Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

STEPS - an approach for human mobility modeling

In this paper we introduce Spatio-TEmporal Parametric Stepping (STEPS) - a simple parametric mobility model which can cover a large spectrum of human mobility patterns. STEPS makes abstraction of spatio-temporal preferences in human mobility by using a power law to rule the nodes movement. Nodes in STEPS have preferential attachment to favorite locations where they spend most of their time. Via simulations, we show that STEPS is able, not only to express the peer to peer properties such as inter-ontact/contact time and to reflect accurately realistic routing performance, but also to express the structural properties of the underlying interaction graph such as small-world phenomenon. Moreover, STEPS is easy to implement, exible to configure and also theoretically tractable

Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video

Viral videos can reach global penetration traveling through international channels of communication similarly to real diseases starting from a well-localized source. In past centuries, disease fronts propagated in a concentric spatial fashion from the the source of the outbreak via the short range human contact network. The emergence of long-distance air-travel changed these ancient patterns. However, recently, Brockmann and Helbing have shown that concentric propagation waves can be reinstated if propagation time and distance is measured in the flight-time and travel volume weighted underlying air-travel network. Here, we adopt this method for the analysis of viral meme propagation in Twitter messages, and define a similar weighted network distance in the communication network connecting countries and states of the World. We recover a wave-like behavior on average and assess the randomizing effect of non-locality of spreading. We show that similar result can be recovered from Google Trends data as well.Comment: 10 page

Determination of the spatial and temporal variation of tropospheric water vapour using CGPS networks

Tropospheric water vapour is the main limiting factor in using GPS to determine crustal deformation at highest accuracy. On the other hand, it is an important variable to monitor meteorological and climatic processes. This paper discusses both aspects: the modelling of tropospheric water vapour using meteorological data as well as the determination of the integrated amount of water vapour and its spatiotemporal variation using GPS data. Switzerland has been chosen as experiment area. The Swiss continuous GPS (CGPS) network AGNES is used as a reference network, which represents a realistic scenario for GPS-based water vapour determination. Data of the Swiss numerical weather model aLMo are used for systematic comparison and validation. For the first aspect, integrated tropospheric wet refractivity values are determined from meteorological measurements and compared with GPS path delays. An overall agreement of 1 cm of zenith wet path delay was achieved. For the second aspect a tomographic approach has been developed. A total of 6720 GPS-determined profiles are compared with data of the numerical weather model and radio soundings. The results are statistically evaluated and systematically compared with each other. A correlation between the accuracy and the weather situation was found. Overall, an agreement of 5-7 ppm (refractivity unit) was obtained compared to aLMo. The use of GPS-determined path delays from a permanent GPS network is the recommended method to correct GPS measurements. In all other cases, the two methods presented (COITROPA, COMEDIE) are a feasible alternative to determine path delays accurately. Furthermore, GPS is a convenient application to determine the amount of water vapour in the troposphere. It is demonstrated that the vertical distribution of water vapour can be deduced by applying the tomographic approac

Determination of the spatial and temporal variation of tropospheric water vapour using CGPS networks

Tropospheric water vapour is the main limiting factor in using GPS to determine crustal deformation at highest accuracy. On the other hand, it is an important variable to monitor meteorological and climatic processes. This paper discusses both aspects: the modelling of tropospheric water vapour using meteorological data as well as the determination of the integrated amount of water vapour and its spatiotemporal variation using GPS data. Switzerland has been chosen as experiment area. The Swiss continuous GPS (CGPS) network AGNES is used as a reference network, which represents a realistic scenario for GPS-based water vapour determination. Data of the Swiss numerical weather model aLMo are used for systematic comparison and validation. For the first aspect, integrated tropospheric wet refractivity values are determined from meteorological measurements and compared with GPS path delays. An overall agreement of 1 cm of zenith wet path delay was achieved. For the second aspect a tomographic approach has been developed. A total of 6720 GPS-determined profiles are compared with data of the numerical weather model and radio soundings. The results are statistically evaluated and systematically compared with each other. A correlation between the accuracy and the weather situation was found. Overall, an agreement of 5-7 ppm (refractivity unit) was obtained compared to aLMo. The use of GPS-determined path delays from a permanent GPS network is the recommended method to correct GPS measurements. In all other cases, the two methods presented (COITROPA, COMEDIE) are a feasible alternative to determine path delays accurately. Furthermore, GPS is a convenient application to determine the amount of water vapour in the troposphere. It is demonstrated that the vertical distribution of water vapour can be deduced by applying the tomographic approac

On the nucleon self-energy in nuclear matter

We consider the nucleon self-energy in nuclear matter in the absence of Pauli blocking. It is evaluated using the partial-wave analysis of $NN$ scattering data. Our results are compared with that of a realistic calculation to estimate the effect of this blocking. It is also possible to use our results as a check on the realistic calculations.Comment: 6 pages, 2 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:

Single particle spectrum and binding energy of nuclear matter

In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The variation in the binding energy value introduced by the parabolic approximation is quantitatively analyzed in detail. It is found that the approximation can introduce an uncertainty of 1-2 MeV near the saturation density.Comment: 6 Latex pages, 3 postscript figure

Neutron star properties and the equation of state of neutron-rich matter

We calculate total masses and radii of neutron stars (NS) for pure neutron matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We use realistic nucleon-nucleon (NN) interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.Comment: 13 pages, 9 figures, 1 table; Revised version, accepted for publication in Physical Review