Coarse-graining description of solid systems at nonzero temperature

Multiscale simulation of thin-film lubrication: free-energy-corrected coarse graining

The quasicontinuum method was previously extended to the nonzero temperature conditions by implementing a free-energy correction on non-nodal atoms in coarse-grained solid systems to avoid the dynamical constraint, [Diestler, Wu, and Zeng, J. Chem. Phys. 121, 9279 (2004)]. In this paper, we combine the extended quasicontinuum method and an atomistic simulation to treat the monolayer film lubrication with elastic (nonrigid) substrates. It is shown that the multiscale method with the coarse-graining local elements in the merging regions between the atomistic and continuous descriptions of the substrates can reasonably predict the shear stress profile, the mean separation curve, and the transverse stress profile in the fully atomistic simulation for the tribological system. Moreover, when the nonlocal elements are placed in the merging regions, the inhomogeneous solid atoms in the near regions covered by the cut-off circles of the nonlocal elements replace the homogeneous ones at the equilibrium configuration for the free-energy correction on the non-nodal atoms. The treatment can cause an unphysical sliding between the near and far regions of the upper substrate. It is shown that if the free-energy correction on the non-nodal atoms in the coarse-grained merging regions is removed, the multiscale method can still well reproduce the shear stress profile, the mean separation curve, and the transverse stress profile obtained from the fully atomistic simulation for the system.

Nonaffine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor D as well as a positive definite scalar χ measuring nonaffinity, i.e., the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of χ and D and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution P(χ,D) and the two-point spatial correlation functions for χ and D. We show that nonaffine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse-graining volume Ω and dimensionality. As a corollary to our work, we identify the field h(χ) conjugate to χ and show that this field may be tuned to produce a transition to a state where the ensemble average <χ> and the correlation length of χ diverge. Our work should be useful as a template for understanding nonaffine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of nonaffine displacements in melting, plastic flow, and the glass transition.

Nonequilibrium multiscale computational model

A computational multiscale method is proposed to simulate coupled, nonequilibrium thermomechanical processes. This multiscale framework couples together thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale. The novel concept of distributed coarse scale thermostats enables subsets of fine scale atoms to be attached to different coarse scale nodes which act as thermostats. The fine scale dynamics is driven by the coarse scale mean field. A coarse-grained Helmholtz free energy is used to derive macroscopic quantities. This new framework can reproduce the correct thermodynamics at the fine scale while providing an accurate coarse-grained result at the coarse scale.

Hybrid atomistic-coarse-grained treatment of multiscale processes in heterogeneous materials: A self-consistent-field approach

A treatment of multiscale quasistatic processes that combines an atomistic description of microscopic heterogeneous ("near") regions of a material with a coarse-grained (quasicontinuum) description of macroscopic homogeneous ("far") regions is presented. The hybrid description yields a reduced system consisting of the original atoms of the near regions plus pseudoatoms (nodes of the coarse-graining mesh) of the far regions, which interact through an effective many-body potential energy V(eff) that depends on the thermodynamic state. The approximate nature of V(eff) gives rise to "ghost forces," which are reflected in spurious heterogeneities close to interfaces between near and far regions. The impact of ghost forces, which afflict all previous hybrid schemes, is greatly diminished by a self-consistent-field hybrid atomistic-coarse-grained (SCF-HACG) methodology. Tests of the SCF-HACG technique on a fully three-dimensional prototypal model [Lennard-Jones (12,6) crystal] yield thermomechanical properties (e.g., local stress) in good agreement with "exact" properties computed in the fully atomistic limit. The SCF-HACG method is also successfully used to characterize the grain boundary in a Lennard-Jones bicrystal.

The significance of lipid composition for membrane activity: New concepts and ways of assessing function

In the last decade or so, it has been realised that membranes do not just have a lipid-bilayer structure in which proteins are embedded or with which they associate. Structures are dynamic and contain areas of heterogeneity which are vital for their formation. In this review, we discuss some of the ways in which these dynamic and heterogeneous structures have implications during stress and in relation to certain human diseases. A particular stress is that of temperature which may instigate adaptation in poikilotherms or appropriate defensive responses during fever in mammals. Recent data emphasise the role of membranes in sensing temperature changes and in controlling a regulatory loop with chaperone proteins. This loop seems to need the existence of specific membrane microdomains and also includes association of chaperone (heat stress) proteins with the membrane. The role of microdomains is then discussed further in relation to various human pathologies such as cardiovascular disease, cancer and neurodegenerative diseases. The concept of modifying membrane lipids (lipid therapy) as a means for treating such pathologies is then introduced. Examples are given when such methods have been shown to have benefit. In order to study membrane microheterogeneity in detail and to elucidate possible molecular mechanisms that account for alteration in membrane function, new methods are needed. In the second part of the review, we discuss ultra-sensitive and ultra-resolution imaging techniques. These include atomic force microscopy, single particle tracking, single particle tracing and various modern fluorescence methods. Finally, we deal with computing simulation of membrane systems. Such methods include coarse-grain techniques and Monte Carlo which offer further advances into molecular dynamics. As computational methods advance they will have more application by revealing the very subtle interactions that take place between the lipid and protein components of membranes - and which are so essential to their function.

An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature

Covering the solid lattice with a finite-element mesh produces a coarse-grained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the two-dimensional Lennard-Jones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress) in excellent agreement with "exact" fully atomistic results.

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. I

A technique that melds an atomistic description of the interfacial region with a coarse-grained description of the far regions of the solid substrates is presented and applied to a two-dimensional model contact consisting of planar solid substrates separated by a monolayer fluid film. The hybrid method yields results in excellent agreement with the "exact" (i.e., fully atomistic) results. The importance of a proper accounting for the elastic response of the substrates, which is reliably and efficiently accomplished through coarse-graining of the far regions, is demonstrated.

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. II

A new hybrid atomistic-coarse-grained (HACG) treatment of reversible processes in multiple-scale systems involving fluid-solid interfaces was tested through isothermal-isobaric Monte Carlo simulations of the quasistatic shearing of a model two-dimensional lubricated contact comprising two planar Lennard-Jones solid substrates that sandwich a softer Lennard-Jones film. Shear-stress profiles (plots of shear stress T(yx) versus lateral displacement of the substrates) obtained by the HACG technique, which combines an atomistic description of the interfacial region with a continuum description of regions well removed from the interface, are compared with "exact" profiles (obtained by treating the whole system at the atomic scale) for a selection of thermodynamic states that correspond to systematic variations of temperature, load (normal stress), film-substrate coupling strength, and film thickness. The HACG profiles are in excellent agreement overall with the exact ones. The HACG scheme provides a reliable description of quasistatic shearing under a wide range of conditions. It is demonstrated that the elastic response of the remote regions of the substrates can have a significant impact on the static friction profile (plot of maximum magnitude of T(yx) versus load).