Pavel M. Lushnikov

Associate professor

 

     Department of Mathematics and Statistics
    MSC03 2150
    University of New Mexico
    Albuquerque, NM 87131-1141

    Phone: +1 (505) 277-2104
    Fax:     +1 (505) 277-5505 


      E-mail:  

Resume
Teaching
Research interests
include a wide range of topics in applied mathematics, nonlinear waves and theoretical physics. Among them are laser fusion and laser-plasma interaction; dynamics of fluids with free surface, Kelvin-Helmholtz instability and nonlinear interactions of surface waves; theory of the wave collapse, singularity formation and its application to plasma physics, hydrodynamics, biology and nonlinear optics; bacterial aggregation, chemotaxis, cell-cell interactions. collapse of bacterial colonies, stochastic Potts model of biological cell; pattern formation in photorefractive crystals and other nonlinear optical media; high-bit-rate optical communication; dispersion-managed optical fiber systems; soliton propagation in optical systems; high performance parallel simulations of optical fiber systems; Bose-Einstein condensation of ultracold dipolar gases.
Publications
Articles in Refereed Journals
  1. P.M. Lushnikov and H.A.Rose. Collective stimulated Brillouin backscatter.
    Submitted to Physical Review Letters (2007). (PDF)
  2. M. Alber, N. Chen, P.M. Lushnikov, and S.A. Newman. Continuous macroscopic limit of a discrete stochastic model for interaction of living cells.
    Physical Review Letters, v. 99, p. 168102 (2007). (PDF)
  3. I. Gabitov, R. Indik, P.M. Lushnikov, L. Mollenauer, and M. Shkarayev. Twin Families of Bisolitons in Dispersion Managed Systems.
    Optics Letters, v. 32, pp. 605-607 (2007). (PDF)
  4. P.M. Lushnikov and H.A.Rose. How much laser power can propagate through fusion plasma?
    Plasma Physics and Controlled Fusion, v. 48, pp. 1501-1513 (2006). (PDF)
  5. M. Alber, N. Chen, T. Glimm and P.M. Lushnikov. Multiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a continuous description.
    Phys. Rev. E, v.73, p.051901 (2006). (PDF)
  6. P.M. Lushnikov, and V.E. Zakharov. On optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface. Physica D, v.203, pp.9-29 (2005). (PDF)
  7. P.M. Lushnikov. Diffusion of optical pulse in dispersion-shifted randomly birefringent optical fibers. Optics Communications, v. 245, pp. 187-192 (2005). (PDF)
  8. P.M. Lushnikov and H.A.Rose. Instability versus equilibrium propagation of laser beam in plasma.
    Physical Review Letters, v.92 (#25), p. 255003 (2004). (PDF)
  9. P.M. Lushnikov. Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous Fluid.
    Physics Letters A, v.329 (#1-2), pp.49-54 (2004). (PDF)
  10. P.M. Lushnikov. Oscillating tails of dispersion-managed soliton. JOSA B, v.21, 1913 (2004). (PDF)
  11. P.M. Lushnikov. Collapse of Bose-Einstein condensate with dipole-dipole interactions. Phys. Rev. A,  v.66 (#5), p. 051601(R) (2002).  (PDF)
  12. P.M. Lushnikov. Fully parallel algorithm for simulating wavelength-division-multiplexed optical fiber systems. Optics Letters, v.27 (#11), pp.939-941 (2002). (PDF)
  13. M. Chertkov, I. Gabitov, P. Lushnikov, J. Moeser, Z. Toroczkai. Pinning method of pulse confinement in optical fiber with random dispersion. J. of the Optical Society of America B, v.19 (#11), pp. 2538-2550 (2002). (PDF)
  14. I.R. Gabitov and P. M. Lushnikov.   Nonlinearity management in dispersion managed system. Optics Letters, v.27 (#2), pp.113-115 (2002).  (PostScript) (PDF)
  15. P.M. Lushnikov.   Dispersion-managed soliton in a strong dispersion map limit. Optics Letters,  v.26 (#20), pp. 1535-1537 (2001).  (PostScript) (PDF)
  16. P.M. Lushnikov, and M. Saffman. Collapse in a forced three dimensional nonlinear Schrodinger equation. Phys. Rev. E, v. 62 (#4), pp. 5793-5796 (2000). (PostScript) (PDF)
  17. P.M. Lushnikov. Dispersion-managed soliton in optical fibers with zero average dispersion. Optics Letters, v. 25 (#16), pp. 1144-1146 (2000).  (PostScript) (PDF)
  18. P.M. Lushnikov. On the boundary of the dispersion-managed soliton existence. JETP Letters, v. 72 (#3), pp. 111-114 (2000).  (PostScript) (PDF)
  19. P.M. Lushnikov, and A.V. Mamaev. Spontaneous hexagon formation in photorefractive crystal with a single pump wave. Optics Letters, v. 24 (#21), pp. 1511-1513 (1999). (PostScript) (PDF)
  20. P.M. Lushnikov. Light propagation in photorefractive crystals: from rings to hexagons. Nature (Priroda Magazine of the Russian Academy of Science, in Russian), v.999 (#11), p. 29 (1998).
  21. P.M. Lushnikov, P. Lodahl, and M. Saffman. Transverse modulational instability of counterpropagating quasi-phase-matched beams in a quadratically nonlinear medium.Optics Letters , v. 23(#21) pp. 1650-1652 (1998).  (PostScript) (PDF)
  22. P.M. Lushnikov.  Two mechanisms of surface wave generation: Kelvin-Helmholtz and Miles instabilities Izvestiya,  Atmospheric and Oceanic Physics, v. 34, 370-377 (1998).   (GZippedPostScript) (PDF)
  23. P.M. Lushnikov. Hexagonal optical structures in photorefractive crystals with a feedback mirror JETP,  v. 86(#3), 614-627 (1998).  (PostScript) (PDF)
  24. P.M. Lushnikov. Dynamic criterion for collapse. JETP Letters, v. 62 (#5), pp. 461-467 (1995).  (GZiippedPostScript) (PDF)
  25. E.A. Kuznetsov, and P.M. Lushnikov. Nonlinear theory of the excitation of waves by a  wind  due to the  Kelvin-Helmholtz instability. JETP v. 81, 332-340 (1995).  (GZippedPostScript) (PDF)
     
Book Chapters
  1. M. Alber, N. Chen, T. Glimm, and P.M. Lushnikov. Two-dimensional Multiscale Model of Cell Motion in a Chemotactic Field, pp. 53-76,
    In Single-Cell-Based Models in Biology and Medicine, Series: Mathematics and Biosciences in Interaction.
    Eds. A.R.A. Anderson, M.A.J. Chaplain, K.A. Rejniak. Birkhauser Verlag Basel/Switzerland (2007). (Link).
Other publications
  1. P.M. Lushnikov and H.A. Rose. Practical Formula for Laser Intensity at Beam Spray Onset.
    LANL report (2006) (xxx.lanl.gov/pdf/physics/0609233).
  2. P.M. Lushnikov. CNLS Research Highlights (2001).
  3. P. M. Lushnikov, and M. Saffman. Collapse and generation of ultrashort optical pulses in a nonlinear optical cavity. Quantum Electronics and Laser Science Conference (QELS 2000). Technical Digest. Postconference Edition.TOPS Vol.40, 7-12 May 2000, San Francisco, CA, USA.
  4. P.M. Lushnikov, and A.V. Mamaev. Hexagonal patterns in photorefractive crystals with feedback for scattered light. Proceedings of "Seventh Topical Meeting on Photorefractive Materials, Effects, and Devices". Elsinore, Denmark, 1999.
  5. P.M.Lushnikov. Dynamical criterion of a collapse in the nonlinear Schroedinger equation. Bulletin of the Russian Academy of Sciences. Physics,  v. 61, suppl., no.1, pp.46-51 (1997).

 

Link to Pavel Lushnikov's web page at the University of New Mexico

Last modified: 08/30/2007.

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