arXiv subjects

Wm. G. Hoover

Publications and source records attributed to Wm. G. Hoover.

27 records · Page 2Linked to original sources

arXiv2010

Well-Posed Two-Temperature Constitutive Equations for Stable Dense Fluid Shockwaves using Molecular Dynamics and Generalizations of Navier-Stokes-Fourier Continuum Mechanics

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

cond-mat.stat-mech↗

arXiv2009

Tensor Temperature and Shockwave Stability in a Strong Two-Dimensional Shockwave

The anisotropy of temperature is studied here in a strong two-dimensional shockwave, simulated with conventional molecular dynamics. Several forms of the kinetic temperature are considered, corresponding to different choices for the local instantaneous stream velocity. A local particle-based definition omitting any "self" contribution to the stream velocity gives the best results. The configurational temperature is not useful for this shockwave problem. Configurational temperature is subject to a shear instability and can give local negative temperatures in the vicinity of the shock front. The decay of sinusoidal shockfront perturbations shows that strong two-dimensional planar shockwaves are stable to such perturbations.

cond-mat.stat-mech↗

arXiv2009

Microscopic and Macroscopic Stress with Gravitational and Rotational Forces

Many recent papers have questioned Irving and Kirkwood's atomistic expression for stress. In Irving and Kirkwood's approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate [1] a fluid in a gravitational field and [2] a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.

nlin.CD↗

arXiv2009

Nonlinear Stresses and Temperatures in Transient Adiabatic and Shear Flows via Nonequilibrium Molecular Dynamics -- Three Definitions of Temperature

We compare nonlinear stresses and temperatures for adiabatic shear flows, using up to 262,144 particles, with those from corresponding homogeneous and inhomogeneous flows. Two varieties of kinetic temperature tensors are compared to the configurational temperatures. This comparison leads to an improved form for the local and instantaneous smooth-particle averaged stream velocity and to a recognition of rotational contributions to the configurational temperature.

nlin.CD↗

arXiv2008

50 Years of Computer Simulation -- a Personal View

In the half century since the 1950s computer simulation has transformed our understanding of physics. The rare, expensive, slow, and bulky mainframes of World War II have given way to today's millions of cheap, fast, desksized workstations and personal computers. As a result of these changes, the theoretical formal view of physics has gradually shifted, so as to focus on the pragmatic and useful. General but vague approaches are being superceded by specific results for definite models. During this evolving change of emphasis I learned, developed, and described my simulation skills at Michigan, at Duke, at Livermore, and in Nevada, while forming increasingly wide-ranging contacts around the world. Computation is now pervasive in all the scientific fields. My own focus has been on the physics of particle simulations, mainly away from equilibrium. I outline my particle work here. It has led me to a model-based understanding of both equilibrium and nonequilibrium physics. There are still some gaps. There is still much to do.

nlin.CD↗

arXiv2008

2D and 3D Dense-Fluid Shear Flows via Nonequilibrium Molecular Dynamics. Comparison of Time-and-Space-Averaged Tensor Temperature and Normal Stresses from Doll's, Sllod, and Boundary-Driven Shear Algorithms

Homogeneous shear flows (with constant strainrate du/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, P(xx) - P(yy), depend on both the thermostat type and the chosen shearflow algorithm. The Doll's and Sllod algorithms predict opposite signs for this stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures, T(xx) > T(zz) > T(yy).

nlin.CD↗

arXiv2008

Nonequilibrium Temperature and Thermometry in Heat-Conducting Phi-4 Models

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We show in detail, for both two- and three-dimensional systems, that the ideal gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the Phi-4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between kinetic temperature and the nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that kinetic temperature, as modeled and imposed by the Nosé-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.

nlin.CD↗

arXiv2002

Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.

nlin.CD↗

arXiv2000

Entropy production and Lyapunov instability at the onset of turbulent convection

Computer simulations of a compressible fluid, convecting heat in two dimensions, suggest that, within a range of Rayleigh numbers, two distinctly different, but stable, time-dependent flow morphologies are possible. The simpler of the flows has two characteristic frequencies: the rotation frequency of the convecting rolls, and the vertical oscillation frequency of the rolls. Observables, such as the heat flux, have a simple-periodic (harmonic) time dependence. The more complex flow has at least one additional characteristic frequency -- the horizontal frequency of the cold, downward- and the warm, upward-flowing plumes. Observables of this latter flow have a broadband frequency distribution. The two flow morphologies, at the same Rayleigh number, have different rates of entropy production and different Lyapunov exponents. The simpler "harmonic" flow transports more heat (produces entropy at a greater rate), whereas the more complex "chaotic" flow has a larger maximum Lyapunov exponent (corresponding to a larger rate of phase-space information loss). A linear combination of these two rates is invariant for the two flow morphologies over the entire range of Rayleigh numbers for which the flows coexist, suggesting a relation between the two rates near the onset of convective turbulence.

nlin.CD↗