Ghosts of order on the frontier of chaos

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderly, completely integrable systems are characterized by phase trajectories confined to low-dimensional, invariant tori. The KAM theory examines what happens to the tori when an integrable system is subjected to a small perturbation and finds that, for small enough perturbations, most of them survive.

The KAM theory is mute about the disrupted tori, but, for two-dimensional systems, Aubry and Mather discovered an astonishing picture: the broken tori are replaced by "cantori," tattered, Cantor-set remnants of the original invariant curves. We seek to extend Aubry and Mather's picture to higher dimensional systems and report two kinds of studies; both concern perturbations of a completely integrable, four-dimensional symplectic map. In the first study we compute some numerical approximations to Birkhoff periodic orbits; sequences of such orbits should approximate any higher dimensional analogs of the cantori. In the second study we prove converse KAM theorems; that is, we use a combination of analytic arguments and rigorous, machine-assisted computations to find perturbations so large that no KAM tori survive. We are able to show that the last few of our Birkhoff orbits exist in a regime where there are no tori.

Frontier experiences from industry-academia consortia

Technology roadmapping has been applied successfully in many industrial organizations. Designed to facilitate and communicate technology strategy and planning, roadmaps (or, as in Europe, route maps) can take a variety of specific forms, depending on the type (opportunities, capabilities, products, technologies, etc.) and particular company context. While roadmaps are generally manifest in a number of "program elements or levels" superimposed upon a timeline, experienced mappers often claim that it is "roadmapping" rather than "the roadmap" that generates the value. This special report focuses primarily on product and technology roadmaps. Following an introduction to the evolution, purpose and applications of corporate/industry roadmapping, four industry-developed articles examine roadmapping in Lucent Technologies, Rockwell Automation, the pharmaceutical/biotechnology industry, and UK-based Domino Printing Sciences.

The local and global dimensions of metalliferous pollution derived from a reconstruction of an eight thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan

Grattan, J.P., Gilbertson, D.D., Hunt, C.O. (2007). The local and global dimensions of metaliferrous air pollution derived from a reconstruction of an 8 thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan. Journal of Archaeological Science 34, 83-110

The mission as a frontier institution in the Spanish american colonies, by Herbert E. Bolton.

http://www.archive.org/details/missionasfrontie00boltrich

In the Ojibway country : a story of early missions on the Minnesota frontier

http://www.archive.org/details/inojibwaycountry00scheiala

The call of the waters; a study of the frontier, by Katharine R. Crowell ...

http://www.archive.org/details/callofwatersstud01crowrich

People and place in the new frontier: an examination of Han and Uyghur ethnic identities

This thesis demonstrates how Han and Uyghur ethnic identities are constructed in urban Xinjiang, how they have evolved over time and how both identities gain their meaning largely from a process of interaction with the ‘other’. It shows that the boundaries that exist between Uyghur and Han hugely influence the identity content of both. Based on over 120 interviews carried out over 3 years, it brings a clear analytical framework and conceptual clarity to the questions of how ethnic identities are constructed and maintained in Xinjiang

Ecology of frontier populations of the invasive grey squirrel (Sciurus carolinensis) in Ireland

The rise in invasive species, together with habitat destruction, is associated with worldwide declines in biodiversity and ecosystem functioning. Management of invasive species, as well as amelioration of invasion impacts, provide challenges to species and ecosystem ecologists and conservation managers. Although any species can become invasive if it is transported to, establishes in and spreads in a new environment outside of its native range, rodents are a particularly frequent invader. Rodent introductions are often inadvertent but are also commonly intentional as these animals are traded and transported as pets and may escape from captivity. Tree squirrel species are attractive to humans and are able to establish populations with only a few founding individuals, making them a group well suited to performing the role of biological invaders. The eastern grey squirrel (Sciurus carolinensis) is the most commonly introduced squirrel species worldwide. This research addressed the grey squirrel invasion and frontier population biology. Novel results were generated through diverse research techniques. Public sighting surveys and hairtube surveys were used to locate the southern frontier of grey squirrel range expansion in Ireland. A 22-month intensive live trapping study of two frontier populations facilitated the collection of personality and demographic data from squirrels in increasing populations. A systematic literature search on grey squirrel demography provided context for the studied populations, among frontier and established introduced populations, as well as those in the native range. Advanced spatially explicit population modeling techniques predicted future range expansion and objectively compared the outcomes of 12 grey squirrel management strategies. The methods and results are discussed in both a basic scientific and applied invasion management context. An improved understanding of the behaviour, population dynamics, and future scenarios at the frontier of species invasions is crucial for managers worldwide and this is provided here for the grey squirrel in Ireland.