IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3106-d1193696.html
   My bibliography  Save this article

Eigenvalue Problem for a Reduced Dynamo Model in Thick Astrophysical Discs

Author

Listed:
  • Evgeny Mikhailov

    (Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
    P. N. Lebedev Physical Institute, 119991 Moscow, Russia
    Center for Advanced Studies, Skolkovo Institute of Science and Technology, 121205 Moscow, Russia)

  • Maria Pashentseva

    (Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia)

Abstract

Magnetic fields of different astrophysical objects are generated by the dynamo mechanism. Dynamo is based on the alpha-effect and differential rotation, which are described using a system of parabolic equations. Their solution is an important problem in magnetohydrodynamics and mathematical physics. They can be solved assuming exponential growth of the solution, which leads to an eigenvalue problem for a differential operator connected with spatial coordinates. Here, we describe a system of equations connected with the generation of magnetic field in discs, which are associated with galaxies and binary systems. For an ideal case of an infinitely thin disc, the eigenvalue problem can be precisely solved. If we take into account the finite thickness of the disc, the problem becomes more difficult. The solution can be found using asymptotical methods based on perturbations of the eigenvalues. Here, we present two different models which describe field evolution for different cases. For the first, we find eigenvalues taking into account linear and quadratic terms for the perturbations in the eigenvalue problem. For the second, we find eigenvalues using only linear terms; this is quite sufficient. Results were verified through numerical modeling, and basic computational tests show proper correspondence between different methods.

Suggested Citation

  • Evgeny Mikhailov & Maria Pashentseva, 2023. "Eigenvalue Problem for a Reduced Dynamo Model in Thick Astrophysical Discs," Mathematics, MDPI, vol. 11(14), pages 1-14, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3106-:d:1193696
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3106/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/14/3106/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Satyajit Chincholkar & Mohd Tariq & Shabana Urooj, 2023. "Large-Signal Stability of the Quadratic Boost Converter Using a Disturbance Observer-Based Sliding-Mode Control," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    2. Evgeny Mikhailov & Tatiana Khasaeva, 2024. "Eigenvalue Problem Describing Magnetorotational Instability in Outer Regions of Galaxies," Mathematics, MDPI, vol. 12(5), pages 1-11, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meng An & Haixiang Zhang, 2023. "High-Dimensional Mediation Analysis for Time-to-Event Outcomes with Additive Hazards Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    2. Abdumauvlen Berdyshev & Dossan Baigereyev & Kulzhamila Boranbek, 2023. "Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model," Mathematics, MDPI, vol. 11(17), pages 1-27, September.
    3. Han-Sol Lee & Changgyun Jin & Chanwoo Shin & Seong-Eun Kim, 2023. "Sparse Diffusion Least Mean-Square Algorithm with Hard Thresholding over Networks," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
    4. Elif Tan & Diana Savin & Semih Yılmaz, 2023. "A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    5. Jun Zhang & Jingjing Zhang & Shangyou Zhang, 2023. "Explicit Symplectic Runge–Kutta–Nyström Methods Based on Roots of Shifted Legendre Polynomial," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    6. Yongou Zhang & Zhongjian Ling & Hao Du & Qifan Zhang, 2023. "Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers," Mathematics, MDPI, vol. 11(18), pages 1-11, September.
    7. Ishtiaq Ali & Muhammad Yaseen & Muhammad Abdullah & Sana Khan & Fethi Bin Muhammad Belgacem, 2023. "An Innovative Numerical Method Utilizing Novel Cubic B-Spline Approximations to Solve Burgers’ Equation," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
    8. Jiaqi Wang & Jianbing Su, 2023. "Boundedness and Compactness of Weighted Composition Operators from α -Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind," Mathematics, MDPI, vol. 11(20), pages 1-27, October.
    9. Ismagil T. Habibullin & Aigul R. Khakimova & Alfya U. Sakieva, 2023. "Miura-Type Transformations for Integrable Lattices in 3D," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    10. Badriah Alamri, 2023. "Solving Integral Equation and Homotopy Result via Fixed Point Method," Mathematics, MDPI, vol. 11(21), pages 1-19, October.
    11. Salman Khalid & Jinwoo Song & Muhammad Muzammil Azad & Muhammad Umar Elahi & Jaehun Lee & Soo-Ho Jo & Heung Soo Kim, 2023. "A Comprehensive Review of Emerging Trends in Aircraft Structural Prognostics and Health Management," Mathematics, MDPI, vol. 11(18), pages 1-42, September.
    12. Jiří Holman, 2023. "Numerical Solution of Transition to Turbulence over Compressible Ramp at Hypersonic Velocity," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    13. Jianyu Wang & Chunhua Fang & Guifeng Zhang, 2023. "Multi-Effective Collocation Methods for Solving the Volterra Integral Equation with Highly Oscillatory Fourier Kernels," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    14. Qiu Lin & Ruisheng Qi, 2023. "Optimal Weak Order and Approximation of the Invariant Measure with a Fully-Discrete Euler Scheme for Semilinear Stochastic Parabolic Equations with Additive Noise," Mathematics, MDPI, vol. 12(1), pages 1-29, December.
    15. Jeffrey A. Hogan & Joseph D. Lakey, 2023. "Spatio–Spectral Limiting on Replacements of Tori by Cubes," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    16. Nazim & Nadeem Ur Rehman & Ahmad Alghamdi, 2023. "On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    17. Li Cheng & Wen-Xiu Ma, 2023. "Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations," Mathematics, MDPI, vol. 11(19), pages 1-8, September.
    18. Jagdish S. Thakur & Archana Thakur & Lawrence G. Lum, 2023. "Mathematical Model to Predict Polyclonal T-Cell-Dependent Antibody Synthesis Responses," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    19. Amira F. Daghistani & Ahmed M. T. Abd El-Bar & Ahmed M. Gemeay & Mahmoud A. E. Abdelrahman & Samia Z. Hassan, 2023. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    20. Sarfraz Nawaz Malik & Nazar Khan & Ferdous M. O. Tawfiq & Mohammad Faisal Khan & Qazi Zahoor Ahmad & Qin Xin, 2023. "Fuzzy Differential Subordination Associated with a General Linear Transformation," Mathematics, MDPI, vol. 11(22), pages 1-17, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3106-:d:1193696. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.