Spin-Motive Forces and Current-Induced Torques in Ferromagnets

In metallic ferromagnets, the spin-transfer torque and spin-motive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spin-orbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spin-motive forces and current-driven magnetization dynamics. The formalism is valid for spin-orbit coupling of any strength and presents a systematic scheme for deriving all possible torque and charge-pumping terms that obey the symmetry requirements imposed by the point group of the system. We demonstrate how the different charge pumping and torque contributions are connected via the Onsager reciprocal relations. The formalism is applied to two important classes of systems: isotropic ferromagnets with non-uniform magnetization and homogeneous ferromagnets described by the point group $C_{2v}$.Comment: Final version accepted by Physical Review

The mechanics of stochastic slowdown in evolutionary games

We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a beneficial mutation may take longer to fixate than a neutral one. More precisely, the fixation time conditioned on the mutant taking over can show a maximum at intermediate selection strength. We show that this phenomenon is present in the prisoner's dilemma, and also discuss counterintuitive slowdown and speedup in coexistence games. In order to establish the microscopic origins of these phenomena, we calculate the average sojourn times. This allows us to identify the transient states which contribute most to the slowdown effect, and enables us to provide an understanding of slowdown in the takeover of a small group of cooperators by defectors: Defection spreads quickly initially, but the final steps to takeover can be delayed substantially. The analysis of coexistence games reveals even more intricate behavior. In small populations, the conditional average fixation time can show multiple extrema as a function of the selection strength, e.g., slowdown, speedup, and slowdown again. We classify two-player games with respect to the possibility to observe non-monotonic behavior of the conditional average fixation time as a function of selection strength.Comment: Accepted for publication in the Journal of Theoretical Biology. Includes changes after peer revie

An empirical investigation of the demand for bananas in Germany

We use econometric methods to investigate consumer demand for bananas and for other fruit in Germany. Monthly household survey data for the period 1986-1998 are analysed. Demand for bananas is significantly responsive to own price, suggesting that policy-induced price increases generate the usual dead-weight losses. Demand is also responsive to income changes, indicating that there is scope for further market expansion as incomes grow. There is evidence that other categories of fruit are both gross and net substitutes for bananas.bananas, fruit, dynamic demand system, Germany, Demand and Price Analysis,