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Using a relation derived from the blob model we obtain an equation giving the Θ temperature of the polymers.
Interfacial adhesion is modeled by nonlinear springs with a force-distance constitutive relation derived from the Lennard Jones potential.
Constitutive contact relations are obtained by integrating the force distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact.
The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators.
Here, ( phi_{text{eff}} ) is the effective volume fraction, which can be found using the following relation derived from the model of Yu and Choi [17]: phi_{text{eff}} = phi left( { 1+ frac{h}{r}} right)^{ 3}, (15 where, h represents liquid thickness.
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The models are based on first order ordinary differential equations together with some constitutive relations derived from models based on ordinary and partial differential equations and other relations based on insight.
Figure 3 shows the dispersion relations derived from the linear Vlasov theory for reference.
The surface excess/chemical potential relations derived from the results of the two methods are almost identical.
The model sums contributions to the rate density from past earthquakes based on predictive scaling relations derived from the precursory scale increase phenomenon.
In [3, 4], certain explicit moment relations derived from the Laplace transform of the first-passage time distribution are applied, but these are only valid under stimulation (supra-threshold regime).
The proximity is a relative measure of pair-wise relations derived from the set of decision trees in the Random Forest method.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com