In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well kn...In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.展开更多
Based on the principle of energy change of alloy formation, the rules for the maximum solid solubility ( C max ) of various transition metals in the metals Ti, Zr and Hf were studied. It is deduced that the C max of t...Based on the principle of energy change of alloy formation, the rules for the maximum solid solubility ( C max ) of various transition metals in the metals Ti, Zr and Hf were studied. It is deduced that the C max of transition metals in the metals Ti, Zr and Hf can be described as a semi empirical equation using three atomic parameters, i.e., electronegativity difference, atomic diameter and electron concentration. From the equation analysis by using experimental data, it shows that atomic size parameter and electronegativity difference are the main factors that affect the C max of the transition metals in the metals Ti, Zr and Hf while electron concentration parameter has the smallest effect on C max .展开更多
文摘In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.
文摘Based on the principle of energy change of alloy formation, the rules for the maximum solid solubility ( C max ) of various transition metals in the metals Ti, Zr and Hf were studied. It is deduced that the C max of transition metals in the metals Ti, Zr and Hf can be described as a semi empirical equation using three atomic parameters, i.e., electronegativity difference, atomic diameter and electron concentration. From the equation analysis by using experimental data, it shows that atomic size parameter and electronegativity difference are the main factors that affect the C max of the transition metals in the metals Ti, Zr and Hf while electron concentration parameter has the smallest effect on C max .
