Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition

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

Deadline for manuscript submissions: 20 May 2025 | Viewed by 280

Special Issue Editor


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Guest Editor
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
Interests: numerical analysis; applied mathematics; computational mathematics; computational mechanics; civil and structural engineering; CAE software
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Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of the previous successful Special Issue “Numerical Computation, Data Analysis and Software in Mathematics and Engineering” in the MDPI journal Mathematics.

In recent years, mathematical models, numerical methods and data analyses have been paid more attention. After the finite element method, the meshless method has been another effective tool for solving science and engineering problems. Numerical methods, such as the finite element method, boundary element method and meshless method, have played important roles in numerical simulations of complicated problems in science, engineering and society fields. Various numerical methods have been presented for solving problems in different fields, and the corresponding computational efficiency, accuracy and convergence have also been studied. With the development of big data, a numerical simulation based on data analysis or big data will be an important direction for science and engineering computation. Furthermore, deep learning is also a new effective approach for analyzing the properties of new materials.

In this Special Issue, we particularly take an interest in manuscripts that report the relevance of numerical computation and data analysis for mathematical and engineering problems. The Special Issue will become an international forum for researchers to summarize the most recent developments of numerical simulations and data analysis within the last five years, especially for new problems. Moreover, manuscripts on the mathematical theories of numerical computation and data analysis for complicated science, engineering or social problems are welcome. We are also interested in the development of the corresponding aspects based on big data, including the corresponding theory, numerical method and the applications.

Software is an important part of numerical computation and data analysis in mathematics and engineering. This Special Issue also concerns the developments of the software of numerical methods, including the finite element method, boundary element method and meshless method, and the methods for data analysis.

Prof. Dr. Yumin Cheng
Guest Editor

Manuscript Submission Information

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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

  • numerical method
  • numerical simulation
  • finite element method
  • boundary element method
  • meshless method
  • mathematical model
  • data analysis
  • software

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Published Papers (1 paper)

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Research

17 pages, 3915 KiB  
Article
The Potential Changes and Stereocilia Movements during the Cochlear Sound Perception Process
by Bin Liu, Junyi Liang, Wenjuan Yao and Chun Xu
Mathematics 2024, 12(16), 2470; https://doi.org/10.3390/math12162470 - 10 Aug 2024
Viewed by 220
Abstract
Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. [...] Read more.
Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. This limitation in measurement capability makes it difficult to fully understand the contribution of stereocilia and transduction channels to cochlear potentials. In view of this, firstly, this article obtains the stereocilia movement generated by basilar membrane (BM) vibration based on the positional relationship between the various structures of the organ Corti. Secondly, Kirchhoff’s law is used to establish an electric field model of the cochlear cavity, and the stereocilia movement is embedded in the electric field by combining the gated spring model. Finally, a force-electric coupling mathematical model of the cochlea is established. The results indicated that the resistance variation between different cavities in the cochlea leads to a sharp tuning curve. As the displacement of the BM increased, the longitudinal potential along the cochlea continued to move toward the base. The decrease in stereocilia stiffness reduced the deflection angle, thereby reducing the transduction current and lymphatic potential. Full article
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