<html data-lt-installed="true">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body style="padding-bottom: 1px;">
On 5/11/23 22:33, Karkee, Rijan wrote:<br>
<blockquote type="cite"
cite="mid:5f651ec981c04217bf0ebdcc2c1bc108@lanl.gov">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<style type="text/css" style="display:none;">P {margin-top:0;margin-bottom:0;}</style>
<div id="divtagdefaultwrapper"
style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;"
dir="ltr">
<p>Hi Lorenzo,</p>
<p><br>
</p>
<p>I saw your tutorial and input files. So it produces Raman
tensor for each displaced atom so if there are 10 atoms then I
have to generate for all.
<br>
</p>
<p><br>
</p>
<p>Quick question, for each atom I see there are three
different tensor. How can we generate the other two? </p>
</div>
</blockquote>
<p><br>
</p>
<p>The Raman tensor has dimension 3x3x(3*nat), it corresponds to
deriving teh dielectric matrix (3x3) with respect to the
displacement of each atom (nat) along eahc cartesian direction
(3), or equivalently along each phonon polarization (3*nat, but
then you need to rotate it to cartesian coordinates). <br>
</p>
<p><br>
</p>
<p>In the example, I only derive epsilon w.r.t. the first atom along
direction x. Because Silicon is so symmetric, all the other
components of the tensor look are identical but rotated. This is
not true in general, however, if the system has symmetry, it is
always possible to use it to reduce the amount of computation, but
it takes some human time, at least once, to write a code that does
it.</p>
<p>hth<br>
</p>
<p><br>
</p>
<p><br>
</p>
<blockquote type="cite"
cite="mid:5f651ec981c04217bf0ebdcc2c1bc108@lanl.gov">
<div id="divtagdefaultwrapper"
style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;"
dir="ltr">
<p>The magnitude looks same but seems rotated by some matrix.
And how does one converts au^-1 in cartesian axis to A^2? For
example in below,
<span>2.524312370 has been converted into <span>0.166309336301E+02</span>
but I could not understand the conversion.
<br>
</span></p>
<p><span><br>
</span></p>
<p><br>
</p>
<p><br>
</p>
<div> Raman tensor (au^-1) in cartesian axis <br>
<br>
atom 1<br>
( 0.000000000 0.000000000
0.000000000 )<br>
( 0.000000000 0.000000000
2.524312370 )<br>
( 0.000000000 2.524312370
0.000000000 )<br>
<br>
( 0.000000000 0.000000000
2.524312370 )<br>
( -0.000000000 -0.000000000
-0.000000000 )<br>
( 2.524312370 0.000000000
-0.000000000 )<br>
<br>
( 0.000000000 2.524312370
0.000000000 )<br>
( 2.524312370 0.000000000
-0.000000000 )<br>
( 0.000000000 -0.000000000
0.000000000 )<br>
<br>
atom 2<br>
( 0.000000000 -0.000000000
-0.000000000 )<br>
( -0.000000000 -0.000000000
-2.493208807 )<br>
( -0.000000000 -2.493208807
-0.000000000 )<br>
<br>
( -0.000000000 -0.000000000
-2.493208807 )<br>
( -0.000000000 -0.000000000
0.000000000 )<br>
( -2.493208807 0.000000000
-0.000000000 )<br>
<br>
( 0.000000000 -2.493208807
-0.000000000 )<br>
( -2.493208807 0.000000000
0.000000000 )<br>
( -0.000000000 -0.000000000
-0.000000000 )<br>
<br>
<br>
Raman tensor (A^2)<br>
<br>
atom # 1 pol. 1<br>
0.603445027917E-14 0.566872601983E-14
0.896024435392E-14<br>
0.347438046377E-14 0.603445027917E-14
0.166309336301E+02<br>
0.182862129672E-15 0.166309336301E+02
0.603445027917E-14<br>
atom # 1 pol. 2<br>
0.128003490770E-14 0.182862129672E-15
0.166309336301E+02<br>
-0.548586389016E-15 -0.182862129672E-15
-0.274293194508E-14<br>
0.166309336301E+02 0.603445027917E-14
-0.148118325034E-13<br>
atom # 1 pol. 3<br>
0.603445027917E-14 0.166309336301E+02
0.603445027917E-14<br>
0.166309336301E+02 0.603445027917E-14
-0.182862129672E-15<br>
0.310865620442E-14 -0.603445027917E-14
0.896024435392E-14</div>
<br>
</div>
<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt"
face="Calibri, sans-serif" color="#000000"><b>From:</b> users
<a class="moz-txt-link-rfc2396E" href="mailto:users-bounces@lists.quantum-espresso.org"><users-bounces@lists.quantum-espresso.org></a> on behalf of
Lorenzo Paulatto <a class="moz-txt-link-rfc2396E" href="mailto:lorenzo.paulatto@cnrs.fr"><lorenzo.paulatto@cnrs.fr></a><br>
<b>Sent:</b> Thursday, May 11, 2023 12:55:32 PM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a><br>
<b>Subject:</b> Re: [QE-users] [EXTERNAL] The phonon code with
Raman and Hubbard U is not implemented</font>
<div> </div>
</div>
<div>
<p><br>
</p>
<div class="moz-cite-prefix">On 11/05/2023 17:28, Lorenzo
Bastonero wrote:<br>
</div>
<blockquote type="cite"
cite="mid:8B9FEB00-0142-4828-A028-13663A3EA6EA@uni-bremen.de">
Dear Rijan,
<div class=""><br class="">
</div>
<div class="">To warn you: these steps are involved, and you
might need to code quite a bit and have to know the theory
behind. Refer to the before mentioned paper.</div>
</blockquote>
<p><br>
</p>
<p>There is a half-way solution, which consists in doing
numerical derivatives of the dielectric constants. This works
with LDA+U with "Atomic" type projections, but not LDA+U+V.
<br>
</p>
<p>I did a tutorial (very simplified) a few years ago, it shoudl
be here:</p>
<p><a class="moz-txt-link-freetext"
href="https://urldefense.com/v3/__https://drive.google.com/drive/folders/0Bzgwv8VZEl9SRDQwckRJVlkyUzA?resourcekey=0-BnSQk84YUeRvCNze9XKCAA&usp=sharing__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBdgStMTw$"
moz-do-not-send="true">https://drive.google.com/drive/folders/0Bzgwv8VZEl9SRDQwckRJVlkyUzA?resourcekey=0-BnSQk84YUeRvCNze9XKCAA&usp=sharing</a><br>
</p>
<p>hth<br>
</p>
<p><br>
</p>
<blockquote type="cite"
cite="mid:8B9FEB00-0142-4828-A028-13663A3EA6EA@uni-bremen.de">
<div class=""><br class="">
</div>
<div class="">If you are willing to do so, you can find the
first steps in example 10 of PW (<a
href="https://urldefense.com/v3/__https://gitlab.com/QEF/q-e/-/tree/develop/PW/examples/example10__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNB0ChW5kw$"
class="moz-txt-link-freetext" moz-do-not-send="true">https://gitlab.com/QEF/q-e/-/tree/develop/PW/examples/example10</a>).</div>
<div class=""><br class="">
</div>
<div class="">Then you might try to have a look in the
PHonon/FD module (<a
href="https://urldefense.com/v3/__https://gitlab.com/QEF/q-e/-/tree/develop/PHonon/FD__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBkY4hHQU$"
class="moz-txt-link-freetext" moz-do-not-send="true">https://gitlab.com/QEF/q-e/-/tree/develop/PHonon/FD</a>).</div>
<div class=""><br class="">
</div>
<div class="">All the best,</div>
<div class="">Lorenzo</div>
<div class=""><br class="">
<div class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0); color:
rgb(0, 0, 0); letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px; -webkit-text-stroke-width:
0px; text-decoration: none; word-wrap: break-word;
-webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0); color:
rgb(0, 0, 0); letter-spacing: normal; text-align:
start; text-indent: 0px; text-transform: none;
white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration: none;
word-wrap: break-word; -webkit-nbsp-mode: space;
line-break: after-white-space;" class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0);
color: rgb(0, 0, 0); letter-spacing: normal;
text-align: start; text-indent: 0px; text-transform:
none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none; word-wrap: break-word; -webkit-nbsp-mode:
space; line-break: after-white-space;" class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0);
color: rgb(0, 0, 0); letter-spacing: normal;
text-align: start; text-indent: 0px;
text-transform: none; white-space: normal;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration: none; word-wrap: break-word;
-webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0);
color: rgb(0, 0, 0); letter-spacing: normal;
text-align: start; text-indent: 0px;
text-transform: none; white-space: normal;
word-spacing: 0px; -webkit-text-stroke-width:
0px; text-decoration: none; word-wrap:
break-word; -webkit-nbsp-mode: space;
line-break: after-white-space;" class="">
<div>
<div class="">********************************</div>
<div class="">Lorenzo Bastonero</div>
<div class=""><br class="">
</div>
<div class="">PhD Student</div>
<div class="">U Bremen Excellence Chair,<br
class="">
Bremen Center for Computational
Materials Science,<br class="">
and MAPEX Center for Materials and Processes</div>
<div class=""><br class="">
</div>
<div class="">University of Bremen</div>
<div class="">Faculty of Production
Engineering</div>
<div class="">TAB-Building, Room 3.32</div>
<div class="">Am Fallturm 1</div>
<div class="">28359 Bremen, DE</div>
<br class="Apple-interchange-newline">
<a
href="https://urldefense.com/v3/__http://www.hmi.uni-bremen.de/__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBUZzapFE$"
class="moz-txt-link-freetext"
moz-do-not-send="true">http://www.hmi.uni-bremen.de/</a></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div><br class="">
<blockquote type="cite" class="">
<div class="">Il giorno 11 mag 2023, alle ore 16:13,
Karkee, Rijan <<a href="mailto:rkarkee@lanl.gov"
class="moz-txt-link-freetext" moz-do-not-send="true">rkarkee@lanl.gov</a>>
ha scritto:</div>
<br class="Apple-interchange-newline">
<div class="">
<div id="divtagdefaultwrapper" dir="ltr"
style="font-style: normal; font-variant-caps:
normal; font-weight: normal; letter-spacing: normal;
text-align: start; text-indent: 0px; text-transform:
none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none; font-size: 12pt; font-family: Calibri,
Helvetica, sans-serif;" class="">
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">Hi Lorenzo,</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class=""><br class="">
</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">Thanks for the information. May I know,
for now, what steps are involved so that I can
compute those steps by hand?</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">I want to know which module to run first
and what would be the input file should include
and likewise for the next steps. </div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class=""><br class="">
</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">Thank you so much.</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class=""><br class="">
</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">Best</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class="">Rijan Karkee</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class=""><br class="">
</div>
<div style="margin-top: 0px; margin-bottom: 0px;"
class=""><br class="">
</div>
</div>
<hr tabindex="-1" style="caret-color: rgb(0, 0, 0);
font-family: Helvetica; font-size: 18px; font-style:
normal; font-variant-caps: normal; font-weight:
normal; letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none; display: inline-block; width: 1267.125px;"
class="">
<span style="caret-color: rgb(0, 0, 0); font-family:
Helvetica; font-size: 18px; font-style: normal;
font-variant-caps: normal; font-weight: normal;
letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none; float: none; display: inline !important;"
class=""></span>
<div id="divRplyFwdMsg" dir="ltr" style="caret-color:
rgb(0, 0, 0); font-family: Helvetica; font-size:
18px; font-style: normal; font-variant-caps: normal;
font-weight: normal; letter-spacing: normal;
text-align: start; text-indent: 0px; text-transform:
none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none;" class="">
<font style="font-size: 11pt;" class=""
face="Calibri, sans-serif"><b class="">From:</b><span
class="Apple-converted-space"> </span>Lorenzo
Bastonero <<a
href="mailto:lbastone@uni-bremen.de"
class="moz-txt-link-freetext"
moz-do-not-send="true">lbastone@uni-bremen.de</a>><br
class="">
<b class="">Sent:</b><span
class="Apple-converted-space"> </span>Thursday,
May 11, 2023 2:11:28 AM<br class="">
<b class="">To:</b><span
class="Apple-converted-space"> </span>Karkee,
Rijan; Quantum ESPRESSO users Forum<br class="">
<b class="">Subject:</b><span
class="Apple-converted-space"> </span>[EXTERNAL]
Re: [QE-users] The phonon code with Raman and
Hubbard U is not implemented</font>
<div class=""> </div>
</div>
<div style="caret-color: rgb(0, 0, 0); font-family:
Helvetica; font-size: 18px; font-style: normal;
font-variant-caps: normal; font-weight: normal;
letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration:
none;" class="">
Dear Rijan,
<div class=""><br class="">
</div>
<div class="">Indeed the computation of Raman
intensities is limited to LDA and Norm-conserving
pseudopotentials.</div>
<div class=""><br class="">
</div>
<div class="">There is an alternative way to compute
both phonons (i.e. peak positions) and intensities
(of each mode). </div>
<div class="">You have to use finite differences for
the phonons and finite electric fields for the
intensities (if you want to know the theory, look
at Umari and Pasquarello, Diamonds and Related
Materials, 2005).</div>
<div class=""><br class="">
</div>
<div class="">These routines are in QE, nevertheless
you will need to do the steps by hand.</div>
<div class=""><br class="">
</div>
<div class="">Currently, we have an automated
workflow for doing such calculations in AiiDA,
which is a workflow manager that automates complex
workflows, for QE and other quantum codes.</div>
<div class="">The code will be published very soon,
and we plan to send an email here once it is
published.</div>
<div class=""><br class="">
</div>
<div class="">So, at the moment, if you are
interested, you can have a look at the
demonstration of AiiDA + QE (<a
href="https://urldefense.com/v3/__https://aiida-qe-demo.readthedocs.io/en/latest/__;!!Bt8fGhp8LhKGRg!DbwBeLMmYIrnyC7VLd4-orYpVCYS7spvVhPfEFwHggBVJv_I2o5dKspdMRW5DKNYoiAGAqSmJ1WuS7chcG1yAe8$"
class="" moz-do-not-send="true">https://aiida-qe-demo.readthedocs.io/en/latest/</a>),
and then get your local implementation and install
aiida (<a
href="https://urldefense.com/v3/__https://aiida.net__;!!Bt8fGhp8LhKGRg!DbwBeLMmYIrnyC7VLd4-orYpVCYS7spvVhPfEFwHggBVJv_I2o5dKspdMRW5DKNYoiAGAqSmJ1WuS7ch19tOXhM$"
class="" moz-do-not-send="true">https://aiida.net</a>)
aiida-quantum espresso, which is the main block
for the future package we will release.</div>
<div class=""><br class="">
</div>
<div class="">HTH,</div>
<div class="">Lorenzo<br class="">
<br class="">
<div dir="ltr" class="">Inviato da iPhone</div>
<div dir="ltr" class=""><br class="">
<blockquote type="cite" class="">Il giorno 11
mag 2023, alle ore 07:55, Karkee, Rijan via
users <<a
href="mailto:users@lists.quantum-espresso.org"
class="moz-txt-link-freetext"
moz-do-not-send="true">users@lists.quantum-espresso.org</a>>
ha scritto:<br class="">
<br class="">
</blockquote>
</div>
<blockquote type="cite" class="">
<div dir="ltr" class="">
<div id="divtagdefaultwrapper" dir="ltr"
style="font-size: 12pt; font-family:
Calibri, Helvetica, sans-serif;" class="">
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
Hello Developers,</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
<br class="">
</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
I saw some plots of Raman spectra in the
tutorial on DFT+U. I was wondering if
Raman spectra with DFT+U and/or DFT+U+V
will be implemented anytime soon or if is
there any simpler way to add in the code
in order for it to have Raman with DFT+U? </div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
As of now, I found that Raman is not
implemented with DFT+U.</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
<br class="">
</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
Thank you,</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
Best</div>
<div style="margin-top: 0px; margin-bottom:
0px;" class="">
Rijan Karkee</div>
</div>
<span class="">_______________________________________________</span><br
class="">
<span class="">The Quantum ESPRESSO community
stands by the Ukrainian</span><br class="">
<span class="">people and expresses its
concerns about the devastating</span><br
class="">
<span class="">effects that the Russian
military offensive has on their</span><br
class="">
<span class="">country and on the free and
peaceful scientific, cultural,</span><br
class="">
<span class="">and economic cooperation
amongst peoples</span><br class="">
<span class="">_______________________________________________</span><br
class="">
<span class="">Quantum ESPRESSO is supported
by MaX (<a
href="https://urldefense.com/v3/__http://www.max-centre.eu__;!!Bt8fGhp8LhKGRg!DbwBeLMmYIrnyC7VLd4-orYpVCYS7spvVhPfEFwHggBVJv_I2o5dKspdMRW5DKNYoiAGAqSmJ1WuS7chO_kspeg$"
class="" moz-do-not-send="true">www.max-centre.eu</a>)</span><br
class="">
<span class="">users mailing list <a
href="mailto:users@lists.quantum-espresso.org"
class="moz-txt-link-freetext"
moz-do-not-send="true">
users@lists.quantum-espresso.org</a></span><br
class="">
<span class=""><a
href="https://urldefense.com/v3/__https://lists.quantum-espresso.org/mailman/listinfo/users__;!!Bt8fGhp8LhKGRg!DbwBeLMmYIrnyC7VLd4-orYpVCYS7spvVhPfEFwHggBVJv_I2o5dKspdMRW5DKNYoiAGAqSmJ1WuS7chrxJ0fqQ$"
class="" moz-do-not-send="true">https://lists.quantum-espresso.org/mailman/listinfo/users</a></span></div>
</blockquote>
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
The Quantum ESPRESSO community stands by the Ukrainian
people and expresses its concerns about the devastating
effects that the Russian military offensive has on their
country and on the free and peaceful scientific, cultural,
and economic cooperation amongst peoples
_______________________________________________
Quantum ESPRESSO is supported by MaX (<a class="moz-txt-link-abbreviated" href="https://urldefense.com/v3/__http://www.max-centre.eu__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBe1qwm-k$" moz-do-not-send="true">www.max-centre.eu</a>)
users mailing list <a class="moz-txt-link-abbreviated moz-txt-link-freetext" href="mailto:users@lists.quantum-espresso.org" moz-do-not-send="true">users@lists.quantum-espresso.org</a>
<a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://lists.quantum-espresso.org/mailman/listinfo/users__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBrqlKd3M$" moz-do-not-send="true">https://lists.quantum-espresso.org/mailman/listinfo/users</a></pre>
</blockquote>
<div class="moz-signature">-- <br>
<small>Dr. Lorenzo Paulatto<br>
IdR @ IMPMC - CNRS UMR 7590 & Sorbonne Université<br>
phone: +33 (0)1 442 79822 / skype: paulatz<br>
<a
href="https://urldefense.com/v3/__http://www.impmc.upmc.fr/*paulatto/__;fg!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBRiF37E8$"
class="moz-txt-link-freetext" moz-do-not-send="true">http://www.impmc.upmc.fr/~paulatto/</a>
- <a
href="https://urldefense.com/v3/__https://anharmonic.github.io/__;!!Bt8fGhp8LhKGRg!Fo8ygVkM_59sAeHnLqjTXbN8q1Um90dSoI25ODoT6335GMMknEiJXbKRYnsLOOdGD7qpaVuG_3fbFIvT5qNBmuve9GA$"
class="moz-txt-link-freetext" moz-do-not-send="true">
https://anharmonic.github.io/</a><br>
23-24/423 B115, 4 place Jussieu 75252 Paris CX 05</small></div>
<lt-container></lt-container></div>
</blockquote>
<div class="moz-signature">-- <br>
<small>Dr. Lorenzo Paulatto<br>
IdR @ IMPMC - CNRS UMR 7590 & Sorbonne Université<br>
phone: +33 (0)1 442 79822 / skype: paulatz<br>
<a href="http://www.impmc.upmc.fr/~paulatto/"
class="moz-txt-link-freetext">http://www.impmc.upmc.fr/~paulatto/</a>
- <a href="https://anharmonic.github.io/"
class="moz-txt-link-freetext">https://anharmonic.github.io/</a><br>
23-24/423 B115, 4 place Jussieu 75252 Paris CX 05<small></small></small></div>
</body>
</html>