836 research outputs found
Complex scale-free networks with tunable power-law exponent and clustering
This article is made available through the Brunel Open Access Publishing Fund. It is distributed under a Creative Commons License (http://creativecommons.org/licenses/by/3.0/). Copyright @ 2013 Elsevier B.V.We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes mm “ambassador” nodes and ll of each ambassador’s descendants where mm and ll are random variables selected from any choice of distributions plpl and qmqm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant mm and the number of selected descendants from each ambassador is the constant ll, the power-law exponent is (2l+1)/l(2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of ll and mm. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.EPSR
About the maximal rank of 3-tensors over the real and the complex number field
High dimensional array data, tensor data, is becoming important in recent
days. Then maximal rank of tensors is important in theory and applications. In
this paper we consider the maximal rank of 3 tensors. It can be attacked from
various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and
Atkinson-Lloyd(1980). They treated the problem in the complex field, and we
will present various bounds over the real field by proving several lemmas and
propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen
Melting transition of an Ising glass driven by magnetic field
The quantum critical behavior of the Ising glass in a magnetic field is
investigated. We focus on the spin glass to paramagnet transition of the
transverse degrees of freedom in the presence of finite longitudinal field. We
use two complementary techniques, the Landau theory close to the T=0 transition
and the exact diagonalization method for finite systems. This allows us to
estimate the size of the critical region and characterize various crossover
regimes. An unexpectedly small energy scale on the disordered side of the
critical line is found, and its possible relevance to experiments on metallic
glasses is briefly discussed.Comment: 4 pages, 3 figure
Pion double charge exchange on 4He
The doubly differential cross sections for the He
reaction were calculated using both a two-nucleon sequential single charge
exchange model and an intranuclear cascade code. Final state interactions
between the two final protons which were the initial neutrons were included in
both methods. At incident pion energies of 240 and 270 MeV the low-energy peak
observed experimentally in the energy spectrum of the final pions can be
understood only if the contribution of pion production is included. The
calculated cross sections are compared with data.Comment: 25 pages, 9 figure
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit
We study the applicability of composite fermion theory to electrons in
two-dimensional parabolically-confined quantum dots in a strong perpendicular
magnetic field in the limit of low Zeeman energy. The non-interacting composite
fermion spectrum correctly specifies the primary features of this system.
Additional features are relatively small, indicating that the residual
interaction between the composite fermions is weak. \footnote{Published in
Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure
Structural Probe of a Glass Forming Liquid: Generalized Compressibility
We introduce a new quantity to probe the glass transition. This quantity is a
linear generalized compressibility which depends solely on the positions of the
particles. We have performed a molecular dynamics simulation on a glass forming
liquid consisting of a two component mixture of soft spheres in three
dimensions. As the temperature is lowered (or as the density is increased), the
generalized compressibility drops sharply at the glass transition, with the
drop becoming more and more abrupt as the measurement time increases. At our
longest measurement times, the drop occurs approximately at the mode coupling
temperature . The drop in the linear generalized compressibility occurs at
the same temperature as the peak in the specific heat. By examining the
inherent structure energy as a function of temperature, we find that our
results are consistent with the kinetic view of the glass transition in which
the system falls out of equilibrium. We find no size dependence and no evidence
for a second order phase transition though this does not exclude the
possibility of a phase transition below the observed glass transition
temperature. We discuss the relation between the linear generalized
compressibility and the ordinary isothermal compressibility as well as the
static structure factor.Comment: 18 pages, Latex, 26 encapsulated postscript figures, revised paper is
shorter, to appear in Phys. Rev.
Quantum spin pumping with adiabatically modulated magnetic barrier's
A quantum pump device involving magnetic barriers produced by the deposition
of ferro magnetic stripes on hetero-structure's is investigated. The device for
dc- transport does not provide spin-polarized currents, but in the adiabatic
regime, when one modulates two independent parameters of this device, spin-up
and spin-down electrons are driven in opposite directions, with the net result
being that a finite net spin current is transported with negligible charge
current. We also analyze our proposed device for inelastic-scattering and
spin-orbit scattering. Strong spin-orbit scattering and more so inelastic
scattering have a somewhat detrimental effect on spin/charge ratio especially
in the strong pumping regime. Further we show our pump to be almost noiseless,
implying an optimal quantum spin pump.Comment: 14 pages, 9 figures. Manuscript revised with additional new material
on spin-orbit scattering and inelastic scattering. Further new additions on
noiseless pumping and analytical results with distinction between weak and
strong pumping regimes. Accepted for publication in Physical Review
Plankton lattices and the role of chaos in plankton patchiness
Spatiotemporal and interspecies irregularities in planktonic populations have been widely observed. Much research into the drivers of such plankton patches has been initiated over the past few decades but only recently have the dynamics of the interacting patches themselves been considered. We take a coupled lattice approach to model continuous-in-time plankton patch dynamics, as opposed to the more common continuum type reaction-diffusion-advection model, because it potentially offers a broader scope of application and numerical study with relative ease. We show that nonsynchronous plankton patch dynamics (the discrete analog of spatiotemporal irregularity) arise quite naturally for patches whose underlying dynamics are chaotic. However, we also observe that for parameters in a neighborhood of the chaotic regime, smooth generalized synchronization of nonidentical patches is more readily supported which reduces the incidence of distinct patchiness. We demonstrate that simply associating the coupling strength with measurements of (effective) turbulent diffusivity results in a realistic critical length of the order of 100 km, above which one would expect to observe unsynchronized behavior. It is likely that this estimate of critical length may be reduced by a more exact interpretation of coupling in turbulent flows
Modified f(G) gravity models with curvature-matter coupling
A modified f(G) gravity model with coupling between matter and geometry is
proposed, which is described by the product of the Lagrange density of the
matter and an arbitrary function of the Gauss-Bonnet term. The field equations
and the equations of motion corresponding to this model show the
non-conservation of the energy-momentum tensor, the presence of an extra-force
acting on test particles and the non-geodesic motion. Moreover, the energy
conditions and the stability criterion at de Sitter point in the modified f(G)
gravity models with curvature-matter coupling are derived, which can degenerate
to the well-known energy conditions in general relativity. Furthermore, in
order to get some insight on the meaning of these energy conditions, we apply
them to the specific models of f(G) gravity and the corresponding constraints
on the models are given. In addition, the conditions and the candidate for
late-time cosmic accelerated expansion in the modified f(G) gravity are studied
by means of conditions of power-law expansion and the equation of state of
matter less than -1/ 3 .Comment: 13 pages, 4 figure
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