Project Overview

The central theme of the research is development of a mathematical and computational framework that enables rational control and design of materials forming by self-assembly processes. The spontaneous character of self-assembly gives great promise for easy and cheap scale-up of devices for commercial use. However, it has eluded researchers how to reproducibly control and design such systems, a difficulty stemming from their inherent stochasticity and emergent behavior. The proposed framework is based on novel mathematical and computational tools that enable, for the first time, modeling of stochastic processes with sufficient accuracy over realistic length and time scales and systematic derivation of coarse-grained approximations used in simulations and control of self-assembly. The project is a collaboration between mathematicians at University of Tennessee, Knoxville and University of Massachusetts, Amherst and chemical engineers at University of Delaware. The project is funded by National Science Foundation under the CDI initiative for the period Sep 2008 – Sep 2012.

Publications

2013

M. A. Katsoulakis, P. Plechac

Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems
(preprint-arXiv:)
J. Chem. Phys. 139 (2013), 074115 (online)

2012

G. Arampatzis, M. A. Katsoulakis, P. Plechac

Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo.
(preprint-arXiv:)
to appear in SIAM J. Numer. Anal.

E. Kalligiannaki, M. A. Katsoulakis, P. Plechac

Spatial multi-level interacting particle simulations and information theory-based error quantification.
(preprint-arXiv: 1208.0730)
to appear in SIAM J. Sci. Comp.

G. Arampatzis, M. A. Katsoulakis, P. Plechac, M. Taufer, L. Xu

Fractional-step kinetic Monte Carlo algorithms and hierarchical parallelization
(preprint-arXiv:1105.4673)
J. Comp. Phys. DOI: 10.1016/j.jcp.2012.07.017,
available in electronic form

2011

N. M. Abukhdeir and D. G. Vlachos

Nano-scale surface pattern evolution in heteroepitaxial bimetallic films
accepted in ACS Nano

Y. Pantazis, M. A. Katsoulakis

Controlled-error approximations for surface diffusion of interacting particles with applications to pattern formation
(preprint-arXiv:1109.2077 [math.PH])
submitted to SIAM Sci. Computing

E. Kalligiannaki, M. A. Katsoulakis, P. Plechac, D. G. Vlachos

Multilevel coarse graining and nano–pattern discovery in many particle stochastic systems
(preprint-arXiv:1109.0459)
J. Comp. Phys. (2011) DOI: 10.1016/j.jcp.2011.12.011 available in electronic form

E. Kalligiannaki, M. A. Katsoulakis, P. Plechac

Coupled coarse-graining and Markov Chain Monte Carlo for lattice systems
in Numerical Analysis and Multiscale Computations, Ed. B. Enguist, O. Runborg, R. Tsai, Lecture Notes on Computational Science and Engineering (LNCSE), Springer, 2011

N.M. Abukhdeir, D. G. Vlachos, M.A. Katsoulakis and M. Plexousakis

Long-time integration methods for mesoscopic models of pattern-forming systems
J. Comp. Phys. 230, 14, 5704-5715, (2011)

M. Salciccioli, M. Stamatakis, S. Caratzoulas, and D. G. Vlachos

A review of multiscale modeling of catalytic reactions: Mechanism development for complexity and emergent behavior
Chem. Eng. Sci. 66, 4319-4355 (2011)

2010

H. Y. Wang, M. Stamatakis, D. A. Hansgen, S. Caratzoulas, and D. G. Vlachos

Understanding mixing of Ni and Pt in the Ni/Pt(111) bimetallic catalyst via molecular simulation and experiments
J. Chem. Phys. 133, 2245031-22450311 (2010)

E. Kalligiannaki, M. A. Katsoulakis, P. Plechac

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
(preprint-arXiv:1006.3781)

M. A. Katsoulakis, P. Plechac, L. Rey-Bellet, D. K. Tsagkarogiannis

Coarse-graining schemes for stochastic lattice systems with short and long-range interactions (arXiv:1006.1506) submitted to Math. Comp.

P. Plechac, M. Rousset,

Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems.
SIAM Multiscale Meth. Sim., 8(2), pp. 498-539 (2010), (preprint)

2009

S. Are, M. A. Katsoulakis, A. Szepessy

Coarse-grained Langevin approximations and spatiotemporal acceleration for kinetic Monte Carlo simulations of diffusion of interacting particles.
Chin. Ann. Math. Ser. B, 30, 6, 653-682, (2009)

M. A. Katsoulakis, P. Plechac, D.G. Vlachos,

Hierarchical pattern discovery in stochastic lattice systems. (preprint)

J. Mascie-Taylor, P. Plechac

Multi-level coarse graining methods for sampling stochastic particle systems.(preprint)

2008

S. Are, M. A. Katsoulakis, P. Plechac, L. Rey-Bellet,

Multi-body interactions in coarse-graining schemes for extended systems.
SIAM J. Sci. Comp., 31(2), pp. 987-1015 (2008),
(preprint)

M.A. Katsoulakis, P. Plechac and L. Rey-Bellet,

Numerical and statistical methods for the coarse-graining of many-particle stochastic systems.
J. Sci. Comp. 37, (2008), 43-71,
(preprint)

2007

Chatterjee, A., Vlachos, D. G.,

Systems tasks in nanotechnology via hierarchical multiscale modeling: Nanopattern formation in heteroepitaxy.
Chem. Eng. Sci. 2007, 62, (18-20), 4852- 4863.

Chatterjee, A., Vlachos, D. G.,

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods.
Journal of Computer-Aided Materials Design 2007, 14, (2), 253-308, invited.

Chatterjee, A., Vlachos, D. G.,

A continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.
J. Chem. Phys. 2007, 127, (3), 0347051-03470516; Selected also for the July 30, 2007 issue of Virtual J. Nanoscale Sci. Tech

Funding

This collaborative project was funded by NSF CMMI under Grant Numbers 0835582 — 0835548 — 0835673