Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff. We show that the Brunet-Derrida formula corresponds to the leading order expansion in the cut-off parameter of both the upper and lower bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula lies outside the allowed band determined from the bounds. If nonlinearities are neglected the upper and lower bounds coincide and are the exact linear speed for all values of the cut-off parameter.Comment: 8 pages, 3 figure

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

Novel metalloporphyrin catalysts for the oxidation of hydrocarbons

Work was done for developing biomimetic oxidation catalysts. Two classes of metalloporphyrin catalysts were studied. The first class of catalysts studied were a novel series of highly substituted metalloporphyrins, the fluorinated iron dodecaphenylporphyrins. These homogeneous metalloporphyrin catalysts were screened for activity as catalysts in the oxidation of hydrocarbons by dioxygen. Results are discussed with respect to catalyst structural features. The second type of catalysts studied were heterogeneous catalysts consisting of metalloporphyrins applied to inorganic supports. Preliminary catalytic testing results with these materials are presented

On Determining Dead Layer and Detector Thicknesses for a Position-Sensitive Silicon Detector

In this work, two particular properties of the position-sensitive, thick silicon detectors (known as the "E" detectors) in the High Resolution Array (HiRA) are investigated: the thickness of the dead layer on the front of the detector, and the overall thickness of the detector itself. The dead layer thickness for each E detector in HiRA is extracted using a measurement of alpha particles emitted from a $^{212}$Pb pin source placed close to the detector surface. This procedure also allows for energy calibrations of the E detectors, which are otherwise inaccessible for alpha source calibration as each one is sandwiched between two other detectors. The E detector thickness is obtained from a combination of elastically scattered protons and an energy-loss calculation method. Results from these analyses agree with values provided by the manufacturer.Comment: Accepted for publication in Nuclear Instruments and Methods in Physics Researc

IGRT After Prostatectomy: Evaluation of Corrective Shifts and Toxicity Using Online Cone Beam CT vs. Weekly Port Films for Target Localization

Purpose/Objective(s): Image guidance (IG) may permit higher radiotherapy (RT) doses (\u3e65 Gy) after radical prostatectomy (RP) without increased toxicity, with improved accuracy and smaller margins. Conebeam (CBCT) allows IGRT with volumetric images. This study evaluated CBCT shifts and toxicity after conformal IGRT, compared to RT with port films. American Society for Therapeutic Radiation Oncology (ASTRO) 52nd Annual Meeting October 31 - November 4, San Diego, C

Identifying metabolites by integrating metabolome databases with mass spectrometry cheminformatics.

Novel metabolites distinct from canonical pathways can be identified through the integration of three cheminformatics tools: BinVestigate, which queries the BinBase gas chromatography-mass spectrometry (GC-MS) metabolome database to match unknowns with biological metadata across over 110,000 samples; MS-DIAL 2.0, a software tool for chromatographic deconvolution of high-resolution GC-MS or liquid chromatography-mass spectrometry (LC-MS); and MS-FINDER 2.0, a structure-elucidation program that uses a combination of 14 metabolome databases in addition to an enzyme promiscuity library. We showcase our workflow by annotating N-methyl-uridine monophosphate (UMP), lysomonogalactosyl-monopalmitin, N-methylalanine, and two propofol derivatives

The Speed of Fronts of the Reaction Diffusion Equation

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.Comment: 7 pages Revtex, 1 figure not include