Non-equilibrium steady states for chains of four rotors

We study a chain of four interacting rotors (rotators) connected at both ends to stochastic heat baths at different temperatures. We show that for non-degenerate interaction potentials the system relaxes, at a stretched exponential rate, to a non-equilibrium steady state (NESS). Rotors with high energy tend to decouple from their neighbors due to fast oscillation of the forces. Because of this, the energy of the central two rotors, which interact with the heat baths only through the external rotors, can take a very long time to dissipate. By appropriately averaging the oscillatory forces, we estimate the dissipation rate and construct a Lyapunov function. Compared to the chain of length three (considered previously by C. Poquet and the current authors), the new difficulty with four rotors is the appearance of resonances when both central rotors are fast. We deal with these resonances using the rapid thermalization of the two external rotors.Comment: Minor changes to reflect the published versio

African Olive (Olea europaea subsp. cuspidata) as an environmental weed in eastern Australia: a review

African Olive, Olea europaea subsp. cuspidata (Wall. ex G.Don) Cif. (family Oleaceae) is a dense-crowned tree introduced into Australia for horticulture in the mid 19th century. In recent decades, African Olive has become an aggressive woody weed, capable of forming a dense and permanent canopy in a wide range of vegetation types in south-west Sydney and beyond. Characteristics of African Olive invasion in south-west Sydney, and its seed dispersal by frugivorous birds are consistent with experience from Norfolk Island and Hawaii. We use records and aerial photographs from Mount Annan Botanic Garden and other bushland areas in south-west Sydney to describe the invasion stages and impacts of African Olive. The capacity for African Olive to establish in both temperate and subtropical zones, underlie the potential for spread well beyond current distribution in New South Wales. Research is now required to further develop control techniques and ecological restoration strategies for areas of heavy African Olive infestation. Mapping of current locations and a coordinated control strategy for African Olive is required to prevent future permanent loss of native plant diversity

Productivity and R&D at the Firm Level in French Manufacturing

In a companion study to that of Griliches and Mairesse for the United States, we have investigated the relationship between output, labor, and physical and R&D capital during the 1972-1977 period for a sample of 182 R&D performing firms in the French nnufacturing industries. Our results are quite comparable to those obtained for the U.S. The relationship between firm productivity and R&D appears both strong and robust in the cross-sectional dimension of the data; it is less so in the time dimension. However, the within-firm estimates are still significant and of a likely order of magnitude.In this respect, they are more satisfactory than the U.S. ones. We show that this is largely due to a better measurement of the variables: (1) the fact that we can use a value-added measure of output instead of sales (or equivalently that we include materials among the factors of the production function); (2) the fact that we can correct the measures of labor, physical capital and output for the double counting or expensing out of the labor, capital and materials components of R&D expenditures.

Roadblock to Trade: The State-Controlled Economy Issue in Antidumping Law Administration

This article will review and analyze the background of the SCE provisions, the operation and limitations of the current law as evidenced by recent cases, and the proposed legislation currently before Congress

Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle-Lanford functions, and the exposition is essentially self-contained