Search

We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to satisfy a generalized monotonicity condition, which is weaker than the standard monotone assumptions. Under mild conditions on parameters, we establish the fixed-time stability of the proposed dynamical system. In addition, we consider an explicit forward Euler discretization of the dynamical system leading to a new forward backward algorithm for which we present the convergence analysis. Applications to other optimization problems such as Constrained Optimization Problems (COPs), Mixed Variational Inequalities (MVIs), and Variational Inequalities (VIs) are presented and some numerical examples are given to illustrate the theoretical results.

Tribological phenomena such as adhesion, friction, and wear can undermine the functionality of devices and applications based on the diamond-silica interface. Controlling these phenomena is highly desirable, but difficult since extrinsic factors, such as the surface termination by adsorbed species, can deeply affect the reactivity of diamond and its resistance to wear. In this work, we investigate the effects of diamond oxidation by massive ab initio molecular dynamics simulations of silica sliding against diamond surfaces considering different surface orientations, O-coverages, and tribological conditions. Our findings reveal a dual role of oxygen that depends on coverage. At full coverage, the adsorbed oxygen is very effective in friction and wear reduction because the repulsion with the silica counter-surface prevents the formation of chemical bonds across the interface. At reduced coverage and high pressure, Si-O-C bonds are anyway established. In this situation the presence of oxygen results detrimental as it weakens the surface C-C bonds making the surface more vulnerable to wear. Indeed we observed atomic wear on the C(110) surface at 50% O-coverage under harsh tribological conditions. The mechanisms of friction reduction and atomistic wear are explained through the analysis of the electronic properties and surface-surface interactions. Overall, our accurate in silico experiments shed light into the effects of adsorbed oxygen on the tribological behavior of diamond and show how oxidized diamond can be worn by silica.

Despite its unrivaled hardness, diamond can be severely worn during the interaction with others, even softer materials. In this work, we calculate from first-principles the energy and forces necessary to induce the atomistic wear of diamond, and compare them for different surface orientations and passivation by oxygen, hydrogen, and water fragments. The primary mechanism of wear is identified as the detachment of carbon chains. This is particularly true for oxidized diamond and diamond interacting with silica. A very interesting result concerns the role of stress, which reveals that compressive stresses can highly favor wear, making it even energetically favorable., Comment: 5 Figures

Diamond displays outstanding chemical, physical, and tribological properties, making it attractive for numerous applications ranging from biomedicine to tribology. However, the reaction of the materials with molecules present in the air, such as oxygen, hydrogen, and water, could significantly change the electronic and tribological properties of the films. In this study, we performed several density functional theory calculations to construct a database for the adsorption energies and dissociation barriers of these molecules on the most relevant diamond surfaces, including C(111), C(001), and C(110). The adsorption configurations, reaction paths, activation energies, and their influence on the structure of diamond surfaces are discussed. The results indicate that there is a strong correlation between adsorption energy and surface energy. Moreover, we found that the dissociation processes of oxygen molecules on these diamond surfaces can significantly alter the surface morphology and may affect the tribological properties of diamond films. These findings can help to advance the development and optimization of devices and antiwear coatings based on diamond.