Thomas Wanner's List of Publications

Publications and Theses by Thomas Wanner

Articles in refereed journals:

  1. Rigorous numerics for the Cahn-Hilliard equation on the unit square
    Revista Matematica Complutense 21(2), pp. 351-426, 2008.
    With Stanislaus Maier-Paape, Ulrich Miller, and Konstantin Mischaikow.
  2. Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation
    Transactions of the American Mathematical Society 360(1), pp. 449-489, 2008.
    With Dirk Blömker and Stanislaus Maier-Paape.
  3. Probabilistic and numerical validation of homology computations for nodal domains
    Electronic Research Announcements of the American Mathematical Society 13, pp. 60-73, 2007.
    With Sarah Day, William D. Kalies, and Konstantin Mischaikow.
  4. Structure of the attractor of the Cahn-Hilliard equation on a square
    International Journal of Bifurcation and Chaos 17(4), pp. 1221-1263, 2007.
    With Stanislaus Maier-Paape and Konstantin Mischaikow.
  5. A Hermite spectral method for the computation of homoclinic orbits and associated functionals
    Journal of Computational and Applied Mathematics 206(2), pp. 986-1006, 2007.
    With Valeriy R. Korostyshevskiy.
  6. Probabilistic validation of homology computations for nodal domains
    Annals of Applied Probability 17(3), pp. 980-1018, 2007.
    With Konstantin Mischaikow.
  7. Complex transient patterns on the disk
    Discrete and Continuous Dynamical Systems, Series A 15(4), pp. 1049-1078, 2006.
    With Jonathan P. Desi and Evelyn Sander.
  8. Topological simplification of nonautonomous difference equations
    Journal of Difference Equations and Applications 12(3-4), pp. 283-296, 2006.
    With Bernd Aulbach.
  9. Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation
    Acta Materialia 53(3), pp. 693-704, 2005.
    With Marcio Gameiro and Konstantin Mischaikow.
  10. Maximum norms of random sums and transient pattern formation
    Transactions of the American Mathematical Society 356(6), pp. 2251-2279, 2004.
  11. Polarization decorrelation in optical fibers with randomly varying elliptical birefringence
    Optics Letters 28(19), pp. 1799-1801, 2003.
    With Brian S. Marks, Curtis R. Menyuk, and John Zweck.
  12. Pattern formation in a nonlinear model for animal coats
    Journal of Differential Equations 191(1), pp. 143-174, 2003.
    With Evelyn Sander.
  13. Invariant foliations and decoupling of non-autonomous difference equations
    Journal of Difference Equations and Applications 9(5), pp. 459-472, 2003.
    With Bernd Aulbach.
  14. Existence and uniqueness of risk-sensitive estimates
    IEEE Transactions on Automatic Control 47(11), pp. 1945-1948, 2002.
    With James Lo.
  15. Enstrophy dynamics of stochastically forced large-scale geophysical flows
    Journal of Mathematical Physics 43(5), pp. 2616-2626, 2002.
    With Dirk Blömker and Jinqiao Duan.
  16. Roughness in surface growth equations
    Interfaces and Free Boundaries 3(4), pp. 465-484, 2001.
    With Dirk Blömker and Stanislaus Maier-Paape.
  17. Spinodal decomposition for the Cahn-Hilliard-Cook equation
    Communications in Mathematical Physics 223(3), pp. 553-582, 2001.
    With Dirk Blömker and Stanislaus Maier-Paape.
  18. Surface roughness in molecular beam epitaxy
    Stochastics and Dynamics 1(2), pp. 239-260, 2001.
    With Dirk Blömker and Stanislaus Maier-Paape.
  19. Slow motion in higher-order systems and $\Gamma$-convergence in one space dimension
    Nonlinear Analysis: Theory, Methods, and Applications 44(1), pp. 33-57, 2001.
    With William D. Kalies and Robert C.A.M. VanderVorst.
  20. Unexpectedly linear behavior for the Cahn-Hilliard equation
    SIAM Journal on Applied Mathematics 60(6), pp. 2182-2202, 2000.
    With Evelyn Sander.
  21. The Hartman-Grobman theorem for Carathéodory type differential equations in Banach spaces
    Nonlinear Analysis: Theory, Methods, and Applications 40(1-8), pp. 91-104, 2000.
    With Bernd Aulbach.
  22. Spinodal decomposition for multicomponent Cahn-Hilliard systems
    Journal of Statistical Physics 98(3-4), pp. 871-896, 2000.
    With Stanislaus Maier-Paape and Barbara Stoth.
  23. Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics
    Archive for Rational Mechanics and Analysis 151(3), pp. 187-219, 2000.
    With Stanislaus Maier-Paape.
  24. Monte Carlo simulations for spinodal decomposition
    Journal of Statistical Physics 95(5-6), pp. 925-948, 1999.
    With Evelyn Sander.
  25. Dissipative quasi-geostrophic dynamics under random forcing
    Journal of Mathematical Analysis and Applications 228(1), pp. 221-233, 1998.
    With James R. Brannan and Jinqiao Duan.
  26. Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Part I: Probability and wavelength estimate
    Communications in Mathematical Physics 195(2), pp. 435-464, 1998.
    With Stanislaus Maier-Paape.
  27. Solutions of nonlinear planar elliptic problems with triangle symmetry
    Journal of Differential Equations 136(1), pp. 1-34, 1997.
    With Stanislaus Maier-Paape.
  28. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
    Physica D 100(3-4), pp. 257-278, 1997.
    With Paul C. Fife, Hansjörg Kielhöfer, and Stanislaus Maier-Paape.
  29. Linearization of random dynamical systems
    Dynamics Reported 4, pp. 203-269, 1995.
  30. Supersolvable and modularly complemented matroid extensions
    European Journal of Combinatorics 12(4), pp. 341-360, 1991.
    With Günter M. Ziegler.
  31. On the chromaticity of certain subgraphs of a q-tree
    Journal of Graph Theory 13(5), pp. 597-605, 1989.

Book chapters:

  1. Phase separation in stochastic Cahn-Hilliard models
    Mathematical Methods and Models in Phase Transitions, edited by A. Miranville, pp. 1-41. Nova Science Publishers, New York, 2005.
    With Dirk Blömker and Stanislaus Maier-Paape.
  2. Invariant foliations for Carathéodory type differential equations in Banach spaces
    Advances in Stability Theory at the End of the 20th Century, edited by A.A. Martynyuk,
    Stability and Control: Theory, Methods and Applications, Vol. 13, pp. 1-14. Taylor and Francis, London, 2003.
    With Bernd Aulbach.
  3. Integral manifolds for Carathéodory type differential equations in Banach spaces
    Six Lectures on Dynamical Systems, edited by B. Aulbach and F. Colonius, pp. 45-119. World Scientific, Singapore, 1996.
    With Bernd Aulbach.

Articles in proceedings:

  1. Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence
    In: Optical Fiber Communication Conference 2003, Technical Digest, pp. 370-372, 2003.
    With Brian S. Marks, Curtis R. Menyuk, and John Zweck.
  2. Spinodal decomposition: A survey of recent results
    In: B. Fiedler, K. Gröger, and J. Sprekels (editors), Equadiff 99, Proceedings of the International Conference on Differential Equations, Volume 2, pp. 1288-1299, World Scientific, 2000.
    With Stanislaus Maier-Paape and Evelyn Sander.
  3. Spinodal decomposition for the stochastic Cahn-Hilliard equation
    In: B. Fiedler, K. Gröger, and J. Sprekels (editors), Equadiff 99, Proceedings of the International Conference on Differential Equations, Volume 2, pp. 1265-1267, World Scientific, 2000.
    With Dirk Blömker and Stanislaus Maier-Paape.
  4. Spinodal decomposition in the linear Cahn-Hilliard model
    Zeitschrift für Angewandte Mathematik und Mechanik 78(S3), pp. S1003-S1004, 1998.
    With Stanislaus Maier-Paape.
  5. Qualitative behavior of random differential equations
    In: D. Bainov and A. Dishliev (editors), Proceedings of the Fifth International Colloquium on Differential Equations, Volume 2, pp. 242-257. SCT Publishing, 1995.

Book reviews:

  1. Review of Computational Homology by T. Kaczynski, K. Mischaikow, and M. Mrozek
    SIAM Review, 48(1), pp. 202-204, 2006.

Theses:

  1. Zur Linearisierung zufälliger dynamischer Systeme
    PhD-thesis, Universität Augsburg, 172 pp., 1993.
  2. Invariante Faserbündel und topologische Äquivalenz bei dynamischen Prozessen
    Master's thesis, Universität Augsburg, 135 pp., 1991.

Manuscripts submitted for publication:

  1. Topology-guided sampling of nonhomogeneous random fields
    With Konstantin Mischaikow.
  2. Verified homology computations for nodal domains
    With Sarah Day and William D. Kalies.

Coming soon:

  1. A high order test discretization for unsymmetric meshless methods
    With Andrew Corrigan and John Wallin.
  2. Homological characterization of microstructure response fields in polycrystals
    With Edwin R. Fuller and David M. Saylor.
  3. The dynamics of nucleation in stochastic Cahn-Morral systems
    With Jonathan P. Desi, Hanein Edrees, Joseph J. Price, and Evelyn Sander.
  4. A semi-implicit spectral method for stochastic nonlocal phase-field models
    With Tina Hartley.

As for preprints or reprints please send e-mail to me at wanner@math.gmu.edu.

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Last modified on September 17, 2008.