Research interests

monte carlo methods, numerical analysis, modeling and simulation, phase transitions and metastability, random graphs and networks

Grants

  • NSF-DMS-1818726. "Stochastic Methods for Complex Systems" (joint PI with G. Simpson), 8/01/2018--7/31/2021
  • NSF-DMS-1522398. "Algorithms for Complex Systems" (sole PI), 8/15/2015--7/31/2018

    • Publications

    computational methods
  • Optimizing weighted ensemble sampling of steady states
           arXiv:1806.00860v2 (with D.M. Zuckerman)
  • Generalizing parallel replica dynamics: trajectory fragments, asynchronous computing, and PDMPs
           arXiv:1802.09444v3
  • Analysis and optimization of weighted ensemble sampling
           (2018) ESAIM: Mathematical Modelling and Numerical Analysis 52(2018), 1219--1238
  • Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics
           (2018) SIAM Multiscale Model. Simul. 16(1), 1--27 (with T. Wang and P. Plecháč)
  • Analysis of estimators for adaptive Kinetic Monte Carlo
           (2016) Comm. App. Math. and Comp. Sci. 11(2), 171--186 (with S. Chill and G. Simpson)
  • A mathematical framework for exact milestoning
           (2016) SIAM Multiscale Model. Simul. 14(1), 301--322 (with J.M. Bello-Rivas and R. Elber)
  • The parallel replica method for computing equilibrium averages of Markov chains
           (2015) Monte Carlo Methods Appl. 21(4), 255--273
  • Adaptive multilevel splitting in molecular dynamics simulations
           (2015) ESAIM: Proceedings and Surveys 48, 215--225 (with T. Lelièvre, C. Mayne and I. Teo)
  • The parallel replica method for simulating long trajectories of Markov chains
           (2014) Appl. Math Res. Express 2014(2), 332--352 (with T. Lelièvre and G. Simpson)
  • Mathematical analysis of temperature accelerated dynamics
           (2014) SIAM Multiscale Model. Simul. 12(1), 290--317 (with T. Lelièvre)

    • random graphs and lattice models
  • On the phase transition curve in a directed exponential random graph model
           (2018) Adv. Appl. Prob. 50(1), 272--301 (with L. Zhu)
  • Lattice gas models with long range interactions
           (2017) J. Math. Phys. 58(2), 023301 (with L. Zhu)
  • Asymptotic structure and singularities in constrained directed graphs
           (2015) Stoch. Proc. Appl. 125(11), 4154--4177 (with L. Zhu)
  • Emergent structures in large networks
           (2013) J. Appl. Prob. 50, 883--888 (with C. Radin)

    • percolation
  • Percolation of hard disks
           (2014) J. Appl. Prob. 51(1), 235--246

    • phase transitions
  • Rigidity in Solids
           (2011) J. Stat. Phys. 144, 1247--1255 (with C. Radin)
  • First order phase transition in a model of quasicrystals
           (2011) J. Phys. A: Math. Theor. 44, 255001 (with C. Radin)
  • Dilatancy transition in a granular model
           (2011) J. Stat. Phys. 143, 215--225 (with C. Radin)
  • First order phase transition of a long polymer chain
           (2011) J. Phys. A: Math. Theor. 44, 065004 (with C. Radin)
  • Random close packing in a granular model
           (2010) J. Math. Phys. 51, 113302 (with C. Radin)
  • Layering in crumpled sheets
           (2010) Europhys. Lett. 91, 56003 (with C. Radin)
  • Random loose packing in granular matter
           (2009) J. Stat. Phys. 135, 1--23 (with C. Radin)

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