Dimensional change of wool fabrics in the process of a tumble-drying cycle

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Currently domestic tumble dryers are popularly used for drying garments; however, excessive drying and the inappropriate way of tumble agitation could waste energy and cause damage to or the dimensional change of garments. Shrinkage of wool fabrics during tumble drying causes a serious problem for wool garments. The current study investigated the shrinkage of untreated and Chlorine-Hercosett–finished wool fabrics at different drying times. Temperature of air in the tumble dryer, temperature of fabric, moisture content of fabric, and dimensional change at different drying times were measured. For the duration of the tumble drying, the rise of fabric temperature and the reduction of moisture content on the wool fabric were investigated to explore their relationship to the shrinkage of wool fabrics in the tumble-drying cycle. It was found that the tumble-drying process can be divided into different stages according to the temperature change trend of wool fabrics. The shrinkage mechanisms of the untreated and the treated fabrics were different. The dimensional change of untreated wool fabric was caused mainly by felting shrinkage during tumble drying. Chlorine-Hercosett–finished wool fabric can withstand the tumble-drying process without noticeable felting shrinkage due to the surface modification and resin coating of surface scales of wool fibers. The finding from the current research provides further understanding of the shrinkage behavior of wool fabrics during the tumble-drying process, leading to optimizing operational parameters at specific stages of a tumble-drying cycle

M5-branes and Wilson Surfaces

We investigate the M5-brane description of the Wilson surface operators in six-dimensional (2,0) superconformal field theory from AdS/CFT correspondence. We consider the Wilson surface operators in high-dimensional representation, whose description could be M5-brane string soliton solutions in $AdS_7\times S^4$ background. We construct such string soliton solutions from the covariant M5-brane equations of motion and discuss their properties. The supersymmetry analysis shows that these solutions are half-BPS. We also discuss the subtle issue on the boundary terms.Comment: 30 pages, Latex; little revision;Typos corrected, references added, JHEP published versio

Hausdorff dimension of certain sets arising in continued fraction expansions

AbstractThis paper is concerned with the fractional dimensions of some sets of points with their partial quotients obeying some restrictions in their continued fraction expansions. The Hausdorff dimension of the following set, which shares a dichotomy law according to Borel–Bernstein's theorem, is completely determinedE(ϕ)={x∈[0,1):an(x)⩾ϕ(n), i.o. n}. Our result significantly strengthens the results of Good and Lúczak

On the fast Khintchine spectrum in continued fractions

For $x\in [0,1)$, let $x=[a_1(x), a_2(x),...]$ be its continued fraction expansion with partial quotients ${a_n(x), n\ge 1}$. Let $\psi : \mathbb{N} \rightarrow \mathbb{N}$ be a function with $\psi(n)/n\to \infty$ as $n\to \infty$. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set E(\psi):=\Big{x\in [0,1): \lim_{n\to\infty}\frac{1}{\psi(n)}\sum_{j=1}^n\log a_j(x)=1\Big} is completely determined without any extra condition on $\psi$.Comment: 10 page