My research is mainly in the area of applied analysis and calculus of variations. The problems under consideration arise from a variety of applications from materials science, fluid mechanics and biology and give rise to systems of nonlinear partial differential equations exhibiting self-organizing behavior. These difficult mathematical problems can often be successfully approached by the direct method of calculus of variations and singular perturbation techniques.

Currently, my ongoing projects include asymptotic analysis of energy-driven pattern formation problems in the presence of non-local effects, with major applications to ultrathin ferromagnetic films and nanotechnology. Other projects involve modeling, analysis and simulations of rare events in noise-driven systems and studies of multiscale, multiphysics problems, with particular applications to NASA's space exploration systems.

- PhD, Physics, Boston University, 1998
- MSc, Applied Mathematics and Physics, Moscow Institute of Physics and Technology, 1993

- Calculus of variations, analysis of nonlinear PDEs, mathematical physics
- Pattern formation and front propagation phenomena
- Reaction-diffusion equations and their applications to embryonic development
- Stochastic analysis of rare events
- Multiphysics modeling

- C. B. Muratov and X. Zhong, "Threshold phenomena for symmetric decreasing radial solutions of reaction-diffusion equations”, Discr. Cont. Dyn. Syst. A 37, 915-944 (2017).
- R. G. Lund, G. D. Chaves-O'Flynn, A. D. Kent and C. B. Muratov, "A reduced model for precessional switching of thin-film nanomagnets under the influence of spin-torque”, Phys. Rev. B 94, 144425 (2016).
- H. Knuepfer, C. B. Muratov and M. Novaga, "Low density phases in a uniformly charged liquid”, Commun. Math. Phys. 345, 141-183 (2016).
- C. B. Muratov and M. Novaga, "On well-posedness of variational models of charged drops”, Proc. Roy. Soc. Lond. A 472, 20150808 (2016).
- J. Lu, V. Moroz and C. B. Muratov, “Orbital-free density functional theory of out-of-plane charge screening in graphene”, J. Nonlin. Sci. 25, 1391-1430 (2015).
- C. B. Muratov, V. V. Osipov and E. Vanden-Eijnden, "Energy barriers for bit-encoding states based on 360-degree domain walls in ultrathin ferromagnetic nanorings”, J. Appl. Phys. 117, 17D118 (2015).
- A. Cesaroni, C. B. Muratov and M. Novaga, "Front propagation in geometric and phase field models of stratified media”, Arch. Rat. Mech. Anal. 216, 153-191 (2015).
- D. Goldman, C. B. Muratov and S. Serfaty, "The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement via the renormalized energy”, Arch. Rat. Mech. Anal. 212, 445-501 (2014).
- H. Knuepfer and C. B. Muratov, "On an isoperimetric problem with a competing non-local term. II. The general case”, Commun. Pure Appl. Math. 67, 1974-1994 (2014).
- M. Chermisi and C. B. Muratov, "One-dimensional Neel walls under applied external fields”, Nonlinearity 26, 2935-2950 (2013).
- D. Goldman, C. B. Muratov and S. Serfaty, "The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density." Arch. Rat. Mech. Anal. 210, 581-613 (2013).
- H. Knuepfer and C. B. Muratov, "On an isoperimetric problem with a competing non-local term. I. The planar case”, Commun. Pure Appl. Math. 66, 1129-1162 (2013).
- H. Knuepfer and C. B. Muratov, "Domain structure of bulk ferromagnetic crystals in applied fields near saturation”, J. Nonlin. Sci. 21, 921-962 (2011).
- P. V. Gordon, C. Sample, A. Berezhkovskii, C. B. Muratov and S. Y. Shvartsman, "Local kinetics of morphogen gradients”, Proc. Natl. Acad. Sci. USA 108, 6157-6162 (2011).
- C. B. Muratov, "Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions”, Commun. Math. Phys. 299, 45-87 (2010).
- M. Lucia, C. B. Muratov, and M. Novaga, "Existence of traveling waves of invasion for Ginzburg-Landau-type problems in infinite cylinders”, Arch. Rat. Mech. Anal. 188, 475-508 (2008).
- C. B. Muratov, E. Vanden Eijnden, and W. E, "Noise can play an organizing role for the recurrent dynamics in excitable media”, Proc. Natl. Acad. Sci. USA 104, 702-707 (2007).
- R. E. L. DeVille, E. Vanden Eijnden, and C.B. Muratov, "Two distinct mechanisms of coherence in randomly perturbed dynamical systems”, Phys. Rev. E 72, 031105 (2005).
- C. B. Muratov, "Theory of domain patterns in systems with long-range interactions of Coulomb type”, Phys. Rev. E 66, 066108 (2002).