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).
( en francais (in French).
Publications:
en anglais (in English).
(
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
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,
[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, [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.
[58]
S. Lee, A. Mikelić, M. F. Wheeler, T. Wick
: Phase-field modeling of proppant-filled fractures in a poroelastic medium,
Comput. Methods Appl. Mech. Engrg. 312 (2016), p. 509-541. doi: 10.1016/j.cma.2016.02.008.
Articles publiés en 2017:
[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, Comp. Appl. Math., Vol. 36 (2017), 1431-1462. 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,
Vietnam J. Math., 45 (2017), 103-125. Special Issue dedicated to Willi Jaeger, DOI: 10.1007/s10013-016-0199-6.
[61] A. Marciniak-Czochra,
A. Mikelić:
Shadow limit for parabolic-ODE systems through a cut-off argument,
Rad HAZU. Matematicke Znanosti. Vol. 21 = 532 (2017), 99--116.
[62] G. Scovazzi, M. F. Wheeler,
A. Mikelić , S. Lee:
Analytical and variational numerical methods for unstable miscible displacement flows in porous media,
Journal of Computational Physics, 335 (2017), 444-496.
Articles publiés en 2018:
[63]
Th. Carraro,, A. Mikelić, E. Marusić- Paloka
: Effective pressure boundary condition for the filtration through porous medium via
homogenization,
Nonlinear Analysis Series B: Real World Applications, Vol. 44 (2018), 149-172.
[64]
A. Mikelić:
An introduction to the homogenization modeling of non-Newtonian and electrokinetic flows
in porous media,
Dans Lecture Notes in Mathematics (Vol. 2212, pp. 171--227). Springer Verlag 2018. Chapitre dans
"New trends in non-newtonian fluid mechanics and complex flow" , Lecture Notes in Mathematics C.I.M.E. Series, Springer, correspondant au CIME-CISM Course "New trends in non-newtonian fluid mechanics and complex flows", Levico Terme, Italie, 28/8- 2/9/2016.
[65]
A. Marciniak-Czochra, A. Mikelić, T. Stiehl:
Renormalization group second order approximation for singularly perturbed nonlinear ordinary differential equations,
Mathematical Methods in the Applied Sciences, Vol. 41 (2018), 5691--5710.
[66]
S. Lee, A. Mikelić, M. F. Wheeler, T. Wick
: Phase-field modeling of two phase fluid filled fractures in a poroelastic medium,
SIAM Multiscale Model. Simul., Vol. 16 (2018), 1542--1580.
Articles publiés en 2019:
[67]
A. Mikelić, J. Tambač:
Derivation of a poroelastic elliptic membrane shell model,
Applicable Analysis, Vol. 98 (1--2) (2019), 136--161. doi: 10.1080/00036811.2018.1430784.
[68]
C.J. van Duijn, A. Mikelić, T. Wick:
A monolithic phase-field model of a fluid-driven fracture in a nonlinear poroelastic medium,
Mathematics and Mechanics of Solids, Vol. 24 (5) (2019), 1530-1555..
Les articles acceptés
pour publication
Quelques
prépublications
(Some preprints)