1,043 research outputs found
Author Lev Raphael reads from his work at the Michigan Writers Series
No full textInternationally acclaimed author and Greater Lansing resident, Lev Raphael, reads from his memoir "My Germany". He recounts his travels to the NAZI labor camp where his mother was held during World War II and coming to terms with his mother's traumatic past. Introduced by Michigan State University Librarian Michael Rodriguez at an event held at the MSU Main Library. Part of the Michigan State University Libraries' Michigan Writers Series
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics
Get PDFWe provide a description of the far-field encountered in the diffraction
problem resulting from the interaction of a monochromatic plane-wave and a
right-angled no-contrast penetrable wedge. To achieve this, we employ a
two-complex-variable framework and use the analytical continuation formulae
derived in (Kunz Assier, QJMAM, 76(2), 2023) to recover the wave-field's
geometrical optics components, as well as the cylindrical and lateral
diffracted waves. We prove that the corresponding cylindrical and lateral
diffraction coefficients can be expressed in terms of certain
two-complex-variable spectral functions, evaluated at some given points
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
Get PDFWe apply the stationary phase method developed in (Assier, Shanin \&
Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a
quarter-plane. The wave field is written as a double Fourier transform of an
unknown spectral function. We make use of the analytical continuation results
of (Assier \& Shanin, QJMAM, 72(1), 2018) to uncover the singularity structure
of this spectral function. This allows us to provide a closed-form far-field
asymptotic expansion of the field by estimating the double Fourier integral
near some special points of the spectral function. All the known results on the
far-field asymptotics of the quarter-plane problem are recovered, and new
mathematical expressions are derived for the secondary diffracted waves in the
plane of the scatterer
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics
Get PDFWe provide a description of the far-field encountered in the diffraction problem resulting from the interaction of a monochromatic plane-wave and a right-angled no-contrast penetrable wedge. To achieve this, we employ a two-complex-variable framework and use the analytical continuation formulae derived in (Kunz & Assier, QJMAM, 76(2), 2023) to recover the wavefield’s geometrical optics components, as well as the cylindrical and lateral diffracted waves. We prove that the corresponding cylindrical and lateral diffraction coefficients can be expressed in terms of certain two-complex-variable spectral functions, evaluated at some given points
A CONTRIBUTION TO THE MATHEMATICAL THEORY OF DIFFRACTION:PART II: RECOVERING THE FAR-FIELD ASYMPTOTICS OF THE QUARTER-PLANE PROBLEM
No full textWe apply the stationary phase method developed in (Assier, Shanin & Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral function. We make use of the analytical continuation results of (Assier & Shanin, QJMAM, 72(1), 2018) to uncover the singularity structure of this spectral function. This allows us to provide a closed-form far-field asymptotic expansion of the field by estimating the double Fourier integral near some special points of the spectral function. All the known results on the far-field asymptotics of the quarter-plane problem are recovered, and new mathematical expressions are derived for the secondary diffracted waves in the plane of the scatterer
A CONTRIBUTION TO THE MATHEMATICAL THEORY OF DIFFRACTION:PART II: RECOVERING THE FAR-FIELD ASYMPTOTICS OF THE QUARTER-PLANE PROBLEM
No full textWe apply the stationary phase method developed in (Assier, Shanin & Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral function. We make use of the analytical continuation results of (Assier & Shanin, QJMAM, 72(1), 2018) to uncover the singularity structure of this spectral function. This allows us to provide a closed-form far-field asymptotic expansion of the field by estimating the double Fourier integral near some special points of the spectral function. All the known results on the far-field asymptotics of the quarter-plane problem are recovered, and new mathematical expressions are derived for the secondary diffracted waves in the plane of the scatterer
Vertex green's functions of a quarter-plane: Links between the functional equation, additive crossing and Lamé functions
Get PDFIn our previous work (Assier & Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter-plane. In particular, we showed that the unknown spectral function satisfies a condition of additive crossing about its branch set. In this paper, we study a very similar class of spectral problem, and show how the additive crossing can be exploited in order to express its solution in terms of Lamé functions. The solutions obtained can be thought of as tailored vertex Green's functions whose behaviours in the near-field are directly related to the eigenvalues of the Laplace-Beltrami operator. This is important since the correct near-field behaviour at the tip of the quarter-plane had so far never been obtained via a multivariable complex analysis approach
Deep machine learning of topological states of quantum matter
No full textauthor: Raphael KaubrueggerMasterarbeit Universität Innsbruck 201
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