A Mathematical Description of the Critical Point in Phase Transitions

dc.contributor.authorBilge, Ayşe Hümeyra
dc.contributor.authorPekcan, Önder
dc.date.accessioned2021-01-31T20:03:48Z
dc.date.available2021-01-31T20:03:48Z
dc.date.issued2013
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractLet y(x) be a smooth sigmoidal curve, y((n)) be its nth derivative and {x(m,i)} and {x(a,i)}, i = 1, 2, ... , be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {x(m,i)} and {x(a,i)} are both convergent and they have a common limit x(c) that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x(0), y(0)) is always the point (x(0), y(0)) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point t(c) is located in between the zero of the third derivative t(a) and the inflection point t(m) of the transition curve and as the strength of activation (measured by the parameter k/eta of the SIR model) increases, the phase transition occurs earlier in time and the critical point, t(c), moves toward t(a).en_US
dc.description.sponsorshipTubitaken_US
dc.identifier.citation10
dc.identifier.doi10.1142/S0129183113500654en_US
dc.identifier.issn0129-1831en_US
dc.identifier.issn0129-1831
dc.identifier.issue10en_US
dc.identifier.scopus2-s2.0-84882764288en_US
dc.identifier.scopusqualityQ3
dc.identifier.urihttps://hdl.handle.net/20.500.12469/3855
dc.identifier.urihttps://doi.org/10.1142/S0129183113500654
dc.identifier.volume24en_US
dc.identifier.wosWOS:000324541100001en_US
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.institutionauthorBilge, Ayşe Hümeyra
dc.institutionauthorPekcan, Mehmet Önder
dc.language.isoenen_US
dc.publisherWorld Scientific Publ Co Pte Ltden_US
dc.relation.journalInternational Journal of Modern Physics Cen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectGelationen_US
dc.subjectPhase Transitionen_US
dc.subjectEpidemic Modelsen_US
dc.titleA Mathematical Description of the Critical Point in Phase Transitionsen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isAuthorOfPublication1b50a6b2-7290-44da-b8d5-f048fea8b315
relation.isAuthorOfPublicatione5459272-ce6e-44cf-a186-293850946f24
relation.isAuthorOfPublication.latestForDiscovery1b50a6b2-7290-44da-b8d5-f048fea8b315

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