Billiards

  1. Conjugate Pairing in the three dimensional periodic Lorentz gas C. P. Dettmann, G. P. Morriss and L. Rondoni, Phys. Rev. E 52, R5746-R5748 (1995) pdf
  2. Hamiltonian formulation of the Gaussian isokinetic thermostat. C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 54, 2495-2500 (1996) pdf ps
  3. The field dependence of Lyapunov exponents for nonequilibrium systems G. P. Morriss, C. P. Dettmann and D. J. Isbister, Phys. Rev. E, 54 4748-4654 (1996) pdf
  4. Crisis in the periodic Lorentz gas. C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 4782-4790 (1996) pdf (4.9M)
  5. Self-similar magnetoresistance of a semiconductor Sinai billiard, R. P. Taylor, R. Newbury, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann, N. Zhu, H. Guo, A. Delage, P. J. Kelly and Z. Wasilewski, Phys. Rev. Lett., 78, 1952-1955 (1997) pdf ps[Physical experiment demonstrating tunable chaos and self-similar magnetoresistance fluctuations]
  6. Stability ordering of cycle expansions C. P. Dettmann and G. P. Morriss, Phys. Rev. Lett. 78, 4201-4204 (1997) pdf ps arxiv
  7. Irreversibility, diffusion and multifractal measures in thermostatted systems, C. P. Dettmann, G. P. Morriss, and L. Rondoni, Chaos, Solitons and Fractals 8, 783-792 (1997)
  8. Recent results for the thermostatted Lorentz gas, G. P. Morriss, C. P. Dettmann and L. Rondoni, Physica A 240, 84-95 (1997)
  9. Fractal behavior in the magnetoresistance of chaotic billiards, R. Newbury, R. P. Taylor, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann and T. M. Fromhold, Jpn. J. Appl. Phys. 36,3991-3995 (1997)
  10. Fractal transistors, R. P. Taylor, A. P. Micolich, R. Newbury, C. P. Dettmann and T. M. Fromhold, Semicond. Sci. Tech. 12,1459-1464 (1997)
  11. Geometry-induced fractal behavior in a semiconductor billiard, A. P. Micolich, R. P. Taylor, R. Newbury, J. P. Bird, R. Wirtz, C. P. Dettmann, Y. Aoyagi and T. Sugano, J. Phys.: Cond. Mat. 10,1339-1347 (1998)
  12. Experimental and theoretical investigations of clusters in the magneto-fingerprints of Sinai billiards, R. P. Taylor, A. P. Micolich, R. Newbury, T. M. Fromhold, C. P. Dettmann and C. R. Tench, Mat. Sci. Eng. B 51, 212-215 (1998)
  13. Experimental and theoretical investigations of electron dynamics in a semiconductor Sinai billiard, A. P. Micolich, R. P. Taylor, R. Newbury, C. P. Dettmann and T. M. Fromhold, Aust. J. Phys. 51, 547-555 (1998)
  14. Microscopic chaos from Brownian motion? C. P. Dettmann, E. G. D. Cohen and H. van Beijeren, Nature 401, 875-875 (1999) ps.gz (1.0M when uncompressed) arxiv
  15. The existence of Burnett coefficients in the periodic Lorentz gas, N. I. Chernov and C. P. Dettmann, Physica A 279, 37-44 (2000) ps arxiv
  16. Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 101, 775-817 (2000) ps.gz (28 pages; 2.1M when uncompressed) arxiv
  17. Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589-599 (2001) ps arxiv
  18. The Burnett expansion of the periodic Lorentz gas, C. P. Dettmann, Ergod. Th. Dyn. Sys. 23, 481-491 (2003) ps arxiv
  19. Open circular billiards and the Riemann hypothesis, L. A. Bunimovich and C. P. Dettmann, Phys. Rev. Lett. 94 100201 (2005) ps pdf RH day slides
  20. Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates L. A. Bunimovich and C. P. Dettmann, EPL, 80 40001 (2007). pdf arxivanimation (6.1M)
  21. Directional emission from an optical microdisk resonator with a point scatterer C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL, 82 34002 (2008). pdf arxiv
  22. Internal and external resonances of dielectric disks, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL, 87, 34003 (2009). pdf arxiv
  23. Survival probability for the stadium billiard, C. P. Dettmann and O. Georgiou, Physica D, 238, 2395-2403 (2009). pdf arxiv animation (30.5M)
  24. Unidirectional Emission from Circular Dielectric Microresonators with a Point Scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Phys. Rev. A, 80, 063813 (2009). [Selected to appear in the PRA "Kaleidoscope"] pdf arxiv poster
  25. Transmission and reflection in the stadium billiard: Time-dependent asymmetric transport, C. P. Dettmann and O. Georgiou, Phys. Rev. E 83 036212 (2011). [Selected to appear in the PRE "Kaleidoscope"] pdf arxiv poster
  26. Open mushrooms: Stickiness revisited, C. P. Dettmann and O. Georgiou, J. Phys. A.: Math. Theor. 44 195102 (2011). [Highlighted in a JPA Insights article.] pdf arxiv poster
  27. Escape of particles in a time-dependent potential well, D. R. Costa, C. P. Dettmann and E. D. Leonel, Phys. Rev. E, 83 066211 (2011). pdf
  28. Scaling invariance for the escape of particles from a periodically corrugated waveguide, E. D. Leonel, D. R. Costa and C. P. Dettmann, Phys. Lett. A 376 421-425 (2012). pdf
  29. New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis, C. P. Dettmann, J. Stat. Phys. 146 181-204 (2012). pdf arxiv animation (4.8M)
  30. Escape and transport for an open bouncer: Stretched exponential decays, C. P. Dettmann and E. D. Leonel, Physica D 241 403-408 (2012). pdf arxiv
  31. Recurrence of particles in static and time varying oval billiards, E. D. Leonel and C. P. Dettmann, Phys. Lett. A 376 1669-1674 (2012). pdf arxiv
  32. Quantifying intermittency in the open drivebelt billiard, C. P. Dettmann and O. Georgiou, Chaos 22 026113 (2012). pdf arxiv
  33. Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration, A. L. P. Livorati, T. Kroetz, C. P. Dettmann, I. L. Caldas, E. D. Leonel, Phys. Rev. E 86 036203 (2012). pdf arxiv
  34. Ergodicity of a single particle confined in a nanopore, S. Bernardi, J. S. Hansen, F. Frascoli, B. D. Todd and C. P. Dettmann, J. Stat. Phys. 148 1156-1169 (2012). pdf
  35. Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings, J. A. de Oliveira, C. P. Dettmann, D. R. Costa and E. D. Leonel, Phys. Rev. E 87 062904 (2013). pdf
  36. Periodic compression of an adiabatic gas: Intermittency enhanced Fermi acceleration, C. P. Dettmann and E. D. Leonel, EPL 103 40003 (2013). pdf
  37. Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard, A. L. P. Livorati, M. S. Palmero, C. P. Dettmann, I. L. Caldas, E. D. Leonel, J. Phys. A.: Math. Theor., 47 365101 (2014). arxiv
  38. Diffusion in the Lorentz gas, C. P. Dettmann, Commun. Theor. Phys. 62 521-540 (2014). pdf arxiv
  39. Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos 24 043130 (2014). arxiv pdf
  40. Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations, D. R. Costa, C. P. Dettmann and E. D. Leonel, Commun. Nonlin. Sci. Numer. Sim. 20 871-881 (2015). pdf
  41. Circular, elliptic and oval billiards in a gravitational field, D. R. Costa, C. P. Dettmann and E. D. Leonel, Commun. Nonlin. Sci. Numer. Sim., 22 731-746 (2015). pdf
  42. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism, D. R. Costa, C. P. Dettmann, J. A. de Oliveira and E. D. Leonel, Chaos 25 033109 (2015). pdf.
  43. Network connectivity in non-convex domains with reflections, O. Georgiou, M. Z. Bocus, M. R. Rahman, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett. 19 427-430 (2015). pdf arxiv.
  44. On the statistical and transport properties of a non-dissipative Fermi-Ulam model, A. L. P. Livorati, C. P. Dettmann, I. L. Caldas, E. D. Leonel, Chaos 25 103107 (2015). pdf.
  45. Crises in a dissipative bouncing ball model, A. L. P. Livorati, I. L. Caldas, C. P. Dettmann and E. D. Leonel, Phys. Lett. A 379 2830-2838 (2015). arxiv.
  46. Universal hitting time statistics for integrable flows, C. P. Dettmann, J. Marklof and A. Strombergsson, J. Stat. Phys. 166 714-749 (2017). arxiv pdf.
  47. Linear and nonlinear stability of periodic orbits in annular billiards, C. P. Dettmann and V. Fain, Chaos 27 043106 (2017). arxiv.
  48. Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model, A. L. P. Livorati, M. S. Palmero, G. Diaz Iturry, C. P. Dettmann, I. L. Caldas and E. D. Leonel, Commun. Nonlin. Sci. Numer. Sim. 55 225-236 (2018).
  49. Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse, C. P. Dettmann, V. Fain and D. Turaev, Nonlinearity 31 667-700 (2018). arxiv.
  50. Transition from normal to ballistic diffusion in a one-dimensional impact system, A. L. P. Livorati, T. Kroetz, C. P. Dettmann, I. L. Caldas and E. D. Leonel, Phys. Rev. E 97 032205 (2018). pdf.
  51. The Iris billiard: Critical geometries for global chaos, G. Page, C. Antoine, C. P. Dettmann and J. Talbot, Chaos 30 123105 (2020). pdf.
  52. Spherical billiards with almost complete escape, C. P. Dettmann and M. R. Rahman, Chaos 31 123119 (2021). pdf.
  53. A billiard in an open circle and the Riemann zeta function L. A. Bunimovich and C. P. Dettmann (submitted). pdf.
  54. Conference paper: Far-field emission pattern of a dielectric circular microresonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2007, 4 197-200 (2007)
  55. Conference paper: TM and TE directional modes of an optical microdisk resonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2008, 4, 65-68 (2008). pdf
  56. Conference paper: Optical microdisk resonator with a small but finite size scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Third International Conference on Mathematical Modelling of Wave Phenomena (MMWP08), 287-289 (2008). pdf
  57. Conference paper: Systematization of All Resonance Modes in Circular Dielectric Cavities, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2009, 763-766 (2009). pdf
  58. Conference paper: Microdisk resonators with two point scatterers, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2011, 462-464 (2011). pdf
  59. Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics 698 111-128 (2017). pdf arxiv.
  60. Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.
  61. Book chapter: Recent advances in open billiards with some open problems, C. P. Dettmann, in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C. Sprott, World Scientific, 2011) arxiv [Image featured in Plus magazine]

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