Scaling property of ideal granitic sequences

Quantification of granite textures and structures using a mathematical model for characterization of granites has been a long-term attempt of mathematical geologists over the past four decades. It is usually difficult to determine the influence of magma properties on mineral crystallization forming fined-grained granites due to its irregular and fine-grained textures. The ideal granite model was originally developed for modeling mineral sequences from first and second-order Markov properties. This paper proposes a new model for quantifying scale invariance properties of mineral clusters and voids observed within mineral sequences. Sequences of the minerals plagioclase, quartz and orthoclase observed under the microscope for 104 aplite samples collected from the Meech Lake area, Gatineau Park, Québec were used for validation of the model. The results show that the multi-scale approaches proposed in this paper may enable quantification of the nature of the randomness of mineral grain distributions. This, in turn, may be related to original properties of the magma

Bridgeness: A Local Index on Edge Significance in Maintaining Global Connectivity

Edges in a network can be divided into two kinds according to their different roles: some enhance the locality like the ones inside a cluster while others contribute to the global connectivity like the ones connecting two clusters. A recent study by Onnela et al uncovered the weak ties effects in mobile communication. In this article, we provide complementary results on document networks, that is, the edges connecting less similar nodes in content are more significant in maintaining the global connectivity. We propose an index named bridgeness to quantify the edge significance in maintaining connectivity, which only depends on local information of network topology. We compare the bridgeness with content similarity and some other structural indices according to an edge percolation process. Experimental results on document networks show that the bridgeness outperforms content similarity in characterizing the edge significance. Furthermore, extensive numerical results on disparate networks indicate that the bridgeness is also better than some well-known indices on edge significance, including the Jaccard coefficient, degree product and betweenness centrality.Comment: 10 pages, 4 figures, 1 tabl

Large normally hyperbolic cylinders in a priori stable Hamiltonian systems

We prove the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems

Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands

Recent proposals of topological flat band (TFB) models have provided a new route to realize the fractional quantum Hall effect (FQHE) without Landau levels. We study hard-core bosons with short-range interactions in two representative TFB models, one of which is the well known Haldane model (but with different parameters). We demonstrate that FQHE states emerge with signatures of even number of quasi-degenerate ground states on a torus and a robust spectrum gap separating these states from higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.Comment: 4 pages, 6 figure