[seminar] Seminar na IF-u srijeda, 06.11.2019. u 15:00h - dr. Anže Lošdorfer Božić - ispravan naslov izlaganja
Damir Dominko
ddominko at ifs.hr
Wed Oct 23 11:48:42 CEST 2019
****
*Institut za fiziku, Bijenička cesta 46,*
*predavaonica u zgradi Mladen Paić*
**srijeda, 06.11.2019. u 15:00 sati*
*
**
*Hyperuniformity and classification of order on the sphere*
*Dr. Anže Lošdorfer Božić*
*Institut Jožef Stefan, Ljubljana, Slovenija*
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.
******Voditelji seminara IF-a: Ivan Balog <mailto:balog at ifs.hr> i Damir
Dominko <mailto:ddominko at ifs.hr>**
--
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: ddominko at ifs.hr
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