| 11. |
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| 12. |
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| 13. |
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| 14. |
- Engström, Christian
(författare)
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Inverse bounds and bulk properties of complex-valued two-component composites
- 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. 194-213
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Tidskriftsartikel (refereegranskat)abstract
- The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quantified in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the effective permittivity, we present a general scheme to estimate the microstructural parameters such as the volume fraction and the anisotropy of two-component composites. The estimates are given as bounds, that is, the largest parameter region which is compatible with the available information. Thus, more information produces better estimates on the microstructural parameters. The method, which uses complex-valued measurements of bulk properties of the composite, is illustrated by numerical examples.
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| 15. |
- Engström, Christian
(författare)
-
Inverse bounds of two-component composites
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:3, s. 666-679
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented for estimating microstructural parameters from permittivity measurements of two-component composites. This structural information is described by a particular positive measure in the Stieltjes integral representation of the effective permittivity. The dependence on the geometrical structure can be reduced to the problem of calculating the moments of the measure. We present a method that uses measurement data at a set of distinct frequencies or temperatures to calculate bounds on several moments. These inverse bounds are improved when the volume fraction is known or the material is isotropic. Composites with known geometrical structure illustrate the method.
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| 16. |
- Engström, Christian, et al.
(författare)
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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:1, s. 231-247
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Tidskriftsartikel (refereegranskat)abstract
- We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.
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| 17. |
- Gosse, Laurent, et al.
(författare)
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Existence, uniqueness, and a constructive solution algorithm for a class of finite Markov moment problems
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 68:6, s. 1618-1640
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Tidskriftsartikel (refereegranskat)abstract
- We consider a class of finite Markov moment problems with an arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the nonunique solution families. Moreover, we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution.
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| 18. |
- 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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| 19. |
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| 20. |
- Helsing, Johan, et al.
(författare)
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An extended charge-current formulation of the electromagnetic transmission problem
- 2020
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 80:2, s. 951-976
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Tidskriftsartikel (refereegranskat)abstract
- A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all wavenumbers in the closed upper half-plane belonging to argument sets for which Maxwell's equations have unique solutions. This includes the challenging combination of a real positive wavenumber in the outer region and an imaginary wavenumber inside the object. The formulation, or variants thereof, is particularly suitable for numerical field evaluations as confirmed by examples involving both smooth and nonsmooth objects.
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