Lenya Ryzhik

How to reach me

• Paper mail:
  Department of Mathematics
  Stanford University
  Stanford CA 94305
  USA
  
  
• Office: 383Y
  
• E-mail: ryzhik@math.stanford.edu
  
• Phone: (650) 721-2113 (Office)
  
• Fax: (650)-725-4066
  

Teaching

• Lecture Notes on Complex Analysis - translation of several chapters from "Introduction to Complex Analysis" by B. Shabat
  
• Winter 2009:
  PDEs and Diffusions, Math227
  
• Winter 2003:
  (Applied Analysis Lecture Notes).
  
• Fall 2008:
  (Fall Analysis Lecture Notes).

  Stanford Applied Math seminar

  Chicago CAMP/Nonlinear PDE Seminar

  Communications in Mathematical Sciences

  Nonlinearity (the journal, that is)

  Some of my preprints and publications:

  Click after the title to see the paper.
  
  • Exit times for diffusions with incompressible drifts (with G. Iyer, A. Novikov and A. Zlatos), (pdf), Preprint, 2009.
  • Asymptotics of the phase of the solutions of the random Schr\"odinger equation (with G. Bal and T. Komorowski), (pdf), Preprint, 2009.
  • The non-local Fisher-KPP equation: traveling waves and steady states (with H. Berestycki, G. Nadin and B. Perthame), (pdf), Preprint, 2009.
  • Limit of fluctuations of solutions of Wigner Equation (with T. Komorowski and Sz. Peszat), (pdf), Preprint, 2008.
  • Travelling fronts for the thermodiffusive system with arbitrary Lewis numbers (with F. Hamel), (pdf), to appear in Archive Rational Mechanics and Analysis, 2009.
  • Stability of generalized transitions fronts (with A. Mellet, J, Nolen and J.-M. Roquejoffre), (pdf), to appear in Communications in PDEs, 2009.
  • The explosion problem in a flow (with H. Berestycki, A. Kiselev and A. Novikov), (pdf), to appear in Journal d'Analyse Mathematiques, 2009.
  • Traveling waves in a one-dimensional random medium (with J. Nolen), (pdf), to appear in Ann. de l'Inst. Henri Poincare, C. Analyse non lineaire, 2009.
  • Propagation and quenching in a reactive Burgers-Boussinesq system (with P. Constantin, J.-M. Roquejoffre and N. Vladimirova), (pdf), Nonlinearity, 21, 2008, 221--271.
  • Traveling waves for the Keller-Segel system with Fisher birth terms (with G. Nadin and B. Perthame), (pdf), Interfaces and Free Boundaries, 10, 2008, 517-538.
  • On asymptotics of a tracer advected in a locally self-similar, correlated flow (with T. Komorowski), (pdf), Asymptotic Analysis, 53, 2007, 159--187.
  • Relaxation in reactive flows, (with P. Constantin and A. Novikov), (pdf), Geometric and Functional Analysis, 18, 2008, 1145-1167.
  • KPP pulsating front speed-up by flows, (with A. Zlatos), (pdf), Communications in Mathematical Sciences, 5, 2007, 575-593.
  • Moderate dispersion in scalar conservation laws (with B. Perthame), (pdf), Communications in Mathematical Sciences, 5, 2007, 473-484.
  • Self-averaging from lateral diversity in the Ito-Schroedinger equation, (with G. Papanicolaou and K. Solna), (pdf), Multiscale Modeling and Simulation, 6, 2007, 468--492.
  • Passive tracer in a slowly decorrelating random flow with a large mean, (with T. Komorowski), (pdf), Nonlinearity, 20, 2007, 1215-1239.
  • Traveling waves in 2D reactive Boussinesq systems with no-slip boundary conditions, (with P. Constantin and M. Lewicka), (pdf), Nonlinearity, 19, 2006, 2605-2615.
  • Diffusion and Mixing in a Fluid Flow, (with P. Constantin, A. Kiselev and A. Zlatos),(pdf), Annals of Mathematics, 68, 2008, 643--674..
  • Wave field correlations in weakly mismatched random media (with G. Bal), (pdf), Stochastics and Dynamics, 2006, 301-328.
  • Existence of pulsating waves in a model of flames in sprays (with P. Constantin, K. Domelevo and J.-M. Roquejoffre), (pdf), Journal of the European Mathematical Society, 8, 2006, 555--584.
  • The stochastic acceleration problem in two dimensions (with T. Komorowski), (pdf), Israel Journal of Mathematics, 155, 2006, 157--204.
  • Non-adiabatic KPP fronts with an arbitrary Lewis number (with F. Hamel), (pdf), Nonlinearity, 18, 2005, 2881-2902.
  • Bounds on the speed of propagation of the KPP fronts in a cellular flow (with A. Novikov), (pdf), Archive for Rational Mechanics and Analysis, 184, 2007, 23--48.
  • Flame capturing with an advection-reaction-diffusion model (with N. Vladimirova and G. Weirs), (ps), Combustion Theory and Modeling, 10, 2006, 727-747.
  • Traveling fronts in porous media: existence and a singular limit (with P. Gordon), (pdf), Proceedings of the Royal Society London A, 462, 2006, 1965-1985.
  • Diffusion in a weakly random Hamiltonian flow (with T. Komorowski), (pdf), Communications in Mathematical Physics, 263, 2006, 277-323.
  • Quenching of reaction by cellular flows (with A. Fannjiang and A. Kiselev), (pdf), Geometric and Functional Analysis, 16, 2006, 40-69.
  • The quantum scattering limit for a regularized Wigner equation (with B. Perthame), (pdf), Methods and Applications of Analysis, 11, 2004, 447-464.
  • Non-Planar Fronts in Boussinesq Reactive Flows (with H. Berestycki and P. Constantin), (pdf), Ann. de l'Inst. Henri Poincar\'e, C. Analyse non lin\'eaire, 23, 2006, 407-437.
  • The KPP system in a periodic flow with a heat loss (with P. Gordon and N. Vladimirova), (ps,pdf ), Nonlinearity, 18, 2005, 571-589.
  • Quenching and propagation in KPP reaction-diffusion equations with a heat loss (with H. Berestycki, F. Hamel and A. Kiselev), (pdf), Archive for Rational Mechanics and Analysis, 178, 2005, 57-80.
  • Stability of time reversed waves in changing media (with G. Bal), (pdf), Discrete and Continuous Dynamical Systems A, 12, 2005, 793 - 815.
  • Time splitting for the Liouville equation in a random medium (with G. Bal), (pdf), Communications in Mathematical Sciences, 3, 2004, 515 - 534.
  • Boundary layers for cellular flows at high Peclet numbers (with A. Novikov and G. Papanicolaou), (ps,pdf)), Communications in Pure and Applied Mathematics, 58, 2005, 867-922.
  • Exponential decay for the fragmentation or cell-division equation (with B. Perthame), (pdf), Journal of the Differential Equations, 210, 2005, 155-177.
  • Time splitting for wave equations in random media (with G. Bal), (pdf), Model. Math. Anal. Num. (M2AN), 38, 2004, 961-987.
  • Flame Enhancement and Quenching in Fluid Flows (with N. Vladimirova, P. Constantin, A. Kiselev and O. Ruchaiskiy), (ps), Combustion Theory and Modeling, 7, 2003, 487 - 508.
  • Fronts in reactive convection: bounds, stability and instability (with P. Constantin and A. Kiselev), (ps), Communications in Pure and Applied Mathematics, 56, 2003, 1781-1803.
  • Self-averaging of Wigner transforms in random media (with G. Bal and T. Komorowski), (ps), Communications in Mathematical Physics, 242, 2003, 81-135.
  • Statistical stability in time reversal (with G. Papanicolaou and K. Solna), (ps), SIAM Journal of Applied Mathematics, 64, 2004, 1133-1155.
  • Stability in a nonlinear population maturation model (with S. Mischler and B. Perthame) (ps), M3AS (Mathematical Models & Methods in Applied Science), 12, 2002, 1751-1772.
  • Self-averaging in time reversal for the parabolic wave equation (with G. Bal and G. Papanicolaou), (ps), Stochastics and Dynamics, 2, 2002, 507-531.
  • The parabolic wave approximation and time reversal (with G. Papanicolaou and K. Solna), (ps), Matematica Contemporanea, 23, 2002, 139-159.
  • Time reversal and refocusing in random media (with G. Bal), (ps), SIAM Journal of Applied Mathematics, 63, 2003, 1475-1498.
  • Radiative transport limit for the random Schroedinger equation (with G. Bal and G. Papanicolaou), (ps), Nonlinearity, 15, 2002, 513-529.
  • Time Reversal for Classical Waves in Random Media (with G. Bal), (ps), Comptes rendus de l'Academies Sciences - Serie I/Mathematique, 333, 2001, 1041-1046.
  • Wave transport for a scalar model of the Love waves (with G. Bal), (ps), Wave Motion, 36, 2002, 49-66.
  • An upper bound for the bulk burning rate for systems (with A. Kiselev), (ps), Nonlinearity, 14, 2001, 1297-1310.
  • Quenching of flames by fluid advection (with P. Constantin and A. Kiselev), (ps), Communications in Pure and Applied Mathematics, 54, 2001, 1320--1342.
  • Enhancement of the traveling front speeds in reaction-diffusion equations with advection (with A. Kiselev), (ps), Ann. de l'Inst. Henri Poincar\'e, C. Analyse non lin\'eaire, 18, 2001, 309--358.
  • Wave transport along surfaces with random impedance (with G. Bal, V. Freilikher and G. Papanicolaou), (ps) Physical Review B, 62, 2000, 6228-6240.
  • Bulk burning rate in passive - reactive diffusion (with P. Constantin, A. Kiselev and A. Oberman), (ps), Archive for Rational Mechanics, 154, 2000, 53-91.
  • Probabilistic theory of transport processes with polarization (with G.Bal and G.Papanicolaou), (ps) SIAM Journal of Applied Mathematics, 60, 2000, 1639 - 1666.
    
  • Radiative Transfer of Sound Waves in a Random Flow: Turbulent Scattering and Mode-Coupling (with A.Fannjiang), (ps), SIAM Journal of Applied Mathematics, 61, 2001, 1545-1577.
    
  • Diffusive energy scattering from weakly random surfaces (with G.Bal and G.Papanicolaou), (ps), Journal of Mathematical Physics, 40, 1999, 4813-4827.
  • Diffusion approximation of radiative transfer problems with interfaces (with G.Bal), (ps)SIAM Journal of Applied Mathematics, 60, 2000, 1887-1912.
    
  • Transport theory for acoustic waves with reflection and transmission at interfaces (with G.Bal, J.B.Keller and G.Papanicoalou), (ps), Wave Motion, 30, 1999, 303-327.
    
  • Level sets in turbulent front propagation (with P.Constantin and A.Kiselev), (ps), Preprint, 1998.
    
  • Radiative transport in a periodic structure (with G.Bal, A.Fannjiang and G.Papanicolaou), (ps), Journal of Statistical Physics 95 (1/2):479-494, 1999.
  • Waves and transport (with G.Papanicolaou), IAS/Park City Mathematics Series, Vol. 5, L. Caffarelli and Weinan E, eds., AMS, 1998, pp. 305-382.
  • Evolution of trajectories correlations in steady random flows (with A.Fannjiang and G.Papanicolaou) (ps).
    In `Proceedings of Symposia in Applied Mathematics', Volume 54, R. Spigler and S. Venakides editors, American Mathematical Society, (1998), 105-130.
  • Transport equations for waves in a half space (with J.Keller and G.Papanicolaou) (ps).
    Comm. PDE's, 22, (1997), 1869-1910.
  • Transport equations for elastic and other waves in random media (with J.Keller and G.Papanicolaou) (ps). Wave Motion 24, (1996), 327-370
    
  • Stability of the P to S energy ratio in the diffusive regime (with George Papanicolaou and Joseph B. Keller) (ps). Bulletin of the Seismological Society of America 86, (1996), 1107-1115. Erratum. 86, (1996), p. 1997.
  • On the complete algebra of symmetries of integrable systems (with E.Schulman), Theor. Math. Phys. 95, 1993, 387-392.

  Curriculum Vitae

  Click here to see a more or less up to date vita. (pdf)
  
  

  Grants

  • NSF grant DMS-9971742 "Radiative transport theory for waves", August 1999-August 2002.
  • ONR grant N00014-02-1-0089 "Time-Reversal for Waves in Random Media", November 2001-2004.
  • Alfred P. Sloan Research Fellowship, 2002-2004.
  • NSF grant DMS-0203537 ``Propagation of fronts and waves in complex media'', 2002-2005.
  • DARPA-ONR grant N00014-04-1-0224 "Time Reversal for Electromagnetic Waves in Random Media", 2004-2009.
  • NSF grant DMS-0604687 ``The Kinetic Theory of Waves and Reactive-Diffusive Fronts'', 2006-2009.
  • NSF FRG grant DMS-0854952 "Stochastics and Dynamics: Asymptotic problems", 2009-2012.
  • NSF grant DMS-0908507 "Waves and Fronts in Heterogeneous Media", 2009-2012.

  Links

  Here are some links related to Israel.