Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

We derive an orthotropic model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data

On the complex singularities of the inverse Langevin function

We study the inverse Langevin function $\mathscr{L}^{-1}(x)$ because of its importance in modelling limited-stretch elasticity where the stress and strain energy become infinite as a certain maximum strain is approached, modelled here by $x\to1$. The only real singularities of the inverse Langevin function $\mathscr{L}^{-1}(x)$ are two simple poles at $x=\pm1$ and we see how to remove their effects either multiplicatively or additively. In addition, we find that $\mathscr{L}^{-1}(x)$ has an infinity of complex singularities. Examination of the Taylor series about the origin of $\mathscr{L}^{-1}(x)$ shows that the four complex singularities nearest the origin are equidistant from the origin and have the same strength; we develop a new algorithm for finding these four complex singularities. Graphical illustration seems to point to these complex singularities being of a square root nature. An exact analysis then proves these are square root branch points.Comment: 25 pages, 10 figures, 4 tables, 50 equations, 28 reference

Erratum to: Determination of the Blockage Effect on a Thermal Anemometer using a Small Open Jet Wind Tunnel

Due to problems that have occurred during the conversion of the article into PDF format, and the resulting loss of many special characters, a new correct version of the article is published below. When an object, specifically an anemometer, is presented before a wind tunnel the flow field will be altered deflecting the flow around the anemometer creating what is commonly known as the Blockage Effect. Directly comparing a thermal anemometer with a vane anemometer in the same flow field, the velocity measured by the thermal anemometer may be significantly different to that measured by the vane anemometer as a result of blockage. In this paper we consider the blockage created by a thermal anemometer. A simple mathematical model is derived to directly compare the thermal anemometer with a primary standard vane anemometer. The calibration results obtained are compared with those obtained by the manufacturer and an ISO/IEC 17025 accredited laboratory chosen as the Reference Laboratory for the purposes of the paper. We conclude with an analysis of the results, discussing the differences in the measured output and postulating how these results may be unified

Rare copy number variations in adults with tetralogy of Fallot implicate novel risk gene pathways.

Structural genetic changes, especially copy number variants (CNVs), represent a major source of genetic variation contributing to human disease. Tetralogy of Fallot (TOF) is the most common form of cyanotic congenital heart disease, but to date little is known about the role of CNVs in the etiology of TOF. Using high-resolution genome-wide microarrays and stringent calling methods, we investigated rare CNVs in a prospectively recruited cohort of 433 unrelated adults with TOF and/or pulmonary atresia at a single centre. We excluded those with recognized syndromes, including 22q11.2 deletion syndrome. We identified candidate genes for TOF based on converging evidence between rare CNVs that overlapped the same gene in unrelated individuals and from pathway analyses comparing rare CNVs in TOF cases to those in epidemiologic controls. Even after excluding the 53 (10.7%) subjects with 22q11.2 deletions, we found that adults with TOF had a greater burden of large rare genic CNVs compared to controls (8.82% vs. 4.33%, p = 0.0117). Six loci showed evidence for recurrence in TOF or related congenital heart disease, including typical 1q21.1 duplications in four (1.18%) of 340 Caucasian probands. The rare CNVs implicated novel candidate genes of interest for TOF, including PLXNA2, a gene involved in semaphorin signaling. Independent pathway analyses highlighted developmental processes as potential contributors to the pathogenesis of TOF. These results indicate that individually rare CNVs are collectively significant contributors to the genetic burden of TOF. Further, the data provide new evidence for dosage sensitive genes in PLXNA2-semaphorin signaling and related developmental processes in human cardiovascular development, consistent with previous animal models

Rare CNV burden in 340 unrelated adults with tetralogy of Fallot and/or pulmonary atresia.

a<p>Rare autosomal CNVs>10 kb and <6.5 Mb in size in individuals of European ancestry. Inclusion of three subjects with anomalies >6.5 Mb in a secondary analysis did not change the overall results (data not shown). Note that the above results also do not include 49 subjects of European ancestry with typical 1.5 to 3 Mb 22q11.2 deletions in the TOF group (all syndromic); see text for details on the results if these subjects had been included.</p>b<p>Fisher's exact test.</p

Rare large CNVs (>500 kb) in 43 of 433 unrelated adults with tetralogy of Fallot.

<p>Case, subjects from discovery sample (n = 433) with TOF; Locus, cytogenetic location of CNV; CNV start, hg18 (NCBI Build 36.1, March 2006); CNV size, in base pairs; CN, type of copy number aberration; Very rare, not found in 2,773 controls (•), see text for details; Confirmed, by qPCR and/or FISH (•) or not done (ND); Origin, <i>de novo</i> or inherited (where known); # of genes, number of known genes overlapped by a CNV as annotated in the Database of Genomic Variants (<a href="http://projects.tcag.ca/variation/" target="_blank">http://projects.tcag.ca/variation/</a>; September 2011); Candidate gene(s), selected based on reported cardiovascular system involvement; References derived from systematic searches of human (e.g., Online Mendelian Inheritance in Man; <a href="http://www.omim.org/" target="_blank">http://www.omim.org/</a>) and model organism (e.g., Mouse Genome Informatics; <a href="http://www.informatics.jax.org/" target="_blank">http://www.informatics.jax.org/</a>) databases presented in Table 4 in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen.1002843.s001" target="_blank">Supporting Information S1</a>.</p>a<p><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen-1002843-g002" target="_blank">Figure 2</a> in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen.1002843.s001" target="_blank">Supporting Information S1</a>.</p>b<p><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen-1002843-t003" target="_blank">Table 3</a>.</p>c<p>Neighbor of a top disease gene (GATA4, NKX2-5, TBX5), as identified in the pathway analysis (Table 11 in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen.1002843.s001" target="_blank">Supporting Information S1</a>).</p>d<p>Non-European ancestry.</p>f<p>Previously reported by our group <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen.1002843-Costain1" target="_blank">[21]</a>.</p>g<p>Figure 3 in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002843#pgen.1002843.s001" target="_blank">Supporting Information S1</a>.</p

Functional clusters of candidate genes for tetralogy of Fallot.

<p>Diagram of results of pathway analyses comparing rare CNVs in cases and controls. Five overlapping functional clusters involved 19 gene-sets; functional neighbors of three known candidate genes identified another cluster (circle size indicates relative number of cases involved).</p

West Antarctic Ice Sheet retreat driven by Holocene warm water incursions.

Glaciological and oceanographic observations coupled with numerical models show that warm Circumpolar Deep Water (CDW) incursions onto the West Antarctic continental shelf cause melting of the undersides of floating ice shelves. Because these ice shelves buttress glaciers feeding into them, their ocean-induced thinning is driving Antarctic ice-sheet retreat today. Here we present a multi-proxy data based reconstruction of variability in CDW inflow to the Amundsen Sea sector, the most vulnerable part of the West Antarctic Ice Sheet, during the Holocene epoch (from 11.7 thousand years ago to the present). The chemical compositions of foraminifer shells and benthic foraminifer assemblages in marine sediments indicate that enhanced CDW upwelling, controlled by the latitudinal position of the Southern Hemisphere westerly winds, forced deglaciation of this sector from at least 10,400 years ago until 7,500 years ago-when an ice-shelf collapse may have caused rapid ice-sheet thinning further upstream-and since the 1940s. These results increase confidence in the predictive capability of current ice-sheet models