12,956 research outputs found
Classification of scale-free networks
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
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
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
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
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
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
- …