Dynamical Inequality in Growth Models

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.Comment: 6 pages, 4 figure

Is There a Role for Producer and Consumer Subsidy Equivalents in Trade Negotiations

International Relations/Trade,

A characterization of quasi-rational polygons

The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.Comment: 15 pages, 9 figure

Exobiology and the search for biological signatures on Mars

In preparation for a Mars Rover/Sample return mission, the mission goals and objectives must be identified. One of the most important objectives must address exobiology and the question of the possibility of the origin and evolution of life on Mars. In particular, key signatures or bio-markers of a possible extinct Martian biota must be defined. To that end geographic locations (sites) that are likely to contain traces of past life must also be identified. Sites and experiments are being defined in support of a Mars rover sample return mission. In addition, analyses based on computer models of abiotic processes of CO2 loss from Mars suggest that the CO2 from the atmosphere may have precipitated as carbonates and be buried within the Martian regolith. The carbon cycle of perennially frozen lakes in the dry valley of Antarctica are currently being investigated. These lakes were purported to be a model system for the ancient Martian lakes. By understanding the dynamic balance between the abiotic vs. biotic cycling of carbon within this system, information is gathered which will enable the interpretation of data obtained by a Mars rover with respect to possible carbonate deposits and the processing of carbon by biological systems. These ancient carbonate deposits, and other sedimentary units would contain traces of biological signatures that would hold the key to understanding the origin and evolution of life on Mars, as well as Earth