Computational Dynamics and Conley Index Theory

• A database schema for the analysis of global dynamics of multiparameter systems  
  SIAM Journal on Applied Dynamical Systems 8, pp. 757-789, 2009.
  With Z. Arai, H. Kokubu, K. Mischaikow, H. Oka, and P. Pilarczyk.


• Topological horseshoes of traveling waves for a fast-slow predator-prey system
  Journal of Dynamics and Differential Equations 19, pp. 623-654, 2007.
  With M. Gameiro, T. Gedeon, H. Kokubu, K. Mischaikow, and H. Oka.


• Polygonal approximation of flows
  Topology and Its Applications 154, pp. 2501-2520, 2007.
  With E. Boczko and K. Mischaikow.


• A computational approach to Conley's decomposition theorem  
  Journal of Computational and Nonlinear Dynamics 1, pp. 312-319, 2006.
  With H. Ban.


• An algorithmic approach to chain recurrence
  Foundations of Computational Mathematics 5, pp. 409-449, 2005.
  With K. Mischaikow and R.C.A.M. van der Vorst.

Computational Topology

• chom - a cubical homology program
  

      Theory and Algorithms

• Verified homology computations for nodal domains
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 7, pp. 1695-1726, 2009.
  With S. Day and T. Wanner.


• Probabilistic and numerical validation of homology computations for nodal domains
  Electronic Research Announcements of the American Mathematical Society 13, pp. 60-73, 2007.
  With S. Day, K. Mischaikow, and T. Wanner.


• Topological characterization of spatial-temporal chaos
  Physical Review E 70, Article 035203 (Rapid communication), 2004.
  With M. Gameiro and K. Mischaikow.


• Cubical approximation and computation of homology
  Banach Center Publications 47, pp. 115-131, 1999.
  With K. Mischaikow and G. Watson.

      Applications

• Three-dimensional analysis of solid oxide fuel cell Ni-YSZ anode interconnectivity
  Microscopy and Microanalysis 15, pp. 71-77, 2009.
  With J.R. Wilson, M. Gameiro, K. Mischaikow, P. Voorhees, and S.A. Barnett.


• On the detection of simple points in higher dimensions using cubical homology
  IEEE Transactions on Image Processing 15(8), pp. 2462-2469, 2006.
  With M. Niethammer, K. Mischaikow, and A. Tannenbaum.


• Analysis of blood vessel topology by cubical homology
  Proceedings of International Conference on Imagine Processing 2002, vol 2, pp. 969-972, 2002.
  With M. Niethammer, A.N. Stein, P. Pilarczyk, K. Mischaikow, and A. Tannenbaum.

Variational Methods and Second-Order Lagrangian Systems

• Closed characteristics on singular energy levels of second-order Lagrangian systems
  Journal of Differential Equations 244, pp. 555-581, 2008.
  With M. Wess.


• Closed characteristics of second-order Lagrangians
  Proceedings of the Royal Society of Edinburgh A 134, pp. 143-158, 2004.
  With R.C.A.M. van der Vorst.


• Slow motion in higher-order systems and gamma-convergence in one space dimension
  Nonlinear Analysis: Theory, Methods, and Applications 44, pp. 33-57, 2001.
  With R.C.A.M. van der Vorst and T. Wanner.
  


• Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems
  Communications in Mathematical Physics 214, pp. 573-592, 2000.
  With J. Kwapisz, J.B. van den Berg, and R.C.A.M. van der Vorst.


• Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
  Communications in Mathematical Physics 193, pp. 337-371, 1998.
  With J. Kwapisz, and R.C.A.M. van der Vorst.


• On the asymptotic behavior of a phase-field model for elastic phase transitions
  Journal of Dynamics and Differential Equations 9, pp. 289-306, 1997.
  


• Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
  Journal of Differential Equations 131, pp. 209-228, 1996.
  With R.C.A.M. van der Vorst.


• On a dynamical model for phase transformation in nonlinear elasticity
  Fields Institute Communications 5, pp. 255-269, 1996.
  With P.J. Holmes.


• Regularized Models of Phase Transformation in One-Dimensional Nonlinear Elasticity
  Ph.D. thesis, Cornell University, 1996. (2 MB)

W.D. Kalies, March 2009.