Applications holomorphes propres d'un domaine quasi-disqué sur un domaine disqué

A result of F. Berteloot and G. Patrizio [F. Berteloot, G. Patrizio, A cartan theorem for proper holomorphic mappings of complete circular domains, Adv. Math. 153 (2000) 342-352] states that if f is a proper holomorphic map between two bounded complete circular domains Ω₁ and Ω₂ in Cn+1 (n?1), such that f−1{0}={0} and such that the principal part fp of the Taylor expansions of f at the origine is nondegenerated i.e. fp−1{0}={0}, then f=fp.Here, we give a partial extension of this result to the case where f is a nondegenerated proper holomorphic map between a quasi-circular domain Ω₁ and a complete circular domain Ω₂, which are pseudo-convex but not necessarily bounded.We show that if f and its principal part fp are nondegenerated at the origine, then fp−1(Ω₂)=Ω₁.     

集值优化问题Benson真有效解的高阶Fritz John型最优性条件

本文讨论的是集值优化问题Benson真有效解的高阶Fritz John型最优性条件,利用Aubin和Fraukowska引入的高阶切集和凸集分离定理,在锥-似凸映射的假设条件下,获得了带广义不等式约束的集值优化问题Benson真有效解的高阶Fritz John型必要和充分性条件.     

A Flow feature detection framework for large-scale computational data based on incremental proper orthogonal decomposition and data mining

ABSTRACT

A framework based on incremental proper orthogonal decomposition (iPOD) and data mining to perform large-scale computational data analysis is presented. It includes iPOD to incrementally reduce data dimensions and decouple dynamic flow structures in massive CFD data; data mining to classify and identify candidate global regions of interest (ROIs) for focused analysis; feature detection to capture key flow features and ultimate ROIs (UROIs); and targeted data storage and visualisation. Quantitative results show that iPOD is able to process large datasets that overwhelm the batch-POD, leading to 4–16× data reduction in the temporal domain. Data mining and feature detection algorithms, respectively, identify 50–70% of the spatial domain with high probability of flow feature occurrence and only 2–30% containing key flow features. The UROI and associated data can be selectively stored and visualised. In contrast to batch-POD, iPOD reduces memory usage by more than 10× and time by up to 75%.     

Free-form deformation,mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation

ABSTRACT

In this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.     

双波长比值光谱差异度指数用于人体舌苔舌质分离

舌苔舌质信息定量描述作为中医舌诊的重要内容,直接影响到中医临床舌诊的准确性。基于生物医学光子学理论,利用高光谱技术,提出一种基于双波长比值光谱差异度指数进行人体舌质舌苔分离的光谱分析新方法。首先采集被测对象371.200～992.956 nm之间共343个波长的舌体高光谱信息,随机选取15位被测对象进行光谱特征分析。绘制15位被测对象舌质舌苔全波段光谱曲线并进行比较,通过观察发现,舌质舌苔反射光特征差异与血红蛋白在该波段的光学特征变化相吻合,在500～750 nm之间,水对光的吸收很少,而舌体表面布满血管,光的吸收主要受到血红蛋白的影响,基于舌质舌苔在573和700 nm两波段光谱吸收差异,计算双波长比值,提取舌质舌苔光谱特征差异度指数,根据个体差异,分别提取不同被测对象舌质舌苔光谱特征差异指标,进行舌质舌苔区域分离,实验结果发现,对同一被测对象舌体苔质提取光谱差异度指数SDI,舌苔舌质光谱差异度指数存在一定差异性,由于个体的不同,具有各自明显的舌质、舌体差异度指数分割线,实验结果表明,运用双波长比值光谱差异度指数的光学表达形式能够用于舌质舌苔分离,同时该方法也能够为进一步中医临床舌诊提供客观依据。     

International journal of computational fluid dynamics real-time prediction of unsteady flow based on POD reduced-order model and particle filter

An integrated method consisting of a proper orthogonal decomposition (POD)-based reduced-order model (ROM) and a particle filter (PF) is proposed for real-time prediction of an unsteady flow field. The proposed method is validated using identical twin experiments of an unsteady flow field around a circular cylinder for Reynolds numbers of 100 and 1000. In this study, a PF is employed (ROM-PF) to modify the temporal coefficient of the ROM based on observation data because the prediction capability of the ROM alone is limited due to the stability issue. The proposed method reproduces the unsteady flow field several orders faster than a reference numerical simulation based on Navier–Stokes equations. Furthermore, the effects of parameters, related to observation and simulation, on the prediction accuracy are studied. Most of the energy modes of the unsteady flow field are captured, and it is possible to stably predict the long-term evolution with ROM-PF.     

Analyzing the fluctuating pressures acting on a circular cylinder using stochastic decomposition

Fluctuating wind pressures acting on bluff bodies are influenced by approaching turbulence and signature (body-induced) turbulence. For a circular cylinder, the signature turbulence is closely related to the formation of Karman vortex shedding. In this paper, proper orthogonal decomposition (POD) and spectral proper transformation techniques (SPT) are applied to the pressure fluctuations acting on a circular cylinder. The physical relationships between the decomposed modes and vortex shedding are discussed to identify the dominant aerodynamic behavior (lift or drag) and to evaluate its contribution to overall behavior. The effect of Reynolds number (Re) is also addressed. It is found that the application of POD and SPT can separate the along-wind and across-wind effects on the cylinder model in both subcritical and supercritical regimes. In contrast to POD, the SPT mode is formulated in the frequency domain, and the dynamic coherent structures can be defined in terms of amplitude and phase angle, which allows detection of the advection features of vortex shedding. In addition, it is observed that the energy contribution of the shedding induced lift force increases with Re and gradually becomes a dominant aerodynamic force at Reynolds numbers in the supercritical regime.     

Interpolation-based reduced-order modelling for steady transonic flows via manifold learning

This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved treatment of the nonlinearities involved in varying the inflow conditions to obtain an accurate prediction of shocks. The reduced-order representation of the data is derived using the Isomap ML method, which is applied to a set of sampled computational fluid dynamics (CFD) data. In order to develop a ROM that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced-order representation to the full CFD solution space is introduced. The proposed ROM, called Isomap+I, is applied to the two-dimensional NACA 64A010 airfoil and to the 3D LANN wing. The results are compared to those obtained by proper orthogonal decomposition plus interpolation (POD+I) and to the full-order CFD model.     

Preparation of Nd-doped BiFeO3 films and their electrical properties

The Nd-doped BiFeO₃ thin films were prepared on SnO₂(FTO) substrates spin-coated by the sol–gel method using Nd(NO₃)₃·6H₂O, Fe(NO₃)₃·9H₂O and Bi(NO₃)₃·5H₂O as raw materials. The microstructure and electric properties of the BiFeO₃ thin films were characterized and tested. The results indicate that the diffraction peak of the Nd-doped BiFeO₃ films is shifted towards right as the doping amounts are increased. The structure is transformed from the rhombohedral to pseudotetragonal phase. The crystal grain is changed from an elliptical to irregular polyhedron. Structure transition occurring in the Bi_0.85Nd_0.15FeO₃ films gives rise to the largest Pr of 64 μC/cm². The leakage conductance of the Nd doped thin films is reduced. The dielectric constant and dielectric loss of Bi_0.85Nd_0.15FeO₃ thin film at 10 kHz are 190 and 0.017 respectively.     

Stability results for properly quasi convex vector optimization problems

In this paper, we discuss the stability of the sets of (weak) minimal points and (weak) efficient points of vector optimization problems. Assuming that the objective functions are (strictly) properly quasi convex, and the data ofthe approximate problems converges to the data of the original problems in the sense of Painlevé–Kuratowski, we establish the Painlevé–Kuratowski set convergence of the sets of (weak) minimal points and (weak) efficient points of the approximate problems to the corresponding ones of original problem. Our main results improve and extend the results of the recent papers.