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Sato-Crutchfield formulation for some Evolutionary Games
The Sato-Crutchfield equations are studied analytically and numerically. The
Sato-Crutchfield formulation is corresponding to losing memory. Then
Sato-Crutchfield formulation is applied for some different types of games
including hawk-dove, prisoner's dilemma and the battle of the sexes games. The
Sato-Crutchfield formulation is found not to affect the evolutionarily stable
strategy of the ordinary games. But choosing a strategy becomes purely random
independent on the previous experiences, initial conditions, and the rules of
the game itself. Sato-Crutchfield formulation for the prisoner's dilemma game
can be considered as a theoretical explanation for the existence of cooperation
in a population of defectors.Comment: 9 pages, 3 figures, accepted for Int. J. Mod. Phys.
Capillary waves at the liquid-vapor interface and the surface tension of water models
Capillary waves occurring at the liquid-vapor interface of water are studied
using molecular dynamics simulations. In addition, the surface tension,
determined thermodynamically from the difference in the normal and tangential
pressure at the liquid-vapor interface, is compared for a number of standard
three- and four-point water models. We study four three-point models (SPC/E,
TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and
TIP4P-Ew). All of the models examined underestimate the surface tension; the
TIP4P-Ew model comes closest to reproducing the experimental data. The surface
tension can also be determined from the amplitude of capillary waves at the
liquid-vapor interface by varying the surface area of the interface. The
surface tensions determined from the amplitude of the logarithmic divergence of
the capillary interfacial width and from the traditional thermodynamic method
agree only if the density profile is fitted to an error function instead of a
hyperbolic tangent function.Comment: 11 pages, 8 figures, 7 tables. Accepted for publication in J. Chem.
Phys. [v2: Added references, corrected minor errors
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