The Simplest Viscous Flow

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

Identyfikatory

DOI

10.12921/cmst.2021.0000017

• Języki publikacji: EN

Abstrakty

EN

We illustrate an atomistic periodic two-dimensional stationary shear flow, ux = h x˙ i = ˙y, 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} : H(q, p) ≡ K(p) + Φ(q) + ˙ Pqp. Choosing qp → ypx the resulting motion equations are consistent with steadily shearing periodic boundaries with a strain rate (dux/dy) = ˙. 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.

Słowa kluczowe

EN

shear flow; statistical physics; Hamiltonian Molecular Dynamics; periodic boundaries; fractals

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2021
• Tom: Vol. 27, No. 3
• Strony: 109--119
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Hoover Wm. G.

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

autor

Hoover C. G.

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

Bibliografia

• [1] T.C. Germann, K. Kadau, Trillion-Atom Molecular Dynamics Becomes a Reality, Journal of Modern Physics C 19, 1315–1319 (2008).
• [2] W.T. Ashurst, Dense Fluid Shear Viscosity and Thermal Conductivity via Nonequilibrium Molecular Dynamics, University of California, Davis (1974).
• [3] S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Method, The Journal of Chemical Physics 81, 511–519 (1984).
• [4] S. Nosé, Molecular Dynamics Method for Simulations in the Canonical Ensemble, Molecular Physics 52, 255–268 (1984).
• [5] Wm.G. Hoover, Canonical Dynamics. Equilibrium Phase-Space Distributions, Physical Review A 31, 1695–1697 (1985).
• [6] Wm.G. Hoover, Adiabatic Hamiltonian Deformation, Linear Response Theory, and Nonequilibrium Molecular Dynamics, [In:] Systems Far from Equilibrium, Ed. L. Garrido, Springer-Verlag, Berlin (1980).
• [7] K.P. Travis, Wm.G. Hoover, C.G. Hoover, A.B. Hass, What is Liquid? [in two dimensions], Computational Methods in Science and Technology 27, 5–23 (2021).
• [8] Wm.G. Hoover, 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, 109–116 (2015).
• [9] B.L. Holian, W.G. Hoover, H.A. Posch, Resolution of Loschmidt’s Paradox: The Origin of Irreversible Behavior in Reversible Atomistic Dynamics, Physical Review Letters 59, 10–13 (1987).
• [10] W.G. Hoover, H.A. Posch, B.L. Holian, M.J. Gillan, M. Mareschal, C.M. Massobrio, Dissipative Irreversibility from Nosé’s Reversible Mechanics, Molecular Simulation 1, 79–86 (I987).
• [11] J.C. Sprott, Some Simple Chaotic Flows, Physical Review E 50, R647 (1994).
• [12] Wm.G. Hoover, Remark on “Some Simple Chaotic Flows”, Physical Review E 51, 759–760 (1995).
• [13] Wm.G. Hoover, O. Kum, H.A. Posch, Time-Reversible Dissipative Ergodic Maps, Physical Review E 53, 2123–2129 (1996).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).