Research Interests:

Research projects for prospective graduate students

(contact me by e-mail for more details)
  1. Topic I: algorithms and numerical analysis for stochastic particle dynamics (funding available)
    development and analysis coarse-graining and sampling algorithms for large particle systems with applications in modeling of polymers and macromolecules, magnetic systems
    basic knowledge of stochastic processes and probability is required, good computational skills and familiarity with Monte Carlo methods will be plus.
  2. Topic II: fast algorithms for PDEs in high dimensions
    development, analysis and implementation of algorithms based on multi-resolution analysis.
  3. Topic III: numerical methods for processing large data set
    development and implementation of algorithms for fast extraction of information from large data sets.
  4. Topic IV: approximation of singular solutions to PDEs
    approximation and numerical analysis of solution to certain PDEs that exhibit finite-time singularity.

Preprints:

Recent preprints:

2010
10-3: Best-fit quasi-equilibrium ensembles: a general approach to statistical closure of underresolved Hamiltonian dynamics II
10-2: Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
10-1: Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

2009
09-3: Multi-level coarse graining methods for sampling stochastic particle systems.
09-2: Hierarchical pattern discovery in stochastic lattice systems
09-1: Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems

2008
08-1: Multi-body interactions in coarse-graining schemes for extended systems.
08-2: Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach.

2007
07-1: Mathematical strategies in the coarse-graining of extensive systems: error quantification and adaptivity.
07-2: Numerical studies of a coarse-grained approximation of dynamics of an atomic chain
07-3: Microscopic simulation of epidermal growth on corralled membrane surfaces
07-4: Numerical and statistical methods for the coarse-graining of many-particle stochastic systems. (review)
07-5: Best-fit quasi-equilibrium ensembles: a general approach to statistical closure of underresolved Hamiltonian dynamics.

2006
06-1: Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

2005
05-1: Mathematical tools for error analysis of coarse-graining of lattice systems.
05-2: Error analysis of coarse-grained kinetic Monte Carlo method.

Some older (1997-2004) preprints available in PostScript/PDF format can be downloaded here

Selected publications:

 
  • Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems.
    •   SIAM Multiscale Modeling and Simulations 8, (2010), No 2, pp. 498-539 (with M. Rousset), (SIAM reprint) (preprint)
     
  • Multi-body interactions in coarse-graining schemes for extended systems.
    •   SIAM J. Sci. Comp. (2008), (with S. Are, and M.A. Katsoulakis, and L. Rey-Bellet), (preprint)
     
  • Numerical and statistical methods for the coarse-graining of many-particle stochastic systems.
    •   J. Sci. Comp. 37, (2008), 43-71 (with M.A. Katsoulakis, and L. Rey-Bellet), (preprint)
     
  • Microscopic simulation of epidermal growth on corralled membrane surfaces
    •   Biophysical Journal , 94, No 5, ahead of print on-line as doi:10.1529/biophysj.107.106484, (2007) (A. M. Niehaus, D. Vlachos, J. S. Edwards, and R. Tribe), (preprint)
     
  • Mathematical strategies in the coarse-graining of extensive systems: error quantification and adaptivity.
    •   J. Non-Newtonian Fluid Mech., in press, available on-line 21 May, (2007) (with M.A. Katsoulakis, L. Rey-Bellet and D. Tsagkarogiannos), (preprint)
     
  • Numerical studies of a coarse-grained approximation of dynamics of an atomic chain.
    •   Intl. J. Multiscale Comp. Eng. , 5, No 5, 351-367, (2007) (with P. Lin), (preprint)
     
  • Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
    •   ESAIM Math. Meth. Anal. Numer., 47, 627-660, (2007) (with M.A. Katsoulakis, L. Rey-Bellet and D. Tsagkarogiannos), (preprint)
     
  • Error analysis of coarse-graining for stochastic lattice dynamics
    •  SIAM J. Numer. Analysis , 44, pp.2270-2296, (2006) (with M.A. Katsoulakis and A. Sopasakis), (SIAM reprint)
     
  • Mesoscopic modeling for continuous spin lattice systems: Model problems and micromagnetics application.
    •  J. Stat. Phys. ,119, No.1-2, 347-389, (2005) (with M.A. Katsoulakis and D. Tsagkarogiannis), (preprint)
     
  • Convergence for stabilisation of degenerately convex minimisation problems.
    •  Interfaces and Free Boundaries , 6, 253-269, (2004) (with S. Bartels, C. Carstensen and A. Prohl), (preprint)
     
  • Singular and regular solutions of a non-linear parabolic system
    •  Nonlinearity, 161, No.6, 2083-2097, (2003) (with V. Sverak), (reprint)
     
  • A visco-elasto-plastic model for phase transformations.
    •  Math. Methods in Appl. Sciences, 25, 1281-1298, (2002), (with T. Roubicek)
     
  • On  self-similar singular solutions of the complex Ginzburg-Landau equation.
    •  Comm. Pure and Appl. Math. , 54, 1215-1242, (2001), (with V. Sverak), (preprint)
     
  • Numerical analysis of a relaxed variational model of hysteresis.
    •  RAIRO Modelisation Math. et Analyse Numer., 35, 865-878, (2001) (with C. Carstensen), (preprint)
     
  • Numerical analysis of compatible phase transitions in elastic solids
    • SIAM J. Numer. Analysis, 37,2061-2081, (2000), (with C. Carstensen), (preprint)
     
  • Finite element computation of macroscopic quantities in nonconvex minimisation problems and applications in materials science
    • In: A. M. Saendig, W. Schiehlen, W.L. Wendland (eds.): ``Multifield Problems. State of the Art.'', Springer-Verlag, Berlin, pp. 69-79, (2000).
    (with S. Bartels, C. Carstensen)
     
  • PARASOL: integrated environment for solution of sparse linear systems
    • In High Performance Computing, Kluwer New York (1999).
    (with P. Amestoy, I.S. Duff, J-Y L'Excellent)
     
  • Vertex models on Feynman diagrams
    • Phys. Lett. A, 248, No 1, 37-48 (1998), (with D.A. Johnston)
     
  • Equivalence of ferromagnetic spin models on trees and random graphs.
    • J. Phys. A, Math. Gen. , 31, No.2, 475-482 (1998), (with D.A. Johnston)
     
  • Adaptive algorithms for scalar non-convex variational problems.
    • Appl. Numer. Math. 26, No.1-2, 203-216 (1998), (with C. Carstensen)
     
  • On functional separately convex hulls.
    • Discrete Comput. Geom. 19, No.1, 105-130 (1998), (with J. Matousek)
     
  • Numerical solution of the scalar double-well problem allowing microstructure.
    • Math. Comput. 66, No.219, 997-1026 (1997), (with C. Carstensen)
     
  • Potts models on Feynman diagrams.
    • J. Phys. A, Math. Gen. 30, No.21, 7349-7363 (1997), (with D.A. Johnston)
     
  • Symmetry breaking Hopf bifurcations in equations with O(2) symmetry with application to the Kuramoto-Sivashinsky equation.
    • J. Comput. Phys. 131, No.1, 181-192, (1997), (with F. Amdjadi, P.J. Aston)
     
  • Local numerical analysis of Hopf bifurcation.
    • SIAM J. Numer. Anal. 33, No.3, 1150-1168 (1996), (with V. Janovsky)
     
  • Spin glasses on thin graphs.
    • Nucl. Phys. B 450, No. 3, 730-752 (1995), (with C.F. Baillie, W. Janke, D.A. Johnston)
     
  • Numerical analysis of subspace-breaking Takens-Bogdanov points.
    • IMA J. Numer. Anal. 15, No.2, 265-290 (1995), (with V. Janovsky)
     
  • Numerical applications of equivariant reduction techniques.
    • in Bifurcation and symmetry. ISNM 104, 203-213 (1992), (with V. Janovsky)
     
  • Computer-aided analysis of imperfect bifurcation diagrams. I: Simple bifurcation point and isola formation centre.
    • SIAM J. Numer. Anal. 29, No.2, 498-512 (1992), (with V. Janovsky)
     
  • Asymptotic analysis of perturbed Takens-Bogdanov points.
    • J. Comput. Appl. Math. 36, No.3, 349-359 (1991), (with V. Janovsky)
     

    Restricted access:
    Archive for ongoing projects

    Last modified: by Petr Plechac