Time scales friction mechanics

The value of ( used here corresponds to 10 3 of its value in room temperature aqueous solutions. [80] On the one hand, using such weak friction improves the sampling efficiency in the simulations and does not affect equilibrium structural properties. On the other hand, the dynamical properties that we observe may be different from those probed by SM-FRET techniques, which would not be able to resolve conformational dynamics on such fast time scales. Thus, the relevance of the following analysis of dynamical properties relies on the assumption that increasing the friction will not significantly alter our main conclusions. It is interesting to note in this context that the folding mechanism in similar models has been observed to be relatively insensitive to the value of the friction coefficient. [81]... 

Contacts mechanics in the MHz range is much different from its low-frequency counterpart. For instance, static friction coefficients probed with MHz excitation are often much above 1. Contact mechanics at short time scales should be of substantial practical relevance. 

In order to illustrate the use of the iGLE and WiGLE models for polymerization reactions, we have studied several phenomenological forms of the polymer PMF of Fig. 5. In the studies to date, the nonstationary frictions have always included the form of Eq. (28) and as such are apphcable only to dense polymerizations. This class would certainly include solid-state polymerization (SSP) as long as none of the other quenching mechanisms discussed above were also operative, and the assumptions of the separation of time scales in the environmental motion are satisfied. In SSP, the heterogeneity in the environment would further require the use of the WiGLE dynamics with the possible inclusion of a time dependence in the w parameter. 

Velocity / Frequency Relationship. The characteristic temperature-dependent line shapes for each polymer, as determined by bulk dynamic mechanical or dielectric experiments from literature (4), were used as a comparison to our fnctional measurements. For the comparison to be valid the literature data must be adjusted to match the same frequency (time-scale) of the friction experiment. The conversion procedure of scan velocity to frequency has been described in previously (7), whereby a contact diameter was calculated to convert the scan velocity to a frequency by simple division. The contact diameter thus allows a gauge for the time the probe tip affects a point on the polymer surface. For the given radius of curvature of 20 nm, applied load=10 nN, adhesive load=15 nN, and assuming a bulk storage modulus, the contact diameter can be estimated by JKR theory to be 18.7 nm. Thus for a scan velocity of 40 pm/sec the equiv ent frequency of measurement is 2000 Hz and all tabulated tanS data used are scaled accordingly to this frequency for comparison. 

Naturally, the results of dimensional analysis discussed above and their consequences were not known to the ship builders of the 19th century. Since the time of Rankine, the total drag resistance of a ship has been divided into three parts the surface friction, the stern vortex and the bow wave. However, the concept of Newtonian mechanical similarity, known at that time, only stated that for mechanically similar processes the forces vary as F p l2 v2. Scale-up was not considered for assessing the effect of gravity. 

Owing to its properties, nanodiamond like the classical diamond is an attractive material for many applications. For the time being, however, just a limited number of industrial scale processes has really been established due to its inhomogeneity and the variable quality available from different suppHers. Pioneers in this area are the countries of the former Soviet Union where by now access has been made to various fields of applicahon. The examples given herein comprise processes developed to an industrial scale already as weU as such stUl operahve on a laboratory scale. They include the preparation of composites and coatings, mechanical apphcations to reduce friction or to modify surfaces, uses in electro-deposition or biomedical apphcahons. 

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