The structure of borders in a small world

Geographic borders are not only essential for the effective functioning of government, the distribution of administrative responsibilities and the allocation of public resources, they also influence the interregional flow of information, cross-border trade operations, the diffusion of innovation and technology, and the spatial spread of infectious diseases. However, as growing interactions and mobility across long distances, cultural, and political borders continue to amplify the small world effect and effectively decrease the relative importance of local interactions, it is difficult to assess the location and structure of effective borders that may play the most significant role in mobility-driven processes. The paradigm of spatially coherent communities may no longer be a plausible one, and it is unclear what structures emerge from the interplay of interactions and activities across spatial scales. Here we analyse a multi-scale proxy network for human mobility that incorporates travel across a few to a few thousand kilometres. We determine an effective system of geographically continuous borders implicitly encoded in multi-scale mobility patterns. We find that effective large scale boundaries define spatially coherent subdivisions and only partially coincide with administrative borders. We find that spatial coherence is partially lost if only long range traffic is taken into account and show that prevalent models for multi-scale mobility networks cannot account for the observed patterns. These results will allow for new types of quantitative, comparative analyses of multi-scale interaction networks in general and may provide insight into a multitude of spatiotemporal phenomena generated by human activity.Comment: 9 page

Accelerating random walks by disorder

We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial displacements of the random walk. Unlike ordinary random walks which are slowed down for all values of the relative weight of source and target, non-local superdiffusive processes show distinct regimes of attenuation and acceleration for increased source and target weight, respectively. Consequently, spatial inhomogeneities can facilitate the spread of superdiffusive processes, in contrast to common belief that external disorder generally slows down stochastic processes. Our results are based on a novel type of fractional Fokker-Planck equation which we investigate numerically and by perturbation theory for weak disorder.Comment: 8 pages, 5 figure

Dirac Hartree-Fock for Finite Nuclei Employing realistic Forces

We discuss two different approximation schemes for the self-consistent solution of the {\it relativistic} Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear matter calculations, whereas in the second approach the local-density approximation is used to account for the effects of correlations. The results obtained by the two methods are very similar. Employing a realistic one-boson-exchange potential (Bonn~A), the predictions for energies and radii of $^{16}$O and $^{40}$Ca come out in substantially better agreement with experiment as compared to non-relativistic approaches. As a by-product of our study, it turns out that the Fock exchange-terms, ignored in a previous investigation, are not negligible.Comment:

Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials

We analyze the spin-orbit coupling term in the nuclear energy density functional in terms of a zero-range NN-contact interaction and finite-range contributions from two-pion exchange. We show that the strength of the spin-orbit contact interaction as extracted from high-precision nucleon-nucleon potentials is in perfect agreement with that of phenomenological Skyrme forces employed in non-relativistic nuclear structure calculations. Additional long-range contributions from chiral two-pion exchange turn out to be relatively small. These explicitly density-dependent contributions reduce the ratio of the isovector to the isoscalar spin-orbit strength significantly below the Skyrme value 1/3. We perform a similar analysis for the strength function of the $(\vec \nabla \rho)^2$-term and find values not far from those of phenomenological Skyrme parameterizations.Comment: 10 pages, 3 figures, accepted for publication in Physical Review C70 (2004

Thematic mapper research in the earth sciences: Small scale patches of suspended matter and phytoplankton in the Elbe River Estuary, German Bight and Tidal Flats

A Thematic Mapper (TM) field experiment was followed by a data analysis to determine TM capabilities for analysis of suspended matter and phytoplankton. Factor analysis showed that suspended matter concentration, atmospheric scattering, and sea surface temperature can be retrieved as independent factors which determine the variation in the TM data over water areas. Spectral channels in the near infrared open the possibility of determining the Angstrom exponent better than for the coastal zone color scanner. The suspended matter distribution may then be calculated by the absolute radiance of channel 2 or 3 or the ratio of both. There is no indication of whether separation of chlorophyll is possible. The distribution of suspended matter and sea surface temperature can be observed with the expected fine structure. A good correlation between water depth and suspended matter distribution as found from ship data can now be analyzed for an entire area by the synoptic view of the TM scenes

Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei

The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include

Effective DBHF Method for Asymmetric Nuclear Matter and Finite Nuclei

A new decomposition of the Dirac structure of nucleon self-energies in the Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the equation of state for asymmetric nuclear matter. The effective coupling constants of $\sigma$, $\omega$, $\delta$ and $\rho$ mesons with a density dependence in the relativistic mean field approach are deduced by reproducing the nucleon self-energy resulting from the DBHF at each density for symmetric and asymmetric nuclear matter. With these couplings the properties of finite nuclei are investigated. The agreement of charge radii and binding energies of finite nuclei with the experimental data are improved simultaneously in comparison with the projection method. It seems that the properties of finite nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We may conclude that the properties of the asymmetric nuclear matter and finite nuclei could be well described by the new decomposition approach of the G matrix.Comment: 16 pages, 5 figure

Momentum-Dependent Mean Field Based Upon the Dirac-Brueckner Approach for Nuclear Matter

A momentum-dependent mean field potential, suitable for application in the transport-model description of nucleus-nucleus collisions, is derived in a microscopic way. The derivation is based upon the Bonn meson-exchange model for the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear matter. The properties of the microscopic mean field are examined and compared with phenomenological parametrizations which are commonly used in transport-model calculations.Comment: 15 pages text (RevTex) and 4 figures (postscript in a separate uuencoded file), UI-NTH-930