Mathematical Analysis in Materials Science and Spectral Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 947

Special Issue Editors

Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Interests: inverse problems and wave imaging; partial differential equations; mathematical materials science; asymptotic and spectral analysis; numerical analysis and scientific computing; finite element method

E-Mail Website
Guest Editor
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Interests: inverse problems; wave scattering and imaging; numerical analysis; scientific computing

Special Issue Information

Dear Colleagues,

Materials science is an interdisciplinary field focused on the investigation and engineering of novel materials. Mathematical analysis plays a fundamental role in the development of a comprehensive understanding of material mechanisms. Thus, this Special Issue is dedicated to original research and reviews on mathematical analysis in materials science and spectral theory. Topics of interest include inverse problems, imaging, partial differential equations, spectral analysis, numerical analysis and scientific computing, and machine learning in material science.

Dr. Hongjie Li
Dr. Xianchao Wang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical analysis
  • spectral analysis
  • engineering materials
  • scientific computing
  • machine learning

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

27 pages, 5709 KiB  
Article
Influence of the Schottky Junction on the Propagation Characteristics of Shear Horizontal Waves in a Piezoelectric Semiconductor Semi-Infinite Medium
by Xiao Guo, Yilin Wang, Chunyu Xu, Zibo Wei and Chenxi Ding
Mathematics 2024, 12(4), 560; https://doi.org/10.3390/math12040560 - 13 Feb 2024
Cited by 2 | Viewed by 705
Abstract
In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of [...] Read more.
In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of biased electric fields. Then, considering the propagation of a shear horizontal wave in the piezoelectric semiconductor semi-infinite medium, two equivalent mathematical models are established. In the first mathematical model, the Schottky junction is theoretically treated as an electrically imperfect interface, and an interface characteristic length is utilized to describe the interface effect of the Schottky junction. To legitimately confirm the interface characteristic length, a second mathematical model is established, in which the Schottky junction is theoretically treated as an electrical gradient layer. Finally, the dispersion and attenuation curves of shear horizontal waves are numerically calculated using these two mathematical models to discuss the influence of the Schottky junction on the dispersion and attenuation characteristics of shear horizontal waves. Utilizing the equivalence of these two mathematical models and the above numerical results, the numerical value of the interface characteristic length is reliably legitimately confirmed; this value is independent of the thickness of the upper metal layer, the doping concentration of the lower n-type piezoelectric semiconductor substrate, and biasing electric fields. Only the biasing electric field parallel to the Schottky junction can provide an evident influence on the attenuation characteristics of shear horizontal waves and enhance the interface effect of the Schottky junction. Since the second mathematical model is also a validation of our previous mathematical model established through the state transfer equation method, some numerical results calculated using these two mathematical models are compared with those obtained using the previous method to verify the correctness and superiority of the research work presented in this paper. Since these two mathematical models can better calculate the dispersion and attenuation curves of high-frequency waves in micro- and nano-scale piezoelectric semiconductor materials, the establishment of mathematical models and the revelation of physical mechanisms are fundamental to the analysis and optimization of micro-scale resonators, energy harvesters, and amplifications. Full article
(This article belongs to the Special Issue Mathematical Analysis in Materials Science and Spectral Theory)
Show Figures

Figure 1

Back to TopTop