Pavel M. Lushnikov:

Researh interests

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Video of Skoltech Colloquium Popular Lecture on singularities and wavebreaking (in Russian)

Strong turbulence in critical 2D nonlinear Schrodinger equation

Supported by NSF grant DMS 0807131

(a)Snapshot of absolute value of psi vs. spatial coordinates (x,y). (b)Snapshot of density plot for psi shows collapse decay with emission of cylindrical waves.

Probability distribution function

shows algebraic tails due to collapses:

Microscopic vs. macroscopic dynamics of biological cells due to contact interaction and chemotaxis

  1. P.M. Lushnikov, N. Chen, and M. Alber. Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact.
    Physical Review E, v. 78, p. 061904 (2008). (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. 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).
  4. 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)

Simulation of early vascular network formation. Left: Microsopic Monte Carlo simulation of dynamics of 15 000 cells. Each cell has fluctuating shape. Right: simualtion of cellular density in macrosopic model. Scale bar represent volume fraction of cells.

Cross sections of the volume fraction in 2D for (a) Monte Carlo microscopic simulation, (b) Keller-Segel macroscopic model (no contact cell-cellinteractions) and (c) Macroscopic nonlinear diffusion equation coupled with chemotaxis:

Laser fusion and laser-plasma interactions
  1. P.M. Lushnikov and H.A.Rose. Collective stimulated Brillouin backscatter.
    Submitted to Physical Review Letters (2007). (PDF)
  2. 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)
  3. 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)
Dispersion-managed soliton in optical fiber communications
  1. 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)
  2. P.M. Lushnikov. Diffusion of optical pulse in dispersion-shifted randomly birefringent optical fibers. Optics Communications, v. 245, pp. 187-192 (2005). (PDF)
  3. P.M. Lushnikov. Oscillating tails of dispersion-managed soliton. JOSA B, v.21, 1913 (2004). (PDF)
  4. P.M. Lushnikov. Fully parallel algorithm for simulating wavelength-division-multiplexed optical fiber systems. Optics Letters, v.27 (#11), pp.939-941 (2002). (PDF)
  5. 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)
  6. I.R. Gabitov and P. M. Lushnikov.   Nonlinearity management in dispersion managed system. Optics Letters, v.27 (#2), pp.113-115 (2002).  (PostScript) (PDF)
  7. P.M. Lushnikov.   Dispersion-managed soliton in a strong dispersion map limit. Optics Letters,  v.26 (#20), pp. 1535-1537 (2001).  (PostScript) (PDF)
  8. P.M. Lushnikov. Dispersion-managed soliton in optical fibers with zero average dispersion. Optics Letters, v. 25 (#16), pp. 1144-1146 (2000).  (PostScript) (PDF)
  9. P.M. Lushnikov. On the boundary of the dispersion-managed soliton existence. JETP Letters, v. 72 (#3), pp. 111-114 (2000).  (PostScript) (PDF)
Nonlinear Schrodinger equation for dispersion-managed optical fiber system:

Oscillating tails of dispersion-managed soliton.

Curve 1: numerical simulation.

Curve 2: analytical prediction:

More about research coming soon

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

Last modified: 02/03/2009.