Some conceptual thoughts toward nanoscale oriented friction in a model of articular cartilage

Toward a Governing Mechanism of Nanoscale Articular Cartilage (Physiologic) Lubrication: Smoluchowski-type Dynamics in Amphiphile Proton Channels

“…It may cause a certain deterioration of the first lamella, requiring adjustment to the new situation. If the system is equipped with additional amphiphile molecules [31], such a load may cause their translocation, and at the same time, emergence of a new micellar structure prone to facilitate lubrication [1]. If the magnitude of the applied load is increased, then more lamellae are prone to their structural rearrangement.…”

“…still applies, if one assumed that the protons under confinement would walk subdiffusively, their root mean-squared displacement, denoted by l rmsq had to cease upon increasing time t, such as l rmsq ≡ l rmsq (t) ∼ t µ with 0 < µ < 1/2. In other words, the value of D H + should be assumed t-dependent, causing D H + (t) ∼ t 2µ−1 to decrease in an algebraic way [31]. Another option that one would not discard is the logarithmic (even Sinai-type or billiard-involving) diffusion which also decelerates in its tempo when compared with its standard counterpart [32].…”

“…Another option that one would not discard is the logarithmic (even Sinai-type or billiard-involving) diffusion which also decelerates in its tempo when compared with its standard counterpart [32]. In the present study, following others [11,28,31], we wish however to focus on the power-law behavior of the diffusion function.…”

“…Thus, for comparison, let us consider three cases of the prototype H + -channel studied in [31] (Fig. 5), and being of relevance to the overall nano-tribological depiction we are addressing.…”

“…5), and being of relevance to the overall nano-tribological depiction we are addressing. When transforming previous studies [11,31] into our present scheme with close analogy to [33], one would list them as follows. If at the first instance x 0,…”