Dynamics of an active crosslinker on a chain and aspects of the dynamics of polymer networks
| dc.contributor.advisor | Muller-Nedebock, Kristian K. | en_ZA |
| dc.contributor.author | Moller, Karl | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Physics. | en_ZA |
| dc.date.accessioned | 2011-11-22T09:02:15Z | en_ZA |
| dc.date.accessioned | 2011-12-05T13:19:02Z | |
| dc.date.available | 2011-11-22T09:02:15Z | en_ZA |
| dc.date.available | 2011-12-05T13:19:02Z | |
| dc.date.issued | 2011-12 | en_ZA |
| dc.description | Thesis (MSc)--Stellenbosch University, 2011. | en_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: Active materials are a subset of soft matter that is constantly being driven out of an equilibrium state due to the energy input from internal processes such as the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP), as found in biological systems. Firstly, we construct and study a simple model of a flexible filament with an active crosslinker/molecular motor. We treat the system on a mesoscopic scale using a Langevin equation approach, which we analyse via a functional integral approach using the Martin-Siggia-Rose formalism. We characterise the steady state behaviour of the system up to first order in the motor force and also the autocorrelation of fluctuations of the position of the active crosslink on the filament. We find that this autocorrelation function does not depend on the motor force up to first order for the case where the crosslinker is located in the middle of the contour length of the filament. Properties that characterise the elastic response of the system are studied and found to scale with the autocorrelation of fluctuations of the active crosslink position. Secondly, we give a brief overview of the current state of dynamical polymer network theory and then propose two dynamical network models based on a Cayley-tree topology. Our first model takes a renormalisation approach and derive recurrence relations for the coupling constants of the system. The second model builds on the ideas of an Edwards type network theory where Wick’s theorem is employed to enforce the constraint conditions. Both models are examined using a functional integral approach. | en_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: Aktiewe stelsels is ’n subveld van sagte materie fisika wat handel oor sisteme wat uit ekwilibruim gedryf word deur middel van interne prossesse, soos wat gevind word in biologiese stelsels. Eerstens konstruëer en bestudeer ons ’n model vir ’n buigbare filament met ’n aktiewe kruisskakelaar of molekulêre motor. Ons formuleer die stelsel op ’n mesoskopiese skaal deur gebruik te maak van ’n Langevin vergelyking formalisme en bestudeer die stelsel deur gebruik te maak van funksionaal integraal metodes deur middel van die Martin-Siggia-Rose formalisme. Dit laat ons in staat om die tydonafhankle gedrag van die stelsel te bestudeer tot op eerste orde in die motorkrag. Ons is ook in staat om die outokorrelasie fluktuasies van die posisie van die aktiewe kruisskakelaar te karakteriseer. Ons vind dat die outokorrelasie onafhanklink is van die motorkrag tot eerste orde in die geval waar die kruisskakelaar in die middel van die filament geleë is. Die elastiese eienksappe van die sisteem word ook ondersoek en gevind dat die skaleer soos die outokorrelasie van die fluktuasies van die aktiewe kruisskakelaar posisie. Tweedens gee ons ’n vlugtige oorsig van die huidige toestand van dinamiese polimeer netwerk teorie en stel dan ons eie twee modelle voor wat gebasseer is op ’n Caylee-boom topologie. Ons eerste model maak gebruik van ’n hernormering beginsel en dit laat ons toe om rekurrensierelasies vir die koppelingskonstates te verkry. Die tweede model bou op idees van ’n Edwards tipe netwerk teorie waar Wick se teorema ingespan word om die beperkingskondisies af te dwing. Beide modelle word met funksionaal integraal metodes bestudeer. | af_ZA |
| dc.format.extent | 94 p. : ill. | |
| dc.identifier.uri | http://hdl.handle.net/10019.1/18001 | en_ZA |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | |
| dc.subject | Dynamics | en_ZA |
| dc.subject | Active systems | en_ZA |
| dc.subject | Polymer networks | en_ZA |
| dc.subject | Theoretical physics | en_ZA |
| dc.subject | Dissertations -- Physics | en_ZA |
| dc.subject | Theses -- Physics | en_ZA |
| dc.subject | Network models | en_ZA |
| dc.subject | Mathematical models | en_ZA |
| dc.subject | Martin-Siggia-Rose formalism | en_ZA |
| dc.title | Dynamics of an active crosslinker on a chain and aspects of the dynamics of polymer networks | en_ZA |
| dc.type | Thesis | en_ZA |