The effect of wavy leading edges on aerofoil–gust interaction noise

High-order accurate numerical simulations are performed to investigate the effects of wavy leading edges (WLEs) on aerofoil–gust interaction (AGI) noise. The present study is based on periodic velocity disturbances predominantly in streamwise and vertical directions that are mainly responsible for the surface pressure fluctuation of an aerofoil. In general, the present results show that WLEs lead to reduced AGI noise. It is found that the ratio of the wavy leading-edge peak-to-peak amplitude (LEA) to the longitudinal wavelength of the incident gust (_λg${\lambda }_g$) is the most important factor for the reduction of AGI noise. It is observed that there exists a tendency that the reduction of AGI noise increases with LEA/_λg$\mathrm{LEA}/{\lambda }_g$ and the noise reduction is significant for LEA/_λg≥0.3$\mathrm{LEA}/{\lambda }_g\ge 0.3$. The present results also suggest that any two different cases with the same LEA/_λg$\mathrm{LEA}/{\lambda }_g$ lead to a strong similarity in their profiles of noise reduction relative to the straight leading-edge case. The wavelength of wavy leading edges (LEW), however, shows minor influence on the reduction of AGI noise under the present gust profiles used. Nevertheless, the present results show that a meaningful improvement in noise reduction may be achieved when 1.0≤LEW/_λg≤1.5$1.0\le \mathrm{LEW}/{\lambda }_g\le 1.5$. In addition, it is found that the beneficial effects of WLEs are maintained for various flow incidence angles and aerofoil thicknesses. Also, the WLEs remain effective for gust profiles containing multiple frequency components. It is discovered in this paper that WLEs result in incoherent response time to the incident gust across the span, which results in a decreased level of surface pressure fluctuations, hence a reduced level of AGI noise.     

Molecular Structure of Heterocycles: 3. Semiempirical MO Calculations and Karplus-Type Dihedral Angle Dependence for the Coupling Constant Relationship of Some 4,5-Dihydro-5-Hydroxy- 5(3)-Halomethylisoxazoles

Molecular modeling by semiempirical MO calculations (AM1) was used to predict configurational and conformational preferences of a series of 4,5-dihydro-5- hydroxy-5(3)-halomethylisoxazoles. The relationship among dihedral angles calculated and the experimental ¹H NMR coupling constants, J³{Ha,b-H}, are established with Karplus-Type Equation.

     

Global supersymmetry on curved spaces in various dimensions

We propose methods towards a systematic determination of d  -dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hⁿ⁺¹${\mathbb{H}}^{n+1}$ and compact spheres Sⁿ${\mathbb{S}}^n$ or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S¹×Sⁿ${\mathbb{S}}^1\times {\mathbb{S}}^n$, with n<6$n<6$. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres S^d${\mathbb{S}}^d$ if d>5$d>5$ (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.     

Co-registration of the distribution of wall shear stress and 140 complex plaques of the aorta

Previous studies provide evidence that atherosclerosis develops in vascular regions exposed to low wall shear stress (WSS) and high oscillatory shear index (OSI). 4D flow MRI was analyzed in 70 stroke patients with complex plaques (≥ 4 mm thickness, ulcerated or superimposed thrombi) and in 12 young healthy volunteers. The segmental distribution of peak systolic WSS_systole and OSI was quantified in analysis planes positioned directly at the location of 140 complex plaques found in the 70 patients. In addition, WSS_systole and OSI were evaluated in 8 standard analysis planes distributed along the aorta. Complex plaques were predominantly found at the inner curvature of the aortic arch and of the descending aorta. High OSI was co-located with the segments mostly affected by complex plaque while WSS_systole demonstrated a homogenous distribution. In standard analysis planes, patients demonstrated significantly (p < 0.01) altered distribution of wall parameters compared to volunteers (reduced WSS_systole in 91% of aortic wall segments, increased OSI in 48% of segments). OSI distribution was asymmetric with higher values at the inner curvature of the aorta. While WSS and OSI showed expected changes in patients compared to healthy controls, their distribution pattern at complex plaques indicated a more complex and heterogeneous relationship than previously anticipated.     

Feasibility of Q-Band EPR Dosimetry in Biopsy Samples of Dental Enamel, Dentine and Bone

Electron paramagnetic resonance (EPR) dosimetry of tooth enamel in X-band has been established as a suitable method for individual reconstruction of doses 0.1 Gy and higher. The objective was to demonstrate the feasibility of using Q-band EPR in small biopsy tooth enamel samples to provide accurate measurements of radiation doses. Q-band spectra of small (<10 mg) irradiated samples of dentine and bone were studied to investigate the possibility of using Q-band EPR for dose measurements in those materials if there are limited amounts of enamel available, and there is no time for the chemical sample preparation required for accurate X-band measurements in dental enamel. Our results have shown that Q-band provides accurate measurements of radiation doses higher than 0.5 Gy in tooth enamel biopsy samples as small as 2 mg. Q-band EPR spectra in powdered dentine and bone demonstrated significantly higher resolution and sensitivity than in conventional X-band measurements.     

Christoffel Words and Markoff Triples: An Algebraic Approach

We introduce a family of modules, called Markoff modules, generated by a cluster-mutation-like iterative process. We show that these modules are combinatorially similar to Christoffel words. Furthermore, we construct a bijective map between the set of Markoff module triples and the set of proper Markoff triples. This allows us to interpret the uniqueness conjecture for Markoff numbers within an algebraic framework.     

Fibonacci-like growth of numerical semigroups of a given genus

We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if n _g is the number of numerical semigroups of genus g, we prove that $$\lim_{g \rightarrow \infty} n_g \varphi^{-g} = S $$ where $\varphi = \frac{1 + \sqrt{5}}{2}$ is the golden ratio and S is a constant, resolving several related conjectures concerning the growth of n _g . In addition, we show that the proportion of numerical semigroups of genus g satisfying f<3m approaches 1 as g→∞, where m is the multiplicity and f is the Frobenius number.     

Characteristic Formulas of Partial Heyting Algebras

The goal of this paper is to generalize a notion of characteristic (or Jankov) formula by using finite partial Heyting algebras instead of the finite subdirectly irreducible algebras: with every finite partial Heyting algebra we associate a characteristic formula, and we study the properties of these formulas. We prove that any intermediate logic can be axiomatized by such formulas. We further discuss the correlations between characteristic formulas of finite partial algebras and canonical formulas. Then with every well-connected Heyting algebra we associate a set of characteristic formulas that correspond to each finite relative subalgebra of this algebra. Finally, we demonstrate that in many respects these sets enjoy the same properties as regular characteristic formulas. In the last section we outline an approach how to generalize these obtained results to the broad classes of algebras.     

NP-hardness of deciding convexity of quartic polynomials and related problems

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.