12,956 research outputs found

    Classification of scale-free networks

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    While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.Comment: 6 Pages, 6 Figures, 1 tabl

    Lattice dynamics and correlated atomic motion from the atomic pair distribution function

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    The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born von-Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRD of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.Comment: 9 pages, 11 figure

    Improved Photocatalytic Performance via Air-Plasma Modification of Titanium Dioxide: Insights from Experimental and Simulation Investigation

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    Commercial titanium dioxide is successfully plasma-treated under ambient conditions for different time periods, leading to reduced crystallite size and the creation of oxygen vacancies. Density functional theory-based calculations reveal the emergence of additional localized states close to the conduction band, primarily associated with under-coordinated titanium atoms in non-stoichiometric titanium-oxide systems. The plasma-treated samples exhibit improved photocatalytic performance in the degradation of methylene blue compared to untreated samples. Moreover, the 4-hour plasma-treated photocatalyst demonstrates commendable stability and reusability. This work highlights the potential of cost-effective plasma treatment as a simple modification technique to significantly enhance the photocatalytic capabilities of titanium dioxide.Comment: Manuscript and Supplementary material include

    The AF structure of non commutative toroidal Z/4Z orbifolds

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    For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

    Orbital ordering and enhanced magnetic frustration of strained BiMnO3 thin films

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    Epitaxial thin films of multiferroic perovskite BiMnO3 were synthesized on SrTiO3 substrates, and orbital ordering and magnetic properties of the thin films were investigated. The ordering of the Mn^{3+} e_g orbitals at a wave vector (1/4 1/4 1/4) was detected by Mn K-edge resonant x-ray scattering. This peculiar orbital order inherently contains magnetic frustration. While bulk BiMnO3 is known to exhibit simple ferromagnetism, the frustration enhanced by in-plane compressive strains in the films brings about cluster-glass-like properties.Comment: 8 pages, 4 figures, accepted to Europhysics Letter

    Implications of the B20 Crystal Structure for the Magneto-electronic Structure of MnSi

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    Due to increased interest in the unusual magnetic and transport behavior of MnSi and its possible relation to its crystal structure (B20) which has unusual coordination and lacks inversion symmetry, we provide a detailed analysis of the electronic and magnetic structure of MnSi. The non-symmorphic P2_13 spacegroup leads to unusual fourfold degenerate states at the zone corner R point, as well as ``sticking'' of pairs of bands throughout the entire Brillouin zone surface. The resulting Fermi surface acquires unusual features as a result of the band sticking. For the ferromagnetic system (neglecting the long wavelength spin spiral) with the observed moment of 0.4 \mu_B/Mn, one of the fourfold levels at R in the minority bands falls at the Fermi energy (E_F), and a threefold majority level at k=0 also falls at E_F. The band sticking and presence of bands with vanishing velocity at E_F imply an unusually large phase space for long wavelength, low energy interband transitions that will be important for understanding the unusual resistivity and far infrared optical behavior.Comment: Nine two-column pages with eight figures include
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