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

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

ANALYSIS OF THE ROLE OF TWO AUTOPHAGY PATHWAY RELATED GENES, BECN1 AND TSC1, IN MURINE MAMMARY GLAND DEVELOPMENT AND DIFFERENTIATION

The mammary gland is a dynamic organ that undergoes the majority of its development in the postnatal period in four stages; mature virgin, pregnancy, lactation, and involution. Every stage relies on tightly regulated cellular proliferation, programmed cell death, and tissue remodeling mechanisms. Misregulation of autophagy, an intracellular catabolic process to maintain energy stores, has long been associated with mammary tumorigenesis and other pathologies. We hypothesize that appropriate regulation and execution of autophagy are necessary for proper development of the mammary ductal tree and maintenance of the secretory epithelia during late pregnancy and lactation. To test this hypothesis we examined the role of two genes during development of the mammary gland. Beclin1 (Becn1) is an essential autophagy gene. Since the Becn1 knockout model is embryonic lethal, we have generated a Becn1 conditional knockout (cKO). We used two discrete mammary gland-specific Cre transgenic lines to interrogate the role of BECN1 during development. We report that MMTV-CreD; Becn1fl/fl mice have a hyper-branching phenotype and WAP-Cre; Becn1fl/- mice are unable to sustain a lactation phase. Becn1 mutants exhibit abnormal glandular morphology during pregnancy and after parturition. Moreover, when autophagy is chemically inhibited in vitro, mammary epithelial cells have an increased mean number of lipid droplets per cell. MTOR inhibits autophagy upstream of BECN1; we looked higher in the regulatory pathway for regulatory candidates. It has been well characterized that Tuberous sclerosis complex 1 (TSC1), in a heterodimer with its primary binding partner TSC2, inhibits MTOR signaling via inhibition of RHEB. Using the Tsc1 floxed model we generated a mammary gland specific Tsc1 cKO and found that these mice phenocopy the Becn1 cKO mice, including a gross lactation failure. Tsc1 cKO glands have altered morphology, retained lipid droplets in secretory epithelia, and an overall increase in MTOR signaling. We show that TSC1 and BECN1 are interacting partners, and that the interaction is nutrient responsive. These results suggest that Becn1 and Tsc1 are necessary for proper mammary gland development and differentiation. Furthermore, we have demonstrated a novel murine protein-protein interaction and an important link between regulation of MTOR pathway and regulation of autophagy in a developmental context

Evaluation of high temperature structural adhesives for extended service, phase 4

The evaluation of three phenylquinoxaline polymers as high temperature structural adhesives is presented. These included an experimental crisskubjabke oiktner (X-PQ) and two experimental materials (PPQ-2501) and (PPQ-HC). Lap shear, crack extension, and climing drum peel specimens were fabricated from all three polymers, and tested after thermal, combined thermal/humidity, and stressed Skydrol exposure. All three polymers generally performed well as adhesives at initial test temperatures from 219K (-67 F) to 505K (450 F) and after humidity exposure. The 644K (700 F) cured test specimens exhibited superior Skydrol resistance and thermal stability at 505K (450 F) when compared to the 602K (625 F) cured test specimens

Temperature Dependence of Homogeneous Nucleation Rates for Water: Near Equivalence of the Empirical Fit of Wölk and Strey, and the Scaled Nucleation Model

It is pointed out that the temperature fitting function of Wölk and Strey [J. Phys. Chem. 105, 11683 (2001)], recently shown to convert the Becker-Döring [Ann. Phys. (Leipzig) 24, 719 (1935)] nucleation rate into an expression in agreement with much of the experimental water nucleation rate data, also converts the Becker-Döring rate into a form nearly equivalent with the scaled nucleation rate model, Jscaled=Joc exp[-16πΩ3(Tc/T-1)3/3(ln S)2]. In the latter expression Joc is the inverse thermal wavelength cubed/sec, evaluated at Tc

Conflict of Laws -- Constitutionality of State Statutes Governing Ability of Nonresident Aliens to Receive Property Under American Wills: Zschernig v. Miller

An excellent illustration of the vertical conflict of laws problem involves the ability of nonresident aliens to receive property under American wills. Traditionally, under the American federal system,the acquisition and transmission of property located within a state has been controlled by state law. Yet article I, section 10 of the United States Constitution imposes strict limitations on a state\u27s power to deal with matters having a bearing on international relations, such matters being within the ambit of the national government. The supremacy of the national government in the general field of foreign affairs has been given continuous recognition by the United States Supreme Court.\u27 The issue, then, is whether a state statute governing the capacity of a non-resident alien to inherit property under an American will is unconstitutional as an intrusion by the state into the area of foreign affairs