Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterization of the Cone and Applications in Banach Spaces

Abstract

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods.     

An explicit algorithm for monotone variational inequalities

We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under only the assumptions of continuity and monotonicity of the operator and existence of solutions.     

Structure of 6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, <'6>He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.     

Weak coupling of a Reynolds model and a Stokes model for hydrodynamic lubrication

The Reynolds model is a reduced Stokes model, valid for narrow lubrication regions. In order to be able to handle locally non‐narrow regions such as pits or grooves, often displaying rapid geometrical variations, there is a need to be able to transit to the more accurate Stokes model. A fundamental problem is how to couple the two models in a numerical simulation, preferably allowing for different meshes in the different domains. In this paper, we present a weak coupling method for Reynolds and Stokes models for lubrication computations, including the possibility of cavitation in the different regions. The paper concludes with a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal boundary discretization by variational data assimilation

A variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near the boundary rather than boundary conditions is shown. Assimilating data that have been produced by the same model on a finer grid, in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under‐resolved boundary layer and wrong wave velocity. Copyright © 2010 John Wiley & Sons, Ltd.     

First‐Principles Investigation of Anisotropic Electron and Hole Mobility in Heterocyclic Oligomer Crystals

Based on quantum chemistry calculations combined with the Marcus–Hush electron transfer theory, we investigated the charge‐transport properties of oligothiophenes (nTs) and oligopyrroles (nPs) (n=6, 7, 8) as potential p‐ or n‐type organic semiconductor materials. The results of our calculations indicate that 1) the nPs show intrinsic hole mobilities as high as or even higher than those of nTs, and 2) the vertical ionization potentials (VIPs) of the nPs are about 0.6–0.7 eV smaller than the corresponding VIPs of the nTs. Based on their charge‐transport ability and hole‐injection efficiency, the nPs have potential as p‐type organic semiconducting materials. Furthermore, it was also found that the maximum values of the electron‐transfer mobility for the nTs are larger by one‐to‐two orders of magnitude than the corresponding maximum values of hole‐transfer mobility, which suggests that the nTs have the potential to be developed as promising n‐type organic semiconducting materials owing to their electron mobility.     

基于第一性原理的无铅无机钙钛矿Cs3Bi2X9(X=Cl、Br、I)光电性能表面效应研究

用基于第一性原理的密度泛函理论方法,对Cs₃Bi₂X₉(X=Cl、Br、I)的光电特性进行理论计算,并系统阐述这3种晶体的表面效应对光电性能的影响。结果表明,3种材料的光学特性由铋原子和卤素原子最外层p轨道上的价电子主导。在可见光区中,材料的吸收峰会随卤素原子序数的增加呈现红移,其中一维结构的Cs₃Bi₂Cl₉表面结构在光吸收能力上尤为特别且敏感;二维结构的Cs₃Bi₂Br₉光吸收能力会受厚度影响;零维结构的Cs₃Bi₂I₉非常稳定,且几乎不受表面特性和晶体厚度的影响。