Slip and stress from low shear rate nonequilibrium molecular dynamics: The transient-time correlation function technique

Exact Response Theory for Time-Dependent and Stochastic Perturbations

The exact, non perturbative, response theory developed within the field of non-equilibrium molecular dynamics, also known as TTCF (transient time correlation function), applies to quite general dynamical systems. Its key element is called the dissipation function because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time-independent external perturbations, and then it has been extended to time-dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated with, e.g., linear response theory. The present work includes time-dependent stochastic perturbations in the theory using the Karhunen-Loève theorem. This leads to three different investigations of a given process. In the first, a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigation, one averages over both initial conditions and stochastic coefficients. We conclude by illustrating the applicability of the resulting exact response theory with simple examples.

A review of recent advances and applications of machine learning in tribology

In tribology, a considerable number of computational and experimental approaches to understand the interfacial characteristics of material surfaces in motion and tribological behaviors of materials have been considered to date. Despite being useful in providing important insights on the tribological properties of a system, at different length scales, a vast amount of data generated from these state-of-the-art techniques remains underutilized due to lack of analysis methods or limitations of existing analysis techniques. In principle, this data can be used to address intractable tribological problems including structure-property relationships in tribological systems and efficient lubricant design in a cost and time effective manner with the aid of machine learning. Specifically, data-driven machine learning methods have shown potential in unraveling complicated processes through the development of structure-property/functionality relationships based on the collected data. For example, neural networks are incredibly effective in modeling non-linear correlations and identifying primary hidden patterns associated with these phenomena. Here we present several exemplary studies that have demonstrated the proficiency of machine learning in understanding these critical factors. A successful implementation of neural networks, supervised, and stochastic learning approaches in identifying structure-property relationships have shed light on how machine learning may be used in certain tribological applications. Moreover, ranging from the design of lubricants, composites, and experimental processes to studying fretting wear and frictional mechanism, machine learning has been embraced either independently or integrated with optimization algorithms by scientists to study tribology. Accordingly, this review aims at providing a perspective on the recent advances in the applications of machine learning in tribology. The review on referenced simulation approaches and subsequent applications of machine learning in experimental and computational tribology shall motivate researchers to introduce the revolutionary approach of machine learning in efficiently studying tribology.