Publications

    Submitted Articles

  1. B.A. Farmer, M. Luskin, P. Plechac, G. Simpson. Spin-Diffusions and Diffusive Molecular Dynamics. [arXiv]
  2. G. Simpson, D. Watkins. Relative Entropy Minimization over Hilbert Spaces via Robbins-Monro. [arXiv]
  3. Published Articles

  4. J.L. Marzuola, S.G. Raynor, G. Simpson. Nonlinear Bound States in a Schrodinger--Poisson System with External Potential. SIAM Journal on Applied Dynamical Systems, 16(1), 2017. [arXiv]
  5. A.D. Jones, G. Simpson, W. Wilson. Conservative Integrators for a Toy Model of Weak Turbulence. Journal of Computational and Applied Mathematics, 325, 113-124, 2017.[arXiv]
  6. Y. Cher, G. Simpson, C. Sulem. Local Structure of Singular Profiles for a Derivative Nonlinear Schrodinger Equation. SIAM Journal on Applied Dynamical Systems, 16(1), 514-545, 2017. [arXiv]
  7. D. Aristoff, S.T. Chill, G. Simpson. Analysis of estimators for adaptive Kinetic Monte Carlo. Communications in Applied Mathematics and Computational Science, 11(2), 171-186, 2016. [arXiv]
  8. R. Cote, C. Munoz, D. Pilod, G. Simpson. Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons. Archive for Rational Mechanics and Analysis, 220(2), 639-710, 2016. [arXiv]
  9. M. Luskin, G. Simpson, D.J. Srolovitz. A Theoretical Examination of Diffusive Molecular Dynamics, SIAM Journal on Applied Mathematics, 76(6), 2176-2196, 2016.
  10. D. Olson, S. Shukla, G. Simpson, D. Spirn. Petviashvilli's Method for the Dirichlet Problem. Journal of Scientific Computing, 66(1), 297-320, 2016. [arXiv]
  11. F. J. Pinski, G. Simpson, A. M. Stuart, H. Weber. Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions. SIAM Journal on Scientific Computing, 37(6), A2733-A2757, 2015. [arXiv]
  12. F. J. Pinski, G. Simpson, A. M. Stuart, H. Weber. Kullback-Leibler approximation for probability measures on infinite dimensional spaces. SIAM Journal on Mathematical Analysis, 47(6), 4091-4122, 2015. [arXiv]
  13. D. M. Ambrose, G. Simpson. Local Existence Theory for Derivative Nonlinear Schrödinger Equations with Non-Integer Power Nonlinearities. SIAM Journal on Mathematical Analysis, 47(3), 2241-2264,2015. [arXiv]
  14. A. Binder, T. Lelievre, G. Simpson. A Generalized Parallel Replica Dynamics. Journal of Computational Physics, 284, 595-616, 2015. [arXiv]
  15. D. Aristoff, T. Lelievre, G. Simpson. The parallel replica method for simulating long trajectories of Markov chains. AMRX, 2014(2), 332-352, 2014. [arXiv]
  16. J. L. Marzuola, S. Raynor, G. Simpson. Dynamics near a minimal mass soliton for a generalized Korteweg-de Vries equation. Dynamical Systems, 29 (2), 285-299, 2014. [arXiv]
  17. X. Liu, G. Simpson, C. Sulem. Focusing Singularity in a Derivative Nonlinear Schrodinger Equation. Physica D, 262:45-58, 2013. [pdf][arXiv]
  18. J.E. Colliander, J.L. Marzuola, T. Oh, G. Simpson. Behavior of a Model Dynamical System with Applications to Weak Turbulence. Experimental Mathematics, 22(3):250-264, 2013 [pdf][arXiv]
  19. G. Simpson, M. Luskin. Numerical Analysis of Parallel Replica Dynamics. M2AN, 47:1287-1314, 2013. [pdf][arXiv]
  20. D. Ginsberg, G. Simpson. Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation. DCDS-B, 18(5):1305-1321, 2013. [pdf][arXiv]
  21. X. Liu, G. Simpson, C. Sulem. Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrodinger Equation. Journal of Nonlinear Science, 23:557-583, 2013. [pdf][arXiv]
  22. D.M. Ambrose, G. Simpson, J.D. Wright, D.G. Yang. Ill-Posedness of Degenerate Dispersive Equations. Nonlinearity, 25(9): 2655--2680, 2012. [pdf][arXiv]
  23. D. Pelinovsky, G. Simpson, M.I. Weinstein. Polychromatic Solitons in a Periodic and Nonlinear Maxwell System. SIADS, 11(1):478--506, 2012. [pdf][arXiv][animations]
  24. G. Simpson, I. Zwiers. Vortex Collapse for the L2-Critical Nonlinear Schrodinger Equation. Journal of Mathematical Physics, 52(8):083503, 2011. [pdf][arXiv][codes]
  25. G. Simpson, M.I. Weinstein. Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations. MMS, 9(3):955--990, 2011. [pdf][arXiv]
  26. G. Simpson, M. Spiegelman. Solitary Wave Benchmarks in Magma Dynamics. Journal of Scientific Computing, 49(3):268--290, 2011. [pdf][SpringerLink]
  27. R. Asad, G. Simpson. Embedded Eigenvalues and the Nonlinear Schrodinger Equation. Journal of Mathematical Physics, 52:033511, 2011. [pdf][arXiv][codes]
  28. J.L. Marzuola, G. Simpson. Spectral Analysis for Matrix Hamiltonian Operators. Nonlinearity, 24:389-429, 2011. [pdf][codes]
  29. J. Colliander, G. Simpson, and C. Sulem. Numerical simulations of the energy- supercritical Nonlinear Schrodinger equation. JHDE, 7:279--296, 2010. [pdf]
  30. J. Marzuola, S. Raynor, and G. Simpson. A System of ODEs for a Perturbation of a Minimal Mass Soliton. Journal of Nonlinear Science , 20:425--461, 2010. [pdf]
  31. G. Simpson, M. Spiegelman, and M.I. Weinstein. A Multiscale Model of Partial Melts 2: Numerical Results. Journal of Geophysical Research -- Solid Earth, 115, B04411. [pdf]
  32. G. Simpson, M. Spiegelman, and M.I. Weinstein. A Multiscale Model of Partial Melts 1: Effective Equations. Journal of Geophysical Research -- Solid Earth, 115, B04410. [pdf]
  33. G. Simpson, C. Sulem, and P.L. Sulem. Arrest of Langmuir wave collapse by quantum effects. PRE , 80:5, 056405, 2009. [pdf]
  34. G. Simpson and M.I. Weinstein. Asymptotic stability of ascending solitary magma waves. SIAM J. Math. Anal., 40:1337--1391, 2008. [pdf]
  35. G. Simpson, M.I. Weinstein and P. Rosenau. On a Hamiltonian PDE arising in magma dynamics. DCDS-B, 10:903--924, 2008. [pdf]
  36. G. Simpson, M. Spiegelman, and M.I. Weinstein. Degenerate dispersive equations arising in the study of magma dynamics. Nonlinearity, 20:21--49, 2007. [pdf]
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