Učni načrt predmeta

Predmet:
Kozmos v kapljici tekočega kristala
Course:
Universe in a Droplet of Liquid Crystal
Študijski program in stopnja /
Study programme and level
Študijska smer /
Study field
Letnik /
Academic year
Semester /
Semester
Nanoznanosti in nanotehnologije, 3. stopnja / 1 1
Nanosciences and Nanotechnologies, 3rd cycle / 1 1
Vrsta predmeta / Course type
Izbirni
Univerzitetna koda predmeta / University course code:
NANO3-884
Predavanja
Lectures
Seminar
Seminar
Vaje
Tutorial
Klinične vaje
work
Druge oblike
študija
Samost. delo
Individ. work
ECTS
15 15 15 10 5

*Navedena porazdelitev ur velja, če je vpisanih vsaj 15 študentov. Drugače se obseg izvedbe kontaktnih ur sorazmerno zmanjša in prenese v samostojno delo. / This distribution of hours is valid if at least 15 students are enrolled. Otherwise the contact hours are linearly reduced and transfered to individual work.

Nosilec predmeta / Course leader:
prof. dr. Samo Kralj
Sodelavci / Lecturers:
Jeziki / Languages:
Predavanja / Lectures:
slovenščina, angleščina / Slovenian, English
Vaje / Tutorial:
Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:
Prerequisites:

Opravljeni izpiti iz mehanike, elektromagnetizma, moderne fizike (FNM, Univerza v Mariboru, oz. temu ekvivalentni kurzi fizike).

Passed exams in Mechanics, Electromagnetism, and Modern Physics (FNM, University of Maribor, or in equivalent courses).

Vsebina:
Content (Syllabus outline):

1) Predstavitev poglavitnih tekoče-kristalnih (TK) faz.
2) Zlom simetrije in umeritveno polje.
3) Topološki defekti (TD):
- TD v TK v orientacijski in translacijski urejenosti,
- topološki naboj: univerzalna definicija,
- analogije med TD v TK in drugih področjih fizike (magnetni monopol, kozmične strune, vorteksi v superprevodnikih in supertekočinah, skyrmioni v fiziki delcev in magnetizmu, robne in zvite dislokacije v trdni snovi….).
4) Vpliv geometrije “prostora” na TD:
- univerzalni pomen Gaussove ukrivljenosti (Gauss-Bonnetov in Poincarejev teorem),
- vpliv ukrivljenosti “prostora” na lego TD,
- krivinsko inducirana tvorba parov defektantidefekt,
- koncept “paralenega transporta” in analogija s splošno teorijo relativnosti,
- stabilizacija mrež TD.
5) Anihilacija topoloških defektov:
- anihilacija TD v orientacijski in translacijski urejenosti TK,
- analogija z anihilacijo matematično sorodnih TD v kondenzirani materiji in delcev v fiziki osnovnih delcev.
6) Domenska struktura in zlom zvezne simetrije:
- anihilacija TD in rast domen,
- vpliv TD na sedanjo strukturo vesolja: Kibble-Zurkov mehanizem,
- univerzalni vpliv naključnega nereda na domensko strukturo: teorem Imry-Ma.
7) Univerzalni delčni opis narave z lokaliziranimi rešitvami pripadajočih ureditvenih polj.

1) Introduction of key liquid crystalline (LC) phases.
2) Symmetry breaking and gauge fields.
3) Topological defects (TD):
- TD in LCs in orientational and translational degree of ordering,
- topological charge: universal definition,
- analogy between TDs in LCs and other fields of physics (Dirac monopole, cosmic strings, vortices in superconductors and superfluids, skyrmions in particle physics and magnetism, edge and screw dislocations in condensed matter…).
4) Impact of curvature of “space” on TDs:
- universal role of Gaussian curvature (Gauss Bonnet and Poincare theorem),
- impact of curvature on position of TDs,
- curvature driven unbinding of pairs defectantidefect,
- concept of “parallel transport” and analogy with theory of general realativity,
- stabilisation of lattices of TDs.
5) Annihilation of TDs:
- annihilation of TDs in orientational and translational ordering in LCs,
- annihilation of mathematically analogous TDs in condensed matter physics and particle physics,
6) Domain structure and symmetry breaking:
- annihilation of TDs and domain growth,
- impact of TDs on structure of Universe: Kibble-Zurek mechanism,
- universal impact of random-type disorder on domain patterns: Imry-Ma theorem.
7) Universal “particle” description of nature in terms of localized solutions in relevant gauge fields.

Temeljna literatura in viri / Readings:

P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, Clarendon press, Oxford, 1998.
M. Kleman, O.D. Lavrentovich, Soft Matter Physics, Springer-Verlag, New York, 2003.
P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, England, 1995.
W.H. Zurek, Cosmological experiments in condensed matter, Nature 317, 505-508, 1985.

Cilji in kompetence:
Objectives and competences:

Študentje pridobijo poglobljeno znanje iz izbranega področja fizike tekočih kristalov. Preko slednjih spoznajo številne analogne univerzalne pojave v naravi, ki so skupni tako fiziki osnovnih delcev, fiziki kondenzirane materije in kozmologiji.

Students get acquainted with physics of liquid crystals. Phenomena observed in liquid crystals are exploited as testing grounds for several universal phenomena in nature, spanning particle physics, condensed matter and cosmology.

Predvideni študijski rezultati:
Intendeded learning outcomes:

Študenti se seznanijo s številnimi univerzalnimi pojavi v tekočih kristalih, preko katerih dobijo vpogled v bazične zakonitosti narave.

Predmet pripravlja študente za uporabo znanja s področja fizike tekočih kristalov.

Students acquire knowledge on diverse universal phenomena in liquid crystals. Via them they get basic understanding of several fundamental concepts in nature and ability to integrate this understanding in their research work.

This course prepares students to apply knowledge of physics of liquid crystals.

Metode poučevanja in učenja:
Learning and teaching methods:

Predavanja, seminarji, konzultacije.

Lectures, seminar work, consultations.

Načini ocenjevanja:
Delež v % / Weight in %
Assesment:
Ustni izpit
50 %
Oral examination
Naloge ali projekt
50 %
Coursework or project
Reference nosilca / Lecturer's references:
1. HÖLBL, Arbresha, MESAREC, Luka, POLANŠEK, Juš, IGLIČ, Aleš, KRALJ, Samo. Stable assemblies of topological defects in nematic orientational order. ACS omega. 2023, vol. 8, iss. 1, str. 169-179, ilustr. ISSN 2470-1343. https://dk.um.si/IzpisGradiva.php?id=84744, DOI: 10.1021/acsomega.2c07174. [COBISS.SI-ID 137430275]
2. HARKAI, Saša, ROSENBLATT, Charles, KRALJ, Samo. Reconfiguration of nematic disclinations in plane-parallel confinements. Crystals. Jun. 2023, vol. 13, iss. 6, [article no.] 904, 11 str. ISSN 2073-4352. DOI: 10.3390/cryst13060904. [COBISS.SI-ID 156823043]
3. MESAREC, Luka, IGLIČ, Aleš, KRALJ-IGLIČ, Veronika, GÓŹDŹ, Wojciech, VIRGA, Epifanio Giovanni, KRALJ, Samo. Curvature potential unveiled topological defect attractors. Crystals. May 2021, no. 5, 539, str. 1-16, ilustr. ISSN 2073-4352. https://www.mdpi.com/2073-4352/11/5/539, https://repozitorij.uni-lj.si/IzpisGradiva.php?id=135428, DOI: 10.3390/cryst11050539. [COBISS.SI-ID 63076611]
4. FAJMUT, Aleš, PAL, Kaushik, HARKAI, Saša, ČREŠNAR, Dejvid, KUTNJAK, Zdravko, KRALJ, Samo. The core structure of a laboratory-made dust devil-like vortex and its condensed matter analogs. Journal of molecular structure. [Print ed.]. 2021, vol. 1237, str. 30335-1-30335-8. ISSN 0022-2860. DOI: 10.1016/j.molstruc.2021.130335. [COBISS.SI-ID 58279171]
5. HARKAI, Saša, CORDOYIANNIS, George, SUSSER, Adam L., MURRAY, Bryce S., FERRIS, Andrew (avtor dodatnega besedila), ROŽIČ, Brigita, KUTNJAK, Zdravko, ROSENBLATT, Charles, KRALJ, Samo. Manipulation of mechanically nanopatterned line defect assemblies in plane-parallel nematic liquid crystals. Liquid crystals reviews. [in press] 2022, 66 str., ilustr. ISSN 2168-0396. DOI: 10.1080/21680396.2022.2042745. [COBISS.SI-ID 99389443]