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A theory is developed, based upon a capillary equilibrium argument, that accurately predicts when material transfer from one surface to another will occur.
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The macroscopic stresses are determined from the internal forces using equilibrium arguments.
The subgrid scalar variance, needed to parameterise the scalar pdf, has been modelled according to local equilibrium arguments.
The variations in the distributions of stress and strain can be explained in a general way by reference to compatibility and equilibrium arguments.
In both cases it seems natural to try to justify these equilibrium distributions by means of mixing-type, convergence-to-equilibrium arguments (Bohm 1953, Valentini and Westman 2005).
The main purpose of this paper is to investigate in some more detail the extended reaction probability integral in the equilibrium thermodynamic argument and in the cut-off case.
The result was, however, that Boltzmann rethought the basis of his approach and in 1877b produced a conceptually very different analysis, which might be called the combinatorial argument, of equilibrium and evolutions towards equilibrium, and the role of probability theory.
Physical arguments of equilibrium for each element then produced a set of linear simultaneous equations whose solution could be computed.
But the general equilibrium model embodies two arguments about markets that explain why they can spur economic growth, and these can also be applied to real markets.
For instance, Chadli et al. in [31] obtained conditions for the existence of solutions of a sequential equilibrium problem via a viscosity argument under quite strong conditions.
Everyone, government officials and economists alike, is in accordance that only a growing economy can bring finances back into equilibrium but, unfortunately, this obvious argument remains buried under the weight of austerity.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com