Homepage of Markos A. Katsoulakis

Professor



Department of Mathematics and Statistics , UMass, Amherst

710 N. Pleasant Street, Amherst, MA 01003, USA
Room: LGRT 1423G
Tel: (413) 545 1331
Fax: (413) 545 1801
Email: markos [at] math umass edu

Education

Ph.D., Brown University, U.S.A., 1993
B.Sc., National and Kapodistrian University of Athens, Greece, 1987


Recent Preprints

1. arXiv:1311.5710v2 [pdf]
Title: Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations


Selected publications

  • Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo
  • , (with G. Arampatzis and P. Plechac), SIAM Num. Analysis, to appear, (2014).
  • Spatial two-level interacting particle simulations and information theory-based error quantification, (with E. Kalligiannaki and P. Plechac), SIAM Sci. Comp., to appear, (2014).
  • Coarse-graining schemes for stochastic lattice systems with short and long-range interactions, (with Petr Plechac, Luc Rey-Bellet and Dimitrios Tsagkarogiannis), Math. Comp., in press, (2014).
  • Measuring the irreversibility of numerical schemes for reversible stochastic differential equations, (with Y. Pantazis and L. Rey-Bellet.), ESAIM: Mathematical Modelling and Numerical Analysis, doi:10.1051/m2an/2013142, (2014).
  • Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Informa\ tion Theory, (with Y. Pantazis and D.G. Vlachos), BMC Bionformatics, 14:311, doi:10.1186/1471-2105-14-311, (2013).
  • Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended system, (with Petr Plechac), J. Chem. Phys., 139, 07\ 4115, (2013).
  • A Relative Entropy Rate Method for Path Space Sensitivity Analysis of Stationary Complex Stochastic Dynamics, (with Yannis Pantazis), J. Chem. Phys., 138, 054115, (2013).
  • Deterministic Equations for Stochastic Spatial Evolutionary Games, (with Sung-Ha Hwang and , Luc Rey-Bellet), Theoretical Economics, 8, 829–874, (2013).
  • Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms (with Giorgos Arampatzis, Petr Plechac, Michela Taufer, Lifan Xu), J. Comp. Phys., 231, 7795- 7814, (2012).
  • Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems. (with E. Kalligiannaki, P. Plechac and D. G. Vlachos), J. Comp. Phys., 231, 2599-2620, (2012).
  • Long-time integration methods for mesoscopic models of pattern-forming systems, (with N.M\ . Abukhdeir, D. G. Vlachos, and M. Plexousakis), J. Comp. Phys. 230, 5704-5715, (2011).
  • Hybrid Deterministic Stochastic Systems with Microscopic Look-ahead Dynamics, (with A. J. Majda and A. Sopasakis), Comm. Math. Sci. 8, 409-437, (2010), [Special volume dedicated to the sixtieth birthday of Professor Andrew Majda].
  • A Hamilton Jacobi theory for controlled gradient flows in infinite dimensions, (with J. Feng), Arch. Rat. Mech. Analysis 192, 2 , 275-310 (2009).
  • Multi-body interactions in coarse-graining schemes for extended systems (with S. Are, P. Plechac and L. Rey-Bellet), SIAM Sci. Comp., 31, No. 2, 987-1015, (2008).
  • Error control and analysis in coarse-graining of stochastic lattice dynamics (with P. Plechac and A. Sopasakis),SIAM J. Num. Analysis 4 (6), 2270-2296 (2006).
  • Intermittency, metastability and coarse-graining in deterministic/stochastic lattice systems (with A. J. Majda and A. Sopasakis),Nonlinearity 19, 1021-1047, (2006).
  • Mechanistic Principles of Nanoparticle Evolution to Zeolite Crystals (with T. M. Davis, T. O. Drews, H. Ramanan, C. He, J. Dong, H. Schnablegger, E. Kokkoli, A. V. McCormick, R. L. Penn, and M. Tsapatsis), Nature Materials, 5, 400, (2006).
  • Stochastic modeling and simulation of traffic flow: ASEP with Arrhenius look-ahead dynamics, (with A. Sopasakis), SIAM J. Appl. Math., 66, 921-944, (2006).
  • Binomial distribution based τ-leap accelerated stochastic simulation, (with A. Chaterjee and D. G. Vlachos), J. Chem. Phys. 122, 024112 (2005).
  • Coarse-grained stochastic models for tropical convection and climate, (with B. Khouider and A. J. Majda), Proc. Natl. Acad. Sci. USA 100, (2003), 11941-11946.
  • Coarse-grained stochastic processes for lattice systems, (with A. J. Majda and D. G. Vlachos), Proc. Natl. Acad. Sci. USA 100, (2003), 782-787.
  • Hierarchical kinetic Monte Carlo simulations for diffusion of interacting molecules, (with D. G. Vlachos), J. Chem. Phys. 112, 18, (2003).
  • Spectral Methods for Mesoscopic Models In Pattern Formation, (with D. J. Horntrop and D. G. Vlachos), J. Comp. Phys. 173, (2001), 361-390.
  • Mesoscopic Theories for the Diffusion of Interacting Molecules, (with D. G. Vlachos), Phys. Rev. Lett. 85, 18, (2000).
  • From microscopic interactions to macroscopic laws of cluster growth (with D. G. Vlachos), Phys. Rev. Lett. 84, 7, (2000), 1511-1514.
  • Relaxation Schemes for Curvature-Dependent Front Propagation, (with S. Jin and Z. Xin), Comm. Pure Appl. Math. 52, 12, (1999), 1587{1615.
  • 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.
  • Contractive Relaxation Systems and the Scalar Multidimensional Conservation Law, (with A.E. Tzavaras), Comm. P.D.E. 22, (1997), 195-233.
  • Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interactions and Glauber dynamics (with P. E. Souganidis), Comm. Math. Phys., 169, (1995), 61-97.
  • Interacting Particle Systems and Generalized Evolutions of Fronts (with P. E. Souganidis), Arch. Rat. Mech. Anal., 127, (1994), 133-157.
  • Viscosity Solutions of 2nd Order Fully Nonlinear Elliptic Equations with State Constraints, Indiana U. Math. J. 43, (1994), 493-519.

Research

ResearchGate Profile


Teaching

This semester I am teaching:

Math 534: Introduction to Partial Differential Equations

Math 331.1: Ordinary Differential Equations

Past Semesters:

Math 697SC: Computational Methods for Stochastic Systems See link for the class projects