As an example we choose the energy of grain boundaries as a function of their geometric degrees of freedom.
Similarly, it was possible to investigate the existence of optima with respect to two other geometric degrees of freedom, such as tube eccentricity and fin-to-fin spacing.
Similarly, it was possible to investigate the existence of optima with respect to other two geometric degrees of freedom, i.e., tube eccentricity and fin-to-fin spacing.
TEM was first employed to determine the five geometric degrees of freedom (DOFs) of each GB: unit rotation axis, c, rotation angle, θ, and unit GB plane normal, n.
Addressing optically induced interactions between nanoparticles, new results from quantum electrodynamical studies are employed to produce surfaces representing the variation of potential energy with the various geometric degrees of freedom – the positions and orientations of each particle relative to each other, and to the throughput radiation.
A notable finding is that connectomes have high "smallworldness" beyond that arising from geometric and degree considerations alone.
The geometric mean degree of activation for TT is about 50 hydrazide groups per TT molecule, whereas that of the activated group A PS is about 100 saccharide repeats per aldehyde group [ 26].
The advantage of the proposed method lies in the method of solution, i.e., geometric programming where degree of difficulty is less than the degree of difficulty of the previous process (goal geometric programming with weighted sum method).
It worth noting that the proposed methods in this paper are the first to consider geometric continuity with degree reductions.
Examples 1-4 show that the proposed WB-, (G^{0} -, (G^{1} -degree reduction methods in this paper give errors that are less than existing methods with and without continuity conditions; moreover, our methods are the first methods of this kind that consider geometric continuity with degree reductions.
Association of regional and average LV myocardial strain and displacement with LV geometric pattern and degree of AS.
