Overview

My research covers topics in:

• Applied Mathematics

• Numerical Analysis

• Scientific Computing

Publications

Works in Progress

1. Russo, J. D., Copperman, J., Aristoff, D., Simpson, G. & Zuckerman, D. M. Unbiased estimation of equilibrium, rates, and committors from Markov state model analysis. [arXiv]

2. Webber, R. J., Aristoff, D. , & Simpson G. A splitting method to reduce MCMC variance. [arXiv]

Refereed Journal Articles

1. Aristoff, D., Copperman, J., Simpson, G., Webber, R. J. & Zuckerman, D. M. Weighted ensemble: Recent mathematical developments. J. Chem. Phys. 158, 014108 (2023). [pdf]

2. Plecháč, P., Simpson, G. & Troy, J. R. Well-posedness of a random coefficient damage mechanics model*. Applicable Analysis 1–28 (2022). [pdf]

3. Medvedev, G. S. & Simpson, G. A numerical method for a nonlocal diffusion equation with additive noise. Stoch PDE: Anal Comp (2022). [pdf]

4. Jones, F. G. & Simpson, G. Iterate averaging, the Kalman filter, and 3DVAR for linear inverse problems. Numer Algor (2022). [pdf]

5. Swinburne, T. D. et al. Anharmonic free energy of lattice vibrations in fcc crystals from a mean-field bond. Phys. Rev. B 102, 100101 (2020). [pdf]

6. Plecháč, P. & Simpson, G. Sampling from rough energy landscapes. Communications in Mathematical Sciences 18, 2271–2303 (2020). [pdf]

7. Woloszynek, S. et al. Exploring thematic structure and predicted functionality of 16S rRNA amplicon data. PLOS ONE 14, e0219235 (2019). [pdf]

8. Simpson, G. & Watkins, D. Relative entropy minimization over Hilbert spaces via Robbins-Monro. AIMS Mathematics 4, 359–383 (2019). [pdf]

9. Copperman, J., Aristoff, D., Makarov, D. E., Simpson, G. & Zuckerman, D. M. Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture. J. Chem. Phys. 151, 174108 (2019). [pdf]

10. Ambrose, D. M., Gupta, E. D., Moskow, S., Ozornina, V. & Simpson, G. Detection of thin high contrast dielectrics from boundary measurements. J. Phys. Commun. 3, 115016 (2019). [pdf]

11. Ambrose, D. M., Simpson, G., Wright, J. D. & Yang, D. G. Existence theory for magma equations in dimension two and higher. Nonlinearity 31, 4724–4745 (2018). [pdf]

12. Marzuola, J. L., Raynor, S. G. & Simpson, G. Nonlinear Bound States in a Schrödinger–Poisson System with External Potential. SIAM J. Appl. Dyn. Syst. 16, 226–251 (2017). [pdf]

13. Jones, A. D., Simpson, G. & Wilson, W. Conservative integrators for a toy model of weak turbulence. Journal of Computational and Applied Mathematics 325, 113–124 (2017). [pdf]

14. Farmer, B., Luskin, M., Plecháč, P. & Simpson, G. Spin-diffusions and diffusive molecular dynamics. Modelling Simul. Mater. Sci. Eng. 25, 084003 (2017). [pdf]

15. Cher, Y., Simpson, G. & Sulem, C. Local Structure of Singular Profiles for a Derivative Nonlinear Schrödinger Equation. SIAM J. Appl. Dyn. Syst. 16, 514–545 (2017). [pdf]

16. Simpson, G., Luskin, M. & Srolovitz, D. J. A Theoretical Examination of Diffusive Molecular Dynamics. SIAM Journal on Applied Mathematics 76, 2175–2195 (2016). [pdf]

17. Olson, D., Shukla, S., Simpson, G. & Spirn, D. Petviashvilli’s Method for the Dirichlet Problem. J Sci Comput 66, 296–320 (2016). [pdf]

18. Côte, R., Muñoz, C., Pilod, D. & Simpson, G. Asymptotic Stability of High-dimensional Zakharov–Kuznetsov Solitons. Arch Rational Mech Anal 220, 639–710 (2016). [pdf]

19. Aristoff, D., Chill, S. & Simpson, G. Analysis of estimators for Adaptive Kinetic Monte Carlo. Commun. Appl. Math. Comput. Sci. 11, 171–186 (2016). [pdf]

20. Pinski, F. J., Simpson, G., Stuart, A. M. & Weber, H. Kullback–Leibler Approximation for Probability Measures on Infinite Dimensional Spaces. SIAM J. Math. Anal. 47, 4091–4122 (2015). [pdf]

21. Pinski, F. J., Simpson, G., Stuart, A. M. & Weber, H. Algorithms for Kullback–Leibler Approximation of Probability Measures in Infinite Dimensions. SIAM J. Sci. Comput. 37, A2733–A2757 (2015). [pdf]

22. Binder, A., Lelièvre, T. & Simpson, G. A generalized parallel replica dynamics. Journal of Computational Physics 284, 595–616 (2015). [pdf]

23. Ambrose, D. M. & Simpson, G. Local Existence Theory for Derivative Nonlinear Schrödinger Equations with Noninteger Power Nonlinearities. SIAM J. Math. Anal. 47, 2241–2264 (2015). [pdf]

24. Marzuola, J. L., Raynor, S. & Simpson, G. Dynamics near a minimal-mass soliton for a Korteweg–de Vries equation. Dynamical Systems 29, 285–299 (2014). [pdf]

25. Aristoff, D., Lelievre, T. & Simpson, G. The Parallel Replica Method for Simulating Long Trajectories of Markov Chains. Applied Mathematics Research eXpress (2014). [pdf]

26. Simpson, G. & Luskin, M. Numerical analysis of parallel replica dynamics. ESAIM: Mathematical Modelling and Numerical Analysis 47, 1287–1314 (2013). [pdf]

27. Liu, X., Simpson, G. & Sulem, C. Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation. J Nonlinear Sci 23, 557–583 (2013). [pdf]

28. Liu, X., Simpson, G. & Sulem, C. Focusing singularity in a derivative nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena 262, 48–58 (2013). [pdf]

29. Ginsberg, D. & Simpson, G. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. DCDS-B 18, 1305–1321 (2013). [pdf]

30. Colliander, J. E., Marzuola, J. L., Oh, T. & Simpson, G. Behavior of a Model Dynamical System with Applications to Weak Turbulence. Experimental Mathematics 22, 250–264 (2013). [pdf]

31. Ambrose, D. M., Simpson, G., Wright, J. D. & Yang, D. G. Ill-posedness of degenerate dispersive equations. Nonlinearity 25, 2655 (2012). [pdf]

32. Pelinovsky, D. E., Simpson, G. & Weinstein, M. I. Polychromatic Solitary Waves in a Periodic and Nonlinear Maxwell System. SIAM J. Appl. Dyn. Syst. 11, 478–506 (2012). [pdf]

33. Asad, R. & Simpson, G. Embedded eigenvalues and the nonlinear Schrödinger equation. Journal of Mathematical Physics 52, 033511 (2011). [pdf]

34. Simpson, G. & Zwiers, I. Vortex collapse for the L2-critical nonlinear Schrödinger equation. Journal of Mathematical Physics 52, 083503 (2011). [pdf]

35. Simpson, G. & Spiegelman, M. Solitary Wave Benchmarks in Magma Dynamics. J Sci Comput 49, 268–290 (2011). [pdf]

36. Simpson, G. & Weinstein, M. I. Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations. Multiscale Model. Simul. 9, 955–990 (2011). [pdf]

37. Simpson, G., Spiegelman, M. & Weinstein, M. I. A multiscale model of partial melts: 2. Numerical results. Journal of Geophysical Research: Solid Earth 115, (2010). [pdf]

38. Simpson, G., Spiegelman, M. & Weinstein, M. I. A multiscale model of partial melts: 1. Effective equations. Journal of Geophysical Research: Solid Earth 115, (2010). [pdf]

39. Marzuola, J. L. & Simpson, G. Spectral analysis for matrix Hamiltonian operators. Nonlinearity 24, 389 (2010). [pdf]

40. Marzuola, J. L., Raynor, S. & Simpson, G. A System of ODEs for a Perturbation of a Minimal Mass Soliton. J Nonlinear Sci 20, 425–461 (2010). [pdf]

41. Colliander, J., Simpson, G. & Sulem, C. Numerical Simulations of the Energy-Supercritical Nonlinear Schrödinger Equation. J. Hyper. Differential Equations 07, 279–296 (2010). [pdf]

42. Simpson, G., Sulem, C. & Sulem, P. L. Arrest of Langmuir wave collapse by quantum effects. Phys. Rev. E 80, 056405 (2009). [pdf]

43. Simpson, G. & Weinstein, M. I. Asymptotic Stability of Ascending Solitary Magma Waves. SIAM J. Math. Anal. 40, 1337–1391 (2008). [pdf]

44. Simpson, G., I. Weinstein, M. & Rosenau, P. On a Hamiltonian PDE arising in magma dynamics. Discrete & Continuous Dynamical Systems - B 10, 903–924 (2008). [pdf]

45. Simpson, G., Spiegelman, M. & Weinstein, M. I. Degenerate dispersive equations arising in the study of magma dynamics. Nonlinearity 20, 21–49 (2007). [pdf]

Conference Proceedings

1. Weber, R. O., Goel, P., Amiri, S. & Simpson, G. Longitudinal Distance: Towards Accountable Instance Attribution. in Workshops Proceedings for the 29th International Conference on Case-Based Reasoning vol. CEUR Volume 3017 (2021). [pdf]