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<div style="color: rgb(0, 0, 0); font-family: "times new
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12pt; text-align: center;"><strong><b><span
style="font-size:16pt;color:black" lang="HR"><img
src="cid:part1.588BE718.7B4C3118@ifs.hr"
data-mce-src="imap://ddominko@mail.ifs.hr:143/fetch%3EUID%3E/INBOX%3E40129?header=quotebody&part=1.1.2.2&filename=logo_IF_seminar.jpg"
class=""></span></b></strong></div>
<div style="color: rgb(0, 0, 0); font-family: "times new
roman", "new york", times, serif; font-size:
12pt; text-align: center;">
<p style="text-align:center;margin:0px" align="center"><b><span
style="font-family:'century gothic' ,
sans-serif;color:#5f5f5f" lang="EN-GB">Institut za fiziku,
Bijenička cesta 46,</span></b></p>
<p style="text-align:center;margin:0px" align="center"><b><span
style="font-family:'century gothic' ,
sans-serif;color:#5f5f5f" lang="EN-GB">predavaonica u
zgradi Mladen Paić</span></b></p>
<strong><b><span style="font-size:14pt;font-family:'century
gothic' , sans-serif;color:#993300" lang="EN-GB">srijeda,
06.11.2019. u 15:00 sati</span></b><br>
</strong></div>
<div style="color: rgb(0, 0, 0); font-family: "times new
roman", "new york", times, serif; font-size:
12pt; text-align: center;"><strong></strong> </div>
<div style="text-align: center;"><span style="color: rgb(85, 145,
60); font-family: "times new roman", serif;
font-size: 12pt;"><span style="font-size:21.3333px"><b><font
face="times new roman, serif">Hyperuniformity and
classification of order on the sphere</font></b></span></span><font
face="times new roman, serif" color="#55913c"><span
style="font-size: 21.3333px;"></span></font></div>
<div style="text-align: center;"><font face="century gothic,
sans-serif"><span style="font-size: 18.6667px;"><b>Dr. Anže
Lošdorfer Božić</b></span></font></div>
<div style="color: rgb(0, 0, 0); font-family: "times new
roman", "new york", times, serif; font-size:
12pt; text-align: center;"> </div>
<div style="text-align: center;">
<div style="text-align: center;"><font face="century gothic,
sans-serif"><span style="font-size: 14.6667px;"><b>Institut
Jožef Stefan, Ljubljana, Slovenija</b></span></font></div>
</div>
<div style="color: rgb(0, 0, 0); font-family: "times new
roman", "new york", times, serif; font-size:
12pt; text-align: center;"><span
style="font-size:small;font-family:'arial'"></span> </div>
Understanding how particles are arranged on the surface of a
sphere is not only central to numerous physical, biological, soft
matter, and materials systems but also finds applications in
computational problems, approximation theory, and analysis of
geophysical and meteorological measurements. Objects that lie on a
sphere experience constraints that are not present in Euclidean
space and that influence both how the particles can be arranged as
well as their statistical properties. These constraints, coupled
with the curved geometry, require a careful extension of
quantities used for the analysis of particle distributions in
Euclidean space to distributions confined to the surface of a
sphere. I will introduce a framework designed to analyze and
classify structural order and disorder in particle distributions
constrained to the sphere. The classification is based on the
concept of hyperuniformity, which was first introduced 15 years
ago and since then studied extensively in Euclidean space, yet has
only very recently been considered also for spherical surfaces. It
employs a generalization of the structure factor on the sphere,
related to the power spectrum of the corresponding multipole
expansion of particle density distribution. The spherical
structure factor is shown to couple with cap number variance, a
measure of density variations at different scales, allowing us to
analytically derive different forms of the variance pertaining to
different types of distributions. Based on these forms, we
construct a classification of hyperuniformity for scale-free
particle distributions on the sphere and show how it can be
extended to include other distribution types as well. I will
demonstrate that hyperuniformity on the sphere can be defined
either through a vanishing spherical structure factor at low
multipole numbers or through a scaling of the cap number
variance—in both cases extending the Euclidean definition, while
at the same time pointing out crucial differences. The presented
work provides a comprehensive tool for detecting global,
long-range order on spheres and for the analysis of spherical
computational meshes, biological and synthetic spherical
assemblies, and ordering phase transitions in spherically
distributed particles.<br>
<br>
</div>
<div style="color: rgb(0, 0, 0); font-family: arial, helvetica,
sans-serif; font-size: 12pt; text-align: left;"><b><span
style="font-size:12pt;font-family:'century gothic' ,
sans-serif" lang="EN-GB"><b><span
style="font-size:11pt;font-family:'century gothic' ,
sans-serif" lang="EN-GB"> </span></b></span></b><b><span
style="font-size:12pt;font-family:'century gothic' ,
sans-serif" lang="EN-GB"><b><span
style="font-size:11pt;font-family:'century gothic' ,
sans-serif" lang="EN-GB">Voditelji seminara IF-a: <a
href="mailto:balog@ifs.hr">Ivan Balog</a> i <a
href="mailto:ddominko@ifs.hr">Damir Dominko</a></span></b></span></b></div>
<pre class="moz-signature" cols="72">--
Damir Dominko
Research associate
Institute of Physics Zagreb
Bijenicka cesta 46, 02-226
10000 Zagreb, Croatia
office: +385 1 469 8821
cell: +385958172990
e-mail: <a class="moz-txt-link-abbreviated" href="mailto:ddominko@ifs.hr">ddominko@ifs.hr</a></pre>
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