Numerical Simulations of Dynamos Generated in Spherical Couette Flows

We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculiar regime where dynamo action may be obtained for relatively low magnetic Reynolds numbers ($Rm_c\sim 300$). In this dynamical regime (Rossby number $Ro\sim -1$, spheres in opposite direction) at a moderate Ekman number ($E=10^{-3}$), a enhanced shear layer around the inner core might explain the decrease of the dynamo threshold. For lower $E$ ($E=10^{-4}$) this internal shear layer becomes unstable, leading to small scales fluctuations, and the favorable dynamo regime is lost. We also model the effect of ferromagnetic boundary conditions. Their presence have only a small impact on the dynamo onset but clearly enhance the saturated magnetic field in the ferromagnetic parts. Implications for experimental studies are discussed

Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1

Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on the two downward lattice directions emanating from the point of the application of the external force. For systems of finite size, the magnitude of these peaks decreases towards the bottom of the packing, while progressively a broader, central maximum appears between the peaks. The response behaviour displays a remarkable scaling behaviour with system size $N$: while the response in the bulk of the packing scales as $\frac{1}{N}$, on the boundary it is independent of $N$, so that in the thermodynamic limit only the peaks on the lattice directions persist. This qualitative behaviour is extremely robust, as demonstrated by our simulation results with different boundary conditions. We have obtained expressions of the response and higher correlations for any system size in terms of integers corresponding to an underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2 reorganized and rewritten; Details about the simulation procedure added in Sec.3.1. ; A new section, summarizing the final results and the calculation procedure adde

Trapped and excited w modes of stars with a phase transition and R>=5M

The trapped $w$-modes of stars with a first order phase transition (a density discontinuity) are computed and the excitation of some of the modes of these stars by a perturbing shell is investigated. Attention is restricted to odd parity (``axial'') $w$-modes. With $R$ the radius of the star, $M$ its mass, $R_{i}$ the radius of the inner core and $M_{i}$ the mass of such core, it is shown that stars with $R/M\geq 5$ can have several trapped $w$-modes, as long as $R_{i}/M_{i}<2.6$. Excitation of the least damped $w$-mode is confirmed for a few models. All of these stars can only exist however, for values of the ratio between the densities of the two phases, greater than $\sim 46$. We also show that stars with a phase transition and a given value of $R/M$ can have far more trapped modes than a homogeneous single density star with the same value of $R/M$, provided both $R/M$ and $R_{i}/M_{i}$ are smaller than 3. If the phase transition is very fast, most of the stars with trapped modes are unstable to radial oscillations. We compute the time of instability, and find it to be comparable to the damping of the $w$-mode excited in most cases where $w$-mode excitation is likely. If on the other hand the phase transition is slow, all the stars are stable to radial oscillations.Comment: To appear in Physical Review

Formation of Disk Galaxies: Warm Dark Matter and the Angular Momentum problem

We have performed TreeSPH simulations of disk galaxy formation in various warm dark matter (WDM) cosmologies. Our results indicate that for a range of WDM free-streaming masses, the disk galaxy formation angular momentum problem can be completely resolved by going to the WDM structure formation scenario, without having to invoke stellar feedback processes at all. We also confirm our previous suspicion, that part of the angular momentum problem is due to numerical effects, most likely related to the shock capturing, artificial viscosity used in SPH. Furthermore we find that we can match the observed I-band Tully-Fisher (TF) relation, provided that the I-band mass-to-light ratio of disk galaxies is about 0.8. We argue that this is quite a reasonable value in comparison with various dynamical and spectrophotometric estimates, including one given in this paper. We speculate that our success in matching the TF relation may be due to WDM halos being less centrally concentrated than CDM halos and suggest to check this exciting possibility with high resolution simulations, in particular in low Omega_M, WDM cosmologies. Finally, we discuss possible physical candidates for WDM particles extensively. We find that the most promising are neutrinos with weaker or stronger interactions than normal, majorons (light pseudogoldstone bosons) or mirror or shadow world neutrinos.Comment: 50 pages incl. 17 figures. Accepted for publication in Ap

Observational Mass-to-Light Ratio of Galaxy Systems: from Poor Groups to Rich Clusters

We study the mass-to-light ratio of galaxy systems from poor groups to rich clusters, and present for the first time a large database for useful comparisons with theoretical predictions. We extend a previous work, where B_j band luminosities and optical virial masses were analyzed for a sample of 89 clusters. Here we also consider a sample of 52 more clusters, 36 poor clusters, 7 rich groups, and two catalogs, of about 500 groups each, recently identified in the Nearby Optical Galaxy sample by using two different algorithms. We obtain the blue luminosity and virial mass for all systems considered. We devote a large effort to establishing the homogeneity of the resulting values, as well as to considering comparable physical regions, i.e. those included within the virial radius. By analyzing a fiducial, combined sample of 294 systems we find that the mass increases faster than the luminosity: the linear fit gives M\propto L_B^{1.34 \pm 0.03}, with a tendency for a steeper increase in the low--mass range. In agreement with the previous work, our present results are superior owing to the much higher statistical significance and the wider dynamical range covered (about 10^{12}-10^{15} M_solar). We present a comparison between our results and the theoretical predictions on the relation between M/L_B and halo mass, obtained by combining cosmological numerical simulations and semianalytic modeling of galaxy formation.Comment: 25 pages, 12 eps figures, accepted for publication in Ap

Observational evidence for self-interacting cold dark matter

Cosmological models with cold dark matter composed of weakly interacting particles predict overly dense cores in the centers of galaxies and clusters and an overly large number of halos within the Local Group compared to actual observations. We propose that the conflict can be resolved if the cold dark matter particles are self-interacting with a large scattering cross-section but negligible annihilation or dissipation. In this scenario, astronomical observations may enable us to study dark matter properties that are inaccessible in the laboratoryComment: 4 pages, no figures; added references, pedagogical improvements, to appear in PR

The evolution of galaxy groups and of galaxies therein

Properties of groups of galaxies depend sensitively on the algorithm for group selection, and even the most recent catalogs of groups built from redshift-space selection should suffer from projections and infalling galaxies. The cosmo-dynamical evolution of groups from initial Hubble expansion to collapse and virialization leads to a fundamental track (FT) in virial-theorem-M/L vs crossing time. The increased rates of mergers, both direct and after dynamical friction, in groups relative to clusters, explain the higher fraction of elliptical galaxies at given local number density in X-ray selected groups, relative to clusters, even when the hierarchical evolution of groups is considered. Galaxies falling into groups and clusters should later travel outwards to typically 2 virial radii, which is somewhat less than the outermost radius where observed galaxy star formation efficiencies are enhanced relative to field galaxies of same morphological type. An ongoing analysis of the internal kinematics of X-ray selected groups suggests that the radial profiles of line of sight velocity dispersion are consistent with isotropic NFW distributions for the total mass density, with higher (lower) concentrations than LambdaCDM predictions in groups of high (low) mass. The critical mass, at M200 ~ 10^13 M_sun is consistent with possible breaks in the X-ray luminosity-temperature and Fundamental Plane relations. The internal kinematics of groups indicate that the M-T relation of groups should agree with that extrapolated from clusters with no break at the group scale. The analyses of observed velocity dispersion profiles and of the FT both suggest that low velocity dispersion groups (compact and loose, X-ray emitting or undetected) are quite contaminated by chance projections.Comment: Invited review, ESO workshop "Groups of Galaxies in the Nearby Universe", held in Santiago, Chile, 5-9 December 2005, ed. I. Saviane, V. Ivanov & J. Borissova, 16 page

The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improve

A recursive approach to the O(n) model on random maps via nested loops

We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in cutting the O(n) model configurations along their loops so that each elementary piece is a map that may have arbitrary even face degrees. In the induced statistics, these maps are drawn according to a Boltzmann distribution whose parameters (the face weights) are determined by a fixed point condition. In particular, we show that the dense and dilute critical points of the O(n) model correspond to bipartite maps with large faces (i.e. whose degree distribution has a fat tail). The re-expression of the fixed point condition in terms of linear integral equations allows us to explore the phase diagram of the model. In particular, we determine this phase diagram exactly for the simplest version of the model where the loops are "rigid". Several generalizations of the model are discussed.Comment: 47 pages, 13 figures, final version (minor changes with v2 after proof corrections