Covariant Spectator Theory: Foundations and Applications

We provide a short overview of the covariant spectator theory and its applications. The basic ideas are introduced through the example of a ${\phi^4}$ -type theory. High-precision models of the two-nucleon interaction are presented and the results of their use in calculations of properties of the two- and three-nucleon systems are discussed. A short summary of applications of this framework to other few-body systems is also presented.     

Eigenvalue problem for arbitrary linear combinations of a boson annihilation and creation operator

The eigenvalue problem for arbitrary linear combinations kα + μα^? of a boson annihilation operator α and a boson creation operator α^? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α^? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α^? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter.     

Aerosol Catalysis on Nickel Nanoparticles

Nickel nanoparticles produced by spark discharges were used as aerosol catalyst for the formation of methane. The available surface area of the particles was determined using different methods. It was found that the surface area available for nitrogen adsorption and, therefore, for the methanation reaction remained virtually constant during restructuring of the agglomerates while the surface area based on the mobility was significantly reduced. In general, the reaction parameters such as activation energy and reaction rates agree well with the values for single nickel crystals and foils. At temperatures above 350°C the activation energy and the photoelectric activity of the particles decrease indicating the formation of graphite on the particle surface. Also the change of the work function points to the build up of multiple layers of graphite on the particle surface. The surprisingly low temperature for the surface deactivation may indicate an enhanced formation of carbon atoms at the surface.     

Controlled evaporative self-assembly of polymer nanoribbons using oscillating capillary bridges

Evaporative self-assembly (ESA), based on the “coffee-ring” effect, is a versatile technique for assembling particle solutions into mesoscale patterns and structures on different substrates. ESA works with a wide variety of organic and inorganic materials, where the solution is a combination of volatile solvent and nonvolatile solute. Modified ESA methods, such as “stop-and-go flow coating,” use a programmed meniscus “stick–slip” motion to create mesoscale assemblies with controlled shape, size, and architecture. However, current methods are not scalable for increased production volumes or patterning large surface areas. We demonstrate a new ESA method, where an oscillating blade controls the meniscus depinning and drives the evaporative assembly of solutes at the pinned meniscus. Results show that oscillation frequency and substrate speed control time/distance intervals between successive meniscus depinning, and the assembly dimensions depend on solution concentration, oscillation frequency, substrate speed, and meniscus height. We report the mechanism of the meniscus depinning and the control over assembly cross-sectional dimensions. This advance provides a scalable ESA method with faster processing times and maintained advantages. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1545–1551     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Kodaira dimension of irregular varieties

Let f:X→Y be an algebraic fiber space with general fiber F. If Y is of maximal Albanese dimension, we show that κ(X)≥κ(Y)+κ(F).     

Solving the post enrolment course timetabling problem by ant colony optimization

In this work we present a new approach to tackle the problem of Post Enrolment Course Timetabling as specified for the International Timetabling Competition 2007 (ITC2007), competition track 2. The heuristic procedure is based on Ant Colony Optimization (ACO) where artificial ants successively construct solutions based on pheromones (stigmergy) and local information. The key feature of our algorithm is the use of two distinct but simplified pheromone matrices in order to improve convergence but still provide enough flexibility for effectively guiding the solution construction process. We show that by parallelizing the algorithm we can improve the solution quality significantly. We applied our algorithm to the instances used for the ITC2007. The results document that our approach is among the leading algorithms for this problem; in all cases the optimal solution could be found. Furthermore we discuss the characteristics of the instances where the algorithm performs especially well.     

An integral equation arising in a convective heat (mass) transfer problem through a boundary layer

A problem of Lighthill and Levich, where convective heat (mass) transfer occurs through a boundary layer, is considered. This gives rise to a certain integral equation. The unique L₂ solution of a generalized version of this integral equation is obtained providing the solution, in closed form, of the original problem.