This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one

It is shown that a useful relativistic generalization of the conventional spin density s ជ͑r ជ , t͒ for the case of moving electrons is the expectation value (T ជ ͑r ជ , t͒ , T 4 ͑r ជ , t͒) of the four-component Bargmann-Wigner polarization operator T = ͑T ជ , T 4 ͒ ͓Proc. Natl. Acad. Sci. U.S.A. 34, 211 ͑1948͔͒ with respect to the four components of the wave function. An exact equation of motion for this quantity is derived using the one-particle Dirac equation, and the relativistic analogs of the nonrelativistic concepts of spin currents and spin-transfer torques are identified. Using this theoretical framework, in the classical limit the Bargmann-Michel-Telegdi equation ͓Phys. Rev. Lett. 2, 435 ͑1959͔͒ for a relativistic wave packet crossing a nonmagnetic/ferromagnetic interface is derived, to lowest order in the spin-orbit coupling it is shown that a contribution to the polarization current occurs with spin-Hall symmetry, and the spin-transfer torque for the simple "perfect spin filter" model is calculated and discussed.

We performed molecular dynamics simulations of boundary-lubricated sliding, varying the boundary lubricant type, its molecular surface coverage, the substrate roughness, and the load. The resulting load versus friction behavior was then analyzed to study how changes in lubricant type, coverage, and roughness affect the extrapolated friction force at zero load, the so-called Derjaguin offset. A smooth-particle-based evaluation method by the authors, applied here for the first time to visualize the sliding interface between the two layers of boundary lubricant, allowed the definition and calculation of a dimensionless normalized sliding resistance area, which was then related to the Derjaguin offset. This relationship excellently reflects the molecular surface coverage, which determines the physical condition of the lubricant, and can differentiate between some lubricant-specific frictional properties.

van der Waals (vdW) forces play a fundamental role in the structure and behavior of diverse systems. Because of development of functionals that include nonlocal correlation, it is possible to study the effects of vdW interactions in systems of industrial and tribological interest. Here we simulated within the framework of density functional theory (DFT) the adsorption of isooctane (2,2,4-trimethylpentane) and ethanol on an Fe(100) surface, employing various exchange–correlation functionals to take vdW forces into account. In particular, this paper discusses the effect of vdW forces on the magnitude of adsorption energies, equilibrium geometries, and their role in the binding mechanism. According to our calculations, vdW interactions increase the adsorption energies and reduce the equilibrium distances. Nevertheless, they do not influence the spatial configuration of the adsorbed molecules. Their effect on the electronic density is a nonisotropic, delocalized accumulation of charge between the molecule and the slab. In conclusion, vdW forces are essential for the adsorption of isooctane and ethanol on a bcc Fe(100) surface.