tag:blogger.com,1999:blog-15794560883804286972023-11-16T08:37:50.616-08:00Dr. Daniel BalaguéHome PageDaniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-1579456088380428697.post-34153048764696361322020-06-30T19:20:00.003-07:002020-06-30T19:21:53.954-07:00(Almost) Moving!Today, June 30 2020, was my last day working for Case Western Reserve University. I am joining Delft University of Technology (TU Delft) in Delft (Netherlands). Due to COVID19, I am still stuck in the US. But I will move to the Netherlands as soon as I can!Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-70147298400238380912016-10-04T14:18:00.001-07:002017-02-05T14:53:02.769-08:00Python WorkshopToday, October 4th 2016, I gave a Workshop on Python Programming. The <a href="https://sites.google.com/a/case.edu/hpc-upgraded-cluster/hpc-activities/training-resources" target="_blank">materials are available online for free</a>. To find more details, visit my Teaching section!Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-45823864639370623192016-07-12T00:04:00.002-07:002016-07-12T00:06:00.607-07:00Moving (again) and SIAMHello everyone!
I am starting a new position at Case Western Reserve University, in Cleveland OH. I will not have an official email until next Monday. I will keep you posted with new updates.
From 07/12/16 to 07/15/16 you can find me in the SIAM conference on Life Sciences in Boston. Do not miss my talk!Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-65639931326163528122016-01-04T15:53:00.001-08:002016-01-04T15:53:36.747-08:00<h2>
New Submission!</h2>
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After the Winter Break it is time for a little update. The paper <i>A year in Madrid as described through the analysis of geotagged Twitter data,</i> by Travis R. Meyer, Daniel Balagué, Miguel Camacho-Collados, Hao Li, Katie Khuu, P. Jeffrey Brantingham, and Andrea L. Bertozzi, was submitted on December 24th 2015.Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-88784768973902698072015-08-02T00:09:00.001-07:002015-08-02T00:13:51.813-07:00Spoiler Alert!!!Dear Followers,<br />
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Here is something that is about to come out. For more details, we will have a draft quite soon. Be patient ;)<br />
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<b>Detonation Wave in a channel</b></h3>
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<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/x9hTYaasCtw/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/x9hTYaasCtw?feature=player_embedded" width="320"></iframe></div>
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Diffraction of a detonation wave</h3>
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Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-27804386250006125712015-07-27T13:31:00.002-07:002015-07-27T13:32:29.256-07:00Moved!I moved to UCLA! My old email address is no longer working, but you can reach me at<br />
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dbalague [at] math [dot] ucla [dot] eduDaniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-45072900820340590582015-02-05T22:40:00.000-08:002015-02-05T22:41:28.341-08:00InterviewA few days ago I was interviewed by <a href="http://ara.cat/">ara.cat</a> (a Catalan newspaper). You can read the interview in the following <a href="http://catalannetwork.ara.cat/2015/02/02/daniel-balague/" target="_blank">link</a> (it is in Catalan!) Unfortunately, Bing and Google do not do a good job translating from Catalan to English as they get the wrong verb tenses and the wrong pronouns, leading to misunderstandings and nonsense. If you mix the translations from both Bing and Google from Catalan to Spanish you can get the right tenses and the right meaning (in Spanish).<br />
<br />
If you are curious about Catalonia and Spain, you can read the English version of the newspaper in <a href="http://www.ara.cat/en" target="_blank">this link</a>.Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.com0tag:blogger.com,1999:blog-1579456088380428697.post-86235514947936123762014-08-24T18:57:00.000-07:002014-08-25T10:31:16.762-07:00New publications!This week I received in my mail the printed version of the paper <a href="http://dbalague.blogspot.com/2013/05/confinement.html">Confinement for Repulsive-Attractive Kernels</a>, published in Discrete and Continuous Dynamical Systems-B 19, 1227–1248, 2014.<br />
<br />
Moreover, the paper <a href="http://dbalague.blogspot.com/2013/05/millflock.html">Stability Analysis of Flock and Mill rings for 2nd Order Models in Swarming</a> was published in SIAM J. Appl. Math., 74(3), 794–818, 2104.Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-26056173787751485722013-08-23T12:03:00.003-07:002013-08-27T15:00:25.856-07:00Moved!<br />
Hi everyone!<br />
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I just moved to North Carolina! I am going to be at North Carolina State University as a Postdoc for two years.</div>
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Although my old email address will work for a while, I recommend you writing me at my new email:</div>
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<b>dbalague [at] math [dot] ncsu [dot] edu</b></div>
Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-6524245748075862822013-05-29T16:35:00.000-07:002014-08-24T19:28:20.873-07:00Stability Analysis of Flock and Mill rings for 2nd Order Models in Swarming<h2>
<span style="font-size: large; font-weight: normal;">G. Albi, D. Balagué, J. A. Carrillo, J. von Brecht</span></h2>
<br />
<div style="text-align: justify;">
We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. We relate the instability of the flock rings with the instability of the ring solution of the first order model. We observe that repulsive-attractive interactions lead to new configurations for the flock rings such as clustering and fattening formation. Finally, we numerically explore mill patterns arising from this kind of interactions together with the asymptotic speed of the system.</div>
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<a href="http://arxiv.org/pdf/1304.5459v1">arXiv</a> Fri, 19 Apr 2013<br />
<a href="http://dx.doi.org/10.1137/13091779X">SIAM J. Appl. Math</a>., 74(3), 794–818, 2014<br />
<br />
<a href="http://www.giacomoalbi.com/research/simulations">Complementary Materials </a>on Giacomo's web page.Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-74297105210772350582013-05-29T16:12:00.000-07:002018-06-26T10:42:29.596-07:00Dimensionality of Local Minimizers of the Interaction Energy<h2>
<span style="font-weight: normal;"><span style="font-size: large;">D. Balagué, J. A. Carrillo, T. Laurent, G. Raoul</span></span></h2>
<br />
<div style="text-align: justify;">
In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.</div>
<div style="text-align: justify;">
<br /></div>
Journal reference: <a href="http://link.springer.com/article/10.1007%2Fs00205-013-0644-6">Archive for Rational Mechanics and Analysis</a>, 2013.<br />
<a href="http://arxiv.org/abs/1210.6795">arXiv</a> Thu, 25 Oct 2012<br />
<br />
<h3 style="text-align: center;">
<u>Complementary materials</u></h3>
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<br />
<a name='more'></a><br />
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<a href="https://www.blogger.com/blogger.g?blogID=1579456088380428697" name="more"></a><br /></div>
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In this page we show some numerical simulations for the <a href="http://arxiv.org/pdf/1210.6795v1"><i>Dimensionality
of Local Minimizers of the Interaction Energy</i></a>. We will keep the same notation as in the paper to
make this page more readable.
</div>
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<div style="text-align: justify;">
We numerically compute some local minimizers of the discrete interaction energy (2) of $n$ particles located at
$X_1,...,X_n \in \mathbb{R}^N$ $$
E_W^n[X_1,\dots, X_n]:=\frac{1}{2n}\sum_{\substack{i,\,j=1\\j\neq i}}^n W\left(X_i-X_j\right),$$ where $W$ is a radially symmetric repulsive-attractive interaction potential $W(x)=k(|x|)$ given by
$$
k(r)=-\frac{r^\alpha}{\alpha}+\frac{r^\gamma}{\gamma}.
$$
As it is explained in Section 6, to efficiently find local minimizers we solve
$$
\dot{X}_i=-\sum_{\substack{j=1\\j\neq i}}^n m_j \nabla W\left(X_i-X_j\right)
$$
with an explicit Euler scheme with adaptive time step chosen the largest possible such that the discrete
energy decreases. In stiffer situations an explicit Runge-Kutta method is used instead. The results in
Table CM1 are discussed below:
</div>
<br />
<ul>
<li style="text-align: justify;">$\alpha=2.1$: According to Theorem 2, the support of the local
minimizer has zero Hausdorff dimension. In this particular case it is supported on four points. For
this case we have $\gamma=4$.</li>
<br />
<li style="text-align: justify;">$\alpha=1.85$: Following Theorem 1, the Hausdorff dimension must be greater than or equal to $\beta=2-\alpha=2-1.85=0.15$. In fact, in our simulations we observe that the support is a circle
(Hausdorff dimension 1). For this simulation we choose $\gamma=4$.</li>
<br />
<li style="text-align: justify;">$\alpha=1.35$: In this case we observe that particles concentrate on three curves (Hausdorff dimension 1). According to
Theorem 1, the Hausdorff dimension of the support of the local minimizer should be larger than or
equal to $\beta=0.65$. In this case, $\gamma=15$.</li>
<br />
<li style="text-align: justify;">$\alpha=0.85$: From Theorem 1, the Hausdorff dimension of the support of the local minimizer
must be greater than or equal to $\beta=1.15$. We observe that the particles evolve into a concentration
in an annular region. The attractive force is given by $\gamma=4$. </li>
</ul>
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<br />
All the simulations have been done using $n=1,000$ particles.
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<br />
<center>
<b>TABLE CM1:</b> Evolution of particles towards local minimizers of the interaction energy.</center>
<table align="center" border="2" bordercolor="black">
<tbody>
<tr>
<td align="center">Dim </td>
<td align="center">$\alpha=2.1$</td>
<td align="center">$\alpha=1.85$</td>
<td align="center">$\alpha=1.35$</td>
<td align="center">$\alpha=0.85$</td>
</tr>
<tr>
<td align="center">0</td>
<td><iframe allowfullscreen="" frameborder="0" height="120" src="http://www.youtube.com/embed/0TDTAceJjok" width="160"></iframe></td>
<td>$ $</td>
<td>$ $</td>
<td>$ $</td>
</tr>
<tr>
<td align="center">1</td>
<td>$ $</td>
<td><iframe allowfullscreen="" frameborder="0" height="120" src="http://www.youtube.com/embed/2fL_drDKX8c" width="160"></iframe></td>
<td><iframe allowfullscreen="" frameborder="0" height="120" src="http://www.youtube.com/embed/FzSLf3En5uk" width="160"></iframe></td>
<td>$ $</td>
</tr>
<tr>
<td align="center">2</td>
<td>$ $</td>
<td>$ $</td>
<td>$ $</td>
<td><iframe allowfullscreen="" frameborder="0" height="120" src="http://www.youtube.com/embed/50rM1zvipio" width="160"></iframe></td>
</tr>
</tbody></table>
<br />
<br />
Other potentials may lead to very complex patterns. For instance, if we consider the potential
$$k'(r)=\tanh((1-r)a)-b$$
with $a=6$ and $b=0.7$ one obtains the evolution shown in Video CM1.<br />
<br />
<br />
<div style="text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/gNdmPaSciT0" width="420"></iframe>
</div>
<div style="text-align: center;">
<b>Video CM1:</b> Evolution of particles towards local minimizers of the interaction energy for
$k'(r)=\tanh((1-r)a)-b$.
</div>
Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-60897778394835711922013-05-29T15:57:00.002-07:002020-06-25T11:16:08.268-07:00Confinement for Repulsive-Attractive Kernels<h2>
<span style="font-weight: normal;"><span style="font-size: large;">D. Balagué, J. A. Carrillo, Y. Yao</span></span></h2>
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<div style="text-align: justify;">
We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the potential. The arguments apply to the functional setting of probability measures with mildly singular repulsive-attractive potentials and to the functional setting of smooth solutions with a potential being the sum of the Newtonian repulsion at the origin and a smooth suitably growing at infinity attractive potential.</div>
<br />
Discrete and Continuous Dynamical Systems-B 19, 1227–1248, 2014.<br />
<br />
<a href="http://arxiv.org/abs/1210.0602">arXiv</a> Mon, 1 Oct 2012Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-58600678520183511162013-05-29T15:43:00.001-07:002013-05-29T15:55:26.812-07:00Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates<h2>
<span style="font-size: large;"><span style="font-weight: normal;">Daniel Balagué, José Cañizo, Pierre Gabriel</span></span></h2>
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<div style="text-align: justify;">
We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and $+\infty$. Using these estimates we prove a spectral gap result by following the technique in [Caceres, Canizo, Mischler 2011, JMPA], which implies that solutions decay to the equilibrium exponentially fast. The growth and fragmentation coefficients we consider are quite general, essentially only assumed to behave asymptotically like power laws.</div>
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Journal reference: <a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8316">Kinetic and Related Models</a>, Vol. 6, No. 2, pp. 219-243 (2013)<br />
<a href="http://arxiv.org/pdf/1203.6156v2">arXiv</a> Submitted on 28 Mar 2012 (v1), last revised 19 Feb 2013 (v2)Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.comtag:blogger.com,1999:blog-1579456088380428697.post-55045847814032504662013-05-29T15:38:00.000-07:002014-08-24T19:22:04.859-07:00Nonlocal interactions by repulsive-attractive potentials: radial ins/stability<h2>
<span style="font-size: large;"><span style="font-weight: normal;">D. Balagué, J. A. Carrillo, T. Laurent, G. Raoul</span></span></h2>
<br />
In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and attract each other in the long range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. We point out the the conditions of radial ins/stability are sharp.<br />
<br />
<a href="http://arxiv.org/pdf/1109.5258v1">arXiv</a> Sat, 24 Sep 2011<br />
<a href="http://www.sciencedirect.com/science/article/pii/S0167278912002540">Physica D: Nonlinear Phenomena</a>, Volume 260, 1 October 2013, Pages 5–25<br />
<br />Daniel Balaguéhttp://www.blogger.com/profile/16566535976988954973noreply@blogger.com