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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 ...
Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs’ canonical distribution for simple (small) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a qu ...
Chaos in conservative systems, particularly in Hamiltonian systems, is different from chaos in dissipative systems. For example, not only the eigenvalues of the symmetric Jacobian, but also the global Lyapunov exponents of Hamiltonian systems occur in pairs (λ, −λ). In this article, we even s ...
The time-averaged Lyapunov exponents, {λi}, support a mechanistic description of the chaos generated in and by nonlinear dynamical systems. The exponents are ordered from largest to smallest with the largest one desc ...
The 2016 Snook Prize has been awarded to Diego Tapias, Alessandro Bravetti, and David Sanders for their paper “Ergodicity of One-Dimensional Systems Coupled to the Logistic Thermostat”. They introduced a relatively-stiff hyperbolic tangent thermostat force and successfully tested its ability ...
We two had year-long research leaves in Japan, working together fulltime with several Japanese plus Tony De Groot back in Livermore and Harald Posch in Vienna. We summarize a few of the high spots from that very productive year (1989-1990), followed by an additional fifteen years’ work in Liver ...
For a harmonic oscillator, Nosé’s single-thermostat approach to simulating Gibbs’ canonical ensemble with dynamics samples only a small fraction of the phase space. Nosé’s approach has been improved in a series of three steps: [1] several two-thermostat sets of motion equations have been ...
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 r ...
Time-reversible symplectic methods, which are precisely compatible with Liouville’s phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent advantage of such methods. But all numerical methods are susce ...
Shuichi Nosé opened up a new world of atomistic simulation in 1984. He formulated a Hamiltonian tailored to generate Gibbs’ canonical distribution dynamically. This clever idea bridged the gap between microcanonical molecular dynamics and canonical statistical mechanics. Until then the canon ...