Three types of computational soft-matter problems revisited, an own-selection-based opinion

A quest to extend friction law into multiscale soft matter: experiment confronted with theory—a review

“…In the former case, one gets in practice χ = 5/12 ≃ 0.41. The last value lies just in-between two characteristic values as represented [36,77] by partly open (middle) proton/hydrogen-ion channels (figure 6) made up of PL (or amphiphilic) matter, respectively. The scenario with χ = 5/12 yields the most effective transport scenario along an equally effective narrow PL-nanotube with the fractal dimension approaching one (figure 6, lefthand side (l.h.s.)…”

“…To go on, and commencing with the micelles' formation at a mesoscopic level, the Avrami-Kolmogorov [29], albeit dispersive, phase-change kinetic scenario can first be drawn [77]. The near-surface amphiphiles, assembled there as multilayer phases [92], are to be converted to reversed micelles.…”

“…Obtaining a friction-lubrication system in a closed autonomous dynamical ODE (i.e. ordinary differential equation) form, reminiscent qualitatively [36] of a temporal change of Φ from equation (5), and by anticipating a weak coupling among the decisively dependent dynamical variables/fields [29,77,78], one can introduce three distinct mechanical states of PLs by means of an exponent h ranging between [1/3; 4/5]. The lowest value of this interval at 1/3, corresponding to a minimal random-walk exponent close to zero, is exclusively valid upon complete mechanical squeezing of the PL molecule, which is formally unattainable because, on average, even after severe loading conditions, or drastic shear actions, the PL involving matter remains at least slightly hydrated (i.e.…”

“…not completely devoid of water); therefore, the approximation of h > 0 applies. Thus, note formally, that: (a) the exponent, h, obeys h = 1 − (d s /2); another random-walk (d s ) exponent arises; (b) by careful analytic inspection, it is easy to show that the ODE dissipative Φ-type system [77] may take on such a least-dissipation autonomous (closed) form. Especially, upon a restriction that it is maximally unidirectional, thus the passage through a (phospholipidic) nanopore temporarily created within the micellar or vesicular matter after load, would resemble a (random) walk along a tube.…”

All Pairs of Pentagons in Leapfrog Fullerenes Are Nice

“…Among the other interesting issues, we mention the transformations that do not increase the number of vertices but result in isomeric fullerene structures [30,31], migrations of pentagons on nanocones and other portions of the honeycomb lattice [32], fullerene dimer formation [33], and crystal formation involving fullerenes [34].…”