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Mathematics
Special Issues
Mathematical Analysis and Its Application in Astrophysics
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Mathematical Analysis and Its Application in Astrophysics

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

Deadline for manuscript submissions: 15 August 2024 | Viewed by 790

Special Issue Editor

Dr. Zhoujian Cao

E-Mail Website
Guest Editor
The Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, China
Interests: numerical relativity; gravity theory; nonlinear physics; large scale scientific computation

Special Issue Information

Dear Colleagues,

Since the origin of natural science, mathematics has co-developed with astrophysics. Many well-known mathematicians, including Leonhard Euler, Joseph-Louis Lagrange, etc., are also astrophysicists. In recent years, more data about astronomical observations about black holes, cosmology, and other phenomena have been accumulated. Along with these observations, mathematical analysis has played and continues to play a very important role. In addition, deeper mathematical analyses will help people to understand the observational data and explore the fundamental problems.

This Special Issue will gather a collection of articles about mathematical developments related to astrophysical phenomena, including gravitational waves, cosmology, compact objects, accretion disks, and related topics.

Theoretical, simulation, and data analysis-related contributions are welcome. The selection criteria consider the formal and technical soundness, experimental support, and the relevance of the contributions.

Dr. Zhoujian Cao
Guest Editor

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

  • Einstein equation
  • partial differential equation
  • numerical relativity
  • geodesic
  • gravitational wave
  • shadow of black hole
  • self-force
  • effective one body

Published Papers (1 paper)

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Research

11 pages, 809 KiB  
Article
Eigenvalue Problem Describing Magnetorotational Instability in Outer Regions of Galaxies
by Evgeny Mikhailov and Tatiana Khasaeva
Mathematics 2024, 12(5), 760; https://doi.org/10.3390/math12050760 - 4 Mar 2024
Viewed by 627
Abstract
The existence of magnetic fields in spiral galaxies is beyond doubt and is confirmed by both observational data and theoretical models. Their generation occurs due to the dynamo mechanism action associated with the properties of turbulence. Most studies consider magnetic fields at moderate [...] Read more.
The existence of magnetic fields in spiral galaxies is beyond doubt and is confirmed by both observational data and theoretical models. Their generation occurs due to the dynamo mechanism action associated with the properties of turbulence. Most studies consider magnetic fields at moderate distances to the center of the disk, since the dynamo number is small in the marginal regions, and the field growth should be suppressed. At the same time, the computational results demonstrate the possibility of magnetic field penetration into the marginal regions of galaxies. In addition to the action of the dynamo, magnetorotational instability (MRI) can serve as one of the mechanisms of the field occurrence. This research is devoted to the investigation of MRI impact on galactic magnetic field generation and solving the occurring eigenvalue problems. The problems are formulated assuming that the perturbations may possibly increase. In the present work, we consider the eigenvalue problem, picturing the main field characteristics in the case of MRI occurrence, where the eigenvalues are firmly connected with the average vertical scale of the galaxy, to find out whether MRI takes place in the outer regions of the galaxy. The eigenvalue problem cannot be solved exactly; thus, it is solved using the methods of the perturbation theory for self-adjoint operators, where the eigenvalues are found using the series with elements including parameters characterizing the properties of the interstellar medium. We obtain linear and, as this is not enough, quadratic approximations and compare them with the numerical results. It is shown that they give a proper precision. We have compared the approximation results with those from numerical calculations and they were relatively close for the biggest eigenvalue. Full article
(This article belongs to the Special Issue Mathematical Analysis and Its Application in Astrophysics)
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