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Keywords = higher-order Sturm–Liouville problems

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17 pages, 1724 KiB  
Article
Slow Body MHD Waves in Inhomogeneous Photospheric Waveguides
by Istvan Ballai, Fisal Asiri, Viktor Fedun, Gary Verth, Emese Forgács-Dajka and Abdulrahman B. Albidah
Universe 2024, 10(8), 334; https://doi.org/10.3390/universe10080334 - 21 Aug 2024
Cited by 2 | Viewed by 1067
Abstract
The present study deals with the investigation of the oscillatory morphology of guided slow body MHD modes in inhomogeneous magnetic waveguides that appear in the solar photospheric plasmas in the forms of pores or sunspots. The eigenvalues and eigenfunctions related to these waves [...] Read more.
The present study deals with the investigation of the oscillatory morphology of guided slow body MHD modes in inhomogeneous magnetic waveguides that appear in the solar photospheric plasmas in the forms of pores or sunspots. The eigenvalues and eigenfunctions related to these waves in an isothermal plasma are obtained numerically by solving a Sturm-Liouville problem with Dirichlet boundary conditions set at the boundary of the waveguide. Our results show that the inhomogeneities in density (pressure) and magnetic field have a strong influence on the morphology of waves, and higher-order more are sensitive to the presence of inhomogeneity. Our results suggest that he identification of modes just by a simple visual inspection can lead to a misinterpretation of the nature of modes. Full article
(This article belongs to the Special Issue Solar and Stellar Activity: Exploring the Cosmic Nexus)
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15 pages, 782 KiB  
Article
Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States
by Souhardya Sen, Shubham Kumar, Athul Kunjipurayil, Pinku Routaray, Sayantan Ghosh, Probit J. Kalita, Tianqi Zhao and Bharat Kumar
Galaxies 2023, 11(2), 60; https://doi.org/10.3390/galaxies11020060 - 19 Apr 2023
Cited by 20 | Viewed by 3362
Abstract
We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron [...] Read more.
We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme–Hartree–Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS. Full article
(This article belongs to the Special Issue The 10th Anniversary of Galaxies: The Astrophysics of Neutron Stars)
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14 pages, 424 KiB  
Article
Solutions of Sturm-Liouville Problems
by Upeksha Perera and Christine Böckmann
Mathematics 2020, 8(11), 2074; https://doi.org/10.3390/math8112074 - 20 Nov 2020
Cited by 8 | Viewed by 4653
Abstract
This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems. Next, a concrete implementation to the inverse Sturm–Liouville problem algorithm proposed by Barcilon (1974) is [...] Read more.
This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems. Next, a concrete implementation to the inverse Sturm–Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm–Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm–Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
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24 pages, 785 KiB  
Article
Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion
by Upeksha Perera and Christine Böckmann
Mathematics 2019, 7(6), 544; https://doi.org/10.3390/math7060544 - 14 Jun 2019
Cited by 9 | Viewed by 4029
Abstract
In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct [...] Read more.
In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively. Full article
(This article belongs to the Special Issue Numerical Analysis: Inverse Problems – Theory and Applications)
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