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30 Habbaltheorem 1 There exists a Nash equilibrium, i.e. a pair of strategies (µ ⋆ , k ⋆ ) ∈ S 1 × S 2such thatµ ⋆ solves minµ∈S 1j 1 (µ, k ⋆ ) (5)k ⋆ solvesmin j 2 (µ ⋆ , k) (6)k∈S 2For numerical experiments, we considered the minimax (or duel) problemj 2 (µ; k) = −j 1 (µ; k) = −L 1 (ρ; p)which models a game where the first player wants to minimize the pressure drop, while onthe contrary the second player wants to maximize it (or, equivalently, wants to minimizethe drainage of the network).Such a game is also known as a zero-sum game.4. A Computational experimentThe domain Ω is a rectangle. The upper side is Γ V , and the lower is Γ T . Maximumallowed volume fractions are 40% for (TAF) and10% for (aAF).The Nash overall loop converged in three iterations ; each partial optimization took aroundthirty iterations (and two hundred FEM runs) to converge.Converging strategies are presented in figures 1-2-3.In figure-1, the first player (TAF), having the information that the second player (aAF)has played a uniform strategy, plays its optimal strategy which consists, as could be expected,in a single channel, preserving the volume constraint, located at the central lineof the rectangle (thanks to the symmetry of the problem). At its turn, the second player,informed that the first player has played a uniform strategy, simply puts as much antiangiogenicas possible around the tumor Γ T . Quite unexpectedly, (aAF) does not play auniform horizontal density, but creates a small excavation.Then, at the second Nash iteration, the first player knows that the second one has cutoff the way to the tumor, so it starts to develop alternative channels. At the same time,the second player knows now that the TAF has a strong presence within the excavation,which is then filled as shown in figure-2.The final iteration, yielding a numerical Nash equilibrium is shown in figure-3. The resultingporosity distribution in figure-3 does not exhibit any arterial-tree branching structure,but only multiple channels.Multiple channels seem to be the best response of the activators to optimally distributedinhibitors.TAMTAM –Tunis– 2005
A topology Nash game 31Figure 1. First Nash loop iteration.Left: density µ of the TAF. Right: density k of the aAF.5. ReferencesJ.S. Gibson A.F. Jones, H.M. Byrne and J.W. Dold. A mathematical model of the stress inducedduring avascular tumour growth. J. Math. Biol., 40(6):473–499, 2000.T. Borrvall and J. Petersson. Topology optimization using regularized intermediate density control.Comput. Methods Appl. Mech. Eng., 190(37-38):4911–4928, 2001.M.A.J. Chaplain and B.D. Sleeman. Modelling the growth of solid tumours and incorporating amethod for their classification using nonlinear elasticity theory. J. Math. Biol., 31(5):431–473,1993.Araujo R.P. McElwain D.L.S. New insights into vascular collapse and growth dynamics in solidtumors. Journal of Theoretical Biology, 228:335–346, 2004.M. Sarntinoranont F. Rooney M. Ferrari. Interstitial stress and fluid pressure within a growingtumor. Annals of Biomedical Engineering, 31:327–335, 2003.Y.C. Fung. Biomechanics. Mechanical properties of living tissues. 2nd ed. Springer-Verlag NewYork Berlin Heidelberg., 1993.T. Roose P.A. Netti L.L. Munn Y. Boucher R.K. Jain. Solid stress generated by spheroid growthestimated using a linear poroelasticity model. Microvascular Research, 66:204–212, 2003.Schreiner W. Buxbaum P.F. Computer-optimization of vascular trees. IEEE Transactions onBiomedical Engineering, 40(5):482–491, 1993.Helmlinger G. Netti P.A. Lichtenbeld H.C. Melder R.J. Jain R.K. Solid stress inhibits the growthof multicellular tumor spheroids. Nature Biotechnology, 15(8):778–783, 1997.T. Rozvany G. I. N. Zhou M. Birker. Generalized shape optimization without homogenization.Struct Optim., 4:250–254, 1992.TAMTAM –Tunis– 2005
Page 5 and 6: PréfaceOrganiser la seconde éditi
Page 7: Comité d’organisationMohamed Abd
Page 11 and 12: SOMMAIRE / CONTENTSI Conférences I
Page 13 and 14: Equilibre dans un système dynamiqu
Page 15 and 16: Arlequin method: Practical impacts
Page 17 and 18: Application de la méthode de Gauss
Page 19: Conférences InvitéesInvited Prese
Page 22 and 23: 4 Amara et al.1. IntroductionWe are
Page 24 and 25: 6 Amara et al.2.2. The nonlinear Na
Page 26 and 27: 8 Amara et al.4. Numerical resultsW
Page 28 and 29: 10 Auger et al.1. Introduction :Dan
Page 30 and 31: 12 Auger et al.La condition de stab
Page 32 and 33: 14 Auger et al.3.1. Taux de migrati
Page 34 and 35: 16 Auger et al.L’équilibre rapid
Page 36 and 37: 18 Auger et al.[7] BRAVO DE LA PARR
Page 38 and 39: Quelques aspects mathématiques etn
Page 40 and 41: 22 El Alaoui Talibi M.- Modèle d
Page 42 and 43: 24 El Alaoui Talibi M.[3] M. Chamba
Page 44 and 45: 26 Habbal1. IntroductionAngiogenesi
Page 46 and 47: 28 HabbalThe pressure drop denoted
Page 50 and 51: 32 HabbalFigure 2. Second Nash loop
Page 52 and 53: 34 Hauray et al.1. IntroductionWe a
Page 54 and 55: 36 Hauray et al.minimal time interv
Page 56 and 57: 38 Hauray et al.From this last theo
Page 58 and 59: Approximation de l’opérateur d
Page 60 and 61: 42 LemrabetLorsque δ → 0, l’é
Page 62 and 63: 44 Lemrabetavec[∆ ∗ (δ)c = [I
Page 64 and 65: 46 Lemrabet6. Bibliographie[1] N. B
Page 66 and 67: 48 Jaafar-Belaid et al.1. Introduct
Page 68 and 69: 50 Jaafar-Belaid et al.where f(ρ)
Page 70 and 71: 52 Jaafar-Belaid et al.202040406060
Page 73: IIContrôleControl55
Page 76 and 77: 58 Arfaoui1. IntroductionCe travail
Page 78 and 79: 60 ArfaouiLe système adjoint assoc
Page 80 and 81: 62 Arfaoui[3] H. ARFAOUI , « Comma
Page 82 and 83: 64 Benzekri et al.1. Global control
Page 84 and 85: 66 Benzekri et al.ẏ = ∂H∂x =
Page 86 and 87: 0 1 2 3 4 5 668 Benzekri et al.32.5
Page 88 and 89: 70 Akian et al.1. IntroductionWe co
Page 90 and 91: 72 Akian et al.We prove that v t+δ
Page 92 and 93: .74 Akian et al.0.0−1.0Exact solu
Page 94 and 95: 76 Bokanowski et al.1. General fram
Page 96 and 97: 78 Bokanowski et al.One interesting
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80 Bokanowski et al.4. Numerical ex
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Sur les problèmes de contrôle opt
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84 Metouileur lorsque u est dans L
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86 MetouiThéorème 2 Soit ū ε le
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88 Metoui[5] L.S. HOU, S.S. RAVINDR
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Système d’information intégré
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Gestion et modélisation des ressou
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Random perturbations of reduced gra
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Global Optimization of Water Resour
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Global Optimization of Water Resour
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IVEquations DifférentiellesDiffere
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114 B. Abdelkader1. IntroductionTel
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116 B. AbdelkaderNotons que les con
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118 B. AbdelkaderAlors pour tout X
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120 Bouzahir1. IntroductionWe consi
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122 Bouzahirwhere the linear operat
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Goursat boundary value problem forh
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126 A. Guezane-Lakoud et al.3. Func
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128 A. Guezane-Lakoud et al.5. Exis
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ACP neuronale : application à l’
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132 Chitroubl’approximation de la
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134 Chitroubcompression égal à 3.
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136 Chitroub[4] J. P. Nougier, Mét
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138 Ferchichi et al.1. Introduction
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140 Ferchichi et al.soit T −1 = (
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142 Ferchichi et al.[4] G.I. BISCHI
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144 Hafidi1. IntroductionOn étudie
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146 Hafidia ) ∫ Ωpdx → +∞ qu
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148 HafidiLEMME 3.2. On a lim R(θ
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150 Lefebvre1. IntroductionSoit (X
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152 LefebvreOn peut aussi écrire q
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154 Lefebvre5. BibliographieD.R. Co
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156 Meskine1. IntroductionDans le p
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158 Meskinefaibles σ( ∏ L M ,
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160 Meskine[12] E. YA. KHRUSLOV, L.
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162 K. Saoudi1. IntroductionL’ét
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164 K. Saoudice qui montre que la s
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166 K. Saoudieton aboutit au résul
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168 K. Saoudietc 1 + c 2 = 1 ∫(u
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170 K. SaoudiRemarque 3.1. Du lemme
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172 K. Saoudiet∫v(t, x) dxΩest c
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VEstimation d’ErreursError Estima
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178 Achchab et al.1. IntroductionDu
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180 Achchab et al.such that}Xh 2 ={
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182 Achchab et al.[2] B.ACHCHAB, M.
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184 Alla et al.1. IntroductionLes e
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186 Alla et al.3. Position du probl
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IsoValue-0.00070533-0.000604452-0.0
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190 Achchab et al.1. IntroductionLe
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192 Achchab et al.où T hi/2 est le
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IsoValue0.000933570.002800710.00840
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196 El Dabaghi et al.1. Motivation
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198 El Dabaghi et al.0 ≤ λ i ≤
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200 El Dabaghi et al.Figure 4. Mail
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Residual error estimators for the t
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204 Kharrat et al.The step (3) need
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206 Kharrat et al.following estimat
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VIMécanique des FluidesFluid Mecha
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212 Abdelwahed et al.1. Introductio
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214 Abdelwahed et al.Ainsi, suivre
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216 Abdelwahed et al.Figure 3. Isov
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Procédure spectrale avec diagonali
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220 El Guarmah et al.où Ra et P r
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222 El Guarmah et al.M 10 20 25 35
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Simulation de l’onde de crue via
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226 El Dabaghi et al.de R 2 , de fr
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228 El Dabaghi et al.INRIA-MODULEFm
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INRIA-MODULEF230 El Dabaghi et al.I
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232 Amoura et al.1. IntroductionFor
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234 Amoura et al.where u = rot r ψ
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236 Amoura et al.CURRENT FUNCTION5
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238 Frih et al.1. IntroductionLa mo
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240 Frih et al.et dans la fracture,
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242 Frih et al.6. Bibliographie[1]
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244 Hasnaoui et al.1. IntroductionL
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246 Hasnaoui et al.On obtient alors
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248 Hasnaoui et al.5. Conclusion et
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250 Hernane-Boukari1. IntroductionW
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252 Hernane-Boukarianda 3 =−11 +
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254 Kloucha et al.1. Motivation et
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256 Kloucha et al.Si le domaine Λ
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INRIA-MODULEF0INRIA-MODULEF.250INRI
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Dimensions fractales : attracteurs
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262 Lamrini Uahabi et al.4. Attract
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264 Lamrini Uahabi et al.l 0 = λ
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266 Lamrini Uahabi et al.En conséq
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Numerical analysis for the problem
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270 El-Kyal et al.d(u) = 1 2(∇u +
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272 El-Kyal et al.Theorem 3.1 There
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274 Marchand et al.1. IntroductionD
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276 Marchand et al.On remarque en p
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278 Marchand et al.dans la formulat
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280 Mezali et al.1. Motivation et m
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282 Mezali et al.s’annulant sur c
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284 Mezali et al.Temps CPUTemps Ela
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R. Touihri & S. Ghnimi *Méthode de
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288 Touihri et al.Les équations go
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290 Touihri et al.Tol N It (Newt) t
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292 Touihri et al.5. Bibliographie[
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Décomposition de domaine pour un m
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DDM pour les fractures 297et−→
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DDM pour les fractures 299dont l’
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Arlequin method: Practical impacts
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Arlequin method 303of the Arlequin
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Arlequin method 3052.2. Penalized A
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Arlequin method 307refinements of t
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Reduction methods and uncertaintypr
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Reduction methods and uncertainty p
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Reduction methods and uncertainty p
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0.00e+00 1.00e−11 2.00e−11 3.00
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Homogénéisation d’un problème
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Problème de conduction-rayonnement
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Problème de conduction-rayonnement
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Equation d’Hamilton-Jacobi 3231.
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Equation d’Hamilton-Jacobi 325qui
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0Equation d’Hamilton-Jacobi 3272
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Détermination du nombre de région
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Simulation des courants de Foucault
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Une méthode d’accélération de
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Schéma SRNHS 3491. IntroductionUn
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Schéma SRNHS 3513. Application du
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Schéma SRNHS 3535. ConclusionLes r
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Smoothing and compressing surfaces
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Problème de convection en milieu p
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0
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Condensation de masse pour la méth
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Condensation de masse 367montre que
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Condensation de masse 369Le terme h
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Condensation de masse 371Aet Qile f
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VIIIModèles CinétiquesKinetic Mod
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376 Ben Abdallah et al.1. Introduct
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378 Ben Abdallah et al.where B ∓
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380 Ben Abdallah et al.ture that th
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382 Degond et al.1. IntroductionOn
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384 Degond et al.q φ s (x, t)/(|q|
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386 Degond et al.Enfin l’opérate
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Les métaheuristiques : application
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Les métaheuristiques 391simulé fu
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Les métaheuristiques 393Fig. 1 Dia
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Les métaheuristiques 395Fig.4 : R
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Prices after capacity addition in m
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Multi-user elastic demand communica
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Shape optimization 4051. Introducti
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Shape optimization 4072.1. Variatio
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Shape optimization 409(a)(b)(c)(d)F
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Problèmes d’optimisation en éco
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Assimilation de données pour l’e
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Écart à la Réciprocité et ident
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Identification de fissures planes 4
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Algorithme de Kohn et Vogelius 4331
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Algorithme de Kohn et Vogelius 435l
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Algorithme de Kohn et Vogelius 4375
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Résolution d’un problème de Cau
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Problème inverse géométrique 445
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Identification de fissures 4511. In
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−0.5 −0.4 −0.3 −0.2 −0.1
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Application de l’algorithme deNeu
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Complétion de données en élastic
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Complétion de données en élastic
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Analytic extensions on an annulus:a
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Analytic extensions on an annulus 4
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Analytic extensions on an annulus 4
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−1 −0.8 −0.6 −0.4 −0.2 0
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Cauchy problem for Laplace’s equa
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Modélisation asymptotique des onde
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Ondes de relief 479 uuuv 1 1 pu v
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Ondes de relief 481( )ˆeiZw( C e D
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Ondes de relief 4836. Bibliographie
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Régularisation pour l’aéroacous
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Miroir à retournement temporel 491
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Vibro-acoustique instationnaire 497
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Vibro-acoustique instationnaire 499
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Ondes dans les milieux poroélastiq
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The implicitly restarted Arnoldi me
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¨§¨ §IRAM method 509To overcome
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IRAM method 511The application of t
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XIIScience du VivantLife Science513
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516 Achchab1. IntroductionDans la m
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518 AchchabNous montrons dans le pa
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520 Achchab5. Bibliographie[1 ] AIE
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522 Derbel et al.1. IntroductionLa
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524 Derbel et al.On se propose de d
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A Stochastic partial differential e
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528 El Saadidiffusion process to a
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530 El Saadiwhere δ Xi(t) is the D
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532 El Saadi5. References[1] A. L.
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534 Ben Miled et al.1. Introduction
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536 Ben Miled et al.nature de l’e
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538 Ben Miled et al.Ensuite on étu
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Optimal spatial distribution of a b
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542 Mchich et al.at time t. The com
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544 Mchich et al.3∑where r = r i
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XIIIStructureStructure547
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550 Ayadi1. IntroductionConsider a
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552 AyadiFor all 0 ≤ p ≤ i, P p
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554 AyadiFigure 3. The curves above
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Analyse mathématique et numérique
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558 Chamekh et al.2. Modèle de tig
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560 Chamekh et al.Γ sr(s)r(σ)Figu
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Modélisation de l’effet dynamiqu
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564 RahmaniI 2 étant l’identité
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566 Rahmani• ( u 1δ1∫+ ,0u 1δ
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Résolution d’un systéme d’ela
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570 Saidoù u vérifie :n∑n∑j=1
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572 SaidEn effet :∣ u(y, s) 1+α
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Régularisation d’un problème d
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576 Achchab et al.On définit : F +
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578 Achchab et al.3. Estimation a p
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Modélisation d’un pieuR. Aboulai
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582 Aboulaich et al.Figure 1. Struc
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584 Aboulaich et al.5. Résultats n
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XIVThéorie des GraphesGraph Theory
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590 Hlaoui1. IntroductionMore and m
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592 Hlaoui3. The New Graph Represen
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594 Hlaoui1 1 2 3 4 1 1 3 411 421 4
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596 M. Nekri et al.1. IntroductionL
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598 M. Nekri et al.proposés. Ces m
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600 M. Nekri et al.cycle de longueu
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TAMTAM -Tunis- 2005 602
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El Guarmah, M., 218El Kacimi, A., 2
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