Fractional Mathieu Equation with Two Fractional Derivatives and Some Applications
Fractal and FractionalThe importance of this research comes from the several applications of the Mathieu equation and its generalizations in many scientific fields. Two models of fractional Mathieu equations are provided using Katugampola fractional derivatives in the sense ...
Ahmed Salem +2 more
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Spectral Insights into Active Matter: Exceptional Points and the Mathieu Equation [PDF]
EntropyWe show that recent numerical findings of universal scaling relations in systems of noisy, aligning self-propelled particles by Rüdiger Kürstencan robustly be explained by perturbation theory and known results for the Mathieu equation with purely ...
Horst-Holger Boltz, Thomas Ihle
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Influence of material distribution and damping on the dynamic stability of Bernoulli-Euler beams [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2023 The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system ...
Sebastian Garus +7 more
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Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations [PDF]
Opuscula Mathematica, 2022 The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using ...
Kazuki Ishibashi
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Some Novel Analytical Approximations to the (Un)damped Duffing–Mathieu Oscillators
Journal of Mathematics, 2022 Some novel exact solutions and approximations to the damped Duffing–Mathieu-type oscillator with cubic nonlinearity are obtained. This work is divided into two parts: in the first part, some exact solutions to both damped and undamped Mathieu oscillators
Haifa A. Alyousef +3 more
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Mathieu Equation and Elliptic Curve [PDF]
Communications in Theoretical Physics, 2012 12 pages; minor improvement of the Conclusion section, references ...
He, Wei, Miao, Yan-Gang
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The asymptotics of the gap in the Mathieu equation [PDF]
Annals of Physics, 1981 We provide a simple proof that the kth gap, Δ_k, for the Mathieu operator −d^2dx^2 + 2κcos(2x) is Δ_k = 8(κ4)^k[(k − 1)!]^(−2)(1 + o(k^(−2))), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.
Avron, Joseph, Simon, Barry
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Exact WKB analysis and TBA equations for the Mathieu equation
Physics Letters B, 2020 We derive the Thermodynamic Bethe Ansatz (TBA) equations for the exact WKB periods of the Mathieu equation in the weak coupling region. We will use the TBA equations to calculate the quantum corrections to the WKB periods, which are regarded as the ...
Keita Imaizumi
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The Double Points of Mathieu's Differential Equation [PDF]
Mathematics of Computation, 1969 Mathieu’s differential equation, y + ( a −
Blanch, G., Clemm, D. S.
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Influence of Material Defects on the Dynamic Stability of the Bernoulli-Euler Beam [PDF]
Archives of Metallurgy and Materials, 2021 The paper presents the results of tests on dynamic stability of Bernoulli-Euler beam with damages. Damages (cracks) were modeled using three rotational springs.
W. Sochacki, S. Garus, J. Garus
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