12,709 research outputs found
Non-abelian quantum Hall states - exclusion statistics, K-matrices and duality
We study excitations in edge theories for non-abelian quantum Hall states,
focussing on the spin polarized states proposed by Read and Rezayi and on the
spin singlet states proposed by two of the authors. By studying the exclusion
statistics properties of edge-electrons and edge-quasiholes, we arrive at a
novel K-matrix structure. Interestingly, the duality between the electron and
quasihole sectors links the pseudoparticles that are characteristic for
non-abelian statistics with composite particles that are associated to the
`pairing physics' of the non-abelian quantum Hall states.Comment: LaTeX2e, 40 page
The Network Analysis of Urban Streets: A Primal Approach
The network metaphor in the analysis of urban and territorial cases has a
long tradition especially in transportation/land-use planning and economic
geography. More recently, urban design has brought its contribution by means of
the "space syntax" methodology. All these approaches, though under different
terms like accessibility, proximity, integration,connectivity, cost or effort,
focus on the idea that some places (or streets) are more important than others
because they are more central. The study of centrality in complex
systems,however, originated in other scientific areas, namely in structural
sociology, well before its use in urban studies; moreover, as a structural
property of the system, centrality has never been extensively investigated
metrically in geographic networks as it has been topologically in a wide range
of other relational networks like social, biological or technological. After
two previous works on some structural properties of the dual and primal graph
representations of urban street networks (Porta et al. cond-mat/0411241;
Crucitti et al. physics/0504163), in this paper we provide an in-depth
investigation of centrality in the primal approach as compared to the dual one,
with a special focus on potentials for urban design.Comment: 19 page, 4 figures. Paper related to the paper "The Network Analysis
of Urban Streets: A Dual Approach" cond-mat/041124
Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations
The basic conceptual picture and theoretical basis for development of
transport equations in porous media are examined. The general form of the
governing equations is derived for conservative chemical transport in
heterogeneous geological formations, for single realizations and for ensemble
averages of the domain. The application of these transport equations is focused
on accounting for the appearance of non-Fickian (anomalous) transport behavior.
The general ensemble-averaged transport equation is shown to be equivalent to a
continuous time random walk (CTRW) and reduces to the conventional forms of the
advection-dispersion equation (ADE) under highly restrictive conditions.
Fractional derivative formulations of the transport equations, both temporal
and spatial, emerge as special cases of the CTRW. In particular, the use in
this context of L{\'e}vy flights is critically examined. In order to determine
chemical transport in field-scale situations, the CTRW approach is generalized
to non-stationary systems. We outline a practical numerical scheme, similar to
those used with extended geological models, to account for the often important
effects of unresolved heterogeneities.Comment: 14 pages, REVTeX4, accepted to Wat. Res. Res; reference adde
Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects
We show the asymptotic long-time equivalence of a generic power law waiting
time distribution to the Mittag-Leffler waiting time distribution,
characteristic for a time fractional CTRW. This asymptotic equivalence is
effected by a combination of "rescaling" time and "respeeding" the relevant
renewal process followed by a passage to a limit for which we need a suitable
relation between the parameters of rescaling and respeeding. Turning our
attention to spatially 1-D CTRWs with a generic power law jump distribution,
"rescaling" space can be interpreted as a second kind of "respeeding" which
then, again under a proper relation between the relevant parameters leads in
the limit to the space-time fractional diffusion equation. Finally, we treat
the `time fractional drift" process as a properly scaled limit of the counting
number of a Mittag-Leffler renewal process.Comment: 36 pages, 3 figures (5 files eps). Invited lecture by R. Gorenflo at
the 373. WE-Heraeus-Seminar on Anomalous Transport: Experimental Results and
Theoretical Challenges, Physikzentrum Bad-Honnef (Germany), 12-16 July 2006;
Chairmen: R. Klages, G. Radons and I.M. Sokolo
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