9,441 research outputs found
Dequantisation of the Dirac Monopole
Using a sheaf-theoretic extension of conventional principal bundle theory,
the Dirac monopole is formulated as a spherically symmetric model free of
singularities outside the origin such that the charge may assume arbitrary real
values. For integral charges, the construction effectively coincides with the
usual model. Spin structures and Dirac operators are also generalised by the
same technique.Comment: 22 pages. Version to appear in Proc. R. Soc. London
Weakly additive cohomology
In this paper the concept of weakly additive cohomology theory is introduced as a variant of the known concept of additive cohomology theory. It is shown that for a closed A in X the singular homology of the pasi (X, X - A) (with some fixed coefficient gropu) regarded as a furcter of A is a weakly additive cohomology theory on any collectionwise normal space X. Fiirthermore, every compactly supported cohomology theory is weakly additive. The main result is a comparison theorem for two cohomology theories on X both of which are additive or both of which are weakly additive which ercomposses the previously known compauson theorems
Influence of Levantine Artificial Reefs on the fish assemblage of the surrounding seabed
Four Artificial Reef (AR) units were deployed at a 20m depth on a flat hard substrate 3 km west of Haifa, Israel and then surveyed for fish for 12 months. AR units supported 20 times the biomass of control quadrates and their enrichment impact was still significant at a radius of 13m away from units. The 13m values were also significantly higher than those of quadrates adjacent to units, suggesting the existence of a halo of relative depletion within the outer enrichment halo. The main species contributing to this pattern was the migrant herbivore Siganus rivulatus. A decrease in grazing resources is thus suggested as an explanation for creation of this halo. The most consistent AR residents were also Lessepsian migrants - Sargocentron rubrum, nocturnal predators which displayed high microhabitat fidelity and a steady increase in density. The 6 species of migrants recorded accounted for 65.3% of the commercially exploitable biomass and 25.2% of the specimens in the AR site. Other constant AR residents were the groupers Epinephelus costae and Epinephelus marginatus, which are rare and commercially important species. Site protection from fishing and storms were found to be of utmost importance, and design and deployment considerations are discussed
Negative forms and path space forms
We present an account of negative differential forms within a natural
algebraic framework of differential graded algebras, and explain their
relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology
dropped in Proposition 3.2; material slightly reorganize
Gauge Group and Topology Change
The purpose of this study is to examine the effect of topology change in the
initial universe. In this study, the concept of -cobordism is introduced to
argue about the topology change of the manifold on which a transformation group
acts. This -manifold has a fiber bundle structure if the group action is
free and is related to the spacetime in Kaluza-Klein theory or
Einstein-Yang-Mills system. Our results revealed that fundamental processes of
compactification in -manifolds. In these processes, the initial high
symmetry and multidimensional universe changes to present universe by the
mechanism which lowers the dimensions and symmetries.Comment: 8 page
Normal Mode Determination of Perovskite Crystal Structures with Octahedral Rotations: Theory and Applications
Nuclear site analysis methods are used to enumerate the normal modes of
perovskite polymorphs with octahedral rotations. We provide the modes
of the fourteen subgroups of the cubic aristotype describing the Glazer
octahedral tilt patterns, which are obtained from rotations of the
octahedra with different sense and amplitude about high symmetry axes. We
tabulate all normal modes of each tilt system and specify the contribution of
each atomic species to the mode displacement pattern, elucidating the physical
meaning of the symmetry unique modes. We have systematically generated 705
schematic atomic displacement patterns for the normal modes of all 15 (14
rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative
examples how to use these tables to identify the octahedral rotations,
symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing
distortions of the octahedra, and the associated Raman selection
rules. We anticipate that these tables and schematics will be useful in
understanding the lattice dynamics of bulk perovskites and would serve as
reference point in elucidating the atomic origin of a wide range of physical
properties in synthetic perovskite thin films and superlattices.Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed
through link specified within manuscrip
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