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math.AP2020
Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies
Alexander Dabrowski, Ahcene Ghandriche, Mourad Sini
We analyze mathematically the acoustic imaging modality using bubbles as contrast agents. These bubbles are modeled by mass densities and bulk moduli enjoying contrasting scales. T…
math.AP2017
A localized boundary deformation which splits the spectrum of the Laplacian
Alexander Dabrowski
For any Lipschitz domain we construct an arbitrarily small, localized perturbation which splits the spectrum of the Laplacian into simple eigenvalues. We use for this purpose a Had…
math.AP2016★ 1 cited
Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions
Alexander Dabrowski
The first terms of the small volume asymptotic expansion for the splitting of Neumann boundary condition Laplacian eigenvalues due to a grounded inclusion of size ε are derived. An…