2021/06/21 by Hoover, William Graham, Hoover, Carol Griswold
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2106.10788
We illustrate an atomistic periodic two-dimensional stationary shear flow, ux = ⟨ x ⟩ = εy, using the simplest possible example, the periodic shear of just two particles ! We use a short-ranged "realistic" pair potential, ϕ(r<2) = (2-r)6 - 2(2-r)3. Many body simulations with it are capable of modelling the gas, liquid, and solid states of matter. A useful mechanics generating steady shear follows from a special ("Kewpie-Doll" ∼ "qp-Doll") Hamiltonian based on the Hamiltonian coordinates \ q \ and momenta \ p \ : \cal H(q,p) ≡ K(p) + Φ(q) + ε∑ qp. Choosing qp → ypx the resulting motion equations are consistent with steadily shearing periodic boundaries with a strain rate (dux/dy) = ε. The occasional x coordinate jumps associated with periodic boundary crossings in the y direction provide a Hamiltonian that is a piecewise-continuous function of time. A time-periodic isothermal steady state results when the Hamiltonian motion equations are augmented with a continuously variable thermostat generalizing Shuichi Nosé's revolutionary ideas from 1984. The resulting distributions of coordinates and momenta are interesting multifractals, with surprising irreversible consequences from strictly time-reversible motion equations.