On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Nonlinear stabilitty for steady vortex pairs

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.Comment: 25 page

Multibeam Maser Survey of methanol and excited OH in the Magellanic clouds: new detections and maser abundance estimates

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing DOI: 10.1111/j.1365-2966.2008.12888.xPeer reviewe

Comparison of the cardiometabolic profiles of adolescents conceived through ART with those of a non-ART cohort

STUDY QUESTION Is the cardiometabolic health of adolescents conceived through ART worse than that of their counterparts conceived without ART? SUMMARY ANSWER The majority of cardiometabolic and vascular health parameters of adolescents conceived through ART are similar or more favourable, than those of their counterparts of similar age and conceived without ART. WHAT IS KNOWN ALREADY It has been proposed that the cardiometabolic health of offspring conceived with ART may be unfavourable compared to that of their counterparts conceived without ART. The literature pertaining to cardiometabolic health of offspring conceived after ART is contradictory, but generally suggests unfavourable cardiometabolic health parameters, such as an increase in blood pressure (BP), vascular dysfunction and adiposity, as well as unfavourable glucose and lipid profiles. With over 8 million children and adults born through ART worldwide, it is important to investigate whether these early signs of adverse cardiometabolic differences persist into adolescence and beyond. STUDY DESIGN, SIZE, DURATION The Growing Up Healthy Study (GUHS) is a prospective cohort study that recruited 303 adolescents and young adults conceived after ART (aged 13–21 years) and born between 1991 and 2001 in Western Australia. Their health parameters, including cardiometabolic factors, were assessed and compared with counterparts from the Raine Study Generation 2 (Gen2). The 2868 Gen2 participants were born 1989–1992 and are representative of the Western Australian adolescent population. At ∼17 years of age (2013–2017), 163 GUHS participants replicated assessments previously completed by Gen2 at a similar age. PARTICIPANTS/MATERIALS, SETTING, METHODS Cardiometabolic parameters were compared between a total of 163 GUHS and 1457 Gen2 adolescents. Separate male (GUHS n = 81, Gen2 n = 735) and female (GUHS n = 82, Gen2 n = 722) analyses were conducted. Assessments consisted of a detailed questionnaire including health, lifestyle and demographic parameters, anthropometric assessments (height, weight, BMI, waist circumference and skinfold thickness), fasting serum biochemistry, arterial stiffness and BP (assessed using applanation tonometry). Abdominal ultrasonography was used to assess the presence and severity of hepatic steatosis, and thickness of abdominal fat compartments. Non-alcoholic fatty liver disease (NAFLD) was diagnosed if there was sonographic fatty liver in the absence of significant alcohol consumption. Chi2, Fisher’s exact and Mann–Whitney U tests, performed in SPSS V25, examined cohort differences and generalized estimating equations adjusted for the following covariates: singleton vs non-singleton pregnancy, birthweight (z-score), gestational age, BMI, smoking, alcohol consumption in the past 6 months and parent cardiovascular status. Arterial stiffness measures and waist circumference were additionally adjusted for height, and female analyses were additionally adjusted for use of oral contraceptives in the preceding 6 months. MAIN RESULTS AND THE ROLE OF CHANCE In adjusted analyses, GUHS females had a lower BMI (22.1 vs 23.3 kg/m2, P = 0.014), and thinner skinfolds (triceps, subscapular, mid-abdominal; 16.9 vs 18.7 mm, P = 0.021, 13.4 vs 15.0 mm, P = 0.027, 19.7 vs 23.2 mm, P < 0.001, respectively), whereas males were not significantly different. Waist circumference was lower in GUHS adolescents (males: 78.1 vs 81.3 cm, P = 0.008, females: 76.7 vs 83.3 cm, P = 0.007). There were no significant differences between the two groups in glucose, insulin, homeostatic model assessment for insulin resistance, low-density lipoprotein cholesterol, non-high-density lipoprotein cholesterol (non-HDL-C), total cholesterol (TC), alanine aminotransferase and high-sensitivity C-reactive protein in both sexes. In females, serum triglycerides were lower in GUHS adolescents (1.0 vs 1.2 mmol/l, P = 0.029). GUHS males had higher serum HDL-C (1.1 vs 1.0 mmol/l, P = 0.004) and a lower TC/HDL-C ratio (3.2 vs 3.6, P = 0.036). There were no significant differences in the prevalence of NAFLD or steatosis severity scores between the cohorts in males and females. GUHS females had less subcutaneous adipose tissue (9.4 vs 17.9 mm, P < 0.001), whereas GUHS males had greater visceral adipose thickness (44.7 vs 36.3 mm, P < 0.001). There was no significant difference in pre-peritoneal adipose thickness. Pulse wave velocity was lower in GUHS males (5.8 vs 6.3 m/s, P < 0.001) and heart rate corrected augmentation index was lower in GUHS females (−8.4 vs −2.7%, P = 0.048). There were no significant differences in BP or heart rate in males or females between the two groups. LIMITATIONS, REASONS FOR CAUTION Despite the substantial study size and the unique study design of the ART cohort, we were unable to differentiate between different types of ART, due to the low number of ICSI cycles (e.g. IVF vs ICSI), draw definite conclusions, or relate the outcomes to the cause of infertility. Considering the differences in time points when both cohorts were studied, external factors could have changed, which could not be accounted for. Given the observational nature of this study, causation cannot be proven. WIDER IMPLICATIONS OF THE FINDINGS Contrary to our hypothesis and previous findings focussing mainly on childhood, this study reports mostly similar or favourable cardiometabolic markers in adolescents conceived with ART compared to those conceived without ART. The greater visceral adipose thickness, particularly present in males, requires further investigation. While these findings are generally reassuring, future well-designed and appropriately powered studies are required to definitively address the issue of cardiometabolic health in ART adults. STUDY FUNDING/COMPETING INTEREST(S) This project was supported by NHMRC project grant number 1042269 and R.J.H. received education grant funding support from Ferring Pharmaceuticals. R.J.H. is the Medical Director of Fertility Specialists of Western Australia and a shareholder in Western IVF. He has received educational sponsorship from MSD, Merck-Serono and Ferring Pharmaceuticals. P.B. is the Scientific Director of Concept Fertility Centre, Subiaco, Western Australia. J.L.Y. is the Medical Director of PIVET Medical Centre, Perth, Western Australia

Wind turbine blade design review

A detailed review of the current state-of-art for wind turbine blade design is presented, including theoretical maximum efficiency, propulsion, practical efficiency, HAWT blade design, and blade loads. The review provides a complete picture of wind turbine blade design and shows the dominance of modern turbines almost exclusive use of horizontal axis rotors. The aerodynamic design principles for a modern wind turbine blade are detailed, including blade plan shape/quantity, aerofoil selection and optimal attack angles. A detailed review of design loads on wind turbine blades is offered, describing aerodynamic, gravitational, centrifugal, gyroscopic and operational conditions

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Stability of the monoclinic phase in the ferroelectric perovskite PbZr(1-x)TixO3

Recent structural studies of ferroelectric PbZr(1-x)TixO3 (PZT) with x= 0.48, have revealed a new monoclinic phase in the vicinity of the morphotropic phase boundary (MPB), previously regarded as the the boundary separating the rhombohedral and tetragonal regions of the PZT phase diagram. In the present paper, the stability region of all three phases has been established from high resolution synchrotron x-ray powder diffraction measurements on a series of highly homogeneous samples with 0.42 <=x<= 0.52. At 20K the monoclinic phase is stable in the range 0.46 <=x<= 0.51, and this range narrows as the temperature is increased. A first-order phase transition from tetragonal to rhombohedral symmetry is observed only for x= 0.45. The MPB, therefore, corresponds not to the tetragonal-rhombohedral phase boundary, but instead to the boundary between the tetragonal and monoclinic phases for 0.46 <=x<= 0.51. This result provides important insight into the close relationship between the monoclinic phase and the striking piezoelectric properties of PZT; in particular, investigations of poled samples have shown that the monoclinic distortion is the origin of the unusually high piezoelectric response of PZT.Comment: REVTeX file, 7 figures embedde

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium "free-energy" at a mesoscopic/cluster level, and it ensues a nonequilibrium "surface tension" with some peculiar low-T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) Noise-enhanced stabilization of nonequilibrium metastable states; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) resonant propagation of domain walls. The cooperative behavior of our system may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe burst-like relaxation at low T, triggered by the additional surface randomness, with scale-free avalanches which closely resemble the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well- defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality.Comment: 26 pages, 22 figure