Homepage of Markos A. Katsoulakis

Recent Preprints

1. arXiv:1109.2077

Title: Controlled-Error Approximations for Surface Diffusion of Interacting Particles with Applications to Pattern Formation

Authors: Yannis Pantazis, Markos A. Katsoulakis

2. arXiv:1109.0459

Title: Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems

Authors: Evangelia Kalligiannaki, Markos A. Katsoulakis, Petr Plechac, Dionisios G Vlachos

3. arXiv:1105.4673

Title: Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

Authors: Giorgos Arampatzis, Markos A. Katsoulakis, Petr Plechac, Michela Taufer, Lifan Xu

4. arXiv:1007.0723

Title: Deterministic Equations for Stochastic Spatial Evolutionary Games

Authors: Sung-Ha Hwang, Markos A. Katsoulakis, Luc Rey-Bellet

5. arXiv:1006.3781

Title: Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

Authors: Evangelia Kalligiannaki, Markos A. Katsoulakis, Petr Plechac

6. arXiv:1003.1506

Title: Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

Authors: Markos A. Katsoulakis, P.Plechac, L. Rey-Bellet, D. K. Tsagkarogiannis

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Selected publications

• 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).
• 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.
• 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.