

Ce travail présente les résultats numériques et une analyse des fluides Newtonien et viscoélastique du type Phan-Thien-Tanner (PTT), dans une conduite courbe de 180° avec section carrée. Les équations de Navier Stokes sont écrites en coordonnées orthogonales généralisées, et résolues en utilisant la méthode des volumes finis. On montre les résultats numériques pour nombres de Dean (125, 137, 150), ainsi que les profils de vitesses, lignes de courant, vortex dans la zone courbée et la région de sortie. Une étude sur influence de la longueur dans la zone de sortie est réalisée.

Existence results for flows of fluid in a singular bounded domain CHAOS 2010, 3rd Chaotic Modeling and Simulation International Conference, Greece, pp. 1-14. 2010

Steady flows of slightly compressible viscoelastic fluid of Oldroyd type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces k Vξ , where the index ξ characterizes the power growth of the solution near the angular point.

Study of a Perturbed Transport Problem in a Bounded Domain With a Convex Angle Int. J. Open Problems Compt. Math., Vol. 3, No. 4, pp. 497-509. 2010

We consider a perturbed transport problem in a domain having an isolated corner point. We prove the existence and the uniqueness of the solution, for small data in weighted Sobolev spaces V^{k;2}_\xi , where the index  characterizes the power growth of the solution near the angular point.

en collaboration avec C.Guillopé et R.Talhouk Regular global solution for small initial data and incompressible limit for weakly compressible viscoelastic fluids flows Discrete and Continuous Dynamical Systems - Series B (DCDS-B), Vol.14, No. 3, pp. 1001-1028. 2010

We consider compressible viscoelastic fluids satisfying the Oldroyd constitutive law. We prove the local existence (and uniqueness) of flows by a classical fixed point argument. We also prove some global properties of the solutions. In particular, we obtain some a priori estimates which are uniform in the Mach number and prove global existence of weakly compressible fluids flows. We show that weakly compressible flows with well-prepared initial data converge to incompressible ones when the Mach number converges to zero.

Flows of slightly compressible fluids viscoelastic through a regular bounded domain with inflow-outflow boundary conditions Communications on Pure and Applied Analysis (CPAA), Vol.9, No. 3, pp. 625-642. 2010

We study steady isothermal motions of a nonlinear weakly compressible viscoelastic fluids of Oldroyd type in a bounded domain \Omega\subset\mathbb{R}^2, with given non-zero velocities on the boundary of \Omega. We suppose that the pressure p and the extra-stress tensor \tau are prescribed on the part of the boundary corresponding to entering velocities. A uniqueness and existence result for the solution (\mathbf u,p,\tau) is established in W^{2,q}(\Omega)\times W^{1,q}(\Omega)\times W^{1,q}(\Omega) with 2 < q < 3. The proof follows from an analysis of a linearized problem. The fixed point theorem is used to establish the existence of a solution. The solutions of two transport equations for p and \tau are obtained by integration along the streamlines.

Écoulements de fluides viscoélastiques dans des domaines singuliers: Étude mathématique Editions universitaires europeennes EUE, 2010 - 212 pages 2010

Ce travail est consacre a l'analyse mathematique de trois problemes d'ecoulements de fluides viscoelastiques de type Oldroyd. Tout d'abord, nous etudions des ecoulements stationnaires faiblement compressibles dans un domaine singulier avec des conditions au bord de type "rentrante-sortante." Nous etudions aussi le probleme d'ecoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une methode de point fixe (premier et deuxieme problemes) et une decomposition de Helmoltz (deuxieme probleme), nous montrons des resultats d'existence et d'unicite des solutions. Nous etudions egalement le cas d'un ecoulement non stationnaire. Nous montrons un resultat d'existence locale et un resultat d'existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous demontrons aussi la convergence du modele d'ecoulement viscoelastique compressible a faible nombre de Mach vers le modele incompressible lorsque les donnees initiales sont "bien preparees."

Li Shanlan: Une histoire d'innovation chinoise en mathématiques Editions Universitaires Europeennes, 60 pages 2010

Dans ce livre, nous étudions une histoire d'innovation chinoise d'un mathématicien du XIXème siècle. C'est Li Shanlan : traducteur des neuf derniers livres des Éléments et créateur des fameux formules combinatoires, notamment la formule de "Li Renshu". Nous essayons, dans ce travail, de mettre en lumière son stratégie intelligente . Li Shanlan n'a pas jeté le patrimoine des mathématiques chinoises et n'a pas vécu dans le passé en ignorant les progrès qui ont été faits dans l'Ouest.

Languages
Arabic

Native or bilingual proficiency

English

Limited working proficiency

French

Full professional proficiency