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

Intraoperative Indocyanine Green Laser Angiography in Pediatric Autologous Ear Reconstruction.

Skin flap vascularity is a critical determinant of aesthetic results in autologous ear reconstruction. In this study, we investigate the use of intraoperative laser-assisted indocyanine green angiography (ICGA) as an adjunctive measure of skin flap vascularity in pediatric autologous ear reconstruction. Twenty-one consecutive pediatric patients undergoing first-stage autologous total ear reconstruction were retrospectively evaluated. The first 10 patients were treated traditionally (non-ICGA), and the latter 11 patients were evaluated with ICGA intraoperatively after implantation of the cartilage construct and administration of suction. Relative and absolute perfusion units in the form of contour maps were generated. Statistical analyses were performed using independent sample Student t test. Statistically significant differences in exposure and infection were not found between the 2 groups. However, decreased numbers of surgical revisions were required in cases with ICGA versus without ICGA (P = 0.03), suggesting that greater certainty in skin flap perfusion correlated with a reduction in revision surgeries. In cases of exposure, we found an average lowest absolute perfusion unit of 14.3, whereas cases without exposure had an average of 26.1 (P = 0.02), thereby defining objective parameters for utilizing ICGA data in tailoring surgical decision making for this special population of patients. Defined quantitative parameters for utilizing ICGA in evaluating skin flap vascularity may be a useful adjunctive technique in pediatric autologous ear reconstruction

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