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.

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

An algorithm for the direct reconstruction of the dark matter correlation function from weak lensing and galaxy clustering

The clustering of matter on cosmological scales is an essential probe for studying the physical origin and composition of our Universe. To date, most of the direct studies have focused on shear-shear weak lensing correlations, but it is also possible to extract the dark matter clustering by combining galaxy-clustering and galaxy-galaxy-lensing measurements. In this study we develop a method that can constrain the dark matter correlation function from galaxy clustering and galaxy-galaxy-lensing measurements, by focusing on the correlation coefficient between the galaxy and matter overdensity fields. To generate a mock galaxy catalogue for testing purposes, we use the Halo Occupation Distribution approach applied to a large ensemble of N-body simulations to model pre-existing SDSS Luminous Red Galaxy sample observations. Using this mock catalogue, we show that a direct comparison between the excess surface mass density measured by lensing and its corresponding galaxy clustering quantity is not optimal. We develop a new statistic that suppresses the small-scale contributions to these observations and show that this new statistic leads to a cross-correlation coefficient that is within a few percent of unity down to 5 Mpc/h. Furthermore, the residual incoherence between the galaxy and matter fields can be explained using a theoretical model for scale-dependent bias, giving us a final estimator that is unbiased to within 1%. We also perform a comprehensive study of other physical effects that can affect the analysis, such as redshift space distortions and differences in radial windows between galaxy clustering and weak lensing observations. We apply the method to a range of cosmological models and show the viability of our new statistic to distinguish between cosmological models.Comment: 23 pages, 14 figures, accepted by PRD; minor changes to V1, 1 new figure, more detailed discussion of the covariance of the new ADSD statisti

Evaluation of 4 Outcomes Measures in Microtia Treatment: Exposures, Infections, Aesthetics, and Psychosocial Ramifications.

BackgroundIn craniofacial microsomia, microtia and canal atresia pose formidable reconstructive challenges. We review our institutional experience in treating microtia and atresia to identify variables associated with 4 outcomes measures: complications, surgical revisions, aesthetic outcomes, and psychosocial function.MethodsCraniofacial microsomia patients treated at the University of California Los Angeles Craniofacial Clinic between 2008 and 2014 greater than 13 years of age (n = 68) were reviewed for microtia and atresia treatment and outcomes.ResultsIn total, 91.2% of patients diagnosed with craniofacial microsomia presented with microtia, affecting 75 ears. Both a male and right-sided predominance were observed. Fifty-six patients (90.3%) underwent autologous external ear reconstruction at an average age of 8.5 years. Age, type of incision, and size of cartilage framework did not predict total number of surgeries or complications. Severity of ear anomalies correlated with increased number of surgeries (P &lt; 0.001) and decreased aesthetic outcomes (P &lt; 0.001) but not complications. In total, 87.1% of patients with microtia had documented hearing loss, of which the majority were conductive and 18.5% were mixed sensorineural and conductive. Hearing deficits were addressed in 70.4% of patients with external hearing aids, bone anchored hearing aids, or canaloplasty. Of all variables, improvement of psychosocial function was correlated only to hearing loss treatment of any type (P = 0.01).ConclusionsOn evaluation of surgical and patient characteristics, severity of microtia predicted the total number of surgical revisions performed and aesthetic ratings. In addition, we found that the only factor that correlated with improved patient and parent-reported psychosocial outcomes was treatment of hearing loss

Dark Matter Structures in the Universe: Prospects for Optical Astronomy in the Next Decade

The Cold Dark Matter theory of gravitationally-driven hierarchical structure formation has earned its status as a paradigm by explaining the distribution of matter over large spans of cosmic distance and time. However, its central tenet, that most of the matter in the universe is dark and exotic, is still unproven; the dark matter hypothesis is sufficiently audacious as to continue to warrant a diverse battery of tests. While local searches for dark matter particles or their annihilation signals could prove the existence of the substance itself, studies of cosmological dark matter in situ are vital to fully understand its role in structure formation and evolution. We argue that gravitational lensing provides the cleanest and farthest-reaching probe of dark matter in the universe, which can be combined with other observational techniques to answer the most challenging and exciting questions that will drive the subject in the next decade: What is the distribution of mass on sub-galactic scales? How do galaxy disks form and bulges grow in dark matter halos? How accurate are CDM predictions of halo structure? Can we distinguish between a need for a new substance (dark matter) and a need for new physics (departures from General Relativity)? What is the dark matter made of anyway? We propose that the central tool in this program should be a wide-field optical imaging survey, whose true value is realized with support in the form of high-resolution, cadenced optical/infra-red imaging, and massive-throughput optical spectroscopy.Comment: White paper submitted to the 2010 Astronomy & Astrophysics Decadal Surve

Exploring Dark Energy with Next-Generation Photometric Redshift Surveys

The coming decade will be an exciting period for dark energy research, during which astronomers will address the question of what drives the accelerated cosmic expansion as first revealed by type Ia supernova (SN) distances, and confirmed by later observations. The mystery of dark energy poses a challenge of such magnitude that, as stated by the Dark Energy Task Force (DETF), nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. The lack of multiple complementary precision observations is a major obstacle in developing lines of attack for dark energy theory. This lack is precisely what next-generation surveys will address via the powerful techniques of weak lensing (WL) and baryon acoustic oscillations (BAO) -- galaxy correlations more generally -- in addition to SNe, cluster counts, and other probes of geometry and growth of structure. Because of their unprecedented statistical power, these surveys demand an accurate understanding of the observables and tight control of systematics. This white paper highlights the opportunities, approaches, prospects, and challenges relevant to dark energy studies with wide-deep multiwavelength photometric redshift surveys. Quantitative predictions are presented for a 20000 sq. deg. ground-based 6-band (ugrizy) survey with 5-sigma depth of r~27.5, i.e., a Stage 4 survey as defined by the DETF

The Whole is Greater than the Sum of the Parts: Optimizing the Joint Science Return from LSST, Euclid and WFIRST

The focus of this report is on the opportunities enabled by the combination of LSST, Euclid and WFIRST, the optical surveys that will be an essential part of the next decade's astronomy. The sum of these surveys has the potential to be significantly greater than the contributions of the individual parts. As is detailed in this report, the combination of these surveys should give us multi-wavelength high-resolution images of galaxies and broadband data covering much of the stellar energy spectrum. These stellar and galactic data have the potential of yielding new insights into topics ranging from the formation history of the Milky Way to the mass of the neutrino. However, enabling the astronomy community to fully exploit this multi-instrument data set is a challenging technical task: for much of the science, we will need to combine the photometry across multiple wavelengths with varying spectral and spatial resolution. We identify some of the key science enabled by the combined surveys and the key technical challenges in achieving the synergies.Comment: Whitepaper developed at June 2014 U. Penn Workshop; 28 pages, 3 figure