Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J' in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J'. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.Comment: 4+ pages, 3 figure

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

The young stellar population of NGC 4214 as observed with HST. I. Data and methods

We present the data and methods that we have used to perform a detailed UV-optical study of the nearby dwarf starburst galaxy NGC 4214 using multifilter HST/WFPC2+STIS photometry. We explain the process followed to obtain high-quality photometry and astrometry of the stellar and cluster populations of this galaxy. We describe the procedure used to transform magnitudes and colors into physical parameters using spectral energy distributions. The data show the existence of both young and old stellar populations that can be resolved at the distance of NGC 4214 (2.94 Mpc) and we perform a general description of those populations.Comment: 33 pages, 9 figures, and 8 table

Comparing Auditory Noise Treatment with Stimulant Medication on Cognitive Task Performance in Children with Attention Deficit Hyperactivity Disorder: Results from a Pilot Study

Background: Recent research has shown that acoustic white noise (80 dB) can improve task performance in people with attention deficits and/or Attention Deficit Hyperactivity Disorder (ADHD). This is attributed to the phenomenon of stochastic resonance in which a certain amount of noise can improve performance in a brain that is not working at its optimum. We compare here the effect of noise exposure with the effect of stimulant medication on cognitive task performance in ADHD. The aim of the present study was to compare the effects of auditory noise exposure with stimulant medication for ADHD children on a cognitive test battery. A group of typically developed children (TDC) took the same tests as a comparison. Methods: Twenty children with ADHD of combined or inattentive subtypes and twenty TDC matched for age and gender performed three different tests (word recall, spanboard and n-back task) during exposure to white noise (80 dB) and in a silent condition. The ADHD children were tested with and without central stimulant medication. Results: In the spanboard- and the word recall tasks, but not in the 2-back task, white noise exposure led to significant improvements for both non-medicated and medicated ADHD children. No significant effects of medication were found on any of the three tasks. Conclusion: This pilot study shows that exposure to white noise resulted in a task improvement that was larger than the one with stimulant medication thus opening up the possibility of using auditory noise as an alternative, non-pharmacological treatment of cognitive ADHD symptoms

Observation of Parity Nonconservation in Møller Scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (Møller) scattering: A_(PV) = [-175 ± 30(stat)± 20(syst)] X 10^(-9). This first direct observation of parity nonconservation in Møller scattering leads to a measurement of the electron’s weak charge at low energy Q^e_W = -0:053 ± 0:011. This is consistent with the standard model expectation at the current level of precision: sin^2θ_W = (M_Z)_(MS) = 0:2293 ± 0:0024(stat) ± 0:0016(syst) ± 0:0006(theory)

The Initial-Boundary Value Problem in General Relativity

In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.Comment: 11 pages, 2 figures. Contribution to a special volume for Mario Castagnino's seventy fifth birthda

On the Use of Blanketed Atmospheres as Boundary Conditions for Stellar Evolutionary Models

Stellar models have been computed for stars having [Fe/H] = 0.0 and -2.0 to determine the effects of using boundary conditions derived from the latest MARCS model atmospheres. The latter were fitted to the interior models at both the photosphere and at tau = 100, and at least for the 0.8-1.0 solar mass stars considered here, the resultant evolutionary tracks were found to be nearly independent of the chosen fitting point. Particular care was taken to treat the entire star as consistently as possible; i.e., both the interior and atmosphere codes assumed the same abundances and the same treatment of convection. Tracks were also computed using either the classical gray T(tau,T_eff) relation or that derived by Krishna Swamy (1966) to derive the boundary pressure. The latter predict warmer giant branches (by ~150 K) at solar abundances than those based on gray or MARCS atmospheres, which happens to be in good agreement with the inferred temperatures of giants in the open cluster M67 from the latest (V-K)-T_eff relations. Most of the calculations assumed Z=0.0125 (Asplund et al.), though a few models were computed for Z=0.0165 (Grevesse & Sauval) to determine the dependence of the tracks on Z_\odot. Grids of "scaled solar, differentially corrected" (SDC) atmospheres were also computed to try to improve upon theoretical MARCS models. When they were used as boundary conditions, the resultant tracks agreed very well with those based on a standard scaled-solar (e.g., Krishna Swamy) T(tau,T_eff) relation, independently of the assumed metal abundance. Fits of isochrones to the C-M diagram of the [Fe/H] = -2 globular cluster M68 were examined, as was the possibility that the mixing-length parameter varies with stellar parameters.Comment: 54 pages, including 20 figures and 3 tables; accepted (July 2007) for publication in the Astrophysical Journa

Beyond the Fe-P-redox connection: preferential regeneration of phosphorus from organic matter as a key control on Baltic Sea nutrient cycles

Patterns of regeneration and burial of phosphorus (P) in the Baltic Sea are strongly dependent on redox conditions. Redox varies spatially along water depth gradients and temporally in response to the seasonal cycle and multidecadal hydrographic variability. Alongside the well-documented link between iron oxyhydroxide dissolution and release of P from Baltic Sea sediments, we show that preferential remineralization of P with respect to carbon (C) and nitrogen (N) during degradation of organic matter plays a key role in determining the surplus of bioavailable P in the water column. Preferential remineralization of P takes place both in the water column and upper sediments and its rate is shown to be redox-dependent, increasing as reducing conditions become more severe at greater water-depth in the deep basins. Existing Redfield-based biogeochemical models of the Baltic may therefore underestimate the imbalance between N and P availability for primary production, and hence the vulnerability of the Baltic to sustained eutrophication via the fixation of atmospheric N. However, burial of organic P is also shown to increase during multidecadal intervals of expanded hypoxia, due to higher net burial rates of organic matter around the margins of the deep basins. Such intervals may be characterized by basin-scale acceleration of all fluxes within the P cycle, including productivity, regeneration and burial, sustained by the relative accessibility of the water column P pool beneath a shallow halocline

The cryogenic system for the SLAC E158 experiment

E158 is a fixed target experiment at SLAC in which high energy (up to 48 GeV) polarized electrons are scattered off the unpolarized electrons in a 1.5 m long liquid hydrogen target. The total volume of liquid hydrogen in the system is 47.1. The beam can deposit as much as 700 W into the liquid hydrogen. Among the requirements for the system are: that density fluctuations in the liquid hydrogen be kept to a minimum, that the target can be moved out of the beam line while cold and replaced to within 2 mm and that the target survive lifetime radiation doses of up to 1×106 Gy. The cryogenic system for the experiment consists of the target itself, the cryostat containing the target, a refurbished CTI 4000 refrigerator providing more than 1 kW of cooling at 20 K and associated transfer lines and valve boxes. This paper discusses the requirements, design, construction, testing and operation of the cryogenic system. The unique features of the design associated with hydrogen safety and the high radiation field in which the target resides are also covered