On wild ramification in quaternion extensions

Quaternion extensions are often the smallest extensions to exhibit special properties. In the setting of the Hasse-Arf Theorem, for instance, quaternion extensions are used to illustrate the fact that upper ramification numbers need not be integers. These extensions play a similar role in Galois module structure. To better understand these examples, we catalog the ramification filtrations that are possible in totally ramified extensions of dyadic number fields. Interestingly, we find that the catalog depends, for sharp lower bounds, upon the refined ramification filtration, which is associated with the biquatratic subfield. Moreover these examples, as counter-examples to the conclusion of Hasse-Arf, occur only when the refined filtration is, in two different ways, extreme.Comment: 19 pages. This is an extensive revision of the earlier draf

Generational research: between historical and sociological imaginations

This paper reflects on Julia Brannen’s contribution to the development of theory and methods for intergenerational research. The discussion is contextualised within a contemporary ‘turn to time’ within sociology, involving tensions and synergies between sociological and historical imagination. These questions are informed by a juxtaposition of Brannen’s four-generation study of family change and social historian Angela Davis’s exploration women and the family in England between 1945 and 2000. These two studies give rise to complementary findings, yet have distinctive orientations towards the status and treatment of sources, the role of geography in research design and limits of generalisatio

Grain boundary motion in layered phases

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as $\epsilon^{-1/2}$, where $\epsilon$ is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time dependent traveling velocity of the boundary, and especially their dependence on wavenumber. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain boundary motion through curved rolls is the dominant coarsening mechanism.Comment: 16 pages, 5 figure

Properties of pattern formation and selection processes in nonequilibrium systems with external fluctuations

We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection processes. These processes are studied by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by means of numerical simulations.Comment: 15 poages, 8 figure

Evaluation of early and late presentation of patients with ocular mucous membrane pemphigoid to two major tertiary referral hospitals in the United Kingdom

PURPOSE: Ocular mucous membrane pemphigoid (OcMMP) is a sight-threatening autoimmune disease in which referral to specialists units for further management is a common practise. This study aims to describe referral patterns, disease phenotype and management strategies in patients who present with either early or established disease to two large tertiary care hospitals in the United Kingdom.\ud \ud PATIENTS AND METHODS: In all, 54 consecutive patients with a documented history of OcMMP were followed for 24 months. Two groups were defined: (i) early-onset disease (EOD:<3 years, n=26, 51 eyes) and (ii) established disease (EstD:>5 years, n=24, 48 eyes). Data were captured at first clinic visit, and at 12 and 24 months follow-up. Information regarding duration, activity and stage of disease, visual acuity (VA), therapeutic strategies and clinical outcome were analysed.\ud \ud RESULTS: Patients with EOD were younger and had more severe conjunctival inflammation (76% of inflamed eyes) than the EstD group, who had poorer VA (26.7%=VA<3/60, P<0.01) and more advanced disease. Although 40% of patients were on existing immunosuppression, 48% required initiation or switch to more potent immunotherapy. In all, 28% (14) were referred back to the originating hospitals for continued care. Although inflammation had resolved in 78% (60/77) at 12 months, persistence of inflammation and progression did not differ between the two phenotypes. Importantly, 42% demonstrated disease progression in the absence of clinically detectable inflammation.\ud \ud CONCLUSIONS: These data highlight that irrespective of OcMMP phenotype, initiation or escalation of potent immunosuppression is required at tertiary hospitals. Moreover, the conjunctival scarring progresses even when the eye remains clinically quiescent. Early referral to tertiary centres is recommended to optimise immunosuppression and limit long-term ocular damage.\ud \u

Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation

The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of infinite aspect ratio. The stationary solutions are shown to be strongly influenced by the strength of noise. Stationary states for small and large noise strengths appear to be quasi-ordered and disordered respectively. The dynamics of ordering from an initially inhomogeneous state is very slow in the former case and fast in the latter. Both numerical and analytic calculations indicate that the slow dynamics can be characterized by a simple scaling relationship, with a characteristic dynamic exponent of $1/4$ in the intermediate time regime

Two Approaches to Dislocation Nucleation in the Supported Heteroepitaxial Equilibrium Islanding Phenomenon

We study the dislocation formation in 2D nanoscopic islands with two methods, the Molecular Static method and the Phase Field Crystal method. It is found that both methods indicate the same qualitative stages of the nucleation process. The dislocations nucleate at the film-substrate contact point and the energy decreases monotonously when the dislocations are farther away from the island-wetting film contact points than the distance of the highest energy barrier.Comment: 4 page

Effect of body composition methodology on heritability estimation of body fatness

Heritability estimates of human body fatness vary widely and the contribution of body composition methodology to this variability is unknown. The effect of body composition methodology on estimations of genetic and environmental contributions to body fatness variation was examined in 78 adult male and female monozygotic twin pairs reared apart or together. Body composition was assessed by six methods - body mass index (BMI), dual energy x-ray absorptiometry (DXA), underwater weighing (UWW), total body water (TBW), bioelectric impedance (BIA), and skinfold thickness. Body fatness was expressed as percent body fat, fat mass, and fat mass/height2 to assess the effect of body fatness expression on heritability estimates. Model-fitting multivariate analyses were used to assess the genetic and environmental components of variance. Mean BMI was 24.5 kg/m2 (range of 17.8-43.4 kg/m2). There was a significant effect of body composition methodology (p<0.001) on heritability estimates, with UWW giving the highest estimate (69%) and BIA giving the lowest estimate (47%) for fat mass/height2. Expression of body fatness as percent body fat resulted in significantly higher heritability estimates (on average 10.3% higher) compared to expression as fat mass/height2 (p=0.015). DXA and TBW methods expressing body fatness as fat mass/height2 gave the least biased heritability assessments, based on the small contribution of specific genetic factors to their genetic variance. A model combining DXA and TBW methods resulted in a relatively low FM/ht2 heritability estimate of 60%, and significant contributions of common and unique environmental factors (22% and 18%, respectively). The body fatness heritability estimate of 60% indicates a smaller contribution of genetic variance to total variance than many previous studies using less powerful research designs have indicated. The results also highlight the importance of environmental factors and possibly genotype by environmental interactions in the etiology of weight gain and the obesity epidemic.R01 AR046124 - NIAMS NIH HHS; R01 MH065322 - NIMH NIH HHS; T32 HL069772 - NHLBI NIH HHS; R21 DK078867 - NIDDK NIH HHS; R37 DA018673 - NIDA NIH HHS; R01 DK076092 - NIDDK NIH HHS; R01 DK079003 - NIDDK NIH HHS; F32 DK009747 - NIDDK NIH HHS; R01 DA018673 - NIDA NIH HH

Phase-field approach to heterogeneous nucleation

We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe homogeneous as well as heterogeneous nucleation starting from several general hypotheses. Thus we can investigate the influence of grain boundaries, localized impurities, or any general kind of imperfections in a systematic way. We also put forward the applicability of our model to study other physical situations such as island formation, amorphous crystallization, or recrystallization.Comment: 8 pages including 7 figures. Accepted for publication in Physical Review