Quasi-stationary states and the range of pair interactions

"Quasi-stationary" states are approximately time-independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their occurrence for a generic pair interaction V(r \rightarrow \infty) \sim 1/r^a with a > 0, in d>1 dimensions. We generalize analytic calculations known for gravity in d=3 to determine the scaling parametric dependences of their relaxation rates due to two body collisions, and report extensive numerical simulations testing their validity. Our results lead to the conclusion that, for a < d-1, the existence of quasi-stationary states is ensured by the large distance behavior of the interaction alone, while for a > d-1 it is conditioned on the short distance properties of the interaction, requiring the presence of a sufficiently large soft-core in the interaction potential.Comment: 5 pages, 3 figures; final version to appear in Phys. Rev. Let

On stability and spiral patterns in polar disks

To investigate the stability properties of polar disks we performed two-dimensional hydrodynamical simulations for flat polytropic gaseous self-gravitating disks which were perturbed by a central S0-like component. Our disk was constructed to resemble that of the proto-typical galaxy NGC 4650A. This central perturbation induces initially a stationary two-armed tightly-wound leading spiral in the polar disk. For a hot disk (Toomre parameter Q>1.7), the structure does not change over the simulation time of 4.5 Gyr. In case of colder disks, the self-gravity of the spiral becomes dominant, it decouples from the central perturbation and grows, until reaching a saturation stage in which an open trailing spiral is formed, rather similar to that observed in NGC4650A. The timescale for developing non-linear structures is 1-2 Gyr; saturation is reached within 2-3 Gyr. The main parameter controlling the structure formation is the Toomre parameter. The results are surprisingly insensitive to the properties of the central component. If the polar disk is much less massive than that in NGC4650A, it forms a weaker tightly-wound spiral, similar to that seen in dust absorption in the dust disk of NGC2787. Our results are derived for a polytropic equation of state, but appear to be generic as the adiabatic exponent is varied between \gamma = 1 (isothermal) and \gamma = 2 (very stiff).Comment: 14 pages including 23 figures, accepted for publication in Astronomy & Astrophysic

Is the dark matter halo of the Milky Way flattened?

We performed an extended analysis of the parameter space for the interaction of the Magellanic System with the Milky Way (MW). The varied parameters cover the phase space parameters, the masses, the structure, and the orientation of both Magellanic Clouds, as well as the flattening of the dark matter halo of the MW. The analysis was done by a specially adopted optimization code searching for the best match between numerical models and the detailed HI map of the Magellanic System by Bruens et al. (2005). The applied search algorithm is a genetic algorithm combined with a code based on the fast, but approximative restricted N-body method. By this, we were able to analyze more than 10^6 models, which makes this study one of the most extended ones for the Magellanic System. Here we focus on the flattening q of the axially symmetric MW dark matter halo potential, that is studied within the range 0.74<=q<=1.20. We show that creation of a trailing tail (Magellanic Stream) and a leading stream (Leading Arm) is quite a common feature of the Magellanic System-MW interaction, and such structures were modeled across the entire range of halo flattening values. However, important differences exist between the models, concerning density distribution and kinematics of HI, and also the dynamical evolution of the Magellanic System. Detailed analysis of the overall agreement between modeled and observed distribution of neutral hydrogen shows that the models assuming an oblate (q<1.0) dark matter halo of the Galaxy allow for better satisfaction of HI observations than models with other halo configurations.Comment: 19 pages, 20 figures, 2 appendices, accepted for publication in A&

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

The Heckscher-Ohlin Model and the Network Structure of International Trade

This paper estimates for 28 product groups a characteristic parameter that reflects the topological structure of its trading network. Using these estimates, it then describes how the structure of international trade has evolved during the 1980-2000 period. Thereafter, it demonstrates the importance of networks in international trade by explicitly accounting for their scaling properties when testing the prediction of the Heckscher-Ohlin model that factor endowment differentials determine bilateral trade flows. The results suggest that differences in factor endowments increase bilateral trade in goods that are traded in "dispersed" networks. For goods that are traded in "concentrated" networks, factor endowment differentials are less important.Networks, international trade, gravity model

Simulation of cosmic irradiation conditions in thick target arrangements

One approach to simulate 2-pi irradiation conditions of planetary surfaces which has been widely applied in the past are bombardments of so called thick targets. A very large thick target was exposed recently to 2.1 GeV protons at the Bevatron-Bevalac in Berkeley. In a 100x100x180 cm steel-surrounded granodiorite target radioactive medium and high energy spallation products of the incident primary and of secondary particles were analyzed along the beam axis down to depths of 140 g/cm(2) in targets such as Cu, Ni, Co, Fe, T, Si, SiO2 and Al. Activities of these nuclides were exclusively determined via instrumental gamma-ray spectroscopy. Relative yields of neutron capture and spallation products induced in Co and Cu targets during the thick target bombardment are shown as a function of depth. The majority of the medium energy products such as Co-58 from Co targets exhibit a maximum at shallow depths of 40-60 g/cm(2) and then decrease exponentially. In a comparable 600 MeV proton bombarded thick target such a slight maximum for medium energy products was not observed. Rather, Co-58 activities in Co decreased steadily with the highest activity at the surface. The activities of the n-capture product Co-60 increase steadily starting at the surface. This indicates the rapidly growing flux of low energy neutrons within the target