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A Brief Survey of Lévy Walks: with applications to probe diffusion
Karlstad University, Division for Chemistry. (Fysikalisk kemi)
2010 (English)Independent thesis Basic level (degree of Bachelor), 15 credits / 22,5 HE creditsStudent thesisAlternative title
En översikt över Lévyprocesser : applicerat på probdiffusion (Swedish)
Abstract [en]

Lévy flights and Lévy walks are two mathematical models used to describe anomalous diffusion(i.e. those having mean square displacements nonlinearly related to time (as opposed to Brownian motion)). Lévy flights follow probability distributions p(|r|) yielding infinite mean square displacements since some rare steps are very long. Lévy walks, however, have coupled space-time probability distributions penalising very long steps. Both Lévy flights and Lévy walks are dominated by a few long steps, but most steps are much, much smaller. The semi-experimental part ofthis work dealt with how fluorescent probes moved in systems of cationic starch and latex/solutions of dodecyl trimethyl ammonium bromide, respectively. Visually, no Lévy walks couldbe detected. However, mathematical regression suggested enhanced diffusion and subdiffusion. Moreover, time-dependent diffusion coefficients were calculated. Also examined was how Microsoft Excel could be used to generate normal diffusion as well as anomalous diffusion.

Abstract [sv]

Lévyflygningar och Lévypromenader är matematiska modeller som används för att beskriva anomal diffusion (i.e. dessa då medelvärdet av kvadratförflyttningarna är icke-linjärt relaterat tilltiden (till skillnad från Brownsk rörelse)). Lévyflygningar följer sannolikhetsfördelningar p(|r|)som ger oändliga medelkvadratförflyttningar eftersom vissa steg är väldigt långa. Lévypromenader,å andra sidan, har kopplade rum-tid-sannolikhetsfördelningar som kraftigt reducerar demycket långa stegen. Både Lévyflygningar och -promenader domineras av ett fåtal långa steg ävenom de flesta steg är mycket, mycket mindre. Den semiexperimentella delen av detta arbetestuderade hur fluorescerande prober rör sig i katjonisk stärkelse respektive latex/lösningar avdodecyltrimetylammoniumbromid. Inga Lévypromenader kunde ses. Emellertid taladematematisk regression för att superdiffusion och subdiffusion förelåg. Tidsberoende diffusionskoefficienter beräknades också. I detta arbete undersöktes även hur Microsoft Excel kan användas för att generera både normal och anomal diffusion.

Place, publisher, year, edition, pages
2010. , p. 59
Keywords [en]
Fluorescence, Probe, diffusion, Lévy walks, Brownian
National Category
Physical Chemistry
Identifiers
URN: urn:nbn:se:kau:diva-5077OAI: oai:DiVA.org:kau-5077DiVA, id: diva2:288755
Presentation
2010-01-13, 9E126, Karlstads universitet, 13:15 (Swedish)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-02-09 Created: 2010-01-21 Last updated: 2010-02-09Bibliographically approved

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