|
@@ -1,6 +1,6 @@
|
|
|
<!DOCTYPE html>
|
|
|
<html lang="en">
|
|
|
- <!--Copyright (C) 2018 E. Blåsten
|
|
|
+ <!--Copyright (C) 2019 Emilia Blåsten
|
|
|
Permission is granted to copy, distribute and/or modify this
|
|
|
document under the terms of the GNU Free Documentation License,
|
|
|
Version 1.3 or any later version published by the Free Software
|
|
@@ -9,7 +9,7 @@
|
|
|
"LICENSE.html". -->
|
|
|
<head>
|
|
|
<meta charset="utf-8" />
|
|
|
- <title>Research by E. Blåsten</title>
|
|
|
+ <title>Research by Emily Blåsten</title>
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
<link rel="stylesheet" href="include/mathstyles.css">
|
|
|
<link rel="stylesheet" href="include/homepage.css">
|
|
@@ -105,6 +105,17 @@
|
|
|
<ol reversed>
|
|
|
<li>
|
|
|
<a class="anchor" id="Blasten-Li-Liu-Wang-2018"></a>
|
|
|
+ <span class="ref-authors">E. Blåsten, H. Liu, J. Xiao,</span>
|
|
|
+ <span class="ref-title">On an electromagnetic problem
|
|
|
+ in a corner and its applications.</span>
|
|
|
+ <div class="ref-links">
|
|
|
+ <a href="#desc_Blasten-Liu-Xiao-2019">Description</a>
|
|
|
+ <a href="https://arxiv.org/abs/1901.00581">Preprint</a>
|
|
|
+ </div>
|
|
|
+ </li>
|
|
|
+
|
|
|
+ <li>
|
|
|
+ <a class="anchor" id="Blasten-Li-Liu-Wang-2018"></a>
|
|
|
<span class="ref-authors">E. Blåsten, H. Li, H. Liu, Y. Wang,</span>
|
|
|
<span class="ref-title">Localization and
|
|
|
geometrization in plasmon resonances and geometric
|
|
@@ -115,16 +126,7 @@
|
|
|
<a href="https://arxiv.org/abs/1809.08533">Preprint</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
- <li>
|
|
|
- <a class="anchor" id="Blasten-Vesalainen-2018"></a>
|
|
|
- <span class="ref-authors">E. Blåsten, E. V. Vesalainen,</span>
|
|
|
- <span class="ref-title">Non-Scattering Energies and Transmission Eigenvalues in
|
|
|
- <i>H<sup>n</sup></i>.</span>
|
|
|
- <div class="ref-links">
|
|
|
- <a href="#desc_Blasten-Vesalainen-2018">Description</a>
|
|
|
- <a href="http://arxiv.org/abs/1809.04426/">Preprint</a>
|
|
|
- </div>
|
|
|
- </li>
|
|
|
+
|
|
|
<li>
|
|
|
<a class="anchor" id="Blasten-Liu-2018"></a>
|
|
|
<span class="ref-authors">E. Blåsten, H. Liu,</span>
|
|
@@ -147,6 +149,29 @@
|
|
|
<a href="https://arxiv.org/abs/1705.00815">Preprint</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
+ </ol>
|
|
|
+ </p>
|
|
|
+
|
|
|
+ <p>
|
|
|
+ <a class="anchor" id="pubs_accepted"></a>
|
|
|
+ <h3>Accepted in Peer-Reviewed Journals</h3>
|
|
|
+ <ol reversed>
|
|
|
+ <li>
|
|
|
+ <a class="anchor" id="BV2019"></a>
|
|
|
+ <span class="ref-authors">E. Blåsten,
|
|
|
+ E. Vesalainen,</span>
|
|
|
+ <span class="ref-title">Non-Scattering Energies and
|
|
|
+ Transmission Eigenvalues
|
|
|
+ in <i>H<sup>n</sup></i>.</span>
|
|
|
+ <span class="ref-journal">Annales Academiæ Scientiarum
|
|
|
+ Fennicæ Mathematica,</span>
|
|
|
+ <span class="ref-year">accepted 2019.</span>
|
|
|
+ <div class="ref-links">
|
|
|
+ <a href="#desc_BV2019">Description</a>
|
|
|
+ <a href="https://arxiv.org/abs/1809.04426">Preprint</a>
|
|
|
+ </div>
|
|
|
+ </li>
|
|
|
+
|
|
|
<li>
|
|
|
<a class="anchor" id="BlastenTzouWang2017"></a>
|
|
|
<span class="ref-authors">E. Blåsten, L. Tzou,
|
|
@@ -154,47 +179,59 @@
|
|
|
<span class="ref-title">Uniqueness for the inverse
|
|
|
boundary value problem with singular potentials in
|
|
|
2D.</span>
|
|
|
+ <span class="ref-journal">Mathematische Zeitschrift,</span>
|
|
|
+ <span class="ref-year">accepted 2019.</span>
|
|
|
<div class="ref-links">
|
|
|
<a href="#desc_BlastenTzouWang2017">Description</a>
|
|
|
<a href="https://arxiv.org/abs/1704.06397">Preprint</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
+
|
|
|
+ <li>
|
|
|
+ <a class="anchor" id="Pipes3"></a>
|
|
|
+ <span class="ref-authors">E. Blåsten, F. Zouari,
|
|
|
+ M. Louati and M. S. Ghidaoui,</span>
|
|
|
+ <span class="ref-title">Blockage detection in
|
|
|
+ networks: the area reconstruction method.</span>
|
|
|
+ <span class="ref-journal">Mathematics in Engineering,</span>
|
|
|
+ <span class="ref-year">accepted 2019.</span>
|
|
|
+ <div class="ref-links">
|
|
|
+ <a href="#desc_Pipes3">Description</a>
|
|
|
+ <a href="https://arxiv.org/abs/1909.05497">Preprint</a>
|
|
|
+ </div>
|
|
|
+ </li>
|
|
|
+
|
|
|
<li>
|
|
|
<a class="anchor" id="BlastenLiu2016"></a>
|
|
|
<span class="ref-authors">E. Blåsten, H. Liu,</span>
|
|
|
<span class="ref-title"> On corners scattering stably
|
|
|
and stable shape determination by a single far-field
|
|
|
pattern.</span>
|
|
|
+ <span class="ref-journal">Indiana University
|
|
|
+ Mathematics Journal,</span>
|
|
|
+ <span class="ref-year">accepted 2019.</span>
|
|
|
<div class="ref-links">
|
|
|
<a href="#desc_BlastenLiu2016">Description</a>
|
|
|
<a href="https://arxiv.org/abs/1611.03647">Preprint</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
- </ol>
|
|
|
- </p>
|
|
|
|
|
|
- <p>
|
|
|
- <a class="anchor" id="pubs_accepted"></a>
|
|
|
- <h3>Accepted in Peer-Reviewed Journals</h3>
|
|
|
- <ol reversed>
|
|
|
<li>
|
|
|
- <a class="anchor" id="Blasten2018"></a>
|
|
|
- <span class="ref-authors">E. Blåsten,</span>
|
|
|
- <span class="ref-title">Nonradiating sources and
|
|
|
- transmission eigenfunctions vanish at corners and
|
|
|
- edges.</span>
|
|
|
- <span class="ref-journal">SIAM Journal on Mathematical
|
|
|
- Analysis,</span>
|
|
|
- <span class="ref-volume">50,</span>
|
|
|
- <span class="ref-issue">6</span>
|
|
|
- <span class="ref-year">(2018)</span>
|
|
|
- <span class="ref-pages">6255–6270.</span>
|
|
|
+ <a class="anchor" id="Pipes2"></a>
|
|
|
+ <span class="ref-authors">F. Zouari, M. Louati,
|
|
|
+ S. Meniconi, E. Blåsten, M. S. Ghidaoui and
|
|
|
+ B. Brunone,</span>
|
|
|
+ <span class="ref-title">Experimental Verification of
|
|
|
+ the Accuracy and Robustness of Area Reconstruction
|
|
|
+ Method for a Pressurized Water Pipe System.</span>
|
|
|
+ <span class="ref-journal">Journal of Hydraulic
|
|
|
+ Engineering, ASCE,</span>
|
|
|
+ <span class="ref-year">accepted 2019.</span>
|
|
|
<div class="ref-links">
|
|
|
- <a href="#desc_Blasten2018">Description</a>
|
|
|
- <a href="https://doi.org/10.1137/18M1182048">Publication</a>
|
|
|
- <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
|
|
|
+ <a href="#desc_Pipes2">Description</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
+
|
|
|
<li>
|
|
|
<a class="anchor" id="Pipes1"></a>
|
|
|
<span class="ref-authors">F. Zouari, E. Blåsten,
|
|
@@ -204,9 +241,12 @@
|
|
|
detection.</span>
|
|
|
<span class="ref-journal">Journal of Hydraulic
|
|
|
Engineering, ASCE,</span>
|
|
|
- <span class="ref-year">accepted 2018.</span>
|
|
|
+ <span class="ref-volume">145,</span>
|
|
|
+ <span class="ref-issue">6</span>
|
|
|
+ <span class="ref-year">(2019)</span>
|
|
|
<div class="ref-links">
|
|
|
<a href="#desc_Pipes1">Description</a>
|
|
|
+ <a href="https://doi.org/10.1061/(ASCE)HY.1943-7900.0001602">Publication</a>
|
|
|
</div>
|
|
|
</li>
|
|
|
<li>
|
|
@@ -226,6 +266,24 @@
|
|
|
</div>
|
|
|
</li>
|
|
|
<li>
|
|
|
+ <a class="anchor" id="Blasten2018"></a>
|
|
|
+ <span class="ref-authors">E. Blåsten,</span>
|
|
|
+ <span class="ref-title">Nonradiating sources and
|
|
|
+ transmission eigenfunctions vanish at corners and
|
|
|
+ edges.</span>
|
|
|
+ <span class="ref-journal">SIAM Journal on Mathematical
|
|
|
+ Analysis,</span>
|
|
|
+ <span class="ref-volume">50,</span>
|
|
|
+ <span class="ref-issue">6</span>
|
|
|
+ <span class="ref-year">(2018)</span>
|
|
|
+ <span class="ref-pages">6255–6270.</span>
|
|
|
+ <div class="ref-links">
|
|
|
+ <a href="#desc_Blasten2018">Description</a>
|
|
|
+ <a href="https://doi.org/10.1137/18M1182048">Publication</a>
|
|
|
+ <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
|
|
|
+ </div>
|
|
|
+ </li>
|
|
|
+ <li>
|
|
|
<a class="anchor" id="Blasten2017"></a>
|
|
|
<span class="ref-authors">E. Blåsten,</span>
|
|
|
<span class="ref-title">Well-posedness of the Goursat
|
|
@@ -465,6 +523,117 @@
|
|
|
<h2>Description of projects</h2>
|
|
|
<dl>
|
|
|
<dt>
|
|
|
+ <a class="anchor" id="desc_desc_Blasten-Liu-Xiao-2019"></a>
|
|
|
+ <a href="#desc_Blasten-Liu-Xiao-2019">
|
|
|
+ <span class="ref-authors">E. Blåsten, H. Liu,
|
|
|
+ J. Xiao,</span>
|
|
|
+ <span class="ref-title">On an electromagnetic problem
|
|
|
+ in a corner and its applications.</span>
|
|
|
+ </a>
|
|
|
+ </dt>
|
|
|
+ <dd>
|
|
|
+ <p>
|
|
|
+ We consider the topic of scattering produced by
|
|
|
+ electromagnetic sources having a corner, and was done
|
|
|
+ by Blåsten <a href="#desc_Blasten2018">[2018]</a> for
|
|
|
+ acoustic source scattering. This also includes
|
|
|
+ studying the corresponding electromagnetic
|
|
|
+ transmission eigenvalue problem.
|
|
|
+ </p>
|
|
|
+ <p>
|
|
|
+ The conclusions are consistent with those for the
|
|
|
+ acoustic case: namely that corners always radiate, and
|
|
|
+ consequently that a source's shape can be determined
|
|
|
+ by a single far-field measurement if it is known to be
|
|
|
+ in the convex polyhedral class. This gives even more
|
|
|
+ evidence for corners behaving universally in a very
|
|
|
+ unique way, as unlike in the previous studies, the
|
|
|
+ Maxwell equations are not elliptic.
|
|
|
+ </p>
|
|
|
+ </dd>
|
|
|
+
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_BV2019"></a>
|
|
|
+ <a href="#BV2019">
|
|
|
+ <span class="ref-authors">E. Blåsten,
|
|
|
+ E. Vesalainen,</span>
|
|
|
+ <span class="ref-title">Non-Scattering Energies and
|
|
|
+ Transmission Eigenvalues
|
|
|
+ in <i>H<sup>n</sup></i>.</span>
|
|
|
+ </a>
|
|
|
+ </dt>
|
|
|
+ <dd>
|
|
|
+ <p>
|
|
|
+ We extend the study of Blåsten, Päivärinta,
|
|
|
+ Sylvester <a href="#desc_BlastenPaivarintaSylvester2014">[2014]</a>
|
|
|
+ from the Euclidean space to any comformally equivaĺent
|
|
|
+ geometric space, for example the hyperbolic plane in
|
|
|
+ two dimensions.
|
|
|
+ </p>
|
|
|
+ <p>
|
|
|
+ We conclude that potentials which have a hyperbolic
|
|
|
+ corner or a <q>corner</q> made by a <em>horocycle</em>
|
|
|
+ and a line (or higher dimensional equivalents) would
|
|
|
+ always produce non-zero scattering given any non-zero
|
|
|
+ incident wave. Se also show the existence of
|
|
|
+ transmission eigenvalues in these geometries, so we
|
|
|
+ can again conclude that non-scattering energies and
|
|
|
+ transmission eigenvalues are different despite the
|
|
|
+ change in the underlying spatial geometry.
|
|
|
+ </p>
|
|
|
+ </dd>
|
|
|
+
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_Pipes3"></a>
|
|
|
+ <a href="#Pipes3">
|
|
|
+ <span class="ref-authors">E. Blåsten, F. Zouari, M. Louati,
|
|
|
+ and M. S. Ghidaoui,</span>
|
|
|
+ <span class="ref-title">Blockage detection in
|
|
|
+ networks: the area reconstruction method.</span>
|
|
|
+ </a>
|
|
|
+ </dt>
|
|
|
+ <dd>
|
|
|
+ <p>
|
|
|
+ The study is about developing and using an inversion
|
|
|
+ algorithm for the wave equation with the goal of
|
|
|
+ determining the cross-sectional area inside a network,
|
|
|
+ e.g. the water supply network. The large picture idea
|
|
|
+ come from Zouari, Blåsten, Louati,
|
|
|
+ Ghidaoui <a href="#desc_Pipes1">[2019]</a>, i.e. it is
|
|
|
+ based on a time-domain boundary control method.
|
|
|
+ </p>
|
|
|
+ <p>
|
|
|
+ We show that the internal cross-sectional area of a
|
|
|
+ tree network is determined by boundary measurements
|
|
|
+ done at all network boundary ends except one. We
|
|
|
+ present a proof of that, and also explicit numerical
|
|
|
+ code for reconstructing the area given the network
|
|
|
+ geometry.
|
|
|
+ </p>
|
|
|
+ </dd>
|
|
|
+
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_Pipes2"></a>
|
|
|
+ <a href="#Pipes2">
|
|
|
+ <span class="ref-authors">F. Zouari, M. Louati,
|
|
|
+ S. Menicone, E. Blåsten, M. S. Ghidaoui and
|
|
|
+ B. Brunone,</span>
|
|
|
+ <span class="ref-title">Experimental Verification of
|
|
|
+ the Accuracy and Robustness of Area Reconstruction
|
|
|
+ Method for a Pressurized Water Pipe System.</span>
|
|
|
+ </a>
|
|
|
+ </dt>
|
|
|
+ <dd>
|
|
|
+ <p>
|
|
|
+ This is an experimental verification of the method
|
|
|
+ introduced by Zouari, Blåsten, Louati,
|
|
|
+ Ghidaoui <a href="#desc_Pipes1">[2019]</a> We conclude
|
|
|
+ that the method is stable enough for use with
|
|
|
+ experimentally measured noisy data.
|
|
|
+ </p>
|
|
|
+ </dd>
|
|
|
+
|
|
|
+ <dt>
|
|
|
<a class="anchor" id="desc_PipesProceedings1"></a>
|
|
|
<a href="#PipesProceedings1">
|
|
|
<span class="ref-authors">F. Zouari, M. Louati,
|
|
@@ -515,29 +684,7 @@
|
|
|
large particles!
|
|
|
</p>
|
|
|
</dd>
|
|
|
- <dt>
|
|
|
- <a class="anchor" id="desc_Blasten-Vesalainen-2018"></a>
|
|
|
- <a href="#Blasten-Vesalainen-2018">
|
|
|
- <span class="ref-authors">E. Blåsten, E. V. Vesalainen</span>
|
|
|
- <span class="ref-title">Non-Scattering Energies and
|
|
|
- Transmission Eigenvalues
|
|
|
- in <i>H<sup>n</sup></i></span>
|
|
|
- </a>
|
|
|
- </dt>
|
|
|
- <dd>
|
|
|
- <p>
|
|
|
- The article concerns scattering theory for the
|
|
|
- Helmholtz and Schrödinger equations in hyperbolic
|
|
|
- spaces. We show that corners always scatter there too
|
|
|
- despite there being so-called transmission
|
|
|
- eigenvalues, which we show also. This brings the
|
|
|
- results of myself, Päivärinta and
|
|
|
- Sylvester <a href="#BlastenPaivarintaSylvester2014">[2014]</a>,
|
|
|
- and Hu, Salo,
|
|
|
- Vesalainen <a href="http://dx.doi.org/10.1137/15M1032958">[2015]</a>
|
|
|
- into the setting of hyperbolic manifolds.
|
|
|
- </p>
|
|
|
- </dd>
|
|
|
+
|
|
|
<dt>
|
|
|
<a class="anchor" id="desc_Blasten-Liu-2018"></a>
|
|
|
<a href="#Blasten-Liu-2018">
|