On the heat equation and the spectrum of the Dirichlet Laplacian for spiral regions in R^2

We determine the asymptotic behaviour of trace (e^(tΔ_S)) as t ↓ 0 where Δ_S is the Dirichlet Laplacian for a class of spiral regions in R^2

AL-SIC INTERFACE STRUCTURE STUDIED BY HREM

A comparison is made between the two well-known aluminium alloys 2014 and 6061, cold pressed from powder and subsequently extruded, with and without a reinforcement of 30 wt% alpha-SiC particulates. The former one has a strength of 550 MPa and a strain at fracture of 1% while the latter one has a more moderate strength of 415 MPa but a fracture strain of 4%. A high resolution electron microscopy study of the Al SiC interface indicates that proper wetting is achieved in both alloys. A preferred orientation relationship is observed in the 6061 SiC combination: (0001)SiC//{111}Al; [2110BARBAR]SiC//[110]Al. When the (0001)SiC is not parallel to the interface, a stepped interface is observed with the 6061 alloy, with one part of the step parallel to the SiC basal plane and one type of the Al octahedral planes and the other part parallel to another type of Al octahedral planes. In the 2014 alloy the steps seem to be less pronounced probably due the processing route

On the λ-Singularity in the Specific Heat of a Free Boson Gas in a Gravitational Field

We show that the specific latent heat per particle (at a constant volume) of a free boson gas in a weak gravitational field has a λ-type singularity. The magnitude of the jump is proportional to the square root of the field strength for small fields

METAL-CERAMIC INTERFACES PRODUCED BY LASER MELT INJECTION PROCESSING

This paper concentrates on the mechanical performance of various ceramic coatings of Cr2O3 on steel (SAF2205), as produced by CO2 laser processing. It is concluded that a firmly bonded coating of Cr2O3 on steel could be produced by high power laser processing. The actual interface strength of a (Fe,Cr)-spinel applied to stainless steel by laser coating depends strongly on the composition of the substrate and coating materials. The energy release rate was extremely high and delamination occurred by fracture through the coating and partially along the interface, indicating that the interface strength is similar to or higher than the fracture strength of (Fe,Cr)-spinel

Linking Categorical and Dimensional Approaches to Assess Food-Related Emotions

Reflecting the two main prevailing and opposing views on the nature of emotions, emotional responses to food and beverages are typically measured using either (a) a categorical (lexicon-based) approach where users select or rate the terms that best express their food-related feelings or (b) a dimensional approach where they rate perceived food items along the dimensions of valence and arousal. Relating these two approaches is problematic since a response in terms of valence and arousal is not easily expressed in terms of emotions (like happy or disgusted). In this study, we linked the dimensional approach to a categorical approach by establishing mapping between a set of 25 emotion terms (EsSense25) and the valence–arousal space (via the EmojiGrid graphical response tool), using a set of 20 food images. In two ‘matching’ tasks, the participants first imagined how the food shown in a given image would make them feel and then reported either the emotional terms or the combination of valence and arousal that best described their feelings. In two labeling tasks, the participants first imagined experiencing a given emotion term and then they selected either the foods (images) that appeared capable to elicit that feeling or reported the combination of valence and arousal that best reflected that feeling. By combining (1) the mapping between the emotion terms and the food images with (2) the mapping of the food images to the valence–arousal space, we established (3) an indirect (via the images) mapping of the emotion terms to the valence–arousal space. The results show that the mapping between terms and images was reliable and that the linkages have straightforward and meaningful interpretations. The valence and arousal values that were assigned to the emotion terms through indirect mapping to the valence–arousal space were typically less extreme than those that were assigned through direct mapping