Gamma peak search and peak fitting algorithm for a low-resolution detector with applications in gamma spectroscopy

A Savitzky–Golay filtering for smoothing and peak search written in Python is presented in this paper alongside its applications in the list-mode digital data acquisition dual gamma–gamma coincidence bismuth germanate (BGO) detector. The study has demonstrated that the software provides a reliable and effective way to quantify trace amounts of ²²Na and ⁷Be in aerosol samples collected at Resolute Bay, Canada with a critical limit of 3 mBq and 5 Bq respectively for a 20 h counting interval, which are believed to be the inherent limitations of the dual-BGO system.

     

Controlling effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts

The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non‐microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials‐of‐mean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption‐strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer‐like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks. The influence of a positive chi‐parameter in the pure copolymer melt is briefly studied. Quantitative application to fullerenes in specific copolymers of experimental interest is performed, and miscibility predictions are made. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1098–1111     

Structural verification of a tetrahydrotetrazole compound

Tetrahydrotetrazoles are five‐membered‐ring heterocycles containing four contiguous saturated nitrogen atoms. Very few examples of such compounds have been reported in the literature. Our previous attempt at the synthesis of a member of this class of compound suggested that the N—N bonds may be more labile than expected. This finding raised the question as to whether the structures of any of the previously reported tetrahydrotetrazoles had been properly assigned. We have reproduced the synthesis of a reported tetrahydrotetrazole, namely 1,2‐di‐tert‐butyl 3‐phenyl‐1H,2H,3H,10bH‐[1,2,3,4]tetrazolo[5,1‐a]isoquinoline‐1,2‐dicarboxylate, C₂₅H₃₀N₄O₄, and have now confidently confirmed its structure via X‐ray crystallography. However, while sufficiently stable in the crystal phase, we discovered that it remains very labile in solution (having a half‐life of only 15 min at 20 °C in CDCl₃). A tentative reaction pathway for its dissociation based on ¹H NMR spectral evidence is provided.     

Water-induced formation of an alkali-ion dimer in cryptomelane nanorods

Tunneled metal oxides such as α-Mn₈O₁₆ (hollandite) have proven to be compelling candidates for charge-storage materials in high-density batteries. In particular, the tunnels can support one-dimensional chains of K⁺ ions (which act as structure-stabilizing dopants) and H₂O molecules, as these chains are favored by strong H-bonds and electrostatic interactions. In this work, we examine the role of water molecules in enhancing the stability of K⁺-doped α-Mn₈O₁₆ (cryptomelane). The combined experimental and theoretical analyses show that for high enough concentrations of water and tunnel-ions, H₂O displaces K⁺ ions from their natural binding sites. This displacement becomes energetically favorable due to the formation of K²⁺ dimers, thereby modifying the stoichiometric charge of the system. These findings have potentially significant technological implications for the consideration of cryptomelane as a Li⁺/Na⁺ battery electrode. Our work establishes the functional role of water in altering the energetics and structural properties of cryptomelane, an observation that has frequently been overlooked in previous studies.

Water displaces potassium ions and initiates the formation of a homonuclear dimer ion (K²⁺) in the tunnels of hollandite.     

Every diassociative A-loop is Moufang

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.

     

Adhesive bonding of glassy polymer surfaces by an ultrathin layer of a semicrystalline polymer

To develop a greater understanding of interfacial interactions between a semicrystalline polymer and a glassy polymer, adhesion tests were performed on very thin layers of poly(ethylene oxide) (PEO) sandwiched between two layers of poly(tetramethyl bisphenol A polycarbonate) (TMPC). The tests were designed to provide intimate contact between the surfaces while they were heated above the melting point of the PEO and cooled back to room temperature. A contact mechanics approach, based on the Johnson, Kendall, and Roberts theory, was used to determine values of the energy release rate describing the energetic driving force for crack propagation within the interfacial region. The ability to measure crack propagation at large values of the energy release rate was limited by rupture of the silicone elastomer that was used to provide a sufficiently compliant matrix for the adhesion experiment. By cycling the tensile stress at relatively low loading levels, we were able to measure fatigue crack propagation at values of the energy release rate that did not result in failure of the elastomer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3809–3821, 2004     

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

An Average-Stretch Full-Network Model for Rubber Elasticity

Two constitutive models that are based on the classical non-Gaussian, Kuhn-Grün probability distribution function are reviewed. It is shown that all chains of a network cell structure comprised of a finite number of identical chains in an affine deformation referred to principal axes may have the same invariant stretch, if and only if the chains are oriented initially along any of eight directions forming the diagonals of a unit cube. The 4-chain tetrahedral and the 8-chain cubic cell structures are familiar admissible models having this property. An easy derivation of the constitutive equation for the Wu and van der Giessen full-network model of initially identical chains arbitrarily oriented in the undeformed state is presented. The constitutive equations for the neo-Hookean model, the 3 -chain model, and the equivalent 4- and 8-chain models are then derived from the Wu and van der Giessen equation. The squared chain stretch of an arbitrarily directed chain averaged over a unit sphere surrounding all chains radiating from a cross-link junction as its center is determined. An average-stretch, full-network constitutive equation is then derived by approximation of the Wu and van der Giessen equation. This result, though more general in that no special chain cell morphology is introduced, is the same as the constitutive equation for the 4- and 8-chain models. Some concluding remarks on extensions to amended models are presented.