Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data

We consider the one-dimensional focusing nonlinear Schr\"odinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a B\"acklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski

Comparison of coal liquefaction processes. Final report on Task 006

Five processes were studied to determine which could give best results for supplying hydrocarbon fuels to replace petroleum products. The processes were Fischer-Tropsch; M-Gasoline; H-Coal; Exxon Donor Solvent; and Solvent Refined Coal. The conclusions of the study are that all of the processes are considered commercially feasible and, because the different products from the different processes will meet different market demands, any significant future liquids from coal market will probably use some of each of these processes. The anticipated conversion efficiency values are given to indicate resource utilization. Simplified capital costs are approximated for each process. These are used in combination with product amounts and relative values to achieve a cost ranking. Because the study was concerned solely with liquid products, Fischer-Tropsch was at a disadvantage. The remaining four were relatively close and a final decision would depend upon the actual end use requirements. For a situation with residual fuels selling at severe discounts, M-Gasoline and H-Coal (Syncrude Mode) were the better choices

A service evaluation of FIT and anaemia for risk stratification in the two week wait pathway for colorectal cancer

Introduction: New national guidance on urgent referral for investigation for Colorectal Cancer (CRC) included faecal occult blood testing in 2015. We evaluated faecal immunochemical testing (FIT) and anaemia as risk stratification tools in symptomatic patients suspected of having CRC.Methods: Postal FIT was incorporated into the CRC two week wait (2WW) pathway for all patients without rectal bleeding in 2016. Patients were investigated in the 2WW pathway as normal and outcomes of investigations were prospectively recorded. Anaemia was defined as haemoglobin less than 120g/L in women and less than 130g/L in men.Results: FIT kits were sent to 1106 patients with an 80.9% return rate; 810 patients completed investigation with 40 CRCs diagnosed (4.9%). Median FIT results were significantly higher in patients who were anaemic (median 4.8 iqr 0.8-34.1 versus 1.2 iqr 0-6.4, Mann-Whitney p less than 0.001).Some 538 (60.4%) had a result of less than 4 µgHb/gFaeces (limit of detectability) and 621 (69.7%) a result less than 10 µgHb/gFaeces. Sixty per cent of CRCs had a FIT reading of >150 µgHb/gFaeces. Five CRCs diagnosed in patients with a FIT4 µgHb/gFaeces had 97.5% sensitivity and 64.5% specificity for CRC diagnosis. A FIT result of >4 µgHb/gFaeces and/or anaemia had a 100% sensitivity and 45.3% specificity for CRC diagnosis.Conclusion: FIT is most useful at the extremes of detectability; strongly positive readings predict high rates of CRC and other significant pathology, whilst very low readings in the absence of anaemia or palpable rectal mass identify a group with very low risk. High return rates for FIT within this 2WW pathway indicate its acceptability

The Two-Communities Theory and Knowledge Utilization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66698/2/10.1177_000276427902200308.pd

Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

1/f Noise in Electron Glasses

We show that 1/f noise is produced in a 3D electron glass by charge fluctuations due to electrons hopping between isolated sites and a percolating network at low temperatures. The low frequency noise spectrum goes as \omega^{-\alpha} with \alpha slightly larger than 1. This result together with the temperature dependence of \alpha and the noise amplitude are in good agreement with the recent experiments. These results hold true both with a flat, noninteracting density of states and with a density of states that includes Coulomb interactions. In the latter case, the density of states has a Coulomb gap that fills in with increasing temperature. For a large Coulomb gap width, this density of states gives a dc conductivity with a hopping exponent of approximately 0.75 which has been observed in recent experiments. For a small Coulomb gap width, the hopping exponent approximately 0.5.Comment: 8 pages, Latex, 6 encapsulated postscript figures, to be published in Phys. Rev.

Flux noise in high-temperature superconductors

Spontaneously created vortex-antivortex pairs are the predominant source of flux noise in high-temperature superconductors. In principle, flux noise measurements allow to check theoretical predictions for both the distribution of vortex-pair sizes and for the vortex diffusivity. In this paper the flux-noise power spectrum is calculated for the highly anisotropic high-temperature superconductor Bi-2212, both for bulk crystals and for ultra-thin films. The spectrum is basically given by the Fourier transform of the temporal magnetic-field correlation function. We start from a Berezinskii-Kosterlitz-Thouless type theory and incorporate vortex diffusion, intra-pair vortex interaction, and annihilation of pairs by means of a Fokker-Planck equation to determine the noise spectrum below and above the superconducting transition temperature. We find white noise at low frequencies omega and a spectrum proportional to 1/omega^(3/2) at high frequencies. The cross-over frequency between these regimes strongly depends on temperature. The results are compared with earlier results of computer simulations.Comment: 9 pages, 4 PostScript figures, to be published in Phys. Rev.

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.Comment: 56 pages, RevTeX, 20 Figure