S. Amiroudine, F. Zoueshtiagh, and R. Narayanan, Mixing generated by Faraday instability between miscible liquids, Physical Review E, vol.16, issue.1, p.16326, 2012.
DOI : 10.1017/S0022112006001169

URL : https://hal.archives-ouvertes.fr/hal-00787353

W. Batson, F. Zoueshtiagh, and R. Narayanan, The Faraday threshold in small cylinders and the sidewall non-ideality, Journal of Fluid Mechanics, vol.6, pp.496-523, 2013.
DOI : 10.1103/PhysRevLett.78.2357

URL : https://hal.archives-ouvertes.fr/hal-00871919

W. Batson, F. Zoueshtiagh, and R. Narayanan, Dual role of gravity on the Faraday threshold for immiscible viscous layers, Physical Review E, vol.88, issue.6, p.63002, 1988.
DOI : 10.1209/0295-5075/86/14002

URL : https://hal.archives-ouvertes.fr/hal-00915572

W. Batson, Faraday waves in small cylinders and the sidewall non-ideality, 2013.

J. Bechhoefer, V. Ego, S. Manneville, and B. Johnson, An experimental study of the onset of parametrically pumped surface waves in viscous fluids, Journal of Fluid Mechanics, vol.221, issue.-1, pp.325-350, 1995.
DOI : 10.1103/PhysRevLett.62.422

T. B. Benjamin and J. C. Scott, Gravity-capillary waves with edge constraints, Journal of Fluid Mechanics, vol.36, issue.02, pp.241-267, 1979.
DOI : 10.1007/BF00862566

T. B. Benjamin and F. Ursell, The Stability of the Plane Free Surface of a Liquid in Vertical Periodic Motion, Proc. R. Soc. Lond. A, pp.505-515, 1954.
DOI : 10.1098/rspa.1954.0218

S. P. Hopfinger and E. J. , Parametrically forced gravity waves in a circular cylinder and finite-time singularity, J. Fluid Mech, vol.599, pp.205-228, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00268227

S. V. Diwakar, F. Zoueshtiagh, S. Amiroudine, and R. Narayanan, The Faraday instability in miscible fluid systems, Physics of Fluids, vol.27, issue.8, p.84111, 2015.
DOI : 10.1017/S0022112009993417

S. Douady, Experimental study of the Faraday instability, Journal of Fluid Mechanics, vol.15, issue.-1, pp.383-409, 1990.
DOI : 10.1080/14786448308627392

S. Douady and S. Fauve, Pattern Selection in Faraday Instability, Europhysics Letters (EPL), vol.6, issue.3, pp.221-226, 1988.
DOI : 10.1209/0295-5075/6/3/006

W. S. Edwards and S. Fauve, Patterns and quasi-patterns in the Faraday experiment, Journal of Fluid Mechanics, vol.248, issue.-1, 1994.
DOI : 10.1103/PhysRevLett.54.1524

M. Faraday, On the forms and states of fluids on vibrating elastic surfaces, 1831.

S. Fauve, K. Kumar, C. Laroche, D. Beysens, and Y. Garrabos, Parametric instability of a liquid-vapor interface close to the critical point, Physical Review Letters, vol.225, issue.21, pp.68-3160, 1992.
DOI : 10.1017/S0022112091001970

J. Feng, I. Jacobi, and H. Stone, Experimental investigation of the Faraday instability on a patterned surface, Experiments in Fluids, vol.74, issue.5, 2016.
DOI : 10.1063/1.1602936

F. Gallaire, P. Brun, D. Henderson, and J. Miles, Fluid dynamic instabilities: theory and application to pattern forming in complex media Single-mode Faraday waves in small cylinders, Philos Trans A Math Phys Eng Sci. May J. Fluid Mech, vol.13375, issue.213, pp.95-109, 1990.

D. M. Henderson and J. W. Miles, Faraday waves in 2:1 internal resonance, Journal of Fluid Mechanics, vol.6, issue.-1, pp.449-470, 1989.
DOI : 10.1017/S0022112085002701

D. F. Hill, The Faraday resonance of interfacial waves in weakly viscous fluids, Physics of Fluids, vol.28, issue.1, p.158, 2002.
DOI : 10.1017/S0022112059000489

G. W. Hill, On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, vol.8, issue.0, pp.1-36, 1886.
DOI : 10.1007/BF02417081

L. M. Hocking, The damping of capillary???gravity waves at a rigid boundary, Journal of Fluid Mechanics, vol.94, issue.-1, pp.253-266, 1987.
DOI : 10.1146/annurev.fl.11.010179.002103

T. Ito and Y. Kukita, Interface Behavior between Two Fluids Vertically Oscillated in a Circular Cylinder under Nonlinear Contact Line Condition, Journal of Fluid Science and Technology, vol.3, issue.5, pp.690-711, 2008.
DOI : 10.1299/jfst.3.690

T. Ito, Y. Tsuji, and Y. Kukita, Interface Waves Excited by Vertical Vibration of Stratified Fluids in a Circular Cylinder, Journal of Nuclear Science and Technology, vol.381, issue.6, pp.508-521, 1999.
DOI : 10.1063/1.869700

L. Johns and R. Narayanan, Interfacial Instability, Applied Mechanics Reviews, vol.56, issue.2, 2002.
DOI : 10.1115/1.1553448

K. Kumar, Linear theory of Faraday instability in viscous fluids, Proc. R. Soc. Lond. A, pp.1113-1126, 1996.

K. Kumar and L. Tuckerman, Parametric instability of the interface between two fluids, Journal of Fluid Mechanics, vol.6, issue.-1, pp.49-67, 1994.
DOI : 10.1103/PhysRevE.47.R788

L. Landau and B. Levich, Dragging of a Liquid by a Moving Plate, Acta Physicochim, 1942.
DOI : 10.1016/B978-0-08-092523-3.50016-2

L. D. Landau, Fluid MechanicsCourse Of Theoretical Physics) Author: LD Landau, p.106, 1987.

E. Florens and F. Chladni, Waves in Fluids, Entdeckungen über die Theorie des Klanges, 1978.

F. Melde, Ueber die Erregung stehender Wellen eines fadenfOrmigen Korpers, 1860.
DOI : 10.1002/andp.18601850202

J. W. Miles, Surface-Wave Damping in Closed Basins, Proc. R. Soc. Lond. A, pp.459-475, 1967.
DOI : 10.1098/rspa.1967.0081

J. W. Miles, Nonlinear Faraday resonance, Journal of Fluid Mechanics, vol.297, issue.-1, pp.285-302, 1984.
DOI : 10.1017/S002211207600030X

S. T. Milner, Square patterns and secondary instabilities in driven capillary waves, Journal of Fluid Mechanics, vol.6, issue.-1, 1991.
DOI : 10.1017/S0022112083002670

H. W. Muller, Periodic triangular patterns in the Faraday experiment, Physical Review Letters, vol.225, issue.20, pp.3287-3290, 1993.
DOI : 10.1017/S0022112091001970

H. W. Muller, H. Wittmer, C. Wagner, J. Albers, and K. Knorr, Analytic Stability Theory for Faraday Waves and the Observation of the Harmonic Surface Response, Physical Review Letters, vol.452, issue.12, 1997.
DOI : 10.1098/rspa.1996.0056

. Oersted, Wheatstone (1823), and Weber (1825) as predecessors in producing and describing crispations Experimental investigations on the maintenance of vibrations, Bulletin of the Indian Association for the Cultivation of Science, vol.6, pp.1-40, 1813.

C. Tipton, Interfacial Faraday Waves in a Small Cylindrical Cell, 2003.

C. R. Tipton and T. Mullin, An experimental study of Faraday waves formed on the interface between two immiscible liquids, Physics of Fluids, vol.36, issue.7, pp.2336-2341, 2004.
DOI : 10.1080/18811248.1999.9726233

C. Wagner, H. Muller, and K. Knorr, Pattern formation at the bicritical point of the Faraday instability, Physical Review E, vol.271, issue.6, pp.68-066204, 2003.
DOI : 10.1016/0039-6028(92)90905-L

A. Wernet, C. Wagner, D. Papathanassiou, H. Muller, and K. Knorr, Amplitude measurements of Faraday waves, Physical Review E, vol.30, issue.3, p.36305, 2001.
DOI : 10.2514/3.11286

C. Wheatstone, New Experiments on Sound, Annals of Philosophy, N.S, vol.6, pp.81-90, 1823.
DOI : 10.1017/CBO9781139057950.002

F. Zoueshtiagh, S. Amiroudine, and R. Narayanan, Experimental and numerical study of miscible Faraday instability k*exp(-k*h(1)), -k*exp(k*h(1)), q1*exp(-q1*h(1)), -q1*exp, k*exp(k*h(2)), -k*exp, pp.43-55, 2009.

. B=zeros, (N+1)) ; %construction of the B matrix if alpha==0, ,3)=2; B(3:2*(N+1) ,1:2*N)=eye

=. For-i, ,2+i)=1; end end [eigenvecs,eigenvals]=eig(D,1/2*(rho(2)-rho(1))*k^2*B)