Publications

On this page you can find a list of my publications. More detailed information for each paper can be obtained by clicking on its title. The papers are listed in reverse chronological order within each category, with the latest and greatest appearing first. They are enumerated in order of publication. Some of these papers can be found on my arXiv page, and additional information is contained both on Google Scholar and on Semantic Scholar.

In Preparation

83. Evelyn Sander, Thomas Wanner:
    Theory and Numerics of Partial Differential Equations
    Book Manuscript, in preparation, 1007 pages, 2024.

Submitted

82. Justin Thorpe, Thomas Wanner:
    Finding attracting sets using combinatorial multivector fields
    Preprint, submitted for publication, 6 pages, 2024.
81. Thomas Wanner:
    ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes
    Preprint, submitted for publication, 5 pages, 2024.
80. Marian Mrozek, Thomas Wanner:
    Connection matrices in combinatorial topological dynamics
    Preprint, submitted for publication, 115 pages, 2023.

Accepted

79. Jonathan Barmak, Marian Mrozek, Thomas Wanner:
    Conley index for multivalued maps on finite topological spaces
    Foundations of Computational Mathematics, accepted for publication, 43 pages, 2024.

Articles in Refereed Journals

77. Peter Rizzi, Evelyn Sander, Thomas Wanner:
    Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model
    Discrete and Continuous Dynamical Systems, Series B 29(2), pp. 666-701, 2024.
76. Michal Lipinski, Jacek Kubica, Marian Mrozek, Thomas Wanner:
    Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
    Journal of Applied and Computational Topology 7(2), pp. 139-184, 2023.
75. Sayomi Kamimoto, Hye Kyung Kim, Evelyn Sander, Thomas Wanner:
    A computer-assisted study of red coral population dynamics
    Pure and Applied Functional Analysis 7(4), pp. 1307-1337, 2022.
74. Peter Rizzi, Evelyn Sander, Thomas Wanner:
    Inverse norm bounds for fourth-order elliptic operators and equilibrium validation for triblock copolymers
    Communications in Nonlinear Science and Numerical Simulation 115, Paper No. 106789, 27 pages, 2022.
73. Marian Mrozek, Roman Srzednicki, Justin Thorpe, Thomas Wanner:
    Combinatorial vs. classical dynamics: Recurrence
    Communications in Nonlinear Science and Numerical Simulation 108, Paper No. 106226, 30 pages, 2022.
72. Marian Mrozek, Thomas Wanner:
    Creating semiflows on simplicial complexes from combinatorial vector fields
    Journal of Differential Equations 304, pp. 375-434, 2021.
71. Evelyn Sander, Thomas Wanner:
    Equilibrium validation in models for pattern formation based on Sobolev embeddings
    Discrete and Continuous Dynamical Systems, Series B 26(1), pp. 603-632, 2021.
70. Bogdan Batko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner:
    Linking combinatorial and classical dynamics: Conley index and Morse decompositions
    Foundations of Computational Mathematics 20(5), pp. 967-1012, 2020.
69. Jonathan Ariel Barmak, Marian Mrozek, Thomas Wanner:
    A Lefschetz fixed point theorem for multivalued maps of finite spaces
    Mathematische Zeitschrift 294(3-4), pp. 1477-1497, 2020.
68. Patrick O'Neil, Thomas Wanner:
    Analyzing the squared distance-to-measure gradient flow system with k-order Voronoi diagrams
    Discrete & Computational Geometry 61(1), pp. 91-119, 2019.
67. Thomas Wanner:
    Validated bounds on embedding constants for Sobolev space Banach algebras
    Mathematical Methods in the Applied Sciences 41(18), pp. 9361-9376, 2018.
66. Jacek Cyranka, Thomas Wanner:
    Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model
    SIAM Journal on Applied Dynamical Systems 17(1), pp. 694-731, 2018.
65. Pawel Dlotko, Thomas Wanner:
    Rigorous cubical approximation and persistent homology of continuous functions
    Computers & Mathematics with Applications 75(5), pp. 1648-1666, 2018.
63. Jean-Philippe Lessard, Evelyn Sander, Thomas Wanner:
    Rigorous continuation of bifurcation points in the diblock copolymer equation
    Journal of Computational Dynamics 4(1-2), pp. 71-118, 2017.
62. Dirk Blömker, Philipp Wacker, Thomas Wanner:
    Probabilistic estimates of the maximum norm of random Neumann Fourier series
    Communications in Nonlinear Science and Numerical Simulation 47, pp. 348-369, 2017.
61. Thomas Wanner:
    Computer-assisted equilibrium validation for the diblock copolymer model
    Discrete and Continuous Dynamical Systems, Series A 37(2), pp. 1075-1107, 2017.
60. Tomasz Kaczynski, Marian Mrozek, Thomas Wanner:
    Towards a formal tie between combinatorial and classical vector field dynamics
    Journal of Computational Dynamics 3(1), pp. 17-50, 2016.
59. Evelyn Sander, Thomas Wanner:
    Validated saddle-node bifurcations and applications to lattice dynamical systems
    SIAM Journal on Applied Dynamical Systems 15(3), pp. 1690-1733, 2016.
58. Pawel Dlotko, Thomas Wanner:
    Topological microstructure analysis using persistence landscapes
    Physica D: Nonlinear Phenomena 334, pp. 60-81, 2016.
55. Dirk Blömker, Evelyn Sander, Thomas Wanner:
    Degenerate nucleation in the Cahn-Hilliard-Cook model
    SIAM Journal on Applied Dynamical Systems 15(1), pp. 459-494, 2016.
53. Thomas Stephens, Thomas Wanner:
    Rigorous validation of isolating blocks for flows and their Conley indices
    SIAM Journal on Applied Dynamical Systems 13(4), pp. 1847-1878, 2014.
52. Gregory S. Cochran, Thomas Wanner, Pawel Dlotko:
    A randomized subdivision algorithm for determining the topology of nodal sets
    SIAM Journal on Scientific Computing 35(5), pp. B1034-B1054, 2013.
51. Ian Johnson, Evelyn Sander, Thomas Wanner:
    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.
50. Pawel Dlotko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner:
    Coreduction homology algorithm for regular CW-complexes
    Discrete & Computational Geometry 46(2), pp. 361-388, 2011.
49. Jonathan P. Desi, Hanein Edrees, Jonathan Price, Evelyn Sander, Thomas Wanner:
    The dynamics of nucleation in stochastic Cahn-Morral systems
    SIAM Journal on Applied Dynamical Systems 10(2), pp. 707-743, 2011.
48. Marian Mrozek, Thomas Wanner:
    Coreduction homology algorithm for inclusions and persistent homology
    Computers & Mathematics with Applications 60(10), pp. 2812-2833, 2010.
47. Konstantin Mischaikow, Thomas Wanner:
    Topology-guided sampling of nonhomogeneous random processes
    Annals of Applied Probability 20(3), pp. 1068-1097, 2010.
46. Dirk Blömker, Bernhard Gawron, Thomas Wanner:
    Nucleation in the one-dimensional stochastic Cahn-Hilliard model
    Discrete and Continuous Dynamical Systems, Series A 27(1), pp. 25-52, 2010.
45. Thomas Wanner, Edwin R. Fuller Jr., David M. Saylor:
    Homological characterization of microstructure response fields in polycrystals
    Acta Materialia 58(1), pp. 102-110, 2010.
44. Sarah Day, William D. Kalies, Thomas Wanner:
    Verified homology computations for nodal domains
    SIAM Journal on Multiscale Modeling & Simulation 7(4), pp. 1695-1726, 2009.
43. Tina Hartley, Thomas Wanner:
    A semi-implicit spectral method for stochastic nonlocal phase-field models
    Discrete and Continuous Dynamical Systems, Series A 25(2), pp. 399-429, 2009.
42. Stanislaus Maier-Paape, Ulrich Miller, Konstantin Mischaikow, Thomas Wanner:
    Rigorous numerics for the Cahn-Hilliard equation on the unit square
    Revista Matematica Complutense 21(2), pp. 351-426, 2008.
41. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation
    Transactions of the American Mathematical Society 360(1), pp. 449-489, 2008.
40. Sarah Day, William D. Kalies, Konstantin Mischaikow, Thomas Wanner:
    Probabilistic and numerical validation of homology computations for nodal domains
    Electronic Research Announcements of the American Mathematical Society 13, pp. 60-73, 2007.
39. Stanislaus Maier-Paape, Konstantin Mischaikow, Thomas Wanner:
    Structure of the attractor of the Cahn-Hilliard equation on a square
    International Journal of Bifurcation and Chaos 17(4), pp. 1221-1263, 2007.
38. Valeriy R. Korostyshevskiy, Thomas Wanner:
    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.
37. Konstantin Mischaikow, Thomas Wanner:
    Probabilistic validation of homology computations for nodal domains
    Annals of Applied Probability 17(3), pp. 980-1018, 2007.
36. Jonathan P. Desi, Evelyn Sander, Thomas Wanner:
    Complex transient patterns on the disk
    Discrete and Continuous Dynamical Systems, Series A 15(4), pp. 1049-1078, 2006.
35. Bernd Aulbach, Thomas Wanner:
    Topological simplification of nonautonomous difference equations
    Journal of Difference Equations and Applications 12(3-4), pp. 283-296, 2006.
33. Marcio Gameiro, Konstantin Mischaikow, Thomas Wanner:
    Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation
    Acta Materialia 53(3), pp. 693-704, 2005.
31. Thomas Wanner:
    Maximum norms of random sums and transient pattern formation
    Transactions of the American Mathematical Society 356(6), pp. 2251-2279, 2004.
30. Thomas Wanner, Brian S. Marks, Curtis R. Menyuk, John Zweck:
    Polarization decorrelation in optical fibers with randomly varying elliptical birefringence
    Optics Letters 28(19), pp. 1799-1801, 2003.
27. Evelyn Sander, Thomas Wanner:
    Pattern formation in a nonlinear model for animal coats
    Journal of Differential Equations 191(1), pp. 143-174, 2003.
26. Bernd Aulbach, Thomas Wanner:
    Invariant foliations and decoupling of non-autonomous difference equations
    Journal of Difference Equations and Applications 9(5), pp. 459-472, 2003.
25. James T. Lo, Thomas Wanner:
    Existence and uniqueness of risk-sensitive estimates
    IEEE Transactions on Automatic Control 47(11), pp. 1945-1948, 2002.
24. Dirk Blömker, Jinqiao Duan, Thomas Wanner:
    Enstrophy dynamics of stochastically forced large-scale geophysical flows
    Journal of Mathematical Physics 43(5), pp. 2616-2626, 2002.
23. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Roughness in surface growth equations
    Interfaces and Free Boundaries 3(4), pp. 465-484, 2001.
22. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Spinodal decomposition for the Cahn-Hilliard-Cook equation
    Communications in Mathematical Physics 223(3), pp. 553-582, 2001.
21. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Surface roughness in molecular beam epitaxy
    Stochastics and Dynamics 1(2), pp. 239-260, 2001.
20. William D. Kalies, Robert C.A.M. VanderVorst, Thomas Wanner:
    Slow motion in higher-order systems and Gamma-convergence in one space dimension
    Nonlinear Analysis. Theory, Methods & Applications 44(1), pp. 33-57, 2001.
19. Evelyn Sander, Thomas Wanner:
    Unexpectedly linear behavior for the Cahn-Hilliard equation
    SIAM Journal on Applied Mathematics 60(6), pp. 2182-2202, 2000.
18. Bernd Aulbach, Thomas Wanner:
    The Hartman-Grobman theorem for Caratheodory type differential equations in Banach spaces
    Nonlinear Analysis. Theory, Methods & Applications 40(1-8), pp. 91-104, 2000.
17. Stanislaus Maier-Paape, Barbara Stoth, Thomas Wanner:
    Spinodal decomposition for multi-component Cahn-Hilliard systems
    Journal of Statistical Physics 98(3-4), pp. 871-896, 2000.
16. Stanislaus Maier-Paape, Thomas Wanner:
    Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics
    Archive for Rational Mechanics and Analysis 151(3), pp. 187-219, 2000.
13. Evelyn Sander, Thomas Wanner:
    Monte Carlo simulations for spinodal decomposition
    Journal of Statistical Physics 95(5-6), pp. 925-948, 1999.
12. James R. Brannan, Jinqiao Duan, Thomas Wanner:
    Dissipative quasi-geostrophic dynamics under random forcing
    Journal of Mathematical Analysis and Applications 228(1), pp. 221-233, 1998.
11. Stanislaus Maier-Paape, Thomas Wanner:
    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.
9. Stanislaus Maier-Paape, Thomas Wanner:
   Solutions of nonlinear planar elliptic problems with triangle symmetry
   Journal of Differential Equations 136(1), pp. 1-34, 1997.
8. Paul C. Fife, Hansjörg Kielhöfer, Stanislaus Maier-Paape, Thomas Wanner:
   Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
   Physica D: Nonlinear Phenomena 100(3-4), pp. 257-278, 1997.
5. Thomas Wanner:
   Linearization of random dynamical systems
   Dynamics Reported 4, pp. 203-269, 1995.
3. Thomas Wanner, Günter M. Ziegler:
   Supersolvable and modularly complemented matroid extensions
   European Journal of Combinatorics 12(4), pp. 341-360, 1991.
1. Thomas Wanner:
   On the chromaticity of certain subgraphs of a q-tree
   Journal of Graph Theory 13(5), pp. 597-605, 1989.

Book Chapters

64. Thomas Wanner:
    Computer-assisted bifurcation diagram validation and applications in materials science
    Proceedings of Symposia in Applied Mathematics 74, pp. 123-174, 2018.
56. Thomas Wanner:
    Topological analysis of the diblock copolymer equation
    In: Mathematical Challenges in a New Phase of Materials Science, edited by Yasumasa Nishiura, Motoko Kotani, Springer Proceedings in Mathematics & Statistics, Vol. 166, pp. 27-51, Springer-Verlag, 2016.
32. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Phase separation in stochastic Cahn-Hilliard models
    In: Mathematical Methods and Models in Phase Transitions, edited by Alain Miranville, pp. 1-41, Nova Science Publishers, New York, 2005.
28. Bernd Aulbach, Thomas Wanner:
    Invariant foliations for Caratheodory type differential equations in Banach spaces
    In: Advances in Stability Theory at the End of the 20th Century, edited by A.A. Martynyuk, pp. 1-14, Taylor and Francis, London, 2003.
7. Bernd Aulbach, Thomas Wanner:
   Integral manifolds for Caratheodory type differential equations in Banach spaces
   In: Six Lectures on Dynamical Systems, edited by Bernd Aulbach, Fritz Colonius, pp. 45-119, World Scientific, Singapore, 1996.

Articles in Proceedings

29. Thomas Wanner, Brian S. Marks, Curtis R. Menyuk, John Zweck:
    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, Optical Society of America, Washington DC, 2003.
15. Stanislaus Maier-Paape, Evelyn Sander, Thomas Wanner:
    Spinodal decomposition: A survey of recent results
    In: Equadiff 99. Proceedings of the International Conference on Differential Equations, edited by B. Fiedler, K. Gröger, J. Sprekels, Vol. 2, pp. 1288-1299, World Scientific, 2000.
14. Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner:
    Spinodal decomposition for the stochastic Cahn-Hilliard equation
    In: Equadiff 99. Proceedings of the International Conference on Differential Equations, edited by B. Fiedler, K. Gröger, J. Sprekels, Vol. 2, pp. 1265-1267, World Scientific, 2000.
10. Stanislaus Maier-Paape, Thomas Wanner:
    Spinodal decomposition in the linear Cahn-Hilliard model
    ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 78(S3), pp. S1003-S1004, 1998.
6. Thomas Wanner:
   Qualitative behavior of random differential equations
   In: Proceedings of the Fifth International Colloquium on Differential Equations, edited by Drumi Bainov, Angel Dishliev, Vol. 2, pp. 242-257, SCT Publishing, 1995.

Software Packages

78. Thomas Wanner:
    ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes
    Software Package, 10.5281/zenodo.14248929, 2024.
54. Thomas Stephens, Thomas Wanner:
    isoblockval: Rigorous validation of isolating blocks
    Software Package, 10.5281/zenodo.14229876, 2014.

Miscellaneous Writings

57. Sarah Day, Robertus C.A.M. Vandervorst, Thomas Wanner:
    Topology in Dynamics, Differential Equations, and Data
    Physica D: Nonlinear Phenomena 334(1), pp. 1-3, 2016.
34. Thomas Wanner:
    Review of Computational Homology by T. Kaczynski, K. Mischaikow, and M. Mrozek
    SIAM Review 48(1), pp. 202-204, 2006.

Theses

4. Thomas Wanner:
   Zur Linearisierung zufälliger dynamischer Systeme
   PhD thesis, Universität Augsburg, 172 pages, 1993.
2. Thomas Wanner:
   Invariante Faserbündel und topologische Äquivalenz bei dynamischen Prozessen
   Master's thesis, Universität Augsburg, 135 pages, 1991.