This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano-and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.

Hierarchical structures are very common in nature, but only recently have they been systematically studied in materials science, in order to understand the specific effects they can have on the mechanical properties of various systems. Structural hierarchy provides a way to tune and optimize macroscopic mechanical properties starting from simple base constituents and new materials are nowadays designed exploiting this possibility. This can be true also in the field of tribology. In this paper we study the effect of hierarchical patterned surfaces on the static and dynamic friction coefficients of an elastic material. Our results are obtained by means of numerical simulations using a one-dimensional spring-block model, which has previously been used to investigate various aspects of friction. Despite the simplicity of the model, we highlight some possible mechanisms that explain how hierarchical structures can significantly modify the friction coefficients of a material, providing a means to achieve tunability.

Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.

The friction force observed at macroscale is the result of interactions at various lower length scales that are difficult to model in a combined manner. For this reason, simplified approaches are required, depending on the specific aspect to be investigated. In particular, the dimensionality of the system is often reduced, especially in models designed to provide a qualitative description of frictional properties of elastic materials, e.g. the spring-block model. In this paper, we implement for the first time a two dimensional extension of the spring-block model, applying it to structured surfaces and investigating by means of numerical simulations the frictional behaviour of a surface in the presence of features like cavities, pillars or complex anisotropic structures. We show how friction can be effectively tuned by appropriate design of such surface features.

In large photosynthetic chromophore-protein complexes not all chromophores are coupled strongly, and thus the situation is well described by formation of delocalized states in certain domains of strongly coupled chromophores. In order to describe excitation energy transfer among different domains without performing extensive numerical calculations, one of the most popular techniques is a generalization of Förster theory to multichromophoric aggregates (generalized Förster theory) proposed by Sumi [J. Phys. Chem. B 103, 252 (1999)] and Scholes and Fleming [J. Phys. Chem. B 104, 1854 (2000)]. The aim of this paper is twofold. In the first place, by means of analytic continuation and a time convolutionless quantum master equation approach, a theory of emission lineshape of multichromophoric systems or molecular aggregates is proposed. In the second place, a comprehensive framework that allows for a clear, compact and effective study of the multichromophoric approach in the full general version proposed by Jang, Newton and Silbey [Phys. Rev. Lett. 92, 218301 (2004)] is developed.We apply the present theory to simple paradigmatic systems and we show on one hand the effectiveness of time-convolutionless techniques in deriving lineshape operators and on the other hand we show how the multichromophoric approach can give significant improvements in the determination of energy transfer rates in particular when the systems under study are not the purely Förster regime. The presented scheme allows for an effective implementation of the multichromophoric Förster approach which may be of use for simulating energy transfer dynamics in large photosynthetic aggregates, for which massive computational resources are usually required. Furthermore, our method allows for a systematic comparison of multichromophoric Föster and generalized Förster theories and for a clear understanding of their respective limits of validity.