Time-Reversible Ergodic Maps and the 2015 Ian Snook Prizes

• Autorzy: Hoover W. G. , Hoover C. G.

Identyfikatory

DOI

10.12921/cmst.2015.21.03.003

• Języki publikacji: EN

Abstrakty

EN

The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based thermostats and ergostats. Typical solutions are multifractal attractor-repellor phase-space pairs with reversed momenta and unchanged coordinates, (q; p)↔(q;--p). Weak control of the temperature, α p2 and its fluctuation, resulting in ergodicity, has recently been achieved in a threedimensional time-reversible model of a heat-conducting harmonic oscillator. Two-dimensional cross sections of such nonequilibrium flows can be generated with time-reversible dissipative maps yielding æsthetically interesting attractorrepellor pairs. We challenge the reader to find and explore such time-reversible dissipative maps. This challenge is the 2015 Snook-Prize Problem.

Słowa kluczowe

EN

ergodicity; chaos; algorithms; time-reversible flows; maps

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2015
• Tom: Vol. 21, No. 3
• Strony: 161--164
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Hoover W. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

autor

Hoover C. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

Bibliografia

• [1] W. G. Hoover and C. G. Hoover, Simulation and Control of Chaotic Nonequilibrium Systems (World Scientific Publishers, Singapore, 2015).
• [2] H. A. Posch and Wm. G. Hoover, Time-Reversible Dissipative Attractors in Three and Four Phase-Space Dimensions, Physical Review E 55, 6803-6810 (1997).
• [3] W. G. Hoover, J. C. Sprott, and C. G. Hoover, Nonequilibrium Molecular Dynamics and Dynamical Systems Theory for Small Systems with Time-Reversible Motion Equations, Molecular Simulation (in press, 2015).
• [4] W. G. Hoover, O. Kum, and H. A. Posch, Time-Reversible Dissipative Ergodic Maps, Physical Review E 53, 2123-2129 (1996).
• [5] J. Kumi˘cák, Irreversibility in a Simple Reversible Model, Physical Review E 71, 016115 (2005), arχiv nlin/0510016.
• [6] L. Ermann and D. L. Shepelyansky, Arnold Cat Map, Ulam Method, and Time Reversal, arχiv1107.0437.
• [7] W. G. Hoover and C. G. Hoover, Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators, Computational Methods in Science and Technology 21 (to appear, 2015), arχiv 1504.00620.
• [8] D. Faranda, Analysis of Roundoff Errors with Reversibility Test as a Dynamical Indicator, arχiv 1205.3060.