4,353 research outputs found
Nudged-elastic band method with two climbing images: finding transition states in complex energy landscapes
The nudged-elastic band (NEB) method is modified with concomitant two
climbing images (C2-NEB) to find a transition state (TS) in complex energy
landscapes, such as those with serpentine minimal energy path (MEP). If a
single climbing image (C1-NEB) successfully finds the TS, C2-NEB finds it with
higher stability and accuracy. However, C2-NEB is suitable for more complex
cases, where C1-NEB misses the TS because the MEP and NEB directions near the
saddle point are different. Generally, C2-NEB not only finds the TS but
guarantees that the climbing images approach it from the opposite sides along
the MEP, and it estimates accuracy from the three images: the highest-energy
one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the
generalized solid-state NEB (SS-NEB).Comment: 3 pages, 4 figure
Coexistence pressure for a martensitic transformation from theory and experiment: revisiting the bcc-hcp transition of iron under pressure
The coexistence pressure of two phases is a well-defined point at fixed
temperature. In experiment, however, due to non-hydrostatic stresses and a
stress-dependent potential energy barrier, different measurements yield
different ranges of pressure with a hysteresis. Accounting for these effects,
we propose an inequality for comparison of the theoretical value to a plurality
of measured intervals. We revisit decades of pressure experiments on the bcc -
hcp transformations in iron, which are sensitive to non-hydrostatic conditions
and sample size. From electronic-structure calculations, we find a bcc - hcp
coexistence pressure of 8.4 GPa. We construct the equation of state for
competing phases under hydrostatic pressure, compare to experiments and other
calculations, and address the observed pressure hysteresis and range of onset
pressures of the nucleating phase.Comment: 8 pages, 1 figure, 202 citation
OVER-ORDER PREMIUMS AND PRICE WARS IN THE MICHIGAN MILK MARKET
We examine behavior in the Michigan fluid milk market. Over-order premiums exist because fluid milk demands are inelastic. Collusion by cooperatives is required to realize these profits. In absence of collusion, the minimum prices defined by federal milk marketing orders prevails as excess fluid milk is always present. Proprietary firms in Michigan joined the fluid milk cartel because of the threat of a state marketing order. Proprietary firms profits may be increased and information gathered in the short run through price wars that result when behavior deviates from collusion.Demand and Price Analysis,
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