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In this work, we consider the propagation of acoustic waves in unbounded domains characterized by a constant wavenumber, except possibly in a bounded region. The geometry of this inhomogeneity is assumed to be uncertain, and we are particularly interested in studying the propagation of this behavior throughout the physical model considered. A key step in our analysis consists of recasting the physical model-originally set in an unbounded domain-into a computationally manageable formulation based on Volume Integral Equations (VIEs), particularly the Lippmann-Schwinger equation. We show that both the leading operator in this volume integral formulation and its solution depend holomorphically on shape variations of the support of the aforementioned inhomogeneity. This property, known as shape holomorphy, is crucial in the analysis and implementation of various methods used in computational Uncertainty Quantification (UQ). We explore the implications of this result in forward and inverse UQ and provide numerical experiments illustrating and confirming the theoretical predictions.

We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on $\Omega$. Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.

The valence band (VB) structure of an Al0.5TiZrPdCuNi high-entropy alloy (HEA) obtained from X-ray photoelectron spectroscopy has been compared to that recently calculated by Odbadrakh et al, 2019. Both experimental and theoretical VBs show split-band structures typical of alloys composed from the early (TE) and late (TL) transition metals. Accordingly, several properties of this alloy (both in the glassy and crystalline state) associated with the electronic structure (ES), are compared with those of similar TE-TL alloys. The comparison shows in addition to the usual dependence on the total TL content strong effect of alloying with Al on the density of states at the Fermi level, N(EF) and on the magnetic susceptibility of Al0.5TiZrPdCuNi HEA, which is like that of conventional glassy alloys, such as Zr-Cu-Al ones. Despite some similarity between the shapes of theoretical and corresponding experimental VBs there are significant quantitative differences between them which should be taken into account in any future studies of ES in HEAs and other compositionally complex alloys (CCA).

As in any other task, the process of building machine learning models can benefit from prior experience. Meta-learning for classifier selection gains knowledge from characteristics of different datasets and/or previous performance of machine learning techniques to make better decisions for the current modeling process. Meta-learning approaches first collect meta-data that describe this prior experience and then use it as input for an algorithm selection model. In this paper, however, we propose an automatic learning scheme in which we train convolutional networks directly with the information of tabular datasets for binary classification. The goal of this study is to learn the inherent structure of the data without identifying meta-features. Experiments with simulated datasets show that the proposed approach achieves nearly perfect performance in identifying linear and nonlinear patterns, outperforming the traditional two-step method based on meta-features. The proposed method is then applied to real-world datasets, making suggestions about the best classifiers that can be considered based on the structure of the data., Comment: This is a preprint of a work under submission and thus subject to change. 12 pages

A new amorphous alloy system $(TiZrNbCu)_{1-x}Co_x$ covering a broad composition range from the high-entropy (HEA) to Co rich alloys (x$\leqslant$ 0.43) has been fabricated, characterized and investigated. A comprehensive study of the chemical compositions, homogeneity, thermal stability, electronic structure and magnetic and mechanical properties has been performed. All properties change their variations with x within the HEA range. In particular, the average atomic volume deviates from the Vegard's law for x$\ge 0.2$, where also the average atomic packing fraction suddenly changes. The valence band structure, studied with ultraviolet photoemission spectroscopy, shows a split-band shape with 3d-states of Co approaching the Fermi level on increasing x. Due to onset of magnetic correlations magnetic susceptibility rapidly increases for x$\ge 0.25$. Very high microhardness increases rapidly with x. The results are compared with those for similar binary and quinary metallic glasses and with those for Cantor type of crystalline alloys., Comment: 29 pages, 10 figures

We present results of comprehensive study of electronic properties of (TiZrNbCu)(1-x)Ni(x) metallic glasses performed in broad composition range x encompassing both, high entropy (HE) range, and conventional Ni-base alloy concentration range, x >= 0.35. The electronic structure studied by photoemission spectroscopy and low temperature specific heat (LTSH) reveal a split-band structure of density of states inside valence band with d-electrons of Ti, Zr, Nb and also Ni present at Fermi level N(E_F), whereas LTSH and magnetoresistivity results show that variation of N(E_F) with x changes in Ni-base regime. The variation of superconducting transition temperatures with x closely follows that of N(E_F). The electrical resistivities of all alloys are high and decrease with increasing temperature over most of explored temperature range, and their temperature dependence seems dominated by weak localization effects over a broad temperature range (10-300 K). The preliminary study of Hall effect shows positive Hall coefficient that decreases rapidly in Ni-base alloys., Comment: 32 pages, 6 figures

The atomic structure, electronic structure and physical properties of $(TiZrNbCu)_{(1-x)}Ni_x$ (x $\leq$ 0.5) metallic glasses (MG) were studied in both the high-entropy (0

Recent studies (J. Alloys Compd. 695 (2017) 2661) of the electronic structure and properties of $(TiZrNbCu)_{1-x}$$Ni_{x}$ (x$\leq$0.25) amorphous high entropy alloys (a-HEA) have been extended to x=0.5 in order to compare behaviours of a-HEA and conventional Ni-base metallic glasses (MG). The amorphous state of all samples was verified by thermal analysis and X-ray diffraction (XRD). XRD indicated a probable change in local atomic arrangements, i.e. short-range-order (SRO) for x$\geq$0.35. Simultaneously, thermal parameters, such as the first crystallization temperature $T_{x}$ and the liquidus temperature showed a tendency to saturate for x$\geq$0.35 . The same tendency also appeared in the magnetic susceptibility $\chi_{exp}$ and the linear term in the low temperature specific heat {\gamma}. The Debye temperatures and Youngs moduli also tend to saturate for x$\geq$0.35. These unusual changes in SRO and all properties within the amorphous phase seem correlated with the change of valence electron number (VEC) on increasing x., Comment: 13 pages, 6 figures

A comprehensive study of selected properties of four (TiZrNbCu)_1-xNi_x (x \le 0.25) amorphous high entropy alloys (a-HEA) has been performed. The samples were ribbons about 20 \mum thick and their fully amorphous state was verified by X-ray diffraction and thermal analysis. The surface morphology, precise composition and the distribution of components were studied with a Scanning electron microscope (SEM) with an energy dispersive spectroscopy (EDS) attachment. The properties selected were the melting temperature (T_m), the low temperature specific heat (LTSH), the magnetic susceptibility \chi_exp and the Young^,s modulus (E). Whereas LTSH and \chi_exp were measured for the as-cast samples, E was measured both for as-cast samples and relaxed samples (after a short anneal close to the glass transition temperature). The LTSH showed that the electronic density of states at the Fermi level, N_0(E_F), decreases with increasing x, whereas the Debye temperature (\theta_D) increases with x. This is similar to what is observed in binary and ternary amorphous alloys of early transition metals (TE) with late transition metals (TL) and indicates that N_0(E_F) is dominated by the d-electrons of the TE. The LTSH also showed the absence of superconductivity down to 1.8K and indicated the emergence of the Boson peak above 4K in all alloys.The free-electron like paramagnetic contribution to \chi_exp also decreases with x, whereas E, like \theta_D, increases with x, indicating enhanced interatomic bonding on addition of Ni. The applicability of the rule of mixtures to these and other similar HEAs is briefly discussed.

Understanding the formation of bulk metallic glasses (BMG) in metallic systems and finding a reliable criterion for selection of BMG compositions are among the most important issues in condensed matter physics and material science. Using the results of magnetic susceptibility measurements performed on both amorphous and crystallized Cu-Hf alloys (30-70 at% Cu) we find a correlation between the difference in magnetic susceptibilities of corresponding glassy and crystalline alloys and the variation in the glass forming ability (GFA) in these alloys. Since the same correlation can be inferred from data for the properties associated with the electronic structure of Cu-Zr alloys, it seems quite general and may apply to other glassy alloys based on early and late transition metals. This correlation is plausible from the free energy considerations and provides a simple way to select the compositions with high GFA., Comment: 11 pages, 3 figures