Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena et al., Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime

Structural disjoining potential for grain boundary premelting and grain coalescence from molecular-dynamics simulations

We describe a molecular dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain-coalescence in solidification. The method is applied in a comparative study of (i) a Sigma 9 120 degress twist and (ii) a Sigma 9 {411} symmetric tilt boundary in a classical embedded-atom model of elemental Ni. Although both boundaries feature highly disordered structures near the melting point, the nature of the temperature dependence of the width of the disordered regions in these boundaries is qualitatively different. The former boundary displays behavior consistent with a logarithmically diverging premelted layer thickness as the melting temperature is approached from below, while the latter displays behavior featuring a finite grain-boundary width at the melting point. It is demonstrated that both types of behavior can be quantitatively described within a sharp-interface thermodynamic formalism involving a width-dependent interfacial free energy, referred to as the disjoining potential. The disjoining potential for boundary (i) is calculated to display a monotonic exponential dependence on width, while that of boundary (ii) features a weak attractive minimum. The results of this work are discussed in relation to recent simulation and theoretical studies of the thermodynamic forces underlying grain-boundary premelting.Comment: 24 pages, 8 figures, 1 tabl

Monte Carlo Study of Short-Range Order and Displacement Effects in Disordered CuAu

The correlation between local chemical environment and atomic displacements in disordered CuAu alloy has been studied using Monte Carlo simulations based on the effective medium theory (EMT) of metallic cohesion. These simulations correctly reproduce the chemically-specific nearest-neighbor distances in the random alloy across the entire Cu\$_x\$Au\$_{1-x}\$ concentration range. In the random equiatomic CuAu alloy, the chemically specific pair distances depend strongly on the local atomic environment (i.e. fraction of like/unlike nearest neighbors). In CuAu alloy with short-range order, the relationship between local environment and displacements remains qualitatively similar. However the increase in short-range order causes the average Cu-Au distance to decrease below the average Cu-Cu distance, as it does in the ordered CuAuI phase. Many of these trends can be understood qualitatively from the different neutral sphere radii and compressibilities of the Cu and Au atoms.Comment: 9 pages, 5 figures, 2 table

The activation energy for GaAs/AlGaAs interdiffusion

Copyright 1997 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. This article appeared in Journal of Applied Physics 82, 4842 (1997) and may be found at

Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

Inhomogeneous High Frequency Expansion-Free Gravitational Waves

We describe a natural inhomogeneous generalization of high frequency plane gravitational waves. The waves are high frequency waves of the Kundt type whose null propagation direction in space-time has vanishing expansion, twist and shear but is not covariantly constant. The introduction of a cosmological constant is discussed in some detail and a comparison is made with high frequency gravity waves having wave fronts homeomorphic to 2-spheres.Comment: 18 pages, Latex file, accepted for publication in Physical Review

Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations

In modeling nonequilibrium systems one usually starts with a definition of the microscopic dynamics, e.g., in terms of transition rates, and then derives the resulting macroscopic behavior. We address the inverse question for a class of steady state systems, namely complex fluids under continuous shear flow: how does an externally imposed shear current affect the microscopic dynamics of the fluid? The answer can be formulated in the form of invariant quantities, exact relations for the transition rates in the nonequilibrium steady state, as discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett. 101, 240601 (2008)]. Here, we present a more pedagogical account of the invariant quantities and the theory underlying them, known as the nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we investigate the relationship between the transition rates and the shear current in the steady state. We show that a fluctuation relation of the Gallavotti-Cohen type holds for systems satisfying NCDB.Comment: 24 pages, 11 figure

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic properties such as shear-thinning and shear-banding.Comment: 14 pages, 5 figures, Revte

Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W

Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties relevant to screw dislocations in pure W. As well, we perform molecular dynamics simulations of stress-assisted glide using all five potentials to study the dynamic behavior of screw dislocations under shear stress. Dislocations are seen to display thermally-activated motion in most of the applied stress range, with a gradual transition to a viscous damping regime at high stresses. We find that one potential predicts a core transformation from compact to dissociated at finite temperature that affects the energetics of kink-pair production and impacts the mechanism of motion. We conclude that a modified embedded-atom potential achieves the best compromise in terms of static and dynamic screw dislocation properties, although at an expense of about ten-fold compared to central potentials