Generalised Longitudinal Susceptibility for Magnetic Monopoles in Spin Ice

The generalised longitudinal susceptibility $\chi({\bf q}, \omega)$ affords a sensitive measure of the spatial and temporal correlations of magnetic monopoles in spin ice. Starting with the monopole model, a mean field expression for $\chi({\bf q}, \omega)$ is derived as well as expressions for the mean square longitudinal field and induction at a point. Monopole motion is shown to be strongly correlated, and both spatial and temporal correlations are controlled by the dimensionless monopole density $x$ which defines the ratio of the magnetization relaxation rate and the monopole hop rate. Thermal effects and spin lattice relaxation are also considered. The derived equations are applicable in the temperature range where the Wien effect for magnetic monopoles is negligible. They are discussed in the context of existing theories of spin ice and the following experimental techniques: dc and ac-magnetization, neutron scattering, neutron spin echo, and longitudinal and transverse field $\mu$SR. The monopole theory is found to unify diverse experimental results, but several discrepancies between theory and experiment are identified. One of these, concerning the neutron scattering line shape, is explained by means of a phenomenological modification to the theory.Comment: 29 pages, 4 figures; to be published in Phil. Trans A, special issue for Royal Society Theo Murphy Meeting on Magnetic Monopoles in Spin Ice (Nov. 2011, UK). Second version, significantly revised after helpful referee comments. Many typos correcte

The Divergence of Modern Jurisprudence from the Original Intent for Federalist and Tenth Amendment Limitations on the Treaty Power

[Excerpt] “That the federal treaty-making authority is constrained by the other parts of the Constitution does not sound like the stuff of law journals. It seems like common sense. After all, we would not expect someone to argue that the ability to “regulate Commerce” entitles Congress to disregard the Third Amendment and quarter soldiers in our houses. We would not expect to see an argument that the power to “establish Post Offices” enables Congress to disregard the freedom of the press in the First Amendment. So, why is the Tenth Amendment so fully disregarded with respect to treaties?

PORTFOLIO SELECTION UNDER EXPONENTIAL AND QUADRATIC UTILITY

The production or marketing portfolio that is optimal under the assumption of quadratic utility may or may not be optimal under the assumption of exponential utility. In certain cases, the necessary and sufficient condition for an identical solution is that absolute risk aversion coefficients associated with the two utility functions be the same. In other cases, equality of risk aversion coefficients is a sufficient condition only. A comparison is made between use of exponential and quadratic utility in the analysis of a California farmerÂ’s marketing problem.Marketing,

Cigarette Consumption by U.S. Men

Health Economics and Policy,

Fiber optic data transmission

The Ohio University Avionics Engineering Center is currently developing a fiber optic data bus transmission and reception system that could eventually replace copper cable connections in airplanes. The original form of the system will transmit information from an encoder to a transponder via a fiber optic cable. An altimeter and an altitude display are connected to a fiber optic transmitter by copper cable. The transmitter converts the altimetry data from nine bit parallel to serial form and send these data through a fiber optic cable to a receiver. The receiver converts the data using a cable similar to that used between the altimeter and display. The transmitting and receiving ends also include a display readout. After completion and ground testing of the data bus, the system will be tested in an airborne environment