Effect of Loading on the Adhesion and Frictional Characteristics of Top Layer Articular Cartilage Nanoscale Contact: A Molecular Dynamics Study.

Articular cartilage is a water-lubricated naturally occurring biological interface imparting unique mechanical and ultralow frictional properties in bone joints. Although the material of cartilage, synovial fluid composition, and their lubricating modes and properties have been extensively investigated at various scales experimentally, there is still a lack of understanding of load bearing, adhesion, and friction mechanisms of the cartilage-cartilage interface from an atomistic perspective under heavy loads. In this study, the effect of loading on adhesion and frictional behavior in articular cartilage is investigated with a proposed atomistic model for top layer cartilage-cartilage contact in unhydrated conditions using molecular dynamics (MD) simulations. Pull-off tests reveal that cohesive interactions occur at the interface due to formation of heavily interpenetrated atomistic sites leading to stretching and localized pulling of fragments during sliding. Sliding tests show that friction is load- and direction-dependent with the coefficient of friction (COF) obtained in the range of 0.20-0.75 at the interface for sliding in parallel and perpendicular directions to the collagen axis. These values are in good agreement with earlier nanoscale experimental results reported for the top layer cartilage-cartilage interface. The COF reduces with an increase in load and tends to be higher for the parallel sliding case than for the perpendicular case owing to the presence of the constant number of H-bonds. Overall, this work contributes toward understanding sliding in unhydrated biointerfaces, which is the precursor of wear, and provides insights into implant research.

Diffusion with resetting inside a circle.

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.