Diffusion

    Diffusion is the transport of particles, and conclusions from work on diffusion can often be extended to viscosity (transport of momentum), heat conduction (transport of energy) and other transport processes. Deterministic diffusion is the analysis of how apparently random large scale behaviour ("Brownian motion") can arise from microscopic, normally chaotic, dynamics. The work here includes the application of periodic orbit theory in intermittent dynamics where the intermittency can lead to anomolous diffusion laws making direct computation unfeasible, the surprisingly small amount of chaos required for diffusion in near-integrable dynamics and diffusive properties of the Lorentz gas. Diffusion in velocity is also a characteristic of Fermi acceleration in time-dependent systems

  1. Cycle expansions for intermittent diffusion C. P. Dettmann and P. Cvitanovic', Phys. Rev. E 56, 6687-6692 (1997) pdf ps arxiv
  2. 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
  3. 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
  4. 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
  5. 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
  6. Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589-599 (2001) ps arxiv
  7. The Burnett expansion of the periodic Lorentz gas, C. P. Dettmann, Ergod. Th. Dyn. Sys. 23, 481-491 (2003) ps arxiv
  8. 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
  9. 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
  10. 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)
  11. 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
  12. 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
  13. 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
  14. 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
  15. Diffusion in the Lorentz gas, C. P. Dettmann, Commun. Theor. Phys. 62 521-540 (2014). pdf arxiv
  16. 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.
  17. 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.

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