Chebfun and numerical quadrature

Chebfun is a Matlab-based software system that overloads Matlab’s discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun’s fast capabilities for Clenshaw–Curtis and also Gauss–Legendre, –Jacobi, –Hermite, and –Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu, and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation

Conformal Maps to Multiply-Slit Domains and Applications

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [Tee and Trefethen, 2006] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to 'enlarge the region of analyticity' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such maps can be rapidly computed in both periodic and nonperiodic geometries, and apply them to some challenging differential equations

High-temperature Adhesive Development and Evaluation

High-temperature adhesive systems are evaluated for short and long-term stability at temperatures ranging from 232C to 427C. The resins selected for characterization include: NASA Langley developed polyphenylquinoxaline (PPQ), and commercially available polyimides (PI). The primary method of bond testing is single lap shear. The PPQ candidates are evaluated on 6A1-4V titanium adherends with chromic acid anodize and phosphate fluoride etch surface preparations. The remaining adhesives are evaluated on 15-5 PH stainless steel with a sulfuric acid anodize surface preparation. Preliminary data indicate that the PPQ adhesives tested have stability to 3000 hours at 450F with chromic acid anodize surface preparation. Additional studies are continuing to attempt to improve the PPQ's high-performance by formulating adhesive films with a boron filler and utilizing the phosphate fluoride surface preparation on titanium. Evaluation of the polyimide candidates on stainless-steel adherends indicates that the FM-35 (American Cyanamid), PMR-15 (U.S. Polymeric/Ferro), TRW partially fluorinated polyimide and NR 150B2S6X (DuPont) adhesives show sufficient promise to justify additional testing

Convection and heat transfer in layered sloping warm-water\ud aquifers

What convective flow is induced if a geologically-tratified groundwater aquifer is subject to a vertical temperature gradient? How strong is the flow? What is the nett heat transfer? Is the flow stable? How does the convection affect the subsequent species distribution if a pollutant finds its way into the aquifer? This paper begins to address such questions. Quantitative models for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures are formulated. The steady-state profiles are calculated for the temperature and for the fluid specific volume flux (Darcy velocity) parallel to the boundaries in a sloping system subjected to a perpendicular temperature gradient, at low Rayleigh numbers. The conducted and advected heat fluxes are compared and it is shown that the system acts somewhat like a heat pipe. The maximum possible ratio of naturally advected-to-conducted heat transfer is determined, together with the corresponding permeability and thermal conductivity profiles

Vesicular stomatitis virus glycoprotein is necessary for H-2-restricted lysis of infected cells by cytotoxic T lymphocytes

Vesicular stomatitis virus (VSV) elicited cytotoxic thymus-derived lymphocytes (CTLs) in mice of the BALB/c and three congenic strains (BALB.b, BALB.k, BALB.HTG). CTL lysis of VSV-infected fibroblasts from the four strains was restricted by the target cells' major histocompatibility complex (H-2). Target cells were also infected with two temperature-sensitive mutants of VSV, tsM and tsG in which, respectively, the viral matrix protein and glycoprotein are not expressed at 39 degrees (restrictive temperature) on the infected cell's surface membrane. At the restrictive temperature, cells infected with wild-type VSV or tsM were lysed by CTLs, but cells infected with tsG were not. The requirement for the glycoprotein on the target cell was also evident from the ability of antisera to the glycoprotein to block completely CTL lysis of VSV-infected cells

Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend, An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 2014, 36, A1207–A1220), to pricing European-type, early-exercise and discrete-monitored barrier options under a Lévy process. The paper employs Chebfun (cf. Trefethen et al., Chebfun Guide, 2014 (Pafnuty Publications: Oxford), Available online at: http://www.chebfun.org/) in computational finance and provides a quadrature-free approach by applying the Chebyshev series in financial modelling. A significant advantage of using the CONLeg method is to formulate option pricing and option Greek curves rather than individual prices/values. Moreover, the CONLeg method can yield high accuracy in option pricing when the risk-free smooth probability density function (PDF) is smooth/non-smooth. Finally, we show that our method can accurately price options deep in/out of the money and with very long/short maturities. Compared with existing techniques, the CONLeg method performs either favourably or comparably in numerical experiments

AN EMPIRICAL TEST OF THE MUTUALISM DISRUPTION HYPOTHESIS: IMPACTS OF AN ALLELOPATHIC INVADER ON THE ECOPHYSIOLOGY OF A NATIVE FOREST HERB

Understanding how biotic and abiotic contexts modify the strength of species interactions is a key goal in ecology. Mutualism effectiveness is particularly sensitive to environmental conditions, and the invasion of non-native species is hypothesized to be one biotic factor that can drive mutualism disruption between native species and their partners. Using an ecophysiological approach, I tested this mutualism disruption hypothesis using the allelopathic invasive plant, Alliaria petiolata, and examined its impacts on the mutualism between symbiotic arbuscular mycorrhizal fungi (AMF) and Maianthemum racemosum, a common native herb in North America. To establish the potential for mutualism disruption in this system, I measured field concentrations of A. petiolata’s allelochemicals and tested the toxicity of these levels on AMF spore germination in a bioassay. I found that field-detected levels of allyl isothiocyanate, a key component of A. petiolata’s allelochemical profile, reduced spore germination by over 50% relative to controls. Additionally, by assessing fungal abundance in the field, I found that sites invaded by A. petiolata generally have reduced fungal hyphal lengths compared to uninvaded sites. In a separate common garden study, I demonstrated that A. petiolata allelochemicals significantly reduced soil respiration rates around M. racemosum plants, indicating active disruption of AMF associated with the plant roots. To investigate the impacts of mutualism disruption by A. petiolata on M. racemosum, I used a combination of field and greenhouse studies. First, in a short, 2-week field study, I found that A. petiolata allelochemicals reduced physiological function and carbon acquisition in M. racemosum. Second, data from a season-long greenhouse study demonstrated that the physiological declines induced by A. petiolata allelochemicals were persistent and translated into reductions in allocation to key traits, including carbohydrate storage, root growth, and asexual reproduction. Together, these studies indicate that A. petiolata allelochemicals disrupted AMF function, resulting in water stress and altered source-sink dynamics for the native plant, and drove declines in both physiology and allocation to competing functions. Overall, my results suggest that allelopathic invasion is one critical, yet underexplored, biotic context that can dictate the outcome of plant-AMF mutualisms

Application of a Scaled Homogeneous Nucleation-Rate Formalism to Experimental Data at T≪T\u3csub\u3ec\u3c/sub\u3e

It is pointed out that for temperatures T\u3c0.5Tc, where Tc is the critical temperature, the classical steady-state nucleation-rate formalism of Becker and Doring predicts an approximate critical supersaturation ratio Scr (for the onset of nucleation) given by lnScr/Ω3/2~0.53(Tc/T-1)3/2. Ω is a material-dependent quantity approximately equal to the excess surface entropy per molecule. For most substances Ω ~ 2.0 and for associated liquids Ω ~ 1.5.The experimental data (for nucleation from vapor to liquid) from diffusion chamber and nozzle beam studies are found to be consistent with the above expression. The classical theory also predicts that for a supersaturation ratio S corresponding to constant J, lnS/lnScr-1 ~ lnJ/2lnJc, where lnJc is a quantity evaluated at the critical point and is ~ 72 for most materials. Expansion cloud-chamber data for nonane, toluene, and water are also found to be consistent with these approximate scaling laws