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,