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Mathematics
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Applied Mathematics in Astrophysics and Space Science
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Applied Mathematics in Astrophysics and Space Science

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

Deadline for manuscript submissions: 30 October 2024 | Viewed by 12256

Special Issue Editors

Dr. Sanjar Abrarov

E-Mail Website
Guest Editor
1. Thoth Technology Inc., Algonquin Radio Observatory, Achray Road, RR6, Pembroke, ON K8A 6W7, Canada
2. Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
3. Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
Interests: modeling and simulation; numerical methods and approximations; fourier methods and analysis
Prof. Dr. Rehan Siddiqui

E-Mail Website
Guest Editor
1. Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
2. Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
3. Department Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
Interests: atmospheric physics; cloud detection; numerical modelling and simulation; line-by-line computation; forest fires; remote sensing; quantitative radiative transfer; climate change

Special Issue Information

Dear Colleagues,

Human activities in industry and agriculture cause a negative impact on the Atmosphere of the Earth. As a result of the annual rate exceeding 2 ppm of CO2 greenhouse gas emission, we can observe a significant increase in the atmospheric temperature over the last decades. The increase in atmospheric temperature affects weather and climate on the Earth. It also intensifies water evaporation and the formation of clouds. Consequently, this increases chances for ignition of forest and wildfires globally due to thunderstorm lightning. The aerosols and other pollutants including hazardous heavy metal particles and particulate matters that are emitted from cars, thermal power stations, factories, forests and wildfires spoil the quality of air. Development of space technologies for geo-satellite communication and remote sensing may result in space debris that can orbit around the Earth for many decades. The mathematical and computational methods may be used as efficient tools to predict, for example, the dynamics of pollutants in the Earth atmosphere and compute trajectories of the space debris. Therefore, we would like to devote this Special Issue: “Applied Mathematics in Astrophysics and Space Science”, to Mathematical Physics/Engineering related to Astrophysics and Space Science in a broad scope. It includes, but not limited to, Mathematical Physics/Engineering and Computational Mathematics. Theoretical Analysis, Modeling and Simulation as well as Detection, Measurements, Instrumentation and Statistics with mathematical and computational background are also within the scope of this Special Issue. Computational Finance may also be relevant to the Special Issue, if the content of the study is closely related to the above subjects. We would like to encourage researchers specializing in Astrophysics and Space Science to contribute their state of the art to the Special Issue.

Dr. Sanjar Abrarov
Prof. Dr. Rehan Siddiqui
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

  • atmospheric techniques
  • atmospheric chemistry
  • mathematical methods
  • algorithms
  • modeling and simulation
  • radiative transfer
  • remote sensing
  • detection
  • instrumentation

Published Papers (6 papers)

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Research

11 pages, 1797 KiB  
Article
On the Uniqueness of the Solution to the Inverse Problem of Determining the Diffusion Coefficient of the Magnetic Field Necessary for Constructing Analytical Models of the Magnetic Field of Mercury
by Inna Stepanova, Igor Kolotov, Dmitry Lukyanenko and Alexey Shchepetilov
Mathematics 2024, 12(8), 1169; https://0-doi-org.brum.beds.ac.uk/10.3390/math12081169 - 12 Apr 2024
Viewed by 367
Abstract
This paper considers the problem of the uniqueness of the solution to the coefficient inverse problem for the system of equations of magneto-hydrodynamics, the solution to which allows more accurately describing the processes of generating the magnetic field of planets with a magneto-hydrodynamic [...] Read more.
This paper considers the problem of the uniqueness of the solution to the coefficient inverse problem for the system of equations of magneto-hydrodynamics, the solution to which allows more accurately describing the processes of generating the magnetic field of planets with a magneto-hydrodynamic dynamo. The conditions under which it is possible to determine three components of the magnetic induction vector and the magnetic field diffusion coefficient are determined. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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20 pages, 768 KiB  
Article
A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing
by Adelina Bärligea, Philipp Hochstaffl and Franz Schreier
Mathematics 2023, 11(13), 2839; https://0-doi-org.brum.beds.ac.uk/10.3390/math11132839 - 24 Jun 2023
Cited by 1 | Viewed by 955
Abstract
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach [...] Read more.
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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12 pages, 1176 KiB  
Article
Investigation of the Stress-Strain State of a Rectangular Plate after a Temperature Shock
by A. V. Sedelnikov, D. I. Orlov, V. V. Serdakova and A. S. Nikolaeva
Mathematics 2023, 11(3), 638; https://0-doi-org.brum.beds.ac.uk/10.3390/math11030638 - 27 Jan 2023
Cited by 8 | Viewed by 1290
Abstract
In this paper, the temperature shock phenomenon is considered. This phenomenon occurs during the operation of engineering structures on Earth and in outer space. A rectangular plate has been selected as a structural element exposed to temperature shock. It has a rigidly sealed [...] Read more.
In this paper, the temperature shock phenomenon is considered. This phenomenon occurs during the operation of engineering structures on Earth and in outer space. A rectangular plate has been selected as a structural element exposed to temperature shock. It has a rigidly sealed edge and three free edges. A one-dimensional third initial boundary value problem of thermal conductivity was posed and solved to study the stress–strain state of the plate. Fourier’s law was used to solve this problem, taking into account the inertial term, since the temperature shock is a fairly fast-dynamic phenomenon. It was believed that all the thermophysical properties of the plate are constant and do not depend on its temperature. As a result, the temperature field of the plate was obtained after the temperature shock. This temperature field generates temperature stresses inside the plate, which lead to temperature deformations. To determine these deformations, the initial boundary value problem of thermoelasticity was posed and solved in this work. The Sophie Germain equation was used while solving this problem. To describe the plate, the theory of flexible plates was used, taking into account the stresses in the middle surface of the plate. Next, the accuracy of analytical solutions for the points displacement of a homogeneous plate subjected to a temperature shock was investigated. The temperature field was constructed using a numerical simulation. Functions of the displacement vector components were obtained using approximate analytical solutions. The accuracy of approximate analytical solutions for the components of the plate points deformation vector was estimated. The obtained results allow us to describe the stress–strain state of the plate after the temperature shock. The results of this work can be used in the design of engineering structures for both terrestrial and space purposes in terms of stability calculations and the implementation of deformation constraints. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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14 pages, 3438 KiB  
Article
A Two-Domain MATLAB Implementation for Efficient Computation of the Voigt/Complex Error Function
by Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal and Brendan M. Quine
Mathematics 2022, 10(19), 3451; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193451 - 22 Sep 2022
Cited by 1 | Viewed by 3827
Abstract
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the number of the interpolation grid-points is dependent on the input parameter y. The [...] Read more.
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the number of the interpolation grid-points is dependent on the input parameter y. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN molecular spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation, especially at smaller ranges of the parameter x. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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13 pages, 3340 KiB  
Article
On the Highly Accurate Evaluation of the Voigt/Complex Error Function with Small Imaginary Argument
by Yihong Wang, Bin Zhou, Bubin Wang, Rong Zhao, Qi Liu and Minglu Dai
Mathematics 2022, 10(3), 308; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030308 - 19 Jan 2022
Cited by 3 | Viewed by 1567
Abstract
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument y ≤ 0.1. Error analysis and run-time tests in double-precision arithmetic [...] Read more.
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument y ≤ 0.1. Error analysis and run-time tests in double-precision arithmetic reveals that in the real and imaginary parts, the proposed algorithm provides an average accuracy exceeding 10−15 and 10−16, respectively, and the calculation speed is as fast as that reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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14 pages, 1528 KiB  
Article
Super-Accuracy Calculation for the Half Width of a Voigt Profile
by Yihong Wang, Bin Zhou, Rong Zhao, Bubin Wang, Qi Liu and Minglu Dai
Mathematics 2022, 10(2), 210; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020210 - 11 Jan 2022
Cited by 8 | Viewed by 1751
Abstract
A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for [...] Read more.
A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for arbitrary αL/αG ratios. In particular, the accuracy reaches an astonishing 10−34 (quadruple precision) in the domain 0 ≤ αL/αG ≤ 0.2371 ∪ αL/αG ≥ 33.8786. Full article
(This article belongs to the Special Issue Applied Mathematics in Astrophysics and Space Science)
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