Markos Katsoulakis
Professor
Director, Center for Applied Mathematics and Computation
- Address:
Department of Mathematics and
Statistics
University of Massachusetts at Amherst
Amherst, MA 01003
USA
- Telephone:
413-545-1331
413-545-1801 (Fax)
- Email:
markos@math.umass.edu
Courses
Research Interests:
- Nonlinear Partial Differential Equations
- Stochastic Processes
- Statistical Mechanics
- Monte Carlo Methods
Recent Publications:
- Stochastic Ising models and anisotropic front propagation
(with P.E. Souganidis),
J. Stat. Phys. 87, (1997), 63-89.
- Contractive Relaxation Systems and the Scalar
Multidimensional Conservation Law,
(with A.E. Tzavaras), Comm. P.D.E. 22, (1997), 195-233.
- Convergence and Error Estimates of Relaxation Schemes
for Multidimensional Conservation Laws (with G. Kossioris and Ch. Makridakis),
Comm. P.D.E. 24, (1999), 395-423.
- Relaxation Schemes for Curvature-Dependent Front Propagation,
(with S. Jin and Z. Xin), Comm. Pure Appl. Math. 52, 12,
(1999), 1587--1615.
- Multiscale Analysis for Interacting Particles: Relaxation
Systems and Scalar Conservation Laws (with A.E. Tzavaras),
J. Stat. Phys. 96, 3/4, (1999), 715--763.
- From microscopic interactions to macroscopic laws
of cluster growth (with D. G. Vlachos), Phys. Rev. Lett. 84, 7, (2000),
1511-1514.
- Relaxation limits for systems of conservation laws,
satisfying a super-characteristic condition,
(with S. Jin), SIAM J. Appl. Math. 61, 1, (2000), 273-292.
- Mesoscopic Theories for the Diffusion of Interacting Molecules,
(with D. G. Vlachos), Phys. Rev. Lett. 85, 18, (2000), 3898-3901.
- Bridging the gap of multiple scales: From microscopic, to
mesoscopic, to macroscopic models, (with P. Aghalayam, S. Raimondeau, and D. G.
Vlachos), Proceedings of
the ``Foundations of Molecular Modeling and Simulation 2000".
- Stochastic Curvature Flows: Asymptotic Derivation, Level Set Formulation
and Numerical Experiments, (with A. T. Kho), J. Interfaces
and Free Boundaries 3, (2001), 265-290.
- Spectral Methods for Mesoscopic Models In Pattern Formation,
(with D. J. Horntrop and D. G. Vlachos), J. Comp. Phys.
173,
(2001), 361-390.
- Mesoscopic modeling of surface processes,
(with D. G. Vlachos), IMA Vol. Math. Appl. 136 (2003), 179-198.
- Fokker-Planck equations for an equilibrium model of
chromatin folding, (with A. T. Kho and N. Whitaker), G.A.N.G. Preprint 5.9.
-
Validation of mesoscopic
theories and their application to computing concentration
dependent diffusivities, (with T. Basak, R. Lam and D. G. Vlachos),
J. Chem. Phys.
115, (2001), 11278-11288.
-
Homogenization of mesoscopic theories: effective
properties of model membranes,
figures ,
(with R. Lam and D. G. Vlachos),
Amer. Inst. Chem. Eng. (AIChE) Journal, 48, (2002), 1083-1092.
-
Mesoscopic modeling of transport and reaction
in microporous crystalline membranes,
(with M. A. Snyder and D. G. Vlachos),
Chem. Eng. Science, 58, (2003), 895-901.
-
Coarse-grained stochastic processes for lattice systems,
figures ,
(with A. J. Majda and D. G. Vlachos), Proc. Natl. Acad. Sci. USA, 100, (2003), 782-787.
-
Wave initiation through spatiotemporally structured perturbations
(joint with G. Ertl, I. G. Kevrekidis, X. Li, A. Papathanasiou, H.H.Rotermund and
J. Wolff), Phys. Rev. Lett. 90, 14, (2003).
-
Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems,
figures,
(with A. J. Majda and D. G. Vlachos), J. Comp. Phys.
186, (2003), 250-278.
-
Hierarchical kinetic Monte Carlo simulations for diffusion of interacting molecules,
figures ,
(with D. G. Vlachos), accepted to J. Chem. Phys.
- Statistical equilibrium measures in micromagnetics,
(with P. Plechac), submitted.
- A Hamilton Jacobi theory for controlled gradient flows in infinite dimensions,
(with J. Feng), submitted.
Conferences: