Computing derivative-based global sensitivity measures using polynomial chaos expansions

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The {\em derivative-based global sensitivity measures} (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis

Hierarchical adaptive polynomial chaos expansions

Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact significant. Taking into account the sparse structure of the model, advanced techniques such as sparse PCE (SPCE), have been recently proposed to alleviate the computational issue. In this paper, we propose a novel approach to SPCE, which allows one to exploit the model's hierarchical structure. The proposed approach is based on the adaptive enrichment of the polynomial basis using the so-called principle of heredity. As a result, one can reduce the computational burden related to a large pre-defined candidate set while obtaining higher accuracy with the same computational budget

Photocurrent in a visible-light graphene photodiode

We calculate the photocurrent in a clean graphene sample normally irradiated by a monochromatic electromagnetic field and subject to a step-like electrostatic potential. We consider the photon energies $\hbar\Omega$ that significantly exceed the height of the potential barrier, as is the case in the recent experiments with graphene-based photodetectors. The photocurrent comes from the resonant absorption of photons by electrons and decreases with increasing ratio $\hbar\Omega/U_0$. It is weakly affected by the background gate voltage and depends on the light polarization as $\propto\sin^2\gamma$, $\gamma$ being the angle between the potential and the polarization plane.Comment: 5 pages, 3 figure

Notch effects in tensile behavior of AM60 magnesium alloys

The deformation and failure behavior of an AM60 magnesium alloy was investigated using tensile test on circumferentially notched specimens with different notch radii. The strain and stress triaxiality corresponding to the failure point were evaluated using both analytical and finite element analyses. Combining with systematical observations of the fracture surfaces, it is concluded that deformation and failure of AM60 magnesium alloy are notch (constraint) sensitive. The failure mechanisms change from ductile tearing to quasi cleavage with the increase of constraint