Carl Dettmann - Publications


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    Alternative sources: The definitive version is usually available at the publisher's website (click on the journal name) for those with access. Some are available at arXiv , not necessarily in the final form.

    Notes: Publications other than those in or intended for refereed journals are noted in RED, and animations in ORANGE (gallery). Large postscript files are gzipped; pdf are not. In both cases the (uncompressed) size is noted if over 1M. If you have any difficulty printing the files, please ask for a hard copy by emailing Carl.Dettmann at bris.ac.uk

    Topics: (with brief descriptions) Top ten, Billiards, Correlation functions, Diffusion, Fractals, Integrable and related dynamics, Intermittent dynamics, Microresonators, Networks, Number theory, Open systems, Periodic orbits, Plasmas, Relativity and cosmology, Semiconductor billiards, Spatiotemporal dynamics, Thermostats, Time dependent dynamics

    Coauthors: Here and below, links are to home pages. These links break at a rapid rate; corrections very welcome. E. G. Altmann, Y. Aoyagi, S. Bernardi, J. P. Bird, M. Z. Bocus, L. A. Bunimovich, I. L. Caldas, M. A. J. Chaplain, N. I. Chernov, E. G. D. Cohen, P. T. Coleridge, J. P. Coon, N. J. Cornish, D. R. Costa, P. Cvitanovic', P. Dahlqvist, A. Delage, S. Drake, Y. Feng, N. E. Frankel, F. Frascoli T. M. Fromhold, R. M. Gailis, O. Georgiou, H. Guo, J. S. Hansen, T. B. Howard, D. J. Isbister, J. P. Keating, P. J. Kelly, R. Klages, G. Knight, V. Kowalenko, T. Kroetz, E. D. Leonel, D. Lippolis, A. L. P. Livorati, R. Mainieri, A. P. Micolich, G. V. Morozov, G. P. Morriss, R. Newbury, J. A. de Oliveira, S. D. Prado, L. Rondoni, A. S. Sachrajda, A. A. Samoletov, M. M. A. Sieber, N. Sondergaard, T. Sugano, T. Taniguchi, T. Taucher, R. P. Taylor, C. R. Tench, B. D. Todd, H. van Beijeren, G. Vattay, A. Voros, H. Waalkens, Z. Wasilewski, R. Wirtz, N. Zhu

    Current affiliations and collaborations: Brazil: UNESP, Bristol: Quantum chaos, Bristol: Toshiba TRL, Europe: EPS, Gatech: Center for Nonlinear Science, Swinburne: Centre for Molecular Simulation, UK: Collaborative Computational Project 5, UK: Institute of Physics, UK: Mathematical Challenges of Molecular Dynamics (EPSRC network)

    Journal articles

  1. Potential theory and analytic properties of a Cantor set C. P. Dettmann and N. E. Frankel, J. Phys. A.: Math. Theor. 26,1009-1022 (1993)pdf animation (1.4M)
  2. Structure factor of deterministic fractals with rotations C. P. Dettmann and N. E. Frankel, Fractals 1, 253-261 (1993) pdf [New journal at the time; missed from most databases]
  3. Potential theory and analytic properties of self-similar fractal and multifractal distributions. C. P. Dettmann and N. E. Frankel, J. Stat. Phys. 72, 241-275 (1993)
  4. Plasma electrodynamics in the expanding Universe. C. P. Dettmann, N. E. Frankel and V. Kowalenko, Phys. Rev. D 48, 5655-5667 (1993) pdf
  5. Structure factor of Cantor sets C. P. Dettmann, N. E. Frankel and T. Taucher, Phys. Rev. E 49, 3171-3178 (1994) pdf
  6. Fractal basins and chaotic trajectories in multi-black-hole space-times. C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. D, 50, R618-R621 (1994) pdf arxiv
  7. Magnetized plasmas in the early universe R. M. Gailis, C. P. Dettmann, N. E. Frankel and V. Kowalenko, Phys. Rev. D 50,3847-3858 (1994) pdf
  8. Chaos and fractals around black holes C. P. Dettmann, N. E. Frankel and N. J. Cornish, Fractals 3 161-181 (1995) pdf arxiv
  9. 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
  10. Magnetohydrodynamics in the expanding Universe R. M. Gailis, C. P. Dettmann and N. E. Frankel, Phys. Rev. D 52, 6901-6917 (1995) pdf (large: 1.2M)
  11. Chaos in special relativistic dynamics S. Drake, C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. E 53,1351-1361 (1996) pdf
  12. Stochastic dynamics of relativistic turbulence. C. P. Dettmann and N. E. Frankel, Phys. Rev. E 53, 5502-5505 (1996) pdf
  13. Proof of Lyapunov exponent pairing for systems at constant kinetic energy. C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 53, R5545-R5548 (1996) pdf ps["Dettmann-Morriss theorem"; mis-cited 15 times at last count!]
  14. Hamiltonian formulation of the Gaussian isokinetic thermostat. C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 54, 2495-2500 (1996) pdf ps
  15. 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
  16. Crisis in the periodic Lorentz gas. C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 4782-4790 (1996) pdf (4.9M)
  17. Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 55, 3693-3696 (1997) pdf ps arxiv [Origin of the "Nose-Poincare" symplectic integrator]
  18. 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]
  19. Stability ordering of cycle expansions C. P. Dettmann and G. P. Morriss, Phys. Rev. Lett. 78, 4201-4204 (1997) pdf ps arxiv
  20. 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)
  21. Recent results for the thermostatted Lorentz gas, G. P. Morriss, C. P. Dettmann and L. Rondoni, Physica A 240, 84-95 (1997)
  22. 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)
  23. Cycle expansions for intermittent diffusion C. P. Dettmann and P. Cvitanovic', Phys. Rev. E 56, 6687-6692 (1997) pdf ps arxiv
  24. Fractal transistors, R. P. Taylor, A. P. Micolich, R. Newbury, C. P. Dettmann and T. M. Fromhold, Semicond. Sci. Tech. 12,1459-1464 (1997)
  25. 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)
  26. 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)
  27. Computing the diffusion coefficient for intermittent maps: Resummation of stability ordered cycle expansions C. P. Dettmann and P. Dahlqvist, Phys. Rev. E 57, 5303-5310 (1998) pdf ps.gz arxiv
  28. 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)
  29. Thermostats: Analysis and application G. P. Morriss and C. P. Dettmann, Chaos 8,321-336 (1998) ps pdf
  30. Trace formulas for stochastic evolution operators: Weak noise perturbation theory P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, J. Stat. Phys. 93, 981-999 (1998) ps.gz (1.2M when uncompressed) arxiv
  31. Traces and determinants of strongly stochastic operators C. P. Dettmann, Phys. Rev. E 59, 5231-5234 (1999) pdf ps html arxiv
  32. Trace formulas for stochastic evolution operators: Smooth conjugation method P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, Nonlinearity 12, 939-953 (1999) ps arxiv
  33. Spectrum of stochastic evolution operators: Local matrix representation approach P. Cvitanovic', N. Sondergaard, G. Palla, G. Vattay, and C. P. Dettmann, Phys. Rev. E 60, 3936-3941 (1999) pdf ps Two distinct arxiv versions:arxiv arxiv
  34. 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
  35. Hamiltonian for a restricted isoenergetic thermostat C. P. Dettmann, Phys. Rev. E 60,7576-7577 (1999) pdf ps arxiv
  36. 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
  37. 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
  38. Noise corrections to stochastic trace formulas G. Palla, G. Vattay, A. Voros, N. Sondergaard, C. P. Dettmann, Found. Phys. 31, 641-657 (2001). arxiv
  39. Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589-599 (2001) ps arxiv
  40. Stable synchronised states of coupled Tchebyscheff maps, C. P. Dettmann, Physica D 172 88-102 (2002). ps.gz(1.3M when uncompressed) animation (0.3M) arxiv
  41. Lyapunov spectra of periodic orbits for a many-particle system, T. Taniguchi, C. P. Dettmann and G. P. Morriss, J. Stat. Phys. 109 747-764 (2002). pdf ps.gz(1.0M when uncompressed). arxiv
  42. The Burnett expansion of the periodic Lorentz gas, C. P. Dettmann, Ergod. Th. Dyn. Sys. 23, 481-491 (2003) ps arxiv
  43. Fractal asymptotics, C. P. Dettmann, Physica D 187, 214-222 (2004). ps arxiv
  44. Stochastic stabilization of cosmological photons. C. P. Dettmann, J. P. Keating, and S. D. Prado, J. Phys. A.: Math. Theor.37 L377-L383 (2004) pdf. arxiv animation (0.3M) [Featured in the June 2010 issue of Mathematics Today, pdf available here.]
  45. Stochastic stabilization of chaos and the cosmic microwave background. C. P. Dettmann, J. P. Keating and S. D. Prado, Int. J. Mod. Phys. D 13 1461-1468 (2004). pdf
  46. Periodic orbit theory of two coupled Tchebyscheff maps, C. P. Dettmann and D. Lippolis, Chaos, Solitons and Fractals 23 43-54 (2005). ps pdf arxiv
  47. Open circular billiards and the Riemann hypothesis, L. A. Bunimovich and C. P. Dettmann, Phys. Rev. Lett. 94 100201 (2005) ps pdf arxivRH day slides
  48. Thermostats for "slow" configurational modes A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Stat. Phys. 128 1321-1336 (2007) [Origin of the "Nose-Hoover-Langevin" thermostat] pdf arxiv
  49. 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)
  50. 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
  51. 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
  52. Product of n independent uniform random variables, C. P. Dettmann and O. Georgiou, Stat. Prob. Lett., 79, 2501-2503 (2009). pdf
  53. Survival probability for the stadium billiard, C. P. Dettmann and O. Georgiou, Physica D, 238, 2395-2403 (2009). pdf arxiv
  54. Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps, C. P. Dettmann and T. B. Howard, Physica D, 238, 2404-2408 (2009). pdf arxiv early poster
  55. 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
  56. Notes on configurational thermostat schemes, A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Chem. Phys. 132 246101 (2010) pdf arxiv
  57. 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
  58. 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
  59. 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
  60. 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
  61. 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)
  62. 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
  63. Impact of boundaries on fully connected random geometric networks, J. P. Coon, C. P. Dettmann and O. Georgiou, Phys. Rev. E 85 011138 (2012). pdf arxiv
  64. 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
  65. Dependence of chaotic diffusion on the size and position of holes, G. Knight, O. Georgiou, C. P. Dettmann, R. Klages, Chaos 22 023132 (2012). pdf arxiv
  66. Full Connectivity: Corners, edges and faces, J. P. Coon, C. P. Dettmann and O. Georgiou, J. Stat. Phys. 147 758-778 (2012). pdf arxiv poster
  67. Quantifying intermittency in the open drivebelt billiard, C. P. Dettmann and O. Georgiou, Chaos 22 026113 (2012). pdf arxiv
  68. 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
  69. 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
  70. Faster than expected escape for a class of fully chaotic maps, O. Georgiou, C. P. Dettmann, E. G. Altmann, Chaos 22 043115 (2012). arxiv pdf
  71. Open circle maps: Small hole asymptotics, C. P. Dettmann, Nonlinearity 26 307-317 (2013). pdf arxiv
  72. On the connectivity of 2-D random networks with anisotropically radiating nodes, J. P. Coon and C. P. Dettmann, IEEE Commun. Lett. 17 321-324 (2013). pdf
  73. An approximation of the Marcum Q-function with application to the performance analysis of communication systems, M. Z. Bocus, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett. (to appear). arxiv
  74. Escape from a circle and Riemann hypotheses, L. A. Bunimovich and C. P. Dettmann, submitted ps pdf
  75. Connectivity of confined dense networks: Boundary effects and scaling laws, J. P. Coon, C. P. Dettmann and O. Georgiou, submitted pdf arxiv
  76. 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, submitted pdf
  77. Keyhole and Reflection Effects in Network Connectivity Analysis, M. Z. Bocus, C. P. Dettmann, J. P. Coon, M. R. Rahman, submitted arxiv.
  78. Periodic volume fluctuations with infinite horizon: Intermittency enhanced Fermi acceleration, C. P. Dettmann and E. D. Leonel, submitted pdf

    79. Proceedings

  79. Proceedings: Stochastic stabilization of the cosmic microwave background radiation. C. P. Dettmann, J. P. Keating and S. D. Prado, Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, ed M. Novello, S. Perez-Bergliaffa and R. Ruffini, World Scientific, Singapore (2006) ps pdf.
  80. Proceedings: 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, Ninth International Conference on Transparent Optical Networks (ICTON 2007) 4 197-200 (2007)
  81. Proceedings: 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, Tenth International Conference on Transparent Optical Networks (ICTON 2008) 4, 65-68 (2008). pdf
  82. Proceedings: 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
  83. Proceedings: Systematization of All Resonance Modes in Circular Dielectric Cavities, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Eleventh International Conference on Transparent Optical Networks (ICTON 2009) 763-766 (2009). pdf
  84. Proceedings: Microdisk resonators with two point scatterers, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Thirteenth International Conference on Transparent Optical Networks (ICTON 2011) 462-464 (2011). pdf
  85. Proceedings: Towards k-connectivity: Local and global approaches, O. Georgiou, C. P. Dettmann and J. P. Coon (submitted) pdf

    Other publications

  86. 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 ps. Environmental microscopic version, 25 pages ps.
  87. Book review: Time reversibility, computer simulation and chaos, W. G. Hoover, (World Scientific, River Edge NJ, 1999); review published in Amer. J. Phys. 70 558-558 (2002) html
  88. Letter to the editor: C. P. Dettmann, Physics World (2006) html
  89. 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

    90. Unpublished work

  90. Web book contribution: "Stability ordering of cycle expansions" (currently section 20.5) in Classical and Quantum Chaos webbook, P. Cvitanovic' et al html
  91. Poster: Recent developments in periodic orbit theory C. P. Dettmann April 2002. ps
  92. Poster: Averaging quasiperiodic systems, C. P. Dettmann and T. B. Howard, August 2008 pdf

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