20.500.12556/RUL-121467 Ureditvena stanja ograjenega nematskega linearnega polimera v kontinuumskem opisu s tenzorsko vezjo Ordering states of confined nematic linear polymers in continuum description with tensorial constraint V tem delu predstavim tipe stacionarnih ureditev linearnih nematskih polimernih verig, omejenih znotraj krogelne kapside (lupine). Pri tem uporabim poln tenzorski opis problema. Sestavim gostoto proste energije in numerično rešim sistem Euler-Lagrangeovih enačb za številsko gostoto polimernih segmentov in nematski ureditveni tenzor. Obe količini sta zaradi zveznosti polimernih verig povezani s kontinuumsko tenzorsko vezjo. Slednjo vključim v gostoto proste energije po ustreznem kazenskem potencialu. Najdene tipe ureditev prikažem na faznem grafu. V zadnjem delu naloge se ukvarjam še s problemom mehčanja DNA molekul. V modelu zamenjam kazenski potencial izvorov tenzorske vezi 2. reda s kazenskim potencialom 4. reda. Pri tem preverim stabilnost modela in se dotaknem nekaterih perečih vprašanj, kot so lokalno taljenje polimernih verig in prihodnja pričakovanja ter ideje o uporabi modela. In this work I present types of stationary configurations of nematic polymer chains confined inside a spherical capsid. In this problem I use the complete tensor description of nematic ordering. The solutions are acquired by formulating the free energy density and solving the system Euler-Lagrange equations for number density of polymer segments and nematic order tensor. Due to the connectivity of polymer chains, both variables are connected by a continuity constraint. This constraint is integrated into free energy density functional via an appropriate penalty potential. The obtained types of polymer configurations are presented in a phase diagram. In the last part of this work the problem of DNA "softening" \, is addressed. The previous penalty potential of second order is replaced with the penalty potential of fourth order in the sources of the continuity constraint. I check the stability of this modified model and touch on some burning issues such as local melting of polymer chains, future expectations and ideas for the use of this model. tenzorska vez linearni polimeri liotropni tekoči kristali nematski tekoči kristali ureditveni parameter kontinuumski modeli nematski ureditveni tenzor omejeni tekoči kristali "mehčanje" DNA molekul stacionarna ureditev defekti tensor continuity constraint linear polymers lyotropic liquid crystals nematic liquid crystals order parameter continuum models nematic order tensor confined liquid crystals DNA "softening" stationary states defects true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2020-10-11 08:15:02 2020-10-11 08:15:10 2022-09-02 03:59:34 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 113359 32296963 1503.pdf 1503.pdf 1 5EFC6D697F4E5C775D92C6DDC80CC38E 20c2b69098e64567f79aa8b519a9dc8a5864ce08faeac4bfd1641f6df0a68940 e48213ff-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=136395 Fakulteta za matematiko in fiziko 0 0 0