Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Mapping the allowed parameter space for decaying dark matter models

I consider constraints on a phenomenological decaying-dark-matter model, in which two weakly-interacting massive particle (WIMP) species have a small mass splitting, and in which the heavier particle decays to the lighter particle and a massless particle on cosmological timescales. The decay parameter space is parameterized by $v_k$, the speed of the lighter particle in the center-of-mass frame of the heavier particle prior to decay, and the decay time $\tau$. Since I consider the case in which dark-matter halos have formed before there has been significant decay, I focus on the effects of decay in already-formed halos. I show that the $v_k-\tau$ parameter space may be constrained by observed properties of dark-matter halos. I highlight which set of observations is likely to yield the cleanest constraints on $v_k-\tau$ parameter space, and calculate the constraints in those cases in which the effect of decay on the observables can be calculated without N-body simulations of decaying dark matter. I show that for $v_k \gtrsim 5\times 10^3$ km s$^{-1}$, the z=0 galaxy cluster mass function and halo mass-concentration relation constrain $\tau \gtrsim$ 40 Gyr, and that precise constraints on $\tau$ for smaller $v_k$ will require N-body simulations.Comment: 14 pages, 5 figures, references added, replaced to match version published in Phys. Rev.

Galaxy-Galaxy Lensing by Non-Spherical Haloes I:Theoretical Considerations

We use Monte Carlo simulations to investigate the theory of galaxy-galaxy lensing by non-spherical dark matter haloes. The simulations include a careful accounting of the effects of multiple deflections. In a typical data set where the mean tangential shear of sources with redshifts zs ~ 0.6 is measured with respect to the observed symmetry axes of foreground galaxies with redshifts zl ~ 0.3, the signature of anisotropic galaxy-galaxy lensing differs substantially from the expectation that one would have in the absence of multiple deflections. The observed ratio of the mean tangential shears, g+/g-, is strongly suppressed compared to the function that one would measure if the intrinsic symmetry axes of the foreground galaxies were known. Depending upon the characteristic masses of the lenses, the observed ratio of the mean tangential shears may be consistent with an isotropic signal (despite the fact that the lenses are non-spherical), or it may even be reversed from the expected signal (i.e., the mean tangential shear for sources close to the observed minor axes of the lenses may exceed the mean tangential shear for sources close to the observed major axes of the lenses). These effects are caused primarily by the fact that the lens galaxies have, themselves, been lensed and therefore the observed symmetry axes of the lenses differ from their intrinsic symmetry axes. The effects of lensing of the foreground galaxies on the observed function g+/g- cannot be eliminated by the rejection of foreground galaxies with small image ellipticities, nor by focusing the analysis on sources that are located very close to the observed symmetry axes of the foreground galaxies. We conclude that any attempt to use a measurement of g+/g- to constrain the shapes of dark matter galaxy haloes must include Monte Carlo simulations that take multiple deflections properly into account.Comment: 15 pages, 17 figures, submitted to MNRAS, full manuscript with high-resolution version of Fig. 4 can be found at http://firedrake.bu.edu/preprints/preprints.htm

Sensor Fusion of Structure-from-Motion, Bathymetric 3D, and Beacon-Based Navigation Modalities

This paper describes an approach for the fusion of 30 data underwater obtained from multiple sensing modalities. In particular, we examine the combination of imagebased Structure-From-Motion (SFM) data with bathymetric data obtained using pencil-beam underwater sonar, in order to recover the shape of the seabed terrain. We also combine image-based egomotion estimation with acousticbased and inertial navigation data on board the underwater vehicle. We examine multiple types of fusion. When fusion is pe?$ormed at the data level, each modality is used to extract 30 information independently. The 30 representations are then aligned and compared. In this case, we use the bathymetric data as ground truth to measure the accuracy and drijl of the SFM approach. Similarly we use the navigation data as ground truth against which we measure the accuracy of the image-based ego-motion estimation. To our knowledge, this is the frst quantitative evaluation of image-based SFM and egomotion accuracy in a large-scale outdoor environment. Fusion at the signal level uses the raw signals from multiple sensors to produce a single coherent 30 representation which takes optimal advantage of the sensors' complementary strengths. In this papel; we examine how lowresolution bathymetric data can be used to seed the higherresolution SFM algorithm, improving convergence rates, and reducing drift error. Similarly, acoustic-based and inertial navigation data improves the convergence and driji properties of egomotion estimation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86044/1/hsingh-35.pd

On the occupation of X-ray selected galaxy groups by radio AGN since z=1.3

Previous clustering analysis of low-power radio AGN has indicated that they preferentially live in massive groups. The X-ray surveys of the COSMOS field have achieved a sensitivity at which these groups are directly detected out to z=1.3. Making use of Chandra-, XMM- and VLA-COSMOS surveys we identify radio AGN members (10**23.6 < L_1.4GHz/(W/Hz) < 10**25) of galaxy groups (10**13.2 < M_200/M_sun < 10**14.4; 0.1<z<1.3) and study i) the radio AGN -- X-ray group occupation statistics as a function of group mass, and ii) the distribution of radio AGN within the groups. We find that radio AGN are preferentially associated with galaxies close to the center (< 0.2r_200). Compared to our control sample of group members matched in stellar mass and color to the radio AGN host galaxies, we find a significant enhancement of radio AGN activity associated with 10**13.6 < M_200/M_sun < 10**14 halos. We present the first direct measurement of the halo occupation distribution (HOD) for radio AGN, based on the total mass function of galaxy groups hosting radio AGN. Our results suggest a possible deviation from the usually assumed power law HOD model. We also find an overall increase of the fraction of radio AGN in galaxy groups (<1r_200), relative to that in all environments.Comment: 5 pages, 4 figures, accepted for publication in MNRAS Letter

Fluid Models of Many-server Queues with Abandonment

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide first-order approximation for this model. The fluid model solution, which is proved to uniquely exists, serves as the fluid limit of the many-server queue, as the number of servers becomes large. Based on the fluid model solution, first-order approximations for various performance quantities are proposed

Constraints on the shapes of galaxy dark matter haloes from weak gravitational lensing

We study the shapes of galaxy dark matter haloes by measuring the anisotropy of the weak gravitational lensing signal around galaxies in the second Red-sequence Cluster Survey (RCS2). We determine the average shear anisotropy within the virial radius for three lens samples: all galaxies with 19<m_r'<21.5, and the `red' and `blue' samples, whose lensing signals are dominated by massive low-redshift early-type and late-type galaxies, respectively. To study the environmental dependence of the lensing signal, we separate each lens sample into an isolated and clustered part and analyse them separately. We also measure the azimuthal dependence of the distribution of physically associated galaxies around the lens samples. We find that these satellites preferentially reside near the major axis of the lenses, and constrain the angle between the major axis of the lens and the average location of the satellites to =43.7 deg +/- 0.3 deg for the `all' lenses, =41.7 deg +/- 0.5 deg for the `red' lenses and =42.0 deg +/- 1.4 deg for the `blue' lenses. For the `all' sample, we find that the anisotropy of the galaxy-mass cross-correlation function =0.23 +/- 0.12, providing weak support for the view that the average galaxy is embedded in, and preferentially aligned with, a triaxial dark matter halo. Assuming an elliptical Navarro-Frenk-White (NFW) profile, we find that the ratio of the dark matter halo ellipticity and the galaxy ellipticity f_h=e_h/e_g=1.50+1.03-1.01, which for a mean lens ellipticity of 0.25 corresponds to a projected halo ellipticity of e_h=0.38+0.26-0.25 if the halo and the lens are perfectly aligned. For isolated galaxies of the `all' sample, the average shear anisotropy increases to =0.51+0.26-0.25 and f_h=4.73+2.17-2.05, whilst for clustered galaxies the signal is consistent with zero. (abridged)Comment: 28 pages, 23 figues, accepted for publication in A&

The dark matter distribution in z~0.5 clusters of galaxies. I : Determining scaling relations with weak lensing masses

The total mass of clusters of galaxies is a key parameter to study massive halos. It relates to numerous gravitational and baryonic processes at play in the framework of large scale structure formation, thus rendering its determination important but challenging. From a sample of the 11 X-ray bright clusters selected from the excpres sample, we investigate the optical and X-ray properties of clusters with respect to their total mass derived from weak gravitational lensing. From multi-color wide field imaging obtained with MegaCam at CFHT, we derive the shear profile of each individual cluster of galaxies. We perform a careful investigation of all systematic sources related to the weak lensing mass determination. The weak lensing masses are then compared to the X-ray masses obtained from the analysis of XMM observations and assuming hydrostatic equilibrium. We find a good agreement between the two mass proxies although a few outliers with either perturbed morphology or poor quality data prevent to derive robust mass estimates. The weak lensing mass is also correlated with the optical richness and the total optical luminosity, as well as with the X-ray luminosity, to provide scaling relations within the redshift range 0.4<z<0.6. These relations are in good agreement with previous works at lower redshifts. For the L_X-M relation we combine our sample with two other cluster and group samples from the literature, thus covering two decades in mass and X-ray luminosity, with a regular and coherent correlation between the two physical quantities