Michael Frankel

 

Research:          Combustion and Phase Transitions, Nonlinear PDE,
Free Interface Problems, Geometrical Dynamics of Interfaces

                                                                                              

 

SELECTED  PAPERS.

 

 

M. Frankel and G. Sivashinsky, The Effect of Viscosity on Hydrodynamic Stability of Plane Flame Front. Combustion Sci­ence and Technology, 29, (1982), 207-224

 

M. Frankel and G. Sivashinsky, On Effects Due to Thermal Expan­sion and Lewis Number in Spherical Flame Propagation. Combus­tion Science and Technology, 31 (1983), 131-138. 

 

M. Frankel and G. Sivashinsky, On Quenching of Curved Flames. Combustion Science and Technology, 40 (1984), 257-268.

 

J. Flaherty, M. Frankel, V. Roytburd and G. Sivashinsky, Numerical Study of Quenching of Inward Propagating Spherical Flames. Combustion Science and Technology, 43 (1985), 245-257.

 

A. Frenkel and M. Frankel, A Generalization of the Theory of Rayleigh-Benard Instability. International Journal of Physico-Chemical Hydrodynamics, 6, No 6, (1985), 747-750

 

A. Frenkel and M. Frankel, Large-Scale Onset of Rayleigh-Benard Convection Between Well Conducting Slabs. Phys.Rev. A, 31, 4(1985), 2760-2763.

 

M. Frankel and G. Sivashinsky, On the Nonlinear Thermal-Diffusive Theory of Curved Flames. Journal de Physique, 48 (1987), 25-28.(pdf)

 

M. Frankel, On the Weakly-Nonlinear Evolution of a Per­turbed Planar Solid-Liquid Interface. Physica D 27 (1987), 260-266.

 

M. Frankel and G. Sivashinsky, On the Equation of Curved Flame Front. Physica D 30 (1988), 28-42.

 

M. Frankel, On the Nonlinear Evolution of Solid-Liquid Inter­face. Phys. Lett. A, 128, 1-2 (1988), 57-60. (pdf)

 

M. Frankel, A Model of Slow Equilibrium Dynamics of Eco­nomic Expansion. Mathematical Analysis & Application, 132, (1988), 499-513

 

M. Frankel, On a Free Boundary Problem Associated with Combustion and Solidification, Mathematical Modeling & Nu­meri­cal Analysis, 23, 2(1989), 283-291.

 

M. Frankel, On the Nonlinear Dynamics of Flame Fronts in Condensed Combustible Matter, Phys. Lett. A, 140, No. 7,8 (1989), 405-410.

 

M. Frankel, On the Equation of Pulsating Flame Fronts in Solid Fuel Combustion, Physica D 40, (1989), 403-414.

 

M. Frankel, An Equation of Surface Dynamics Modeling Flame Fronts as Density Discontinuity in Potential Flows, Physics of Fluids A 2, No. 10 (1990), 1879-1883. (pdf )

 

M. Frankel, Qualitative Approximation of Oscillatory Flames in Premixed Gas Combustion by a Local Equation of Front Dynamics, SIAM J, Appl. Math, 51, No.3, (1991),673-683 (pdf)

 

M. Frankel and G. Sivashinsky, Surface Evolution Equa­tions Modeling Intrinsic Dynamics of Premixed Flames. "FLUID DYNAMICAL ASPECTS OF COMBUSTION THEORY", ed­ited by M. Onufri and G. Tesei, Pitman (1991),

 

M. Frankel, Free Boundary Problems and Dynamical Geome­try Associated with Flames, "DYNAMICAL ISSUES IN COMBUSTION THEORY", the IMA Volumes in Mathematics and its Applications, P. Fife, A. Linan and F. Williams editors, Springer-Verlag, (1991), pp. 107-127

 

M. Frankel and V Roytburd,  A free boundary problem modeling thermal instabilities: Well-posedness, SIAM J. Math. Anal., 25 (1994), 1357-1374.

 

M. Frankel, V. Roytburd and G. Sivashinsky,  A sequence of period doublings and chaotic pulsations in a free bound­ary problem modeling thermal instabilities, SIAM J. Appl. Math., 54 (1994), 1101-1112 (pdf.)

 

M. Frankel and V. Roytburd,  Complex dynamics of ther­mal instability, Proc. of Dyn. Sys. & Appl., vol 1, G. S Ladde and M. Sambandham ed., Dynamic Publishers, Atlanta (1994), 95-102.

 

L. Filyand, G. Sivashinsky and M. Frankel,  On self-acceleration of outward propagating wrinkled flames, Physica D 72, (1994), 110-118.

 

M. Frankel and V. Roytburd, Dynamical portrait of a model of thermal instability: cascades, chaos, reversed cas­cades and infinite period bifurcations, Int. J. of Bifurcation and Chaos, 4 (1994), 579-593.

 

M. Frankel and V. Roytburd,  A free boundary problem modeling thermal instabilities: Stability and bifurcation, J. of Dyn. Sys. and Diff. Eqs. 6 (1994), 447-486.

 

M. Frankel and V. Roytburd, Finite-dimensional model of thermal instabilities, Appl. Math. Let., 8 (1995), 39-44. (pdf. )

 

M. Frankel, Min Qu and V. Roytburd, On a free interface problem modeling solid combustion and rapid solidification in infinite medium, Dynamical systems and applications, World Scientific series in Applicable Analysis, Vol. 4 (1995), 263-278. (pdf. )

 

M. Frankel,  and V. Roytburd,  On a free boundary model related to solid-state combustion. Comm. Appl. Nonlinear. Anal. 2. No.3,  (1995), 1-22

 

M. Frankel and G. Sivashinsky, Fingering instability in non-adiabatic low Lewis number flames, Phys. Rev. E, 52, No.6 (1995), 6154-6158. (pdf.)

 

M. Frankel, Hamiltonian dynamics of polygons and integrability, Journal of Mathematical Analysis & Applications. 205 (1997), 133-147.

 

M. Frankel,  Turbulent fronts and self-fractalizing ornaments generated by an interface dynamics equation. Int. J. of Bifurcation and Chaos, 7, No.1 (1997), 239-252

 

M. Frankel, Wrinkling and Fractalization of Curves in an Interface Model of Diffusionally Unstable Flames, Appl. Math. Let., 11 (1998), 17-23 (pdf)

 

M. Frankel V. Roytburd G. Sivashinsky, Complex dynamics generated by a sharp interface model of self-propagating high-temperature synthesis, Combust. Theory & Modelling , 2 (1998), 479-496. (pdf.)

 

M. Frankel and V. Roytburd, On dynamics of exothermic interfaces, Contemporary Mathematics 256 (2000), 63-77

 

M. Frankel, L. K. Gross and V. Roytburd, Thermo-kinetically controlled pattern selection, Interfaces and Free Boundaries 2 (2000), 313-330 (pdf.)

 

M. Frankel, G. Kovacic, V. Roytburd and I. Timofeyev, Finite-dimensional dynamical system modeling thermal instabilities, Physica D 137 (2000), 295-315 (pdf.)

 

I. Brailovsky, M. Frankel and G. Sivashinsky, Galloping and spinning modes of subsonic detonation, Combust. Theory Modelling , 4 (2000), 47-60 (pdf file)

 

M. Frankel and V. Roytburd, Finite-dimensional attractors for a free-boundary problem with a kinetic condition , Appl. Math. Letters 15 (2002), 83-87.(pdf)

 

M. Frankel and V. Roytburd,  Compact attractors for a free-boundary model of exothermic phase transitions , EJDE 15 (2002), 1-27

 

M. Frankel and V. Roytburd, Finite-Dimensional Attractor for a One-Phase Stephan Problem with Kinetics, JDDE 15(2003) No.1, 87-106 (pdf. )

 

M. Frankel, P. Gordon and G Sivashinsky, On Disintegration of Near-Limit Cellular Flames Phys. Let 310 (2003)., N.5,6,.389-392 (pdf. )

 

M. Frankel and V. Roytburd, Low fractal dimension of attractors for a one-phase nonequilibrium Stefan problem, DCDS, Suppl, (2003), 281-287  (pdf )

 

M. Frankel and V. Roytburd, Compact attractors for classical solutions of a free interface problem of  SHS and rapid solidification, Adv. In Math. Sci. and Applications, 14 (2004) pp.25-40 (pdf)

 

C. Brauner, M. Frankel, J. Hulshof and G Sivashinsky, Weakly nonlinear asymptotics of the κ-θ model of cellular flames: the Q-S equation, IFB 7(2005), 131-146 (pdf file)

 

M. Frankel and V. Roytburd, Finite-Dimensional Attractors for a Nonequilibrium Stefan Problem with Heat Losses, DCDS, Volume 13, Number 1, June 2005, pp. 35-62 (pdf file)

 

M. Frankel and V. Roytburd, Frequency locking for a combustion synthesis front propagating through a periodic medium, Phys. Let. A Vol 329 /1-2 (2004) pp 68-75 (pdf file)

 

M. Frankel and V. Roytburd, Dynamics of SHS in periodic media,  Nonlinear Analysis, Vol 63/5-7 (2005), pp e1507-e1515 (pdf file)

 

M. Frankel and V. Roytburd, Dynamical structure of one-phase model of solid combustion, , DCDS, Suppl (2005) 287-296. (pdf file)

 

C. Brauner, M. Frankel, J. Hulshof and V. Roytburd, Stability and attractors for Quasi-Sready equation of cellular flames, Interfaces and Free Boundaries 8 (2006), 301-316 (pdf file)

 

M. Frankel, P. Gordon and G Sivashinsky, Stretch-Temperature Model for Flame-Flow Interaction,. Phys. Let. A (2006), in print (pdf file)

 

I. Brailovsky, A. Babchin, M. Frankel, and G. Sivashinsky, Fingering Instability in Water-Oil Displacement, Transport in porous media, Volume 63, Issue 3, June 2006, Pages 363 – 380 (pdf file)

 

M. Frankel and V. Roytburd, Dynamics of thermally-insulated nonequilibrium Stefan problem (2006), Journal of Evolution Equations, in print (pdf file)

 

P. Gordon, M. Frankel and G. Sivashinsky, A reduced model for flame-flow interaction, (2006), CTM, submitted.

 

C. Brauner, M. Frankel, J. Hulshof , A. Lunardy, and G Sivashinsky, ON THE k-q MODEL OF CELLULAR FLAMES: EXISTENCE IN THE LARGE AND ASYMPTOTICS, (2006), DCDS, submitted,

 

I. Brailovsky, A. Babchin, M. Frankel, and G. Sivashinsky, A reduced model for fingering instability in miscible displacement. (2006), submitted,