Publications

The papers linked to below are generally not in their final version.

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Articles submitted for publication

• Determination of output composition in reaction-advection-diffusion systems on network reactors
  Eric Pasewark, Gregory Yablonsky, 2024.

• Chaotic lensed billiards
  Tim Chumley, Maeve Covey and Chris Cox, 2023

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Articles in print or accepted for publication

• Revisiting Maxwell-Smoluchowski theory: low surface roughness in straight channels
  Tim Chumley, Luis Garcia German and Gregory Yablonsky, Chemical Engineering Science, 284 (2023)

• Exact Discretization of Harmonic Tensors
  Matt Wallace and Tim Chumley
  Potential Analysis. 56, 409-421 (2022).

• Knudsen diffusivity in random billiards: spectrum, geometry, and computation
  Tim Chumley, Luis Garcia German
  SIADS (SIAM Journal on Applied Dynamical Systems), 2021, Vol. 20, No. 3: pp. 1655-1682.

• Rolling systems and their billiard limits
  Chris Cox, Bowei Zhao
  Regular and Chaotic Dynamics, 2021, Vol. 26, Issue 1, pages 1-21.

• Entropy Production in Random Billiards
  Tim Chumley
  Discrete and Continuous Dynamical System-A, 2021, 41(3): 1319-1346.

• Rolling and no-slip bouncing in cylinders
  Scott Cook, Chris Cox, and Tim Chumley
  Journal of Geometric Mechanics, 12 (1) 2020, 53-84.

• Explicit Formulas for Reaction Probability in Reaction-Diffusion Experiments
  Matt Wallace, Ari Stern, and Gregory Yablonski
  Computers & Chemical Engineering 125 (2019) 612-622.

• Stability of periodic orbits in no-slip billiards
  C. Cox and H.-K. Zhang
  Nonlinearity 31 (2018) 4443-4471

• Reaction-diffusion on metric graphs: from 3D to 1D
  Matt Wallace and Gregory Yablonsky
  Computers & Mathematics with Applications, Volume 73, Issue 9, 2017, p. 2035-2052.

• No-slip billiards in dimension 2
  Christopher Cox
  Contemporary Math. Volume 698 (2017) 91-110

• Differential Geometry of Rigid Bodies Collisions and Non-standard Billiards
  Christopher Cox
  Discrete and Continuous Dynamical Systems-A, 33 (2016) no. 11, 6065-6099.

• Diffusivity in multiple scattering systems
  Timothy Chumley and Hong-Kun Zhang
  Trans. Amer. Math. Soc. 368 (2016), 109-148.

• Multiple scattering in random mechanical systems and diffusion approximation
  Jasmine Ng and Hongkun Zhang
  Commun. Math. Phys. V. 323, N. 2 (2013).

• From billiards to thermodynamics
  Tim Chumley and Scott Cook
  Computers and Mathematics with Applications, Vol. 65, n. 10 (2013), p. 1596-1613.

• Random billiards with wall temperature and associated Markov chains
  with Scott Cook
  Nonlinearity 25 (2012) 2503-2541.

• Spectral gap for a class of random billiards
  Hong-Kun Zhang
  Commun. Math. Phys. 313, 479-515 (2012).

• The spectrum of the billiard Laplacian of a family of random billiards
  Hong-Kun Zhang
  Journal of Statistical Physics, V. 141, N.6 (2010) 1030-1054.

• Higher order approximations of isochrons
  D. Takeshita
  Nonlinearity, 23 (2010) 1303-1323.

• A general formula for reactant conversion over a single catalyst particle in TAP pulse experiments
  A. Cloninger, G.S. Yablonsky, and J.T. Gleaves
  Chemical Engineering Science, 64 (2009) 21, 4358-4364.

• Harmonic functions on \(\mathbb{R}\)-covered foliations and group actions on the circle
  S. Fenley and K. Parwani
  Erg. Th. Dyn. Syst. 29 (2009) 4, 1141-1161.

• Probabilistic analysis of transport-reaction processes over catalytic particles: theory and experimental testing
  G.S. Yablonsky, A. Mueller, A. Baernstein, X. Zheng, J.T. Gleaves
  Chemical Engineering Science, 64 (2008) 3, 568-581.

• Probing Surface Structure via time-of-escape analysis of gas in Knudsen regime
  G. Yablonsky
  Chemical Engineering Science, Vol. 61, Issue 24, December 2006, pages 7864-7883.

• Dynamics on the space of harmonic functions and the foliated Liouville problem
  A. Zeghib
  Ergodic Theory and Dynamical Systems, 25 (2005), 1-14.

• Knudsen’s cosine law and random billiards
  Gregory Yablonsky
  Chemical Engineering Science 59 (2004) 1541-1556.

• Leafwise holomorphic functions
  A. Zeghib
  Proceedings of the American Mathematical Society, V. 131, n. 6, 1717-1725, 2003.

• Groups that do not act by automorphisms of codimension-one foliations
  D. Witte, Pacific Journal of Math, Vol. 204, No. 1, 2002, 31-42.

• Cartan geometries and Dynamics
  P. Lampe
  Geometriae Dedicata 80 (2000), 29-41.

• Topological Superrigidity and Anosov Actions of Lattices
  Francois Labourie
  Annales Scientifiques de l’ENS, 4e. serie, t. 31, 1998, p. 599-629.

• Actions of discrete linear groups and Zimmer’s conjecture
  Journal of Differential Geometry, vol.42, no. 3, 1995, 554-576.

• The invariant connection of a \(\frac 12\)-pinched Anosov diffeomorphism and rigidity
  Pacific Journal of Mathematics, vol. 171, No. 1, 1995, 139-155.

• Hyperbolic dynamical systems, invariant geometric structures, and rigidity
  Mathematical Research Letters 1, 11-26, 1994.

• The center foliation of an affine diffeomorphism
  Geometriae Dedicata 46, 233-238, 1993.

• Affine actions of higher rank lattices
  Geometric and Functional Analysis Vol. 3. No. 4 1993 p.370-394.

• Connection-preserving actions of lattices in \(SL(n,R)\)
  Israel Journal of Math. 79, 1992, 1-21.

• Geodesic flows on manifolds of negative curvature with smooth horospheric foliations
  Ergodic Theory and Dynamical Systems, (1991), 11, 653-686.

• Anosov flows with smooth foliations and rigidity of geodesic flows in threee-dimensional manifolds of negative curvature
  A. Katok
  Ergodic Theory and Dynamical Systems, 10 (1990) 657-670.

• Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows
  A. Katok
  Ergodic Theory and Dynamical Systems, 9 (1989) 627-632.

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Book and book chapters

• Harmonic functions over group actions
  E. Ronshausen, in Geometry, Rigidity and Group Actions, Ed. B. Farb and D. Fisher, University of Chicago Press, 2011, 59-71.

• Random walks derived from billiards
  in Dynamics, Ergodic Theory, and Geometry, Ed. B. Hasselblatt, Mathematical Sciences Research Institute Publications 54, 2007, pages 179-222.

• A differential-geometric view of normal forms of contractions
  in Modern Dynamical Systems and Applications, Eds.: M. Brin, B. Hasselblatt, Y. Pesin, Cambridge University Press, (2004) 103-121.

• Rigidité, groupe fondamental et dynamique
  Edited by Patrick Foulon, Panoramas et Synthèses, Société Mathématique de France, n. 13, 2002.

• An introduction to cocycle super-rigidity
  Rigidity in dynamics and number theory, Eds.: M. Burger and A. Iozzi. Springer, 2002.

• Ergodic Theory and Dynamics of \(G\)-spaces
  A. Katok. Chapter 9 of Handbook of Dynamical Systems, Vol. Ia, Elsevier, 2002.

• Dynamical Systems and Semisimple Groups: an introduction
  Tracts in Mathematics, 126, Cambridge University Press, 1998.

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Articles not submitted for publication

• The Minimal Entropy Theorem and Mostow Rigidity
  after Besson, Courtois, Gallot, 1996.

• Bounded Representations of Amenable Groupoids and Transference
  S. Durand, 1994.

• Rigidity of Geodesic Flows on Negatively Curved Manifolds of Dimensions 3 and 4
  Anatole Katok, 1989.

• Geodesic Flows on Manifolds of Negative Curvature with Smooth Horospheric Foliations
  Caltech thesis, May 10 1989.