Mikelic Andro's  Home Page


Nom et prénom (Name) : MikelićAndro                          

Lieu et date de naissance (Place and date of birth) :
Split, Dalmatie, CROATIE, le 2 octobre 1956
(Split, Dalmatia, CROATIA, October 2, 1956).

Situation:
Professeur  à l'Université Lyon 1, Faculté des Sciences et Technologie,   Département de Mathématiques
(Professor at the Université Lyon 1,  Department of Mathematics).

CV:
en anglais (in English).


( en francais (in French).


 

Activités actuelles de recherche (Current research activities)

Théorie de l'homogénéisation et applications

(Homogenization theory and applications)

Étude asymptotique approfondie des équations de Navier-Stokes et Euler en milieux poreux et des EDP des écoulements en milieux poreux aléatoires (Detailed asymptotic study of the Navier-Stokes and Euler equations in porous media and of the flows equations in random porous media). Détermination des loi constitutives sur les interfaces milieu poreux / fluide libre (Determination of the constutive relations at the interfaces between a porous medium and a free flow).  Homogénéisation stochastique (Stochastic homogenization). Les applications en environnement et en physiologie mathématique (Applications to environmental problems and to the mathematical physiology)

AMS Subject Classification Index 35B, 35Q, 76D, 76S

Mécanique des fluides, turbulence (Fluid mechanics, turbulence) :

Hydrodynamique statistique (statistical hydrodynamics).
AMS Subject Classification Index 35Q, 76D, 76S

Adresse (Address) :
Institut Camille Jordan, Département de Mathématiques,
Université Claude Bernard  Lyon 1, Campus La Doua,
Bât. Braconnier, Bureau 119, 43, Bd du 11 novembre 1918,
69622 Villeurbanne  Cedex, FRANCE
Téléphone : (33) 0426234548
Télécopie (fax): (33) 0956109885
e-mail: Andro.Mikelic@univ-lyon1.fr


Quelques articles recents
(Some recent articles)

 

 

Articles publiés en 2005 :

 [1] S. Čanić,  A. Mikelić , J. Tambača: A Two-Dimensional Effective Model Describing Fluid-Structure Interaction in Blood Flow: Analysis, Numerical Simulation and Experimental Validation,  Comptes Rendus   Mécanique, Vol. 333 (2005), p. 867-883.

[2]  J. Tambača, S. Čanić, A. Mikelić: Effective model of the fluid flow through elastic tube with variable radius,  Grazer Math. Ber.,  Bericht nr. 348 (2005), pp. 91-112.

[3] S. Čanić, D. Lamponi, A. Mikelić , J. Tambača: Self-Consistent Effective Equations Modeling Blood Flow in Medium-to-Large Compliant Arteries, SIAM Multiscale Model. Simul.,   Vol. 3 (2005), p. 559-596.

 

Articles publiés en 2006 :

 

 

[4] A. Mikelić, V. Devigne, C.J. van Duijn: Rigorous upscaling of the reactive flow through a pore, under dominant Peclet and Damkohler numbers, SIAM J. Math. Anal.,  Vol.  38, Issue 4 (2006), p. 1262-1287. Taylordispersion

 

[5] S. Čanić, J. Tambača, G. Guidoboni, A. Mikelić, C. J. Hartley,  D. Rosenstrauch: Modeling Viscoelastic Behavior of Arterial Walls and their Interaction with Pulsatile Blood Flow,  SIAM J. Appl. Maths, Vol. 67, no. 1 (2006), p.164-193.

[6] A. Mikelić , M. Primicerio: Modelling and homogenizing a problem of sorption/desorption in porous media,  M3AS : Math. Models   Methods Appl. Sci.,  Vol. 16, no. 11 (2006), p. 1751-1782.

[7] M. Cabrera, T. Clopeau, A. Mikelić,  J. Pousin: Approximation de la lubrification pour l'étalement de gouttes en présence d'évaporation, application aux biopuces,  La houille blanche,  No 2 (2006), p. 93-99.

[8]  S. Čanić, C.J. Hartley, D. Rosenstrauch, J. Tambača, G. Guidoboni, A. Mikelić: Blood Flow in Compliant Arteries: An Effective Viscoelastic Reduced Model, Numerics and Experimental Validation,  Annals of Biomedical Engineering,  Vol.  34 (2006), pp. 575 - 592

[9]  N. Neuss, M. Neuss-Radu, A. Mikelić : Effective Laws for the Poisson Equation on Domains with Curved Oscillating Boundaries,    Appl. Anal. , Vol.  85 (2006), no. 5, p. 479--502.

[10] A. Mikelić , M. Primicerio: A diffusion-consumption problem for oxygen in a living tissue perfused by capillaries,  Nonlinear differ. equ. appl. (NoDEA) , Vol. 13, no. 3 (2006), pp.  349-367.

[11] M. Cabrera, T. Clopeau, A. Mikelić,  J. Pousin: Viscous drops spreading with evaporation and applications to DNA biochips,  Progress in Industrial Mathematics at ECMI 2004, Series: Mathematics in Industry, Vol. 8, Di Bucchianico,Alessandro; Mattheij, Robert M.M.; Peletier, Marc Adriaan (Eds.), Springer 2006, p. 320-325.

 

 

 Articles publiés en 2007 :

 

[12] A. Mikelić , C. Rosier  : Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore,   Ann Univ Ferrara,  Vol. 53 (2007), p. 333-359.

[13]  M. Belhadj, E. Cancès, J.F. Gerbeau, A. Mikelić: Homogenization approach to filtration through a fibrous medium, Networks and Heterogeneous Media,  Vol. 2 (2007), p. 529 - 550.

[14] A. Mikelić, G. Guidoboni, S. Čanić : Fluid-Structure Interaction in a Pre-Stressed Tube with Thick Elastic Walls I: The Stationary Stokes Problem,  Networks and Heterogeneous Media,  Vol. 2 (2007), p. 397 - 423.

[15] A. Mikelić : On the justification of the Reynolds equation, describing isentropic compressible flows through a tiny pore, Ann Univ Ferrara, Vol. 53 (2007), p. 95-106.

[16] A. Mikelić, S. Čanić: Homogenization closure for a two-dimensional effective model describing fluid- structure interaction in blood flow, in   "Math Everywhere";  Deterministic and Stochastic Modelling in Biomedicine, economics and Industry,  Dedicated to the 60th Birthday of Vincenzo Capasso, G. Aletti, M. Burger, A. Micheletti, D. Morale (ed.) , Springer Heidelberg,  2007, p. 193-205., 2008.

 

 Articles publiés en 2008 :

 

 [17] O. Iliev, A. Mikelić, P. Popov : On upscaling certain flows in deformable porous media, Multiscale Model. Simul.,  Vol. 7 (2008), no. 1, p. 93-123.

 [18] A. Farina, A. Fasano, A. Mikelić : On the equations governing the flow of mechanically incompressible, but thermally expansible, viscous fluids,   M3AS : Math. Models  Methods Appl. Sci.,  Vol. 18 (2008), no. 6, p. 813-858.

[19]  C.J. van Duijn,  A. Mikelić , I.S. Pop, C. Rosier: Effective Dispersion Equations For Reactive Flows  With Dominant Peclet and Damkohler Numbers,     Advances in Chemical Engineering,  

Guy B. Marin, David West and Gregory S. Yablonsky, editors; Vol 34, 2008, p. 1-45.

 

  [20] A. Mikelić, J. Bruining: Analysis of model equations for stress-enhanced diffusion in coal layers. Part I: Existence of a weak solution.   SIAM Journal of Mathematical Analysis , Volume 40, Issue 4, pp. 1671-1691 (2008).

 

 

 [21] C. Choquet, A. Mikelić : Laplace transform approach to the rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore,   Applicable  Analysis,   Vol. 87, No. 12, December 2008, 1373--1395..

 

 Articles publiés en 2009:

 

 

  [22] A. Mikelić: An existence result for the equations describing a gas-liquid two-phase flow.   Comptes rendus Mécanique , Volume 337, Issue 4, 2009, p. 226-232.

 

[23]  W. Jäger, A. Mikelić, M. Neuss-Radu: Analysis of Differential Equations Modelling the

Reactive Flow through a Deformable System of  Cells,   Arch. Ration. Mech. Anal. , Vol. 192, no. 2 (2009), p. 331-374.

 

  [24] C. Choquet, A. Mikelić: Rigorous upscaling of the reactive flow with finite kinetics and under dominant Peclet number.   Continuum Mechanics and Thermodynamics , Volume 21, 2009, p. 125-140.

 

 

  [25] W. Jäger, A. Mikelić: Modeling effective interface laws for transport phenomena between an unconfined fluid and a porous medium using homogenization   Transport in Porous Media , Volume 78, Number 3, 2009, p. 489-508.

 

 

  [26] A. Mikelić: Rough boundaries and wall laws,   dans Qualitative properties of solutions to partial differential equations, Lecture notes of Necas Center for mathematical modeling, edited by E. Feireisl, P. Kaplicky and J. Malek, , Volume 5, Matfyzpress, Publishing House of the Faculty of Mathematics and Physics Charles University in Prague, Prague, 2009, p. 103-134.

 

 Articles publiés en 2010:

 

[27]   M. Balhoff, A. Mikelić, M.F. Wheeler: Polynomial filtration laws for low Reynolds number flows through porous media,   Transport in Porous Media , Vol. 81, No. 1 (2010), p. 35-60.

 

[28]   G. Allaire, R. Brizzi, A. Mikelić, A. Piatnitski: Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media,   Chemical Engineering Science, Vol. 65 (2010),p. 2292–2300.

 

[29]   G. Allaire, A. Mikelić, A. Piatnitski: Homogenization approach to the dispersion theory for reactive transport through porous media,   SIAM J. Math. Anal., Volume 42, Issue 1, pp. 125-144 (2010).

 

[30]   A. Mikelić, : A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure,   J. Differential Equations, Vol. 248 (2010), pp. 1561-1577.

 

[31]  T. Clopeau, A. Farina, A. Fasano, A. Mikelić: Asymptotic equations for the terminal phase of glass fiber drawing and their analysis, Nonlinear Analysis TMA: Real World Applications, Vol. 11 (2010), p. 4533-4545, , dx.doi.org/10.1016/j.nonrwa. 2008.09.017.

 

[32]   G. Allaire, A. Mikelić, A. Piatnitski: Homogenization of the linearized ionic transport equations in rigid periodic porous media,   J. Math. Phys. 51, 123103 (2010); doi:10.1063/1.35215552010.2010.

 

 Articles publiés en 2011:

 

[33]  A. Farina, A. Fasano,   A. Mikelić : Non-Isothermal Flow of Molten Glass: Mathematical Challenges and Industrial Questions, chapter in Mathematical Models in the Manufacturing of Glass, editor A. Fasano, C.I.M.E. Summer School, Montecatini Terme, Italy 2008, Lecture Notes in Mathematics, 2011,   Volume 2010/2011, 173-224.

 

[34]   S. Čanić, A. Mikelić, T.-B. Kim, G. Guidoboni: Existence of a unique solution to a nonlinear moving-boundary problem of mixed type arising in modeling blood flow,   IMA Volume on Nonlinear Conservation Laws and Applications, edited by Alberto Bressan, Gui-Qiang Chen, Marta Lewicka, and Dehua Wang, Vol 153 (2011), 235 -256.

 

[35]   E. Feireisl, Ph. Laurençot, A. Mikelić: Global-in-time solutions for the isothermal Matovich-Pearson equations,   Nonlinearity, Vol. 24 (2011), p. 277 -292. (doi: 10.1088/0951-7715/24/1/014).

[36]   O. Boiarkine, D. Kuzmin, S. Čanić, G. Guidoboni, A. Mikelić: A positivity-preserving ALE finite element scheme for convection-diffusion equations in moving domains,  Journal of Computational Physics, Vol. 230 (2011) 2896 – 2914.

 

[37]   A. Mikelić, C.J. van Duijn: Rigorous derivation of a hyperbolic model for Taylor dispersion,   M3AS: Mathematical Models and Methods in Applied Sciences, Vol. 21, No. 5 (2011), p. 1095-1120.

 

[38]  W. Jäger, A. Mikelić, M. Neuss-Radu: Homogenization-limit of a model system for interaction of flow, chemical reactions and mechanics in cell tissues,   SIAM J. Math. Anal., Vol. 43, No. 3 (2011), p. 1390--1435. ,

 Articles publiés en 2012:

 

[39]   A. Marciniak-Czochra, A. Mikelić: Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization,   SIAM: Multiscale modeling and simulation, Vol. 10, No. 2 (2012), p. 285-305.

[40]   A. Mikelić, M. F. Wheeler: On the interface law between a deformable porous medium containing a viscous fluid and an elastic body,   M3AS: Mathematical Models and Methods in Applied Sciences, Vol. 22, No. 11 (2012), 1240031 (32 pages). doi: 10.1142/S0218202512500315.

[41]   A. Mikelić, M. F. Wheeler: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system,   Journal of Mathematical Physics, Vol. 53, no. 12 (2012), 123702 (15 pages); doi: 10.1063/1.4764887.

 

 Articles publiés en 2013:

 

[42]   G. Allaire, J.-F. Dufrêche, A. Mikelić , A. Piatnitski : Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media,   Nonlinearity, Vol. 26, p. 881--910, 2013.

 

[43]   A. Mikelić, M. F. Wheeler: Convergence of iterative coupling for coupled flow and geomechanics,   Comput Geosci, Vol. 17 (2013), no. 3, p. 455-462. DOI 10.1007/s10596-012-9318-y.

 

[44]   G. Allaire, R. Brizzi, J.-F. Dufrêche, A. Mikelić , A. Piatnitski : Ion transport in porous media: derivation of the macroscopic equations using up-scaling and properties of the effective coefficients,   Comput Geosci, Vol. 17 (2013), no. 3, p. 479-496, DOI 10.1007/s10596-013-9342-6.

 

[45]   A. Mikelić , S. Necasova, M. Neuss-Radu : Effective slip law for general viscous flows over an oscillating surface,   Mathematical Methods in Applied Sciences M2AS, Vol. 36 (2013), p. 2086-2100, DOI 10.1002/mma.2923.

 

[46]   T. Carraro, C. Goll, A. Marciniak-Czochra, A. Mikelić : Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations,   Journal of Fluid Mechanics, Vol. 732 (2013), p. 510-536, doi: 10.1017/jfm.2013.416.

 

 Articles publiés en 2014:

 

[47]   A.Farina, J. Bodin, T. Clopeau, A. Fasano, L. Meacci, A. Mikelić : Isothermal Water Flows in Low Porosity Porous Media in Presence of Vapor--Liquid Phase Change,   Nonlinear Analysis: Real World Applications, Vol. 15 (2014), p. 306-325. doi:10.1016/j.nonrwa.2011.11.021.

 

[48]   A. Marciniak-Czochra, A. Mikelić : A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium,   Discrete and Continuous Dynamical Systems - Series S (DCDS-S), Vol. 7 (2014), p. 1065-1077.

 

[49]   A. Mikelić , B. Wang, M. F. Wheeler : Numerical convergence study of iterative coupling for coupled flow and geomechanics,   Comput Geosci, Vol. 18 (2014), p. 325–341.

 

[50]   G. Allaire, R. Brizzi, J. F. Dufrêche, A. Mikelić , A. Piatnitski : Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling,   Physica D: Nonlinear Phenomena, Vol. 282 (2014), p. 39-60.

 

 Articles publiés en 2015:

 

[51]   A. Marciniak-Czochra, A. Mikelić : A Rigorous Derivation of the Equations for the Clamped Biot-Kirchhoff-Love Poroelastic plate,   Arch. Rational Mech. Anal., 215 (2015), 1035–1062.

 

[52]   T. Carraro, C. Goll, A. Marciniak-Czochra, A. Mikelić : Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization,   Computer Methods in Applied Mechanics and Engineering, 292 (2015) 195-220.

[53]   A. Mikelić, M. F. Wheeler, T. Wick : A Phase-Field Method For Propagating Fluid-Filled Fractures Coupled To A Surrounding Porous Medium,   SIAM Multiscale Model. Simul., Vol. 13 (2015), no. 1, 367–398.

[54]   A. Mikelić, M. F. Wheeler, T. Wick : A quasistatic phase field approach to fluid filled fractures,   Nonlinearity, 28 (2015), 1371-1399.

 

[55]   A. Mikelić, M. F. Wheeler, T. Wick : Phase-field modeling of a fluid-driven fracture in a poroelastic medium,   Computational Geosciences, Vol. 19(2015), no. 6, 1171-1195.

 

[56]   N. Grosjean, D. Iliev, O. Iliev, R. Kirsch, Z. Lakdawala, M. Lance, M. Michard, A. Mikelić : Experimental and numerical study of the interaction between fluid flow and filtering media on the macroscopic scale,  Separation and Purification Technology, Vol. 156, Part 1 (2015), p. 22-27.

 

 

 Articles publiés en 2016:

 

 

[57]   A. Mikelić, J. Tambača : Derivation of a poroelastic flexural shell model,   SIAM Multiscale Model. Simul., 14-1 (2016), pp. 364-397.

 

Les articles acceptés pour publication

 

 

[58]   S. Lee, A. Mikelić, M. F. Wheeler, T. Wick : Phase-field modeling of proppant-filled fractures in a poroelastic medium,   accepté pour publication dans Comput. Methods Appl. Mech. Engrg., 2016. doi: 10.1016/j.cma.2016.02.008.

 

 

[59]   G. Allaire, O. Bernard, J.-F. Dufrêche, A. Mikelić: Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling,   hal-01215457, accepté pour publication dans Comp. Appl. Math., 2016, doi:10.1007/s40314-016-0321-0.

 

 

[60]   A. Marciniak-Czochra, A. Mikelić: Shadow limits via the renormalization group method and the center manifold method,   accepté pour publication dans Vietnam Journal of Mathematics, Special Issue dedicated to Willi Jaeger, 2016, DOI: 10.1007/s10013-016-0199-6.

 

Quelques prépublications


(Some preprints)

 

[61]   A. Mikelić, M. F. Wheeler, T. Wick : A phase field approach to the fluid filled fracture surrounded by a poroelastic medium,   ICES Report 14-18, July 29, 2014.