Thomas Wanner's List of Publications

Publications and Theses by Thomas Wanner


Articles in refereed journals:

  1. Rigorous continuation of bifurcation points in the diblock copolymer equation
    Journal of Computational Dynamics, to appear.
    With Jean-Philippe Lessard and Evelyn Sander.
  2. Probabilistic estimates of the maximum norm of random Neumann Fourier series
    Communications in Nonlinear Science and Numerical Simulation 47, pp. 348-369, 2017.
    With Dirk Blömker and Philipp Wacker.
  3. Computer-assisted equilibrium validation for the diblock copolymer model
    Discrete and Continuous Dynamical Systems, Series A 37(2), pp. 1075-1107, 2017.
  4. Towards a formal tie between combinatorial and classical vector field dynamics
    Journal of Computational Dynamics 3(1), pp. 17-50, 2016.
    With Tomasz Kaczynski and Marian Mrozek.
  5. Validated saddle-node bifurcations and applications to lattice dynamical systems
    SIAM Journal on Applied Dynamical Systems 15(3), pp. 1690-1733, 2016.
    With Evelyn Sander.
  6. Topological microstructure analysis using persistence landscapes
    Physica D: Nonlinear Phenomena 334(1), pp. 60-81, 2016.
    With Pawel Dlotko.
  7. Degenerate nucleation in the Cahn-Hilliard-Cook model
    SIAM Journal on Applied Dynamical Systems 15(1), pp. 459-494, 2016.
    With Dirk Blömker and Evelyn Sander.
  8. Rigorous validation of isolating blocks for flows and their Conley indices
    SIAM Journal on Applied Dynamical Systems 13(4), pp. 1847-1878, 2014.
    With Thomas Stephens. (Sample software scripts can be found here.)
  9. A randomized subdivision algorithm for determining the topology of nodal sets
    SIAM Journal on Scientific Computing 35(5), pp. B1034-B1054, 2013.
    With Gregory S. Cochran and Pawel Dlotko.
  10. Branch interactions and long-term dynamics for the diblock copolymer model in one dimension
    Discrete and Continuous Dynamical Systems, Series A 33(8), pp. 3671-3705, 2013.
    With Ian Johnson and Evelyn Sander.
  11. Coreduction homology algorithm for regular CW-complexes
    Discrete & Computational Geometry 46(2), pp. 361-388, 2011.
    With Pawel Dlotko, Tomasz Kaczynski, and Marian Mrozek.
  12. The dynamics of nucleation in stochastic Cahn-Morral systems
    SIAM Journal on Applied Dynamical Systems 10(2), pp. 707-743, 2011.
    With Jonathan P. Desi, Hanein Edrees, Joseph J. Price, and Evelyn Sander.
  13. Coreduction homology algorithm for inclusions and persistent homology
    Computers & Mathematics with Applications 60(10), pp. 2812-2833, 2010.
    With Marian Mrozek.
  14. Topology-guided sampling of nonhomogeneous random processes
    Annals of Applied Probability 20(3), pp. 1068-1097, 2010.
    With Konstantin Mischaikow.
  15. Nucleation in the one-dimensional stochastic Cahn-Hilliard model
    Discrete and Continuous Dynamical Systems, Series A 27(1), pp. 25-52, 2010.
    With Dirk Blömker and Bernhard Gawron.
  16. Homology metrics for microstructure response fields in polycrystals
    Acta Materialia 58(1), pp. 102-110, 2010.
    With Edwin R. Fuller and David M. Saylor.
  17. Verified homology computations for nodal domains
    SIAM Journal on Multiscale Modeling & Simulation 7(4), pp. 1695-1726, 2009.
    With Sarah Day and William D. Kalies.
  18. A semi-implicit spectral method for stochastic nonlocal phase-field models
    Discrete and Continuous Dynamical Systems, Series A 25(2), pp. 399-429, 2009.
    With Tina Hartley.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Probabilistic validation of homology computations for nodal domains
    Annals of Applied Probability 17(3), pp. 980-1018, 2007.
    With Konstantin Mischaikow.
  25. 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.
  26. Topological simplification of nonautonomous difference equations
    Journal of Difference Equations and Applications 12(3-4), pp. 283-296, 2006.
    With Bernd Aulbach.
  27. 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.
  28. Maximum norms of random sums and transient pattern formation
    Transactions of the American Mathematical Society 356(6), pp. 2251-2279, 2004.
  29. 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.
  30. Pattern formation in a nonlinear model for animal coats
    Journal of Differential Equations 191(1), pp. 143-174, 2003.
    With Evelyn Sander.
  31. Invariant foliations and decoupling of non-autonomous difference equations
    Journal of Difference Equations and Applications 9(5), pp. 459-472, 2003.
    With Bernd Aulbach.
  32. Existence and uniqueness of risk-sensitive estimates
    IEEE Transactions on Automatic Control 47(11), pp. 1945-1948, 2002.
    With James Lo.
  33. 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.
  34. Roughness in surface growth equations
    Interfaces and Free Boundaries 3(4), pp. 465-484, 2001.
    With Dirk Blömker and Stanislaus Maier-Paape.
  35. 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.
  36. Surface roughness in molecular beam epitaxy
    Stochastics and Dynamics 1(2), pp. 239-260, 2001.
    With Dirk Blömker and Stanislaus Maier-Paape.
  37. 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.
  38. Unexpectedly linear behavior for the Cahn-Hilliard equation
    SIAM Journal on Applied Mathematics 60(6), pp. 2182-2202, 2000.
    With Evelyn Sander.
  39. 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.
  40. 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.
  41. 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.
  42. Monte Carlo simulations for spinodal decomposition
    Journal of Statistical Physics 95(5-6), pp. 925-948, 1999.
    With Evelyn Sander.
  43. 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.
  44. 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.
  45. Solutions of nonlinear planar elliptic problems with triangle symmetry
    Journal of Differential Equations 136(1), pp. 1-34, 1997.
    With Stanislaus Maier-Paape.
  46. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
    Physica D: Nonlinear Phenomena 100(3-4), pp. 257-278, 1997.
    With Paul C. Fife, Hansjörg Kielhöfer, and Stanislaus Maier-Paape.
  47. Linearization of random dynamical systems
    Dynamics Reported 4, pp. 203-269, 1995.
  48. Supersolvable and modularly complemented matroid extensions
    European Journal of Combinatorics 12(4), pp. 341-360, 1991.
    With Günter M. Ziegler.
  49. On the chromaticity of certain subgraphs of a q-tree
    Journal of Graph Theory 13(5), pp. 597-605, 1989.


Book chapters:

  1. Computer-assisted bifurcation diagram validation and applications in materials science
    Proceedings of Symposia in Applied Mathematics, Vol. 74. American Mathematical Society, to appear.
  2. 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.
  3. 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.
  4. 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. Topological analysis of the diblock copolymer equation
    In: Y. Nishiura, M. Kotani (editors), Mathematical Challenges in a New Phase of Materials Science, Springer Proceedings in Mathematics & Statistics 166, pp. 27-51, Springer-Verlag, 2016.
  2. 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.
  3. 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.
  4. 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.
  5. Spinodal decomposition in the linear Cahn-Hilliard model
    Zeitschrift für Angewandte Mathematik und Mechanik 78(S3), pp. S1003-S1004, 1998.
    With Stanislaus Maier-Paape.
  6. 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.


Miscellaneous writings:

  1. Editorial: Topology in dynamics, differential equations, and data
    Physica D: Nonlinear Phenomena 334(1), pp. 1-3, 2016.
    With Sarah Day and Robert C.A.M. VanderVorst.
  2. 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. Cubical approximation and persistent homology of continuous functions
    Submitted for publication, 2016.
    With Pawel Dlotko.
  2. Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model
    Submitted for publication, 2017.
    With Jacek Cyranka.
  3. Analyzing the distance-to-measure gradient flow problem with k-order Voronoi diagrams
    Submitted for publication, 2017.
    With Patrick O'Neil.


In preparation:

  1. Theory and Numerics of Partial Differential Equations (book manuscript, under contract with SIAM)
    With Evelyn Sander.


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

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Last modified on September 6, 2017.