رسالة جامعية
Non-Hermitian Phononics
| العنوان: | Non-Hermitian Phononics |
|---|---|
| المؤلفون: | Mokhtari, Amir Ashkan |
| المساهمون: | Srivastava, Ankit |
| المصدر: | Illinois Institute of Technology ; MMAE / Mechanical, Materials, and Aerospace Engineering |
| سنة النشر: | 2021 |
| المجموعة: | repository.iit (Illinois Institute of Technology) |
| مصطلحات موضوعية: | Mechanical engineering, Aerospace engineering, Acoustics, Metamaterial, Non-Hermitian, Open systems, Phononics, Wave Propagation |
| الوصف: | Non-Hermitian and open systems are those that interact with their environment by the flows of energy, particles, and information. These systems show rich physical behaviors such as unidirectional wave reflection, enhanced transmission, and enhanced sensitivity to external perturbations comparing to a Hermitian system. To study non-Hermitian and open systems, we first present key concepts and required mathematical tools such as the theory of linear operators, linear algebra, biorthogonality, and exceptional points. We first consider the operator properties of various phononic eigenvalue problems. The aim is to answer some fundamental questions about the eigenvalues and eigenvectors of phononic operators. These include questions about the potential real and complex nature of the eigenvalues, whether the eigenvectors form a complete basis, what are the right orthogonality relationships, and how to create a complete basis when none may exist at the outset. In doing so we present a unified understanding of the properties of the phononic eigenvalues and eigenvectors which would emerge from any numerical method employed to compute such quantities. Next, we apply the mentioned theories on the phononic operators to the problem of scattering of in-plane waves at an interface between a homogeneous medium and a layered composite. This problem is an example of a non self-adjoint operator with biorthogonal eigenvectors and a complex spectrum. Since this problem is non self-adjoint, the degeneracies in the spectrum generally represent a coalescing of both the eigenvalues and eigenvectors (exceptional points). These degeneracies appear in both the complex and real domains of the wavevector. After calculating the eigenvalues and eigenvectors, we then calculate the scattered fields through a novel application of the Betti-Rayleigh reciprocity theorem. Several numerical examples showing rich scattering phenomena are presented afterward. We also prove that energy flux conservation is a restatement of the biorthogonality relationship ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| وصف الملف: | application/pdf |
| اللغة: | English |
| العلاقة: | islandora:1024913; http://hdl.handle.net/10560/islandora:1024913Test; http://repository.iit.edu/islandora/object/islandora%3A1024913/datastream/TN/view/Non-Hermitian%20Phononics.jpgTest |
| الإتاحة: | http://hdl.handle.net/10560/islandora:1024913Test http://repository.iit.edu/islandora/object/islandora%3A1024913/datastream/TN/view/Non-Hermitian%20Phononics.jpgTest |
| حقوق: | In Copyright ; http://rightsstatements.org/page/InC/1.0Test/ ; Restricted Access |
| رقم الانضمام: | edsbas.7DF33EF3 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |