Boundaries Merge Research Articles

Plant Communities of the Shetland Islands

(1) The Shetland Islands lie between Scotland and Norway and this study describes the vegetation types found there with reference to both British/Continental and Scandinavian communities. (2) A conspectus of the main plant communities was obtained by recording vegetation plots from fifteen of the islands, from shingle beaches, sand-dunes, salt-marshes, wet meadows, grasslands, blanket peat and heaths. (3) Sixty-five noda were identified and their general characteristics described. These noda were assigned to both recognized and new taxa within seventeen phytosociological classes. (4) A new association of grazed low altitude blanket bogs, the EmpetrumRhytidiadelphus loreus Association is outlined. (5) The factors influencing plant and vegetation distribution in Shetland are discussed; geographical position and physical isolation from seed sources provide the historical basis. (6) While climatic and topographic interaction on the flora have determined the natural vegetation communities, the impact of land-use, particularly grazing, has been to confine these communities to areas inaccessible to sheep. The majority of Shetland's vegetation composition has been determined by grazing. (7) The absence of comparative taxonomic studies, the Islands' geographical position and climate, the influence of salt-spray and intensive land-use produce a merging of community boundaries and difficulties in delimiting discrete associations.

Boolean operations in solid modeling: Boundary evaluation and merging algorithms

Solid modeling plays a key role in electromechanical CAD/CAM, three-dimensional computer graphics, computer vision, robotics, and other disciplines and activities that deal with spatial phenomena. Almost all contemporary solid modeling systems support Boolean operations akin to set intersection, union, and difference on solids. Boundary representations (face/edge/vertex structures) for solids defined through Boolean operations are generated in these modelers by using so-called boundary evaluation and boundary merging procedures. These are the most complex and delicate software modules in a solid modeler. This paper describes boundary evaluation algorithms used by the PADL solid modeling systems developed at the University of Rochester, and discusses other known approaches in terms of concepts that emerged from the PADL work, notably set membership classification and neighborhood manipulation.

Antiferromagnetic classicalXYmodel: A mean-field analysis

The antiferromagnetic classical $\mathrm{XY}$ (planar-rotator) model is analyzed under the mean-field approximation. Phase diagrams are obtained and found to be strongly dependent on the underlying lattice geometry. For bipartite lattices, there exists a second-order transition across a unique phase boundary. For tripartite lattices, there exist two phase boundaries, separating an intermediate "nonhelical" phase from a low-temperature "helical" phase and the high-temperature paramagnetic phase. The two phase boundaries merge into a single critical point at finite temperature and zero magnetic field.

An indication for an intrinsically different coronal temperature

As is well known, the interplanetary magnetic field is the extension of the solar magnetic field, and the solar wind is the extension of the solar corona (Biermann, 1951; Parker, 1958). Consequently, knowledge of these two interplanetary structures reflects a knowledge of the solar corona itself. Calculations of radial proton temperature gradients within magnetic sector boundaries, observed by Helios-1 and Helios-2 heliocentric satellites between 0.3 and 1.0 AU, revealed lower temperatures in the solar corona in the region where these boundaries merge.