Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-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 andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

TRANSFER OF EXCITATION ENERGY BETWEEN PORPHYRIN CENTERS OF A COVALENTLY-LINKED DIMER*

Abstract— Three covalently-linked porphyrin hybrid dimers were synthesized, each containing a metallotetraarylporphyrin [Zn(II), Cu(II), or Ni(II)], and a free base tetraarylporphyrin. Transfer of singlet excitation energy from the metalloporphyrin center to the free base porphyrin center was determined by measuring fluorescence properties. The Zn hybrid dimer displayed excellent intramolecular transfer of energy ( 85%) from the excited singlet state of the Zn(II) chromophore to the free base chromophore. No evidence for such transfer of the excited singlet state energy was found in the Ni(II) or Cu(II) analogues. From our experimental data, the fluorescence quantum yield of the Zn hybrid dimer was the same as for the free base monomer porphyrin (0.11; Seybold and Gouterman, 1969). Thus, the covalent attachment of another fluorescent porphyrin center effectively doubled the antenna size without decreasing the quantum yield even though the fluorescence quantum yield of the Zn(II) containing monomer was substantially less (0.03, according to Seybold and Gouterman, 1969) than that of the free base porphyrin. The donor-acceptor distance and the rate constant for energy transfer were calculated using the Forster equation. Assuming random orientation, a donor-acceptor distance of 15 Å was calculated with an associated rate constant (k_ci) for energy transfer of 1.9 ± 10₉ s_–1.     

Conjugates of Iron-Transporting N-Hydroxylactams with Ciprofloxacin

Screening of a library of novel N-hydroxylactams amenable by the Castagnoli-Cushman reaction identified four lead compounds that facilitated ⁵⁵Fe transport into P. aeruginosa cells (one of these synthetic siderophores was found to be as efficient at promoting iron uptake as the natural siderophores pyoverdine, pyochelin or enterobactin). Conjugates of the four lead siderophores with ciprofloxacin were tested for antibacterial activity against P. aeruginosa POA1 (wild type) and the ∆pvdF∆pchA mutant strain. The antibacterial activity was found to be pronounced against the ∆pvdF∆pchA mutant strain grown in CAA medium but not for the POA1 strain. This may be indicative of these compounds being ‘Trojan horse’ antibiotics. Further scrutiny of the mechanism of the antibacterial action of the newly developed conjugates is warranted.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Reactions of π-allyl with atomic oxygen and hydroxyl on Ag(110)

The oxidation of the adsorbed π-allyl (η³-C₃H₅), prepared on atomic oxygen- and hydroxyl-covered Ag(110) by dissociation of allyl chloride (C₃H₅Cl), is investigated with temperature-programmed desorption and high-resolution electron energy loss spectroscopy. Allyl chloride adsorbs molecularly on oxygen-covered Ag(110) at 110 K. Upon heating to 180 K, some allyl chloride dissociates to form π-allyl and atomic chlorine, and the remainder desorbs molecularly. The π-allyl undergoes combustion to form hydroxyl or carbonate until all of the free oxygen is consumed by 200 K. Migratory insertion of hydroxyl into excess π-allyl commences near 220 and finishes by 250 K, forming adsorbed allyl alcohol (C₃H₅OH), which reacts either with excess hydroxyl near 240 K to form allyl alkoxy (η¹(O)-C₃H₅O) and water, or with π-allyl at 250 K to form allyl alkoxy and propylene (C₃H₆). Th allyl alkoxy evolves acrolein (C₃H₄O) by β-hydrogen elimination near 285 K, and propylene is evolved concurrently as the hydrogen released by this reaction rapidly scavenges π-allyl. Finally, the remaining π-allyl dimerizes to form 1,5-hexadiene (C₆H₁₀), which desorbs at 315 K. The gross observations of reaction pathways and temperatures are used to evaluate important aspects of the thermochemistry of these reactions.     

Synchrotron X‐ray CT characterization of titanium parts fabricated by additive manufacturing. Part I. Morphology

Synchrotron X‐ray tomography has been applied to the study of titanium parts fabricated by additive manufacturing (AM). The AM method employed here was the Arcam EBM^® (electron beam melting) process which uses powdered titanium alloy, Ti64 (Ti alloy with approximately 6%Al and 4%V), as the feed and an electron beam for the sintering/welding. The experiment was conducted on the Imaging and Medical Beamline of the Australian Synchrotron. Samples were chosen to examine the effect of build direction and complexity of design on the surface morphology and final dimensions of the piece.     

Neutral-pion photoproduction off protons in the energy range 0.3 GeV<E(gamma)<3 GeV

Single pi(0) photoproduction has been studied with the CB-ELSA experiment at Bonn using tagged photon energies between 0.3 and 3.0 GeV. The experimental setup covers a very large solid angle of approximately 98% of 4pi. Differential cross sections dsigma/dOmega have been measured. Complicated structures in the angular distributions indicate a variety of different resonances being produced in the s channel intermediate state gammap-->N(*)(Delta(*))-->ppi(0). A combined analysis including the data presented in this letter along with other data sets reveals contributions from known resonances and evidence for a new resonance N(2070)D15.     

Validity of the law of mass action in three-dimensional coagulation processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long-wavelength fluctuations and is a universal function of the macroscopic decay rate.     

Polypropylene/Poly (Trimethylene Terephthalate)–Blend Fibers

Polypropylene (PP)/polyester (PES)–blend fibers were prepared by extruder melt spinning. The polymer blend consisted of PP and a “master batch” (MB) based on polytrimethylene terephthalate (PTT) or polyethylene terephthalate (PET), binary PTT/PET or PP/PTT blends, and also on a ternary PP/(PTT/PET) blend. The phase structure of PP/PES–blend fibers was examined. PES microfibers showed separation from the PP matrix in blend fibers. The impact of MB composition and rheological characteristics on phase structure parameters indicate a significant contribution of the PTT in the binary MB on the length of dispersed PES microfibers in the PP matrix. However, the blends of PP and ternary MB (PP/PTT/PET) have a lower diameter and length of the PES microfibers. The presence of PTT/PET (PES) enhances the structural and mechanical properties of the blend PP/PES fibers. In addition, PTT increases the tensile strength of the PP/PES–blend fibers if a binary MB is used, while the fiber nonuniformity is reduced in the presence of a ternary MB.     

Localization of weakly disordered flat band states

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths ξ that diverge with a variety of unconventional exponents ν, ξ ~ 1 /W ^ν .