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@@ -1,6 +1,6 @@
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<!DOCTYPE html>
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<html lang="en">
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- <!--Copyright (C) 2018 E. Blåsten
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+ <!--Copyright (C) 2019 Emilia Blåsten
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Permission is granted to copy, distribute and/or modify this
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document under the terms of the GNU Free Documentation License,
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Version 1.3 or any later version published by the Free Software
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@@ -9,7 +9,7 @@
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"LICENSE.html". -->
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<head>
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<meta charset="utf-8" />
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- <title>Research by E. Blåsten</title>
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+ <title>Research by Emily Blåsten</title>
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<link rel="stylesheet" href="include/mathstyles.css">
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<link rel="stylesheet" href="include/homepage.css">
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@@ -121,6 +121,17 @@
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<ol reversed>
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<li>
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<a class="anchor" id="Blasten-Li-Liu-Wang-2018"></a>
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+ <span class="ref-authors">E. Blåsten, H. Liu, J. Xiao,</span>
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+ <span class="ref-title">On an electromagnetic problem
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+ in a corner and its applications.</span>
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+ <div class="ref-links">
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+ <a href="#desc_Blasten-Liu-Xiao-2019">Description</a>
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+ <a href="https://arxiv.org/abs/1901.00581">Preprint</a>
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+ </div>
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+ </li>
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+
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+ <li>
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+ <a class="anchor" id="Blasten-Li-Liu-Wang-2018"></a>
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<span class="ref-authors">E. Blåsten, H. Li, H. Liu, Y. Wang,</span>
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<span class="ref-title">Localization and
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geometrization in plasmon resonances and geometric
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@@ -131,16 +142,7 @@
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<a href="https://arxiv.org/abs/1809.08533">Preprint</a>
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</div>
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</li>
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- <li>
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- <a class="anchor" id="Blasten-Vesalainen-2018"></a>
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- <span class="ref-authors">E. Blåsten, E. V. Vesalainen,</span>
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- <span class="ref-title">Non-Scattering Energies and Transmission Eigenvalues in
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- <i>H<sup>n</sup></i>.</span>
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- <div class="ref-links">
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- <a href="#desc_Blasten-Vesalainen-2018">Description</a>
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- <a href="http://arxiv.org/abs/1809.04426/">Preprint</a>
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- </div>
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- </li>
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+
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<li>
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<a class="anchor" id="Blasten-Liu-2018"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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@@ -163,6 +165,29 @@
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<a href="https://arxiv.org/abs/1705.00815">Preprint</a>
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</div>
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</li>
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+ </ol>
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+ </p>
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+
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+ <p>
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+ <a class="anchor" id="pubs_accepted"></a>
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+ <h3>Accepted in Peer-Reviewed Journals</h3>
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+ <ol reversed>
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+ <li>
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+ <a class="anchor" id="BV2019"></a>
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+ <span class="ref-authors">E. Blåsten,
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+ E. Vesalainen,</span>
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+ <span class="ref-title">Non-Scattering Energies and
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+ Transmission Eigenvalues
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+ in <i>H<sup>n</sup></i>.</span>
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+ <span class="ref-journal">Annales Academiæ Scientiarum
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+ Fennicæ Mathematica,</span>
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+ <span class="ref-year">accepted 2019.</span>
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+ <div class="ref-links">
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+ <a href="#desc_BV2019">Description</a>
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+ <a href="https://arxiv.org/abs/1809.04426">Preprint</a>
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+ </div>
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+ </li>
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+
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<li>
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<a class="anchor" id="BlastenTzouWang2017"></a>
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<span class="ref-authors">E. Blåsten, L. Tzou,
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@@ -170,47 +195,59 @@
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<span class="ref-title">Uniqueness for the inverse
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boundary value problem with singular potentials in
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2D.</span>
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+ <span class="ref-journal">Mathematische Zeitschrift,</span>
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+ <span class="ref-year">accepted 2019.</span>
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<div class="ref-links">
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<a href="#desc_BlastenTzouWang2017">Description</a>
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<a href="https://arxiv.org/abs/1704.06397">Preprint</a>
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</div>
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</li>
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+
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+ <li>
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+ <a class="anchor" id="Pipes3"></a>
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+ <span class="ref-authors">E. Blåsten, F. Zouari,
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+ M. Louati and M. S. Ghidaoui,</span>
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+ <span class="ref-title">Blockage detection in
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+ networks: the area reconstruction method.</span>
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+ <span class="ref-journal">Mathematics in Engineering,</span>
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+ <span class="ref-year">accepted 2019.</span>
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+ <div class="ref-links">
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+ <a href="#desc_Pipes3">Description</a>
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+ <a href="https://arxiv.org/abs/1909.05497">Preprint</a>
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+ </div>
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+ </li>
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+
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<li>
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<a class="anchor" id="BlastenLiu2016"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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<span class="ref-title"> On corners scattering stably
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and stable shape determination by a single far-field
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pattern.</span>
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+ <span class="ref-journal">Indiana University
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+ Mathematics Journal,</span>
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+ <span class="ref-year">accepted 2019.</span>
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<div class="ref-links">
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<a href="#desc_BlastenLiu2016">Description</a>
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<a href="https://arxiv.org/abs/1611.03647">Preprint</a>
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</div>
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</li>
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- </ol>
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- </p>
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- <p>
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- <a class="anchor" id="pubs_accepted"></a>
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- <h3>Accepted in Peer-Reviewed Journals</h3>
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- <ol reversed>
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<li>
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- <a class="anchor" id="Blasten2018"></a>
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- <span class="ref-authors">E. Blåsten,</span>
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- <span class="ref-title">Nonradiating sources and
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- transmission eigenfunctions vanish at corners and
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- edges.</span>
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- <span class="ref-journal">SIAM Journal on Mathematical
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- Analysis,</span>
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- <span class="ref-volume">50,</span>
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- <span class="ref-issue">6</span>
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- <span class="ref-year">(2018)</span>
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- <span class="ref-pages">6255–6270.</span>
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+ <a class="anchor" id="Pipes2"></a>
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+ <span class="ref-authors">F. Zouari, M. Louati,
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+ S. Meniconi, E. Blåsten, M. S. Ghidaoui and
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+ B. Brunone,</span>
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+ <span class="ref-title">Experimental Verification of
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+ the Accuracy and Robustness of Area Reconstruction
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+ Method for a Pressurized Water Pipe System.</span>
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+ <span class="ref-journal">Journal of Hydraulic
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+ Engineering, ASCE,</span>
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+ <span class="ref-year">accepted 2019.</span>
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<div class="ref-links">
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- <a href="#desc_Blasten2018">Description</a>
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- <a href="https://doi.org/10.1137/18M1182048">Publication</a>
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- <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
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+ <a href="#desc_Pipes2">Description</a>
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</div>
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</li>
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+
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<li>
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<a class="anchor" id="Pipes1"></a>
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<span class="ref-authors">F. Zouari, E. Blåsten,
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@@ -220,9 +257,12 @@
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detection.</span>
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<span class="ref-journal">Journal of Hydraulic
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Engineering, ASCE,</span>
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- <span class="ref-year">accepted 2018.</span>
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+ <span class="ref-volume">145,</span>
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+ <span class="ref-issue">6</span>
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+ <span class="ref-year">(2019)</span>
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<div class="ref-links">
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<a href="#desc_Pipes1">Description</a>
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+ <a href="https://doi.org/10.1061/(ASCE)HY.1943-7900.0001602">Publication</a>
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</div>
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</li>
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<li>
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@@ -242,6 +282,24 @@
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</div>
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</li>
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<li>
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+ <a class="anchor" id="Blasten2018"></a>
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+ <span class="ref-authors">E. Blåsten,</span>
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+ <span class="ref-title">Nonradiating sources and
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+ transmission eigenfunctions vanish at corners and
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+ edges.</span>
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+ <span class="ref-journal">SIAM Journal on Mathematical
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+ Analysis,</span>
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+ <span class="ref-volume">50,</span>
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+ <span class="ref-issue">6</span>
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+ <span class="ref-year">(2018)</span>
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+ <span class="ref-pages">6255–6270.</span>
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+ <div class="ref-links">
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+ <a href="#desc_Blasten2018">Description</a>
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+ <a href="https://doi.org/10.1137/18M1182048">Publication</a>
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+ <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
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+ </div>
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+ </li>
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+ <li>
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<a class="anchor" id="Blasten2017"></a>
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">Well-posedness of the Goursat
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@@ -481,6 +539,117 @@
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<h2>Description of projects</h2>
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<dl>
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<dt>
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+ <a class="anchor" id="desc_desc_Blasten-Liu-Xiao-2019"></a>
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+ <a href="#desc_Blasten-Liu-Xiao-2019">
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+ <span class="ref-authors">E. Blåsten, H. Liu,
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+ J. Xiao,</span>
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+ <span class="ref-title">On an electromagnetic problem
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+ in a corner and its applications.</span>
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+ </a>
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+ </dt>
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+ <dd>
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+ <p>
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+ We consider the topic of scattering produced by
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+ electromagnetic sources having a corner, and was done
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+ by Blåsten <a href="#desc_Blasten2018">[2018]</a> for
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+ acoustic source scattering. This also includes
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+ studying the corresponding electromagnetic
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+ transmission eigenvalue problem.
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+ </p>
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+ <p>
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+ The conclusions are consistent with those for the
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+ acoustic case: namely that corners always radiate, and
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+ consequently that a source's shape can be determined
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+ by a single far-field measurement if it is known to be
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+ in the convex polyhedral class. This gives even more
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+ evidence for corners behaving universally in a very
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+ unique way, as unlike in the previous studies, the
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+ Maxwell equations are not elliptic.
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+ </p>
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+ </dd>
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+
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+ <dt>
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+ <a class="anchor" id="desc_BV2019"></a>
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+ <a href="#BV2019">
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+ <span class="ref-authors">E. Blåsten,
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+ E. Vesalainen,</span>
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+ <span class="ref-title">Non-Scattering Energies and
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+ Transmission Eigenvalues
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+ in <i>H<sup>n</sup></i>.</span>
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+ </a>
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+ </dt>
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+ <dd>
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+ <p>
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+ We extend the study of Blåsten, Päivärinta,
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+ Sylvester <a href="#desc_BlastenPaivarintaSylvester2014">[2014]</a>
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+ from the Euclidean space to any comformally equivaĺent
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+ geometric space, for example the hyperbolic plane in
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+ two dimensions.
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+ </p>
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+ <p>
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+ We conclude that potentials which have a hyperbolic
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+ corner or a <q>corner</q> made by a <em>horocycle</em>
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+ and a line (or higher dimensional equivalents) would
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+ always produce non-zero scattering given any non-zero
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+ incident wave. Se also show the existence of
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+ transmission eigenvalues in these geometries, so we
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+ can again conclude that non-scattering energies and
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+ transmission eigenvalues are different despite the
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+ change in the underlying spatial geometry.
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+ </p>
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+ </dd>
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+
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+ <dt>
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+ <a class="anchor" id="desc_Pipes3"></a>
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+ <a href="#Pipes3">
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+ <span class="ref-authors">E. Blåsten, F. Zouari, M. Louati,
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+ and M. S. Ghidaoui,</span>
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+ <span class="ref-title">Blockage detection in
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+ networks: the area reconstruction method.</span>
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+ </a>
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+ </dt>
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+ <dd>
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+ <p>
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+ The study is about developing and using an inversion
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+ algorithm for the wave equation with the goal of
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+ determining the cross-sectional area inside a network,
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+ e.g. the water supply network. The large picture idea
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+ come from Zouari, Blåsten, Louati,
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+ Ghidaoui <a href="#desc_Pipes1">[2019]</a>, i.e. it is
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+ based on a time-domain boundary control method.
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+ </p>
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+ <p>
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+ We show that the internal cross-sectional area of a
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+ tree network is determined by boundary measurements
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+ done at all network boundary ends except one. We
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+ present a proof of that, and also explicit numerical
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+ code for reconstructing the area given the network
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+ geometry.
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+ </p>
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+ </dd>
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+
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+ <dt>
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+ <a class="anchor" id="desc_Pipes2"></a>
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+ <a href="#Pipes2">
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+ <span class="ref-authors">F. Zouari, M. Louati,
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+ S. Menicone, E. Blåsten, M. S. Ghidaoui and
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+ B. Brunone,</span>
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+ <span class="ref-title">Experimental Verification of
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+ the Accuracy and Robustness of Area Reconstruction
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+ Method for a Pressurized Water Pipe System.</span>
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+ </a>
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+ </dt>
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+ <dd>
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+ <p>
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+ This is an experimental verification of the method
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+ introduced by Zouari, Blåsten, Louati,
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+ Ghidaoui <a href="#desc_Pipes1">[2019]</a> We conclude
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+ that the method is stable enough for use with
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+ experimentally measured noisy data.
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+ </p>
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+ </dd>
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+
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+ <dt>
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<a class="anchor" id="desc_PipesProceedings1"></a>
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<a href="#PipesProceedings1">
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<span class="ref-authors">F. Zouari, M. Louati,
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@@ -531,29 +700,7 @@
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large particles!
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</p>
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</dd>
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- <dt>
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- <a class="anchor" id="desc_Blasten-Vesalainen-2018"></a>
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- <a href="#Blasten-Vesalainen-2018">
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- <span class="ref-authors">E. Blåsten, E. V. Vesalainen</span>
|
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- <span class="ref-title">Non-Scattering Energies and
|
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- Transmission Eigenvalues
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- in <i>H<sup>n</sup></i></span>
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- </a>
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- </dt>
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- <dd>
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- <p>
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- The article concerns scattering theory for the
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- Helmholtz and Schrödinger equations in hyperbolic
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- spaces. We show that corners always scatter there too
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- despite there being so-called transmission
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- eigenvalues, which we show also. This brings the
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- results of myself, Päivärinta and
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- Sylvester <a href="#BlastenPaivarintaSylvester2014">[2014]</a>,
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- and Hu, Salo,
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- Vesalainen <a href="http://dx.doi.org/10.1137/15M1032958">[2015]</a>
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- into the setting of hyperbolic manifolds.
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- </p>
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- </dd>
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+
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<dt>
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<a class="anchor" id="desc_Blasten-Liu-2018"></a>
|
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<a href="#Blasten-Liu-2018">
|
Emilia Blåsten