This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9505049, DMS-9973393, DMS-0139824, and DMS-0513438.
Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

Publications

1992

1. S.N. Chow and E.S. Van Vleck, A Shadowing Lemma for Random Diffeomorphisms
(1992) Random & Computational Dynamics 1(2) pp. 197-218.

1994

2. R. Shonkwiler and E.S. Van Vleck, Parallel Speed-Up of Monte Carlo Methods for Global Optimization
(1994) J. of Complexity 10 pp. 64-95.

3. S.N. Chow and E.S. Van Vleck, A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs
(1994) SIAM J. Sci. Comp. 15 pp. 959-976.

4. L. Dieci, R.D. Russell and E.S. Van Vleck, Unitary Integrators and Applications to Continuous Orthonormalization Techniques
(1994) SIAM J. Numer. Anal. 31 pp. 261-281.

5. W. Shen and E.S. Van Vleck, Bifurcation Phenomena in a Condensed Two-Phase Combustion Model
(1994) Random & Computational Dynamics 2(2) pp. 227-245.

6. S.N. Chow and E.S. Van Vleck, Shadowing of Lattice Maps
(1994) Contemporary Mathematics 172 pp. 97-116.

1995

7. J.W. Cahn, S.N. Chow and E.S. Van Vleck, Spatially Discrete Nonlinear Diffusion Equations
(1995) Rocky Mount. J. Math. 25 pp. 87-118.

8. E.S. Van Vleck, Numerical Shadowing Near Hyperbolic Trajectories
(1995) SIAM J. Sci. Comp. 16 pp. 1177-1189.

9. C.P. Grant and E.S. Van Vleck, Slowly-Migrating Transition Layers for the Discrete Allen-Cahn and Cahn-Hilliard Equations
(1995) Nonlinearity 8 pp. 861-876.

10. L. Dieci and E.S. Van Vleck, Computation of a Few Lyapunov Exponents for Continuous and Discrete Dynamical Systems
(1995) Appld. Numer. Math. 17 pp. 275-291.

(Click here for PDF version of the paper.)

1996

11. J.W. Cahn and E.S. Van Vleck, Quadrijunctions Do Not Stop Two-Dimensional Grain Growth
(1996) Scripta Mater. 34 pp. 909-912.

12. C.E. Elmer and E.S. Van Vleck, Computation of Traveling Wave Solutions for Spatially Discrete Bistable Reaction-Diffusion Equations
(1996) Appld. Numer. Math. 20 pp. 157-169.

13. S.N. Chow, J. Mallet-Paret and E.S. Van Vleck, Pattern Formation and Spatial Chaos in Spatially Discrete Evolution Equations
(1996) Random & Computational Dynamics 4(2&3) pp. 109-178.

14. S.N. Chow, J. Mallet-Paret and E.S. Van Vleck, Dynamics of Lattice Differential Equations
(1996) Int. J. Bif. and Chaos 6 pp. 1605-1622.

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1997

15. L. Dieci, R.D. Russell and E.S. Van Vleck, On the Computation of Lyapunov Exponents for Continuous Dynamical Systems,
(1997) SIAM J. Numer. Anal. 34 pp. 402-423.

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16. B. Leimkuhler and E.S. Van Vleck, Orthosymplectic Integration of Linear Hamiltonian Systems
(1997) Numer. Math. 77 pp. 269-282.

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17. J.A. Scales and E.S. Van Vleck, Lyapunov Exponents and Localization in Randomly Layered Media
(1997) J. Comp. Phys. 133 pp. 27-42.

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1998

18. A. Rodriguez-Bernal and E. S. Van Vleck, Diffusion Induced Chaos in a Closed Loop Thermosyphon
(1998) SIAM J. Appld. Math. 58 pp. 1072-1093.

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19. A. Rodriguez-Bernal and E.S. Van Vleck, Complex Oscillations in a Closed Thermosyphon
(1998) Int. J. Bif. Chaos. 8 pp. 41-56.

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20. C. Morey, J.A. Scales and E.S. Van Vleck, A Feedback Algorithm for Determining Search Parameters for Monte Carlo Optimization
(1998) J. Comp. Phys. 146 pp. 263-281.

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1999

21. J.W. Cahn, J. Mallet-Paret and E.S. Van Vleck, Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice
(1999) SIAM J. Appld. Math. 59 pp. 455-493.

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22. L. Dieci and E. S. Van Vleck, Computation of Orthonormal Factors for Fundamental Solution Matrices
(1999) Numer. Math. 83 pp. 599-620.

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23. L. Dieci and E. S. Van Vleck, Continuous Orthonormalization for Linear Two-Point Boundary Value Problems Revisited
(1999) IMA Volumes in Mathematics and Its Applications 118 pp. 69-90.

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24. C.E. Elmer and E.S. Van Vleck, Analysis and Computation of Traveling Wave Solutions of Bistable Differential-Difference Equations
(1999) Nonlinearity 12 pp. 771-798.

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25. J. W. Cahn and E.S. Van Vleck, On the Co-existence and Stability of Trijunctions and Quadrijunctions in a Simple Model
(1999) Acta Materialia 47 pp. 4627-4639.

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2000

26. B. Jennings and E.S. Van Vleck, Mosaic Solutions and Spatial Entropy for a Class of Neural Network Models
(2000) Int. J. Bif. Chaos 10 pp. 1661-1676.

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27. K. A. Abell, A.R. Humphries and E.S. Van Vleck, Mosaic Solutions and Spatial Entropy for Spatially Discrete Cahn-Hilliard Equations
(2000) IMA J. Appld. Math. 65 pp. 219-255.

(Click here for POSTSCRIPT version of the paper.)

2001

28. E.S. Van Vleck, Numerical Shadowing Using Componentwise Bounds and a Sharper Fixed Point Result
(2001) SIAM J. Sci. Comp. 22 pp. 787-801.

(Click here for POSTSCRIPT version of the paper.)

29. C.E. Elmer and E.S. Van Vleck, Traveling Waves Solutions for Bistable Differential-Difference Equations with Periodic Diffusion
(2001) SIAM J. Appld. Math. 61 pp. 1648-1679.

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30. K. A. Abell, A.R. Humphries and E.S. Van Vleck, Mosaic Solutions and Entropy for Discrete Coupled Phase-Transition Equations
(2001) Physica D 155 pp. 223-259.

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2002

31. L. Dieci and E.S. Van Vleck, Lyapunov and Other Spectra: A Survey
(2002) Collected Lectures on the Preservation of Stability under Discretization, A Volume Published by SIAM, pp. 197--218.

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32. C.E. Elmer and E.S. Van Vleck, A Variant of Newton's Method for the Computation of Traveling Waves of Bistable Differential Difference Equations
(2002) J. Dyn. Diff. Eqn. 14 pp. 493--517.

(Click here for POSTSCRIPT version of the paper.)

2003

33. C.E. Elmer and E.S. Van Vleck, Existence of Monotone Traveling Fronts for BDF Discretizations of Bistable Reaction-Diffusion Equations
(2003) Journal of Dynamics of Continuous, Discrete and Impulsive Systems, 10A pp. 389--402.

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34. L. Dieci and E.S. Van Vleck, Lyapunov Spectral Intervals: Theory and Computation
(2003) SIAM J. Numer. Anal. 40 pp. 516--542.

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35. C.E. Elmer and E.S. Van Vleck, Anisotropy, Propagation Failure, and Wave Speedup in Traveling Waves of Discretizations of a Nagumo PDE
(2003) J. Comp. Phys. 185 pp. 562--582.

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36. L. Dieci and E.S. Van Vleck, Orthonormal Integrators Based on Householder and Givens Transformations
(2003) Future Generation Computer Systems 19 pp. 363--373.

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2004

J. Collis and E.S. Van Vleck, Efficient Numerical Shadowing Global Error Estimation for High Dimensional Dissipative Systems,
(2004) Advanced Nonlinear Studies 4 pp. 165--188.

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2005

S. Maier-Paape, B. Moore, and E.S. Van Vleck, Spinodal Decomposition for Spatially Discrete Cahn-Hilliard Equations
(2005) Journal of Dynamics of Continuous, Discrete and Impulsive Systems 12 pp. 529--554.

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C.E. Elmer and E.S. Van Vleck, Spatially Discrete FitzHugh-Nagumo Equations,
(2005) SIAM J. Appld. Math. 65 pp. 1153--1174.

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K.A. Abell, C.E. Elmer, A.R. Humphries and E.S. Van Vleck, Computation of Mixed Type Functional Differential Boundary Value Problems
(2005) SIAM J. Appld. Dyn. Sys. 4 pp. 745--771.

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C.E. Elmer and E.S. Van Vleck, Dynamics of Monotone Traveling Fronts for Discretizations of Nagumo PDE's,
(2005) Nonlinearity 18 pp. 1605--1628.

(Click here for POSTSCRIPT version of the paper.)

L. Dieci and E.S. Van Vleck, On the Error in Computing Lyapunov Exponents by QR Methods,
(2005) Numer Math. 101 pp. 619--642.

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B. Wang and E.S. Van Vleck, Attractors for Lattice FitzHugh-Nagumo Systems,
(2005) Physica D 212 pp. 317--336..

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2006

C.M. Elliott, B. Gawron, S. Maier-Paape, and E.S. Van Vleck, Discrete Dynamics for Convex and Non-Convex Smoothing Functionals in PDE Based Image Restoration,
(2006) Comm. Pure Appld. Anal. 5 pp. 181--200.

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W. Liu and E.S. Van Vleck, Turning Points and Traveling Waves in FitzHugh-Nagumo Type Equations,
(2006) J. Diff. Eqn. 225 pp. 381--410.

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M.D. Bateman and E.S. Van Vleck, Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations,
(2006) SIAM J. Appld. Math. 66 pp. 945--976.

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L. Dieci and E.S. Van Vleck, Perturbation Theory for the Approximation of Lyapunov Exponents by QR Methods,
(2006) J. Dyn. Diff. Eqn. 18 pp. 815--840.

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2007

L. Dieci and E.S. Van Vleck, Lyapunov and Sacker-Sell Spectral Intervals,
(2007) J. Dyn. Diff. Eqn. 19 pp. 263--295.

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D. W. Graham, C. W. Knapp, E. S. Van Vleck, K. Bloor, T. B. Lane, and C. E. Graham,
Experimental Demonstration of Chaotic Instability in Biological Nitrification,

(2007) The ISME Journal: Multidisciplinary Journal of Microbial Ecology.

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2008

L. Dieci, M. S. Jolly, R. Rosa, and E.S. Van Vleck, Error in Approximation of Lyapunov Exponents on Inertial Manifolds: the Kuramoto-Sivashinsky Equation,
(2007) to appear in Discrete and Continuous Dynamical Systems.

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L. Dieci and E.S. Van Vleck, On the Error in QR Integration,
(2007) to appear in SIAM J. Numer. Anal..

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A. Scheel and E.S. Van Vleck, Lattice Differential Equations Embedded into Reaction-Diffusion Systems,
(2007) to appear in Proc. Royal Soc. Edinburgh.

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