42,060 research outputs found
Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
An algebraic structure related to discrete zero curvature equations is
established. It is used to give an approach for generating master symmetries of
first degree for systems of discrete evolution equations and an answer to why
there exist such master symmetries. The key of the theory is to generate
nonisospectral flows from the discrete spectral
problem associated with a given system of discrete evolution equations. Three
examples are given.Comment: 24 pages, LaTex, revise
The Luminosity - E_p Relation within Gamma--Ray Bursts and Implications for Fireball Models
Using a sample of 2408 time-resolved spectra for 91 BATSE gamma-ray bursts
(GRBs) presented by Preece et al., we show that the relation between the
isotropic-equivalent luminosity (L_iso) and the spectral peak energy (E_p) in
the cosmological rest frame, L_iso \propto E_p^2, not only holds within these
bursts, but also holds among these GRBs, assuming that the burst rate as a
function of redshift is proportional to the star formation rate. The possible
implications of this relation for the emission models of GRBs are discussed. We
suggest that both the kinetic-energy-dominated internal shock model and the
magnetic-dissipation-dominated external shock model can well interpret this
relation. We constrain the parameters for these two models, and find that they
are in a good agreement with the parameters from the fittings to the afterglow
data (abridged).Comment: 3 pages plus 5 figures, emulateapj style, accepted for publication in
ApJ Letter
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
Correlation between the cohesive energy and the onset of radiation-enhanced diffusion in ion mixing
A correlation between the cohesive energy of elemental solids and the characteristic temperature Tc for the onset of radiation-enhanced diffusion during ion mixing is established. This correlation enables one to predict the onset of radiation-enhanced diffusion for systems which have not yet been investigated. A theoretical argument based on the current models of cascade mixing and radiation-enhanced diffusion is provided as a basis for understanding this observation
Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model
We present an analogy between the classic Gambler's Ruin problem and the
thermally-activated dynamics in periodic Brownian ratchets. By considering each
periodic unit of the ratchet as a site chain, we calculated the transition
probabilities and mean first passage time for transitions between energy minima
of adjacent units. We consider the specific case of Brownian ratchets driven by
Markov dichotomous noise. The explicit solution for the current is derived for
any arbitrary temperature, and is verified numerically by Langevin simulations.
The conditions for vanishing current and current reversal in the ratchet are
obtained and discussed.Comment: 4 pages, 3 figure
Modelling the multi-wavelength emissions from PSR B1259-63/LS 2883: the effects of the stellar disc on shock radiations
PSR B1259-63/LS 2883 is an elliptical pulsar/Be star binary and emits
broadband emissions from radio to TeV -rays. The massive star possesses
an equatorial disc, which is inclined with the orbital plane of the pulsar. The
non-thermal emission from the system is believed to be produced by the pulsar
wind shock and the double-peak profiles in the X-ray and TeV -ray light
curves are related to the phases of the pulsar passing through the disc region
of the star. In this paper, we investigate the interactions between the pulsar
wind and stellar outflows, especially with the presence of the disc, and
present a multi-wavelength modelling of the emission from this system. We show
that the double-peak profiles of X-ray and TeV -ray light curves are
caused by the enhancements of the magnetic field and the soft photons at the
shock during the disc passages. As the pulsar is passing through the equatorial
disc, the additional pressure of the disc pushes the shock surface closer to
the pulsar, which causes the enhancement of magnetic field in the shock, and
thus increases the synchrotron luminosity. The TeV -rays due to the
inverse-Compton (IC) scattering of shocked electrons with seed photons from the
star is expected to peak around periastron which is inconsistent with
observations. However, the shock heating of the stellar disc could provide
additional seed photons for IC scattering during the disc passages, and thus
produces the double-peak profiles as observed in the TeV -ray light
curve. Our model can possibly be examined and applied to other similar
gamma-ray binaries, such as PSR J2032+4127/MT91 213, HESS J0632+057, and LS
I+61303.Comment: 14 pages, 6 figure
Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras
Polynomial-in-time dependent symmetries are analysed for polynomial-in-time
dependent evolution equations. Graded Lie algebras, especially Virasoro
algebras, are used to construct nonlinear variable-coefficient evolution
equations, both in 1+1 dimensions and in 2+1 dimensions, which possess
higher-degree polynomial-in-time dependent symmetries. The theory also provides
a kind of new realisation of graded Lie algebras. Some illustrative examples
are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge
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