| 1. |
- Ammari, Habib, et al.
(författare)
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Subwavelength Localized Modes for Acoustic Waves in Bubbly Crystals With a Defect
- 2018
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 78:6, s. 3316-3335
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Tidskriftsartikel (refereegranskat)abstract
- The ability to control wave propagation is of fundamental interest in many areas of physics. Photonic and phononic crystals have proved very useful for this purpose but, because they are based on Bragg interferences, these artificial media require structures with large dimensions. In [Ammari et al., J. Differential Equations, 263 (2017), pp. 5610-5629], it has been proved that a subwavelength bandgap opening occurs in bubble phononic crystals. To demonstrate the opening of a subwavelength phononic bandgap, a periodic arrangement of bubbles is considered and their subwavelength Minnaert resonance is exploited. In this paper, this subwavelength bandgap is used to demonstrate cavities, very similar to those obtained in photonic and phononic crystals, albeit of deeply subwavelength dimensions. The key idea is to increase the size of a single bubble inside the crystal, thus creating a defect. The goal is then to analytically and numerically show that this crystal has a localized eigenmode close to the defect bubble.
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| 2. |
- Appelö, Daniel, et al.
(författare)
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Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability
- 2006
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 67:1, s. 1-23
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Tidskriftsartikel (refereegranskat)abstract
- Since its introduction the perfectly matched layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limited to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters, which is applicable to all hyperbolic systems and which we prove is well-posed and perfectly matched. We also introduce an automatic method for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell's equations, the linearized Euler equations, and arbitrary 2 x 2 systems in (2 + 1) dimensions.
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| 3. |
- Dao, Tuan Anh, et al.
(författare)
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Viscous Regularization of the MHD Equations
- 2024
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 84:4, s. 1439-1459
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Tidskriftsartikel (refereegranskat)abstract
- Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this paper, we present a new viscous flux to regularize the MHD equations that holds many attractive properties. In particular, we prove that the proposed viscous flux preserves positivity of density and internal energy, satisfies the minimum entropy principle, is consistent with all generalized entropies, and is Galilean and rotationally invariant. We also provide a variation of the viscous flux that conserves angular momentum. To make the analysis more useful for numerical schemes, the divergence of the magnetic field is not assumed to be zero. Using continuous finite elements, we show several numerical experiments, including contact waves and magnetic reconnection.
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| 4. |
- Gustafsson, Bertil, et al.
(författare)
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Incompletely parabolic problems in fluid dynamics
- 1978
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 35, s. 343-357
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Tidskriftsartikel (refereegranskat)
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| 5. |
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