arXiv subjects

Brad Lee Holian

Publications and source records attributed to Brad Lee Holian.

6 recordsLinked to original sources

arXiv2026

Nonequilibrium Maxwell-Demon NEMD formalism for transport: I. Extrapolating shear viscosity to the hydrodynamic limit

The Maxwell-Demon nonequilibrium molecular dynamics method for measuring the shear viscosity divides the fluid simulation cell into two regions of width w in the $x$-direction, with the particles allowed to move freely between the two sides. The Demon maintains equal and opposite regional average particle velocities in the $y$-direction by applying an acceleration needed to sustain the nonequilibrium steady state (NESS), which includes both total force balance and an instantaneous correction for diffusion of particles across boundaries. We show that the driven velocity profile in x is a natural hydrodynamic response and not imposed by the constraint. For the present shear geometry, the measured NESS profile in Eulerian slabs is represented accurately by a piecewise parabolic form, reminiscent of planar Poiseuille flow. The parabolic profile gives an estimate of the kinematic viscosity from work done on the shearing fluid, as well as an entropy production estimate, derived from heat removal by the Nosé-Hoover thermostat that keeps each regional average temperature constant. We show that the mechanical work supplied by the Demon equals the heat removed by the thermostat. Once NESS driving is removed, the parabolic velocity profile relaxes exponentially in short order to sinusoidal, the natural transverse momentum-diffusion eigenmode. Our Maxwell-Demon shear method provides a direct NEMD formalism for obtaining shear viscosity from momentum diffusion, work, and entropy balances. Our results in three dimensions for increasing system size $N$ (the number of particles) demonstrate that shear viscosity approaches an asymptote (the so-called hydrodynamic limit) as $N^{-1/3}$.

cond-mat.stat-mech↗

arXiv2025

When Heating Isn't Cooling in Reverse: Nosé-Hoover Thermostat Fluctuations from Equilibrium Symmetry to Nonequilibrium Asymmetry

Recent laboratory experiments suggest an intrinsic asymmetry between heating and cooling, with heating occurring more efficiently. Two decades earlier, molecular dynamics (MD) simulations had examined a related setup - heating one side of a computational cell while cooling the other via distinct thermostats. We revisit those calculations, recapitulating the underlying theory and showing that earlier MD results already hinted at the observed laboratory asymmetry. Recent realizations of a simple two-dimensional single-particle model, thermostatted in $x$ and $y$ at different temperatures, reproduces key features: at equilibrium, thermostat variables were identical, but under nonequilibrium conditions, the heating variable is weaker than the cooling one. At the same time, MD simulations from four decades ago by Evans and Holian reported a surprising skew in the Nose--Hoover thermostat variable $ξ$ under equilibrium - indicating a statistical bias in energy injection versus extraction. We revisit those results with exact reproduction of their setup. We show that when (1) the center-of-mass velocity is set to zero, (2) integration is done carefully with finite differencing, and (3) sampling is sufficiently long, the distribution of $ξ$ is symmetric and Gaussian with zero mean, as predicted by theory and validated by two independent error estimates. However, in the two-temperature cell, the distribution of thermostat variables become asymmetric, the cold bath requires significantly stronger damping than the hot bath requires anti-damping, with $\langle ξ_x \rangle / \langle ξ_y \rangle = -T_y/T_x$. This exact analytic relation links thermostat effort to thermal bias and the negative rate of change in the entropy of the system. These results identify the microscopic origin of heating-cooling asymmetry as a genuine nonequilibrium effect, consistent with experimental findings.

cond-mat.stat-mech↗

arXiv2025

Chaos in Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Models

We revisit a two-temperature Nosé-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction with high numerical precision. The total contraction rate, interpreted as entropy production, increases nonlinearly with the thermostat anisotropy, deviating from the quadratic dependence expected from linear-response theory, $Λ\propto -δ^{2}$. We compare two fits for $Λ$ as a function of $δ= 0.5 -T_y$: 1) a power law, $Λ\propto -δ^{2.44}$, 2) a quadratic-plus-quartic expansion. While the former captures low-driving behavior slightly better, the latter more accurately describes the strongly driven regime and remains consistent with linear response theory near equilibrium. An empirical linear relation between dissipation and phase-space dimensionality loss is also identified, $Λ\propto (D_{KY}-6) / 3$, where $D_{KY}$ is the approximate Kaplan-Yorke dimension. Our results demonstrate that nonlinear dissipation scaling emerges naturally even in minimal driven systems. Momentum statistics show significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production.

cond-mat.stat-mech↗

arXiv2014

Mesodynamics with implicit degrees for freedom

Mesoscale phenomena -- involving a level of description between the finest atomistic scale and the macroscopic continuum -- can be studied by a variation on the usual atomistic-level molecular dynamics (MD) simulation technique. In mesodynamics, the mass points, rather than being atoms, are mesoscopic in size, for instance representing the centers of mass of polycrystalline grains or molecules. In order to reproduce many of the overall features of fully atomistic MD, which is inherently more expensive, the equations of motion in mesodynamics must be derivable from an interaction potential that is faithful to the compressive equation of state, as well as to tensile de-cohesion that occurs along the boundaries of the mesoscale units. Moreover, mesodynamics diffrers from Newton's equations of motion in that dissipation -- the exchange of energy between mesoparticles and their internal degrees of freedom (DoFs) -- must be described, and so should the transfer of energy between the internal modes of neighboring mesoparticles. We present a formulation where energy transfer between the internal modes of a mesoparticle and its external center-of-mass DoFs occurs in the phase space of mesoparticle coordinates, rather than momenta, resulting in a Galilean invariant formulation that conserves total linear momentum and energy (including the energy internal to the mesoparticles). We show that this approach can be used to describe, in addition to mesoscale problems, conduction electrons in atomic-level simulations of metals, and we demonstrate applications of mesodynamics to shockwave propagation and thermal transport.

physics.chem-ph↗

arXiv2006

The Influence of Interatomic Bonding Potentials on Detonation Properties

The dependence of macroscopic detonation properties of a two-dimensional diatomic (AB) molecular system on the fundamental properties of the molecule were investigated. This includes examining the detonation velocity, reaction zone thickness, and critical width as a function of the exothermicity of the gas-phase reaction and the gas-phase dissociation energy for. Following previous work, molecular dynamics (MD) simulations with a reactive empirical bond-order potential were used to characterize the shock-induced response of a diatomic AB molecular solid, which exothermically reacts to produce gaseous products. MD simulations reveal that there is a linear dependence between the square of the detonation velocity and each of these molecular parameters. The detonation velocities were shown to be consistent with the Chapman-Jouguet model, demonstrating that these dependencies arise from how the Equation of State of the products and reactants are affected.

cond-mat.mtrl-sci↗

arXiv1996

An Einstein Model of Brittle Crack Propagation

We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement with many-body dynamical simulations. The model exhibits lattice-trapping. For loads just above this, the crack velocity rises sharply, reaching a limiting value well below that predicted by elastic continuum theory. We trace the origin of the low limiting velocity to the anharmonicity of the potential well experienced by the crack-tip atom.

cond-mat.mtrl-sci↗