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Department of Mathematical Sciences

Muratov, Cyrill B.

Contact Info
Title: Associate Professor
Email: cyrill.b.muratov@njit.edu
Office: CULM 510
Hours: MR 2-3 (Spring 2014)
Phone: 973-596-5833
Dept: Mathematical Sciences
Webpage: http://web.njit.edu/~muratov

About Me

I am interested in modeling, analysis, and simulations of systems described by nonlinear parabolic and elliptic partial differential equations, with major applications to biology and materials science. The systems under investigation involve spatially distributed positive and negative feedbacks and may be capable of self-organizing behavior, which makes predicting their behavior especially challenging. My research is aimed at developing new approaches to problems of front propagation, pattern formation and self-organization and involves model formulation, asymptotic and variational techniques, numerical simulations, and stochastic analysis, with specific applications in developmental biology.

Education

  • PhD, Physics, Boston University
  • MS, Applied Mathematics and Physics, with Honors, Moscow Institute of Physics and Technology

Courses I Teach

Not teaching any courses this semester

Research Interests

  • Reaction-diffusion equations and their applications
  • Pattern formation and propagation phenomena
  • Calculus of variations, analysis of nonlinear PDEs
  • Modeling and analysis of cell communication in development
  • Stochastic analysis of rare events

Publications

  1. "Geometric strong segregation theory for compositionally asymmetric diblock copolymer melts" C. B. Muratov, M. Novaga, G. Orlandi, and C. J. Garcia-Cervera (submitted to J. Chem. Phys.)
  2. "Front propagation in infinite cylinders. I. A vriational approach." C. B. Muratov and M. Novaga (to be published in Commun. Math. Sci.)
  3. "Theory of 360-degree domain walls in thin ferromagnetic films" C. B. Muratov and V. V. Osipov (to be published in J. Appl. Phys.)
  4. "Compensated optimal grids for elliptic boundary-value problems" F. Posta, S. Y. Shvartsman and C. B. Muratov J. Comput. Phys. 227, 8622-8635 (2008).
  5. "Boundary homogenization for periodic arrays of absorbers" C. B. Muratov and S. Y. Shvartsman Multiscale Model. Simul. 7, 44-61 (2008).
  6. "Existence of traveling waves of invasion for Ginzburg-Landau-type problems in infinite cylinders" M. Lucia, C. B. Muratov, and M. Novaga Arch. Rat. Mech. Anal. 188, 475-508 (2008).
  7. "Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle" C. B. Muratov and E. Vanden-Eijnden Chaos 18, 015111 (2008).
  8. "Front propagation in infinite cylinders. II. The sharp reaction zone limit." C. B. Muratov and M. Novaga Calc. Var. PDE 31, 521-547 (2008).
  9. "Noise can play an organizing role for the recurrent dynamics in excitable media" C. B. Muratov, E. Vanden Eijnden, and W. E Proc. Natl. Acad. Sci. USA 104, 702-707 (2007).
  10. "Quantitative models of developmental pattern formation" G. T. Reeves, C. B. Muratov, T. Schupbach, and S. Y. Shvartsman Devel. Cell 11, 289-300 (2006).
  11. "Non-meanfield deterministic limits in chemical reaction kinetics" R. E. L. DeVille, C. B. Muratov, and E. Vanden Eijnden J. Chem. Phys. 124, 231102 (2006).
  12. "Optimal grid-based methods for thin film micromagnetics simulations" C. B. Muratov and V. V. Osipov J. Comput. Phys. 216, 637-653 (2006).
  13. "Traveling wave solutions of harmonic heat flow" M. Bertsch, C. B. Muratov, and I. Primi Calc. Var. PDE 26, 489-509 (2006).
  14. "Homogenization of boundary conditions for surfaces with regular arrays of traps" A. M. Berezhkovskii, M. I. Monine, C. B. Muratov, and S. Y. Shvartsman J. Chem. Phys. 124, 036103 (2006).
  15. "Two distinct mechanisms of coherence in randomly perturbed dynamical systems" R. E. L. DeVille, E. Vanden Eijnden, and C.B. Muratov Phys. Rev. E 72, 031105 (2005).
  16. "Self-induced stochastic resonance in excitable systems" C.B. Muratov, E. Vanden Eijnden, and Weinan E Physica D 210, 227-240 (2005).
  17. "Signal propagation and failure in discrete autocrine relays" C.B. Muratov and S. Y. Shvartsman Phys. Rev. Lett. 93, 118101 (2004).
  18. "A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type" C.B. Muratov Discrete Cont. Dyn. S., Ser. B 4, 867-892 (2004).
  19. "Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium" M. Lucia, C.B. Muratov, and M. Novaga Commun. Pure Appl. Math. 57, 616-636 (2004).
  20. "Breakup of universality in the generalized spinodal nucleation theory" C.B. Muratov and E. Vanden Eijnden J. Stat. Phys. 114, 605-623 (2004).
  21. "An asymptotic study of the inductive pattern formation mechanism in Drosophila egg development" C.B. Muratov and S.Y. Shvartsman Physica D 186, 93-108 (2003).
  22. "Discrete models of autocrine cell communication in epithelial layers" M. Pribyl, C.B. Muratov and S.Y. Shvartsman Biophys. J. 84, 3624-3635 (2003).
  23. "Free boundary problem and its applications to reaction-diffusion systems of activator-inhibitor type" C.B. Muratov Proceedings of the Conference on Dynamics of Patterns in Reaction-Diffusion Systemsand the Related Topics, RIMS, Kyoto University, 63-78 (2003).
  24. "Long-range signal transmission in autocrine relays" M. Pribyl, C.B. Muratov and S.Y. Shvartsman Biophys. J. 84, 883-896 (2003).
  25. "Transitions in the model of epithelial patterning" M. Pribyl, C.B. Muratov and S.Y. Shvartsman Devel. Dynamics 226, 155-159 (2003).
  26. "Theory of domain patterns in systems with long-range interactions of Coulomb type" C. B. Muratov Phys. Rev. E 66, 066108 (2002).
  27. "Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis" S.Y. Shvartsman, C.B. Muratov and D.A. Lauffenburger Development 129 , 2577-2589 (2002).
  28. "Theory of phase separation kinetics in polymer-liquid crystal systems" C.B. Muratov and W. E J. Chem. Phys. 116, 4723-4734 (2002).
  29. "Stability of the static spike autosolitons in the Gray-Scott model" C.B. Muratov and V.V. Osipov SIAM J. Appl. Math. 62, 1463-1487 (2002).
  30. "Traveling spike autosolitons in the Gray-Scott model" C.B. Muratov and V.V. Osipov Physica D 155, 112-131 (2001).
  31. "Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model" C.B. Muratov and V.V. Osipov Eur. Phys. J. B  22, 213-221 (2001).
  32. "On the well-posedness of the equations for the smoothed phase space distributions function and irreversibility in classical statistical mechanics" C.B. Muratov J. Phys. A: Math. Gen.  34, 4641-4651 (2001).
  33. "Static spike autosolitons in the Gray-Scott model" C.B. Muratov and V.V. Osipov J. Phys. A: Math. Gen.  33, 8893-8916 (2000).
  34. "A quantitative approximation scheme for the traveling wave solutions in the Hodgkin-Huxley model" C.B. Muratov Biophys. J.  79, 2893-2901 (2000).
  35. "Spike autosolitons in the Gray-Scott model" C.B. Muratov and V.V. Osipov CAMS Rep. 9900-10, NJIT, Newark, NJ 07102
  36. "Theory of spike spiral waves in a reaction-diffusion system" C.B. Muratov and V. V. Osipov Phys. Rev. E 60, 242-246 (1999)
  37. "Traveling wave solutions in the Burridge-Knopoff model" C.B. Muratov Phys. Rev. E 59, 3847-3857 (1999)
  38. "Unusual coarsening during phase separation in polymer systems" C.B. Muratov Phys. Rev. Lett. 81, 3699-3702 (1998)
  39. "Instabilities and disorder of the domain patterns in the systems with competing interactions" C.B.Muratov Phys. Rev. Lett.78, 3149-3152 (1997)
  40. "Synchronization, chaos, and the breakdown of the collective domain oscillations in reaction-diffusion systems" C.B. Muratov Phys. Rev. E 55, 1463-1477 (1997)
  41. "Scenarios of domain pattern formation in a reaction-diffusion system" C.B. Muratov and V.V.Osipov Phys. Rev. E 54, 4860-4879 (1996)
  42. "Self-replication and splitting of domain patterns in reaction-diffusion systems with the fast inhibitor" C.B. Muratov Phys. Rev. E 54, 3369-3376 (1996)
  43. "General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems" C.B. Muratov and V.V. Osipov Phys. Rev. E 53, 3101-3116 (1996)
  44. "Ultrafast traveling spike autosolitons in reaction-diffusion systems" V.V. Osipov and C.B. Muratov Phys Rev. Lett. 75, 338-341 (1995)
  45. "Properties of wide-peak autosolitons in electron-hole and gas plasma" V.V. Osipov and C.B. Muratov Phys. Rev. E 50, 3251-3254 (1994)