List of Publications (by area)

For a complete chronological list, click here.

Energy driven pattern formation

  1. "Asymptotically exact formulas for the stripe domains period in ultrathin ferromagnetic films with out-of-plane anisotropy"
    2. A. Bernand-Mantel, V. V. Slastikov and C. B. Muratov
    (submitted).
  2. "Existence of higher degree minimizers in the magnetic skyrmion problem"
    3. C. B. Muratov V. V. Slastikov and T. M Simon
    (submitted).
  3. "An optimal design problem for a charge qubit"
    4. D. Mazzoleni, C. B. Muratov and B. Ruffini
    (submitted).
  4. "Reduced energies for thin ferromagnetic films with perpendicular anisotropy"
    5. G. Di Fratta, C. B. Muratov and V. V. Slastikov
    Math. Models Methods Appl. Sci.34,1861-1904 (2024).
  5. "A variational model of charged drops in dielectrically matched binary fluids: the effect of charge discreteness"
    6. C. B. Muratov, M. Novaga, P. Zaleski
    Arch. Ration. Mech. Anal.248, 76 (2024).
  6. "Thomas-Fermi theory of out-of-plane charge screening in graphene"
    7. V. Moroz and C. B. Muratov
    Proc. R. Soc. A 480, 20230570 (2024).
  7. "Magnetic skyrmions under confinement"
    8. A. Monteil, C. B. Muratov, T. M. Simon and V. V. Slastikov
    Commun. Math. Phys. 404, 1571-1605 (2023).
  8. "Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets"
    9. A. Bernand-Mantel, A. Fondet, S. Barnova, T. M. Simon and C. B. Muratov
    Phys. Rev. B 108, L161405 (2023).
  9. "Transverse domain walls in thin ferromagnetic strips"
    10. M. Morini, C. B. Muratov, M. Novaga and V. V. Slastikov
    Arch. Ration. Mech. Anal. 247, 59 (2023).
  10. "The mathematics of thin structures"
    11. J.-F. Babadjian, G. Di Fratta, I. Fonseca, G. A. Francfort, M. Lewicka and C. B. Muratov
    Quart. Appl. Math. 81, 1-64 (2023).
  11. "A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films"
    12. A. Bernand-Mantel, C. B. Muratov, and V. V. Slastikov
    Proc. Natl. Acad. Sci. USA 119, e2122237119 (2022).
  12. "Conducting flat drops in a confining potential"
    13. C. B. Muratov, M. Novaga and B. Ruffini
    Arch. Rat. Mech. Anal. 243, 1773-1810 (2022).
  13. "A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from ℝ2 to 𝕊2"
    14. A. Bernand-Mantel, C. B. Muratov, and T. M. Simon
    Arch. Rat. Mech. Anal. 239, 219-299 (2021).
  14. "Variational principles of micromagnetics revisited"
    15. G. Di Fratta, C. B. Muratov, F. N. Rybakov and V. V. Slastikov
    SIAM J. Math. Anal. 52, 3580-3599 (2020).
  15. "The voltage-dependent manipulation of few-layer graphene with a scanning tunneling microscopy tip"
    16. M. M. Alyobi, C. J. Barnett, C. B. Muratov, V. Moroz, and R. J. Cobley
    Carbon 163, 379-384 (2020).
  16. "Edge domain walls in ultrathin exchange-biased films"
    17. R. G. Lund, C. B. Muratov, and V. Slastikov
    J. Nonlin. Sci. 30, 1165-1205 (2020).
  17. "Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions"
    18. A. Bernand-Mantel, C. B. Muratov, and T. M. Simon
    Phys. Rev. B 101, 045416 (2020).
  18. "Emergence of non-trivial minimizers for the three-dimensional Ohta-Kawasaki energy"
    19. H. Knuepfer, C. B. Muratov, and M. Novaga
    Pure Appl. Analysis 2, 1-21 (2020).
  19. "A nonlocal isoperimetric problem with dipolar repulsion"
    20. C. B. Muratov and T. M. Simon
    Commun. Math. Phys. 372, 1059-1115 (2019).
  20. "Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films"
    21. V. V. Slastikov, C. B. Muratov, J. M. Robbins and O. A. Tretiakov
    Phys. Rev. B 99, 100403R (2019).
  21. "Magnetic domains in thin ferromagnetic films with strong perpendicular anisotropy"
    22. H. Knuepfer, C. B. Muratov, and F. Nolte
    Arch. Rat. Mech. Anal. 232, 727-761 (2019).
  22. "A universal thin film model for Ginzburg-Landau energy with dipolar interaction"
    23. C. B. Muratov
    Calc. Var. PDE 58, 52 (2019).
  23. "On equilibrium shapes of charged flat drops"
    24. C. B. Muratov, M. Novaga and B. Ruffini
    Commun. Pure Appl. Math. 71, 1049-1073 (2018).
  24. "One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films"
    25. R. G. Lund, C. B. Muratov, and V. Slastikov
    Nonlinearity 31, 728-754 (2018).
  25. "An Old Problem Resurfaces Nonlocally: Gamow's Liquid Drops Inspire Today's Research and Applications"
    26. R. Choksi, C. B. Muratov and I. Topaloglu
    Notices Amer. Math. Soc. 64, 1275-1283 (2017).
  26. "Theory of Dzyaloshinskii domain wall tilt in ferromagnetic nanostrips"
    27. C. B. Muratov, and V. V. Slastikov, A. G. Kolesnikov and O. A. Tretiakov
    Phys. Rev. B 96, 134417 (2017).
  27. "Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii-Moriya interaction"
    28. C. B. Muratov and V. V. Slastikov
    Proc. R. Soc. A 473, 20160666 (2016).
  28. "A reduced model for precessional switching of thin-film nanomagnets under the influence of spin-torque"
    29. R. G. Lund, G. D. Chaves-O'Flynn, A. D. Kent and C. B. Muratov
    Phys. Rev. B 94, 144425 (2016).
  29. "Low density phases in a uniformly charged liquid"
    30. H. Knuepfer, C. B. Muratov and M. Novaga
    Commun. Math. Phys. 345, 141-183 (2016).
  30. "One-dimensional domain walls in thin ferromagnetic films with fourfold anisotropy"
    31. R. G. Lund and C. B. Muratov
    Nonlinearity 29, 1716-1734 (2016).
  31. "On well-posedness of variational models of charged drops"
    32. C. B. Muratov and M. Novaga
    Proc. R. Soc. A 472, 20150808 (2016).
  32. "Uniqueness of one-dimensional Neel wall profiles"
    33. C. B. Muratov and X. Yan
    Proc. R. Soc. A 472, 20150762 (2016).
  33. "Orbital-free density functional theory of out-of-plane charge screening in graphene"
    34. J. Lu, V. Moroz and C. B. Muratov
    J. Nonlin. Sci. 25, 1391-1430 (2015).
  34. "Energy barriers for bit-encoding states based on 360-degree domain walls in ultrathin ferromagnetic nanorings"
    35. C. B. Muratov, V. V. Osipov and E. Vanden-Eijnden
    J. Appl. Phys. 117, 17D118 (2015).
  35. "On an isoperimetric problem with a competing non-local term: Quantitative results."
    36. C. B. Muratov and A. Zaleski
    Ann. Global Anal. Geom. 47, 63-80 (2015).
  36. "The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement via the renormalized energy."
    37. D. Goldman, C. B. Muratov and S. Serfaty
    Arch. Rat. Mech. Anal. 212, 445-501 (2014).
  37. "On an isoperimetric problem with a competing non-local term. II. The general case."
    38. H. Knuepfer and C. B. Muratov
    Commun. Pure Appl. Math. 67, 1974-1994 (2014).
  38. "One-dimensional Neel walls under applied external fields"
    39. M. Chermisi and C. B. Muratov
    Nonlinearity 26, 2935-2950 (2013).
  39. "The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density."
    40. D. Goldman, C. B. Muratov and S. Serfaty
    Arch. Rat. Mech. Anal. 210, 581-613 (2013).
  40. "Micromagnetic Studies of the Effects of Crystalline Anisotropy on the Remanent Magnetization of Ferromagnetic Nanorings"
    41. G. D. Chaves-O'Flynn and C. B. Muratov
    IEEE Trans. Magn. 49, 3125-3128 (2013).
  41. "On an isoperimetric problem with a competing non-local term. I. The planar case."
    42. H. Knuepfer and C. B. Muratov
    Commun. Pure Appl. Math. 66, 1129-1162 (2013).
  42. "Domain structure of bulk ferromagnetic crystals in applied fields near saturation"
    43. H. Knuepfer and C. B. Muratov
    J. Nonlin. Sci. 21, 921-962 (2011).
  43. "Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions"
    44. C. B. Muratov
    Commun. Math. Phys. 299, 45-87 (2010).
  44. "Bit storage by 360-degree domain walls in ferromagnetic nanorings"
    45. C. B. Muratov and V. V. Osipov
    IEEE Trans. Magn. 45, 3207-3209 (2009).
  45. "Geometric strong segregation theory for compositionally asymmetric diblock copolymer melts"
    46. C. B. Muratov, M. Novaga, G. Orlandi, and C. J. Garcia-Cervera
    in "Singularities in nonlinear evolution phenomena and applications", CRM Series, Birkhauser, 2009.
  46. "Theory of 360-degree domain walls in thin ferromagnetic films"
    47. C. B. Muratov and V. V. Osipov
    J. Appl. Phys. 104, 053908 (2008).
  47. "Optimal grid-based methods for thin film micromagnetics simulations"
    48. C. B. Muratov and V. V. Osipov
    J. Comput. Phys. 216, 637-653 (2006).
  48. "Theory of domain patterns in systems with long-range interactions of Coulomb type"
    49. C. B. Muratov
    Phys. Rev. E 66, 066108 (2002).
  49. "Theory of phase separation kinetics in polymer-liquid crystal systems"
    50. C.B. Muratov and W. E
    J. Chem. Phys. 116, 4723-4734 (2002).
  50. "Unusual coarsening during phase separation in polymer systems"
    51. C.B. Muratov
    Phys. Rev. Lett. 81, 3699-3702 (1998).
  51. "Instabilities and disorder of the domain patterns in the systems with competing interactions"
    52. C.B.Muratov
    Phys. Rev. Lett.78, 3149-3152 (1997).

Front propagation

  1. "Threshold phenomena for symmetric decreasing radial solutions of reaction-diffusion equations"
    2. C. B. Muratov and X. Zhong
    Discr. Cont. Dyn. Syst. A 37, 915-944 (2017).
  2. "Front propagation in geometric and phase field models of stratified media"
    3. A. Cesaroni, C. B. Muratov and M. Novaga
    Arch. Rat. Mech. Anal. 216, 153-191 (2015).
  3. "Asymptotic behavior of attractors for inhomogeneous Alen-Cahn equations."
    4. A. Cesaroni, C. B. Muratov and M. Novaga
    RIMS Kokyuroku 1924, 97-114 (2014).
  4. "Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations"
    5. C. B. Muratov and X. Zhong
    Nonlin. Diff. Eq. Appl. 20, 1519-1552 (2013).
  5. "Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders"
    6. P. V. Gordon, C. B. Muratov and M. Novaga
    Calc. Var. PDE 47, 683-709 (2013).
  6. "Global exponential convergence to variational traveling waves in cylinders"
    7. C. B. Muratov and M. Novaga
    SIAM J. Math. Anal. 44, 293--315 (2012).
  7. "Front propagation in infinite cylinders. I. A vriational approach."
    8. C. B. Muratov and M. Novaga
    Commun. Math. Sci. 6, 799-826 (2008).
  8. "Existence of traveling waves of invasion for Ginzburg-Landau-type problems in infinite cylinders"
    9. M. Lucia, C. B. Muratov, and M. Novaga
    Arch. Rat. Mech. Anal. 188, 475-508 (2008).
  9. "Front propagation in infinite cylinders. II. The sharp reaction zone limit."
    10. C. B. Muratov and M. Novaga
    Calc. Var. PDE 31, 521-547 (2008).
  10. "Traveling wave solutions of harmonic heat flow"
    11. M. Bertsch, C. B. Muratov, and I. Primi
    Calc. Var. PDE 26, 489-509 (2006).
  11. "Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium"
    12. M. Lucia, C.B. Muratov, and M. Novaga
    Commun. Pure Appl. Math. 57, 616-636 (2004).
  12. "A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type"
    13. C.B. Muratov
    Discrete Cont. Dyn. S., Ser. B 4, 867-892 (2004).

Signal transmission in tissues

  1. "Generation and motion of interfaces in a mass-conserving reaction-diffusion system"
    2. P. W. Miller, D. Fortunato, C. B. Muratov, M. Novaga, S. Y. Shvartsman
    SIAM J. Appl. Dyn. Syst. 22, 2408-2431 (2023).
  2. "Forced and spontaneous symmetry breaking in cell polarization"
    3. P. W. Miller, D. Fortunato, C. B. Muratov, L. Greengard and S. Y. Shvartsman
    Nature Comp. Sci. 2, 504-511 (2022).
  3. "Efficient approximations for stationary single-channel Ca2+ nanodomains across length scales"
    4. Y. Chen, C. B. Muratov, and V. V. Matveev
    Biophys. J. 119, 1239-1254 (2020).
  4. "Spherical caps in cell polarization"
    5. R. Diegmiller, H. Montanelli, C. B. Muratov and S. Y. Shvartsman
    Biophys. J. 115, 26-30 (2018).
  5. "Eventual self-similarity of solutions for the diffusion equation with nonlinear absorption and a point source"
    6. P. V. Gordon and C. B. Muratov
    SIAM J. Math. Anal. 47, 2903-2916 (2015).
  6. "Local accumulation times for source, diffusion and degradation models in two and three dimensions"
    7. P. V. Gordon, C. B. Muratov and S. Y. Shvartsman
    J. Chem. Phys. 138, 104121 (2013).
  7. "Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source"
    8. P. V. Gordon and C. B. Muratov
    Netw. Heterog. Media 7, 767-780 (2012).
  8. "Self-similar dynamics of morphogen gradients"
    9. C. B. Muratov, P. V. Gordon and S. Y. Shvartsman
    Phys. Rev. E 84, 041916 (2011). See extended version here.
  9. "Local kinetics of morphogen gradients"
    10. P. V. Gordon, C. Sample, A. Berezhkovskii, C. B. Muratov and S. Y. Shvartsman
    Proc. Natl. Acad. Sci. USA 108, 6157-6162 (2011).
  10. "Waves of autocrine signaling in patterned epithelia"
    11. C. B. Muratov and S. Y. Shvartsman
    Math. Model. Nat. Phenom. 5, 46-63 (2010).
  11. "Autocrine signal transmission with extracellular ligand degradation"
    12. C. B. Muratov, F. Posta and S. Y. Shvartsman
    Phys. Biol. 6, 016006 (2009).
  12. "Quantitative models of developmental pattern formation"
    13. G. T. Reeves, C. B. Muratov, T. Schupbach, and S. Y. Shvartsman
    Devel. Cell 11, 289-300 (2006).
  13. "Signal propagation and failure in discrete autocrine relays"
    14. C.B. Muratov and S. Y. Shvartsman
    Phys. Rev. Lett. 93, 118101 (2004).
  14. "An asymptotic study of the inductive pattern formation mechanism in Drosophila egg development"
    15. C.B. Muratov and S.Y. Shvartsman
    Physica D 186, 93-108 (2003).
  15. "Discrete models of autocrine cell communication in epithelial layers"
    16. M. Pribyl, C.B. Muratov and S.Y. Shvartsman
    Biophys. J. 84, 3624-3635 (2003).
  16. "Long-range signal transmission in autocrine relays"
    17. M. Pribyl, C.B. Muratov and S.Y. Shvartsman
    Biophys. J. 84, 883-896 (2003).
  17. "Transitions in the model of epithelial patterning"
    18. M. Pribyl, C.B. Muratov and S.Y. Shvartsman
    Devel. Dynamics 226, 155-159 (2003).
  18. "Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis"
    19. S.Y. Shvartsman, C.B. Muratov and D.A. Lauffenburger
    Development 129, 2577-2589 (2002).
  19. "A quantitative approximation scheme for the traveling wave solutions in the Hodgkin-Huxley model"
    20. C.B. Muratov
    Biophys. J.  79, 2893-2901 (2000).

Cryogenic systems in liquid propellant rockets

  1. "Acoustic modes of a spherical thin shell tank for liquid propellant mass gauging: theory and experiment"
    2. C. B. Muratov, J. Rogers and M. Khasin
    J. Acoust. Soc. Am. 152, 3260-3270 (2022).
  2. "Spectral mass gauging of unsettled liquid with acoustic waves"
    3. J. Feller, A. Kashani, M. Khasin, C. B. Muratov, V. V. Osipov and S. Sharma
    Technical Report, NASA/TM-2018-219876, January 2018.
  3. "Spectral mass gauging of unsettled liquid with acoustic waves"
    4. J. Feller, A. Kashani, M. Khasin, C. B. Muratov, V. V. Osipov and S. Sharma
    IOP Conf. Ser.: Mater. Sci. Eng. 278, 012003 (2017).
  4. "Mitigation of Solid Booster Ignition-Over-Pressure Wave by Water Aerosol Sprays"
    5. V. V. Osipov, M. Khasin, H. Hafiychuk, C. B. Muratov, M. Watson and V. N. Smelyanskiy
    J. Spacecraft Rockets 52, 928-943 (2015).
  5. "Explosion Hazard from a Propellant Tank Breach in Liquid Hydrogen-Oxygen Rockets"
    6. V. V. Osipov, C. B. Muratov, H. Hafiychuk, E. Ponizovskaya-Devine and V. N. Smelyanskiy
    J. Spacecraft Rockets 50, 860-871 (2013).
  6. "Issues of Long-Term Cryogenic Propellant Storage in Microgravity"
    7. C. B. Muratov, V. V. Osipov and V. N. Smelyanskiy,
    Technical Report, NASA/TM-2011-215988, September 2011.
  7. "Nucleate boiling in long-term cryogenic propellant storage in microgravity"
    8. C. B. Muratov, V. V. Osipov, V. N. Smelyanskiy and R. W. Tyson
    IAC-11.A2.6.4.x12034, Proceedings of the 62nd International Astronautical Congress, Cape Town, South Africa, October 2011.
  8. "A dynamical model of rocket propellant loading with liquid hydrogen"
    9. V. V. Osipov, M. J. Daigle, C. B. Muratov, M. Foygel, V. N. Smelyanskiy and M. D. Watson
    J. Spacecraft Rockets 48, 987-998 (2011).
  9. "Cavitation-induced ignition of cryogenic hydrogen-oxygen fluids"
    10. V. V. Osipov, C. B. Muratov, E. Ponizovsakya-Devine, M. Foygel and V. N. Smelyanskiy
    Appl. Phys. Lett. 98, 134102 (2011).
  10. "Dynamic condensation blocking in cryogenic refueling"
    11. V. V. Osipov and C. B. Muratov
    Appl. Phys. Lett. 93, 224105 (2008).

Stochastic analysis

  1. "Importance sampling for thermally induced switching and non-switching probabilities in spin-torque magnetic nanodevices"
    2. Y. Yu, C. B. Muratov, and R. O. Moore
    IEEE Trans. Magn. 55, 7205011 (2019).
  2. "Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle"
    3. C. B. Muratov and E. Vanden-Eijnden
    Chaos 18, 015111 (2008).
  3. "Noise can play an organizing role for the recurrent dynamics in excitable media"
    4. C. B. Muratov, E. Vanden Eijnden, and W. E
    Proc. Natl. Acad. Sci. USA 104, 702-707 (2007).
  4. "Non-meanfield deterministic limits in chemical reaction kinetics"
    5. R. E. L. DeVille, C. B. Muratov, and E. Vanden Eijnden
    J. Chem. Phys. 124, 231102 (2006).
  5. "Two distinct mechanisms of coherence in randomly perturbed dynamical systems"
    6. R. E. L. DeVille, E. Vanden Eijnden, and C.B. Muratov
    Phys. Rev. E 72, 031105 (2005).
  6. "Self-induced stochastic resonance in excitable systems"
    7. C.B. Muratov, E. Vanden Eijnden, and Weinan E
    Physica D 210, 227-240 (2005).

Pattern formartion in reaction-diffusion systems

  1. "A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type"
    2. M. Henry, D. Hilhorst and C. B. Muratov
    Interfaces Free Bound. 20, 297-336 (2018).
  2. "Free boundary problem and its applications to reaction-diffusion systems of activator-inhibitor type"
    3. C.B. Muratov
    Proceedings of the Conference on Dynamics of Patterns in Reaction-Diffusion Systems
    and the Related Topics, RIMS, Kyoto University    , 63-78 (2003).
  3. "Stability of the static spike autosolitons in the Gray-Scott model"
    4. C.B. Muratov and V.V. Osipov
    SIAM J. Appl. Math. 62, 1463-1487 (2002).
  4. "Traveling spike autosolitons in the Gray-Scott model"
    5. C.B. Muratov and V.V. Osipov
    Physica D 155, 112-131 (2001).
  5. "Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model"
    6. C.B. Muratov and V.V. Osipov
    Eur. Phys. J. B  22, 213-221 (2001).
  6. "Static spike autosolitons in the Gray-Scott model"
    7. C.B. Muratov and V.V. Osipov
    J. Phys. A: Math. Gen.  33, 8893-8916 (2000).
  7. "Spike autosolitons in the Gray-Scott model"
    8. C.B. Muratov and V.V. Osipov
    CAMS Rep. 9900-10, NJIT, Newark, NJ 07102
  8. "Theory of spike spiral waves in a reaction-diffusion system"
    9. C.B. Muratov and V. V. Osipov
    Phys. Rev. E 60, 242-246 (1999).
  9. "Synchronization, chaos, and the breakdown of the collective domain oscillations in reaction-diffusion systems"
    10. C.B. Muratov
    Phys. Rev. E 55, 1463-1477 (1997).
  10. "Scenarios of domain pattern formation in a reaction-diffusion system"
    11. C.B. Muratov and V.V.Osipov
    Phys. Rev. E 54, 4860-4879 (1996).
  11. "Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor"
    12. C.B. Muratov
    Phys. Rev. E 54, 3369-3376 (1996)
  12. "General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems"
    13. C.B. Muratov and V.V. Osipov
    Phys. Rev. E 53, 3101-3116 (1996).
  13. "Ultrafast traveling spike autosolitons in reaction-diffusion systems"
    14. V.V. Osipov and C.B. Muratov
    Phys Rev. Lett. 75, 338-341 (1995).
  14. "Properties of wide-peak autosolitons in electron-hole and gas plasma"
    15. V.V. Osipov and C.B. Muratov
    Phys. Rev. E 50, 3251-3254 (1994).

Miscellaneous

  1. "Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation"
    2. K.-S. Chen, C. B. Muratov, and X. Yan
    Math. Eng. 5, 1-52 (2023).
  2. "Layer solutions for a one-dimensional nonlocal model of Ginzburg-Landau type"
    3. K.-S. Chen, C. B. Muratov, and X. Yan
    Math. Model. Nat. Phenom. 12, 68-90 (2017).
  3. "Asymptotic properties of ground states of scalar field equations with a vanishing parameter"
    4. V. Moroz and C. B. Muratov
    J. Eur. Math. Soc. 16, 1081-1109 (2014).
  4. "Boundary homogenization for periodic arrays of absorbers"
    5. C. B. Muratov and S. Y. Shvartsman
    Multiscale Model. Simul. 7, 44-61 (2008).
  5. "Compensated optimal grids for elliptic boundary-value problems"
    6. F. Posta, S. Y. Shvartsman and C. B. Muratov
    J. Comput. Phys. 227, 8622-8635 (2008).
  6. "Homogenization of boundary conditions for surfaces with regular arrays of traps"
    7. A. M. Berezhkovskii, M. I. Monine, C. B. Muratov, and S. Y. Shvartsman
    J. Chem. Phys. 124, 036103 (2006).
  7. "Breakup of universality in the generalized spinodal nucleation theory"
    8. C.B. Muratov and E. Vanden Eijnden
    J. Stat. Phys. 114, 605-623 (2004).
  8. "On the well-posedness of the equations for the smoothed phase space distributions function and irreversibility in classical statistical mechanics"
    9. C.B. Muratov
    J. Phys. A: Math. Gen.  34, 4641-4651 (2001).
  9. "Traveling wave solutions in the Burridge-Knopoff model"
    10. C.B. Muratov
    Phys. Rev. E 59, 3847-3857 (1999).