2019 SNOOK Prizes in Computational Statistical Mechanics
Ruby Valley Research Institute
Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA
E-mail: hooverwilliam@yahoo.com
Received:
Published online: 14 March 2019
DOI: 10.12921/cmst.2019.0000009
Abstract:
The one-dimensional φ4 Model generalizes a harmonic chain with nearest-neighbor Hooke’s-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature: because the quartic tethers act to scatter long-wavelength phonons, φ4 chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the three-dimensional energy surface describing a two-body two-spring chain. That surface can include at least two distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body φ4 problems merit more investigation. Accordingly, the 2019 Prizes honoring Ian Snook (1945-2013) [five hundred United States dollars cash from the Hoovers and an additional $500 cash from the Institute of Bioorganic Chemistry of the Polish Academy of Sciences and the Poznan Supercomputing and Networking Center] will be awarded to the author(s) of the most interesting work analyzing and discussing few-body φ4 models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model’s ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.
Details of the Prize Problem can be found on pages 159-162 of Volume 24 (2) of Computational Methods in Science and Technology (CMST) http://dx.doi.org/10.12921/cmst.2018.0000032 . No Prize was awarded in 2018.
The one-dimensional φ4 Model generalizes a harmonic chain with nearest-neighbor Hooke’s-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature: because the quartic tethers act to scatter long-wavelength phonons, φ4 chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the three-dimensional energy surface describing a two-body two-spring chain. That surface can include at least two distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body φ4 problems merit more investigation. Accordingly, the 2019 Prizes honoring Ian Snook (1945-2013) [five hundred United States dollars cash from the Hoovers and an additional $500 cash from the Institute of Bioorganic Chemistry of the Polish Academy of Sciences and the Poznan Supercomputing and Networking Center] will be awarded to the author(s) of the most interesting work analyzing and discussing few-body φ4 models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model’s ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.
Details of the Prize Problem can be found on pages 159-162 of Volume 24 (2) of Computational Methods in Science and Technology (CMST) http://dx.doi.org/10.12921/cmst.2018.0000032 . No Prize was awarded in 2018.
