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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