A Born scatterer in an acoustical waveguide

Scattering from a Born inhomogeneity in a homogeneous, acoustical waveguide is considered and results compared to the corresponding scattering in a homogeneous, unbounded medium. It is found that the Ewald sphere in the unbounded medium case is replaced by a Ewald "strip" in a waveguide, the strip consisting of many individual Ewald spheres embedded in a ball the radius of which is twice that of an individual sphere. The physics behind the Ewald strip is discussed along with the implications of waveguide Born data.     

Modelling self-ordering behaviour on Ag covered Pt vicinal surfaces

We use computer simulation to explore the formation process of a monolayer of Ag on a stepped Pt(111) substrate and the formation of 3D Pt nanostructures on an Ag covered (111) and (100) Pt substrate. We show that broken lines of Pt nanostructures are preferred at the step edges on the (111) substrate while continuous lines of Pt nanowires are preferred at the step edge on the (100) substrate. This different behaviour is due to the exposed front facet of the nanostructures running along the step, specifically for the (100) stepped substrate a nanowire grown on the step edge has a stable (111) exposed front facet, whereas a nanowire grown on the (111) substrate would have an unstable (100) front facet (depending on the direction of the step). For the Pt nanowires grown on the (100) substrate we show how arriving Pt dimers (and monomers) preferentially move up off the Ag substrate onto the nanowire's (111) facet where they undergo fast diffusion. We also show that these Pt dimers (and monomers) move up and down the nanowire's facet until a vacancy or defect is encountered.     

Efficient algorithms for three‐dimensional axial and planar random assignment problems

Beautiful formulas are known for the expected cost of random two‐dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural “Axial” and “Planar” versions, both of which are NP‐hard. For 3‐dimensional Axial random assignment instances of size n, the cost scales as Ω(1/ n), and a main result of the present paper is a linear‐time algorithm that, with high probability, finds a solution of cost O(n^–1+o(1)). For 3‐dimensional Planar assignment, the lower bound is Ω(n), and we give a new efficient matching‐based algorithm that with high probability returns a solution with cost O(n log n). © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 160–196, 2015     

The effect of hydrogen addition on flammability limit and NOx emission in ultra-lean counterflow CH4/air premixed flames

The effect of hydrogen addition to ultra lean counterflow CH₄/air premixed flames on the extinction limits and the characteristics of NO_x emission was investigated by numerical simulation. Detailed chemistry and complex thermal and transport properties were employed. The results show that the addition of hydrogen can significantly enlarge the flammable region and extend the flammability limit to lower equivalence ratios. If the equivalence ratio is kept constant, the addition of hydrogen increases the emission of NO in a flame due to the enhancement in the rate of the NNH or N₂O intermediate NO formation routes. The addition of hydrogen causes a monotonic decrease in the formation of NO₂ and N₂O, except flames near the extinction limits, where the emission of NO₂ and N₂O first increases, and then decreases with the increase in the fraction of hydrogen. Overall, hydrogen enrichment technology allows stable combustion under ultra lean conditions, resulting in significant CO₂ and NO emission reduction.     

A problem structuring method for ecosystem-based management: The DPSIR modelling process

The purpose of this paper is to learn from Complex Adaptive Systems (CAS) theory to inform the development of Problem Structuring Methods (PSMs) both in general and in the specific context of marine management. The focus on marine management is important because it is concerned with a CAS (formed through the interconnection between natural systems, designed systems and social systems) which exemplifies their particularly ‘wicked’ nature. Recognition of this compels us to take seriously the need to develop tools for knowledge elicitation and structuring which meet the demands of CAS. In marine management, chief among those tools is the DPSIR (Drivers – Pressures – State Changes – Impacts – Responses) model and, although widely applied, the extent to which it is appropriate for dealing with the demands of a CAS is questionable. Such questioning is particularly pertinent in the context of the marine environment where there is a need to not only recognise a broad range of stakeholders (a question of boundary critique) but also to manage competing knowledge (economic, local and scientific) and value claims. Hence this paper emphasises how a CAS perspective might add impetus to the development of a critical perspective on DPSIR and PSM theory and practice to promote a more systemic view of decision-making and policy development.     

Ends of iterated function systems

Guided by classical concepts, we define the notion of ends of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points are then linked to idempotent maps. A commutative diagram illustrates the natural relationships between the infinite walks in a semigroup and components of an attractor in more detail. We show in particular that, if an iterated function system is one-ended, the associated attractor is connected, and ask whether every connected attractor (fractal) conversely admits a one-ended system.     

Physical properties and processing conditions correlations of the ldpe/lldpe tubular blown films

Experiments are carried out to verify a theory developed to correlate the strain history of the polymer during film blowing to the ultimate physical properties of the film. The theory predicts that the amount of strain put into the film once it starts to freeze, defined as strain in the amorphous region and the plastic strain, has a dominant effect on the film properties. Two grades of low and linear low density polyethylene, experimental resins supplied by Mobil chemical company, were used to produce the blown film yielding a 1.25 mil film at the for all experimental runs. Film surface and bulk temperatures, along the machine direction and around the bubble, were measured using the infra-red techniques to identify the points where film starts to crystallize. A video digitization technique was used to measure the bubble kinematics. Film properties were measured using standard ASTM methods. The results indicate a correlation between the amount of strain and a measure of stress with ultimate physical properties of the blown film. This principle leads to the correlation of both the machine and transverse film properties on the same surface. The results obtained can potentially be exploited by designing the blown-film equipment and processing conditions such that optimal bubble stretching produces desired film properties.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

Novel copolymers of styrene. 3. Some ring-substituted propyl 2-cyano-3-phenyl-2-propenoates

Novel trisubstituted ethylenes, ring-substituted propyl 2-cyano-3-phenyl-2-propenoates, RPhCH?C(CN)CO₂C₃H₇ (where R is 2-C₆H₅CH₂O, 3-C₆H₅CH₂O, 4-C₆H₅CH₂O, 4-CH₃COO, 3-CH₃CO, 4-CH₃CONH, 2-CN, 3-CN, 4-CN, 4-(CH₃)₂N, 4-(C₂H₅)₂N) were prepared and copolymerized with styrene. The monomers were synthesized by the piperidine catalyzed Knoevenagel condensation of ring-substituted benzaldehydes and propyl cyanoacetate, and characterized by CHN analysis, IR, ¹H and ¹³C-NMR. All the ethylenes were copolymerized with styrene (M₁) in solution with radical initiation (ABCN) at 70°C. The compositions of the copolymers were calculated from nitrogen analysis and the structures were analyzed by IR, ¹H and ¹³C-NMR. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200–500°C range with residue (2.7–8.6% wt.), which then decomposed in the 500–800°C range.