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Yayın Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction(World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, SerkanWe study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.Yayın Small molecule sorption and desorption in and out of iota-carrageenan gels(Taylor & Francis Group, 2007-08) Ataman, Evren; Pekcan, Mehmet ÖnderSmall molecule sorption and desorption in and out of Iota-Carrageenan was studied by using steady-state fluorescence (SSF) technique. Pyranine dissolved in water used as fluorescence probe. Fluorescence emission intensity, I-p from pyranine was monitored for studying sorption and desorption processes at various temperatures. The Fickian model was applied to produce sorption, D-s, early desorption, D-ed, and desorption, D-d, coefficients. Corresponding activation energies were obtained and found to be 20.5 kJ mol(-1), 7.0 kJ mol(-1) and 34.9 kJ mol(-1), respectively. The observed D-ed value is an order of magnitude smaller than the D-s and D-d coefficients. On the other hand, sorption processes were shown to be twice as fast as desorption processes.Yayın Monovalent and divalent cation effects on phase transitions of iota-carrageenan(Sage Publications Ltd, 2007-01) Kara, Selim; Arda, Ertan; Pekcan, Mehmet ÖnderPhase transitions Of L-carrageenan in a variety of monovalent (Li, Na, K) and divalent (Mg, Ca, Sr) cation solutions were studied during heating and cooling by using photon transmission technique. Photon transmission intensity (I-tr) was monitored against temperature to determine the transition temperatures and activation energies during the heating and cooling processes in the monovalent and divalent systems. Three distinct transition regions were observed during the heating and cooling cycles for the carrageenan-divalent salt system. At the first step of the heating process, dimer groups were transformed into dimers that presented (g-d) transitions, then these dimers were directly converted into a double helix by undergoing a (d-h) transition. In the higher temperature region, a double helix-to-coil (h-c) transition took place. During the cooling process, these transitions are arranged in the order of (c-h), (h-d), and (d-g). The carrageenan-monovalent salt system presented only coil-to-rod-like helix (c-r) and rod-like helix-to-coil (r-c) transitions during the cooling and heating processes, respectively. A hysteresis was observed between (r-c)-(c-r) and (g-d)-(d-g) transitions for the monovalent and divalent cations, respectively.Yayın Study on critical behaviour in N-isopropyl acrylamide gels by using fluorescence technique(Taylor & Francis Group, 2006-11) Kaya Aktaş, Demet; Pekcan, Mehmet ÖnderThe steady state fluorescence (SSF) technique was used to study the sol-gel transition for the solution free radical crosslinking copolymerization of N-isopropyl acrylamide (NIPA), with N,N'-methylenebis (acrylamide) (BIS) as crosslinker in the presence of ammonium persulfate (APS) as an initiator. Pyranine (8-hydroxypyrene-1,3,6-trisulfonic acid, trisodium salt, HPTS) was used as a floroprobe for monitoring the polymerization. Pyranine molecules start to bind to NIPA polymer chains upon the initiation of the polymerization, thus the spectra of the bonded pyranines shift to the shorter wavelengths. The get fraction exponent beta and the weight average degree of polymerization exponent gamma' agree best with the mean-field (Flory-Stockmayer) results near the gel point for various crosslinker contents.Yayın Molecular recognition during sol-gel and gel-sol transition of kappa-iota carrageenan mixtures(Taylor & Francis ltd, 2005-12) Kara, Selim; Arda, Ertan; Pekcan, Mehmet ÖnderSol-gel and gel-sol phase transitions of kappa-iota (kappa-iota) carrageenan mixtures in two types of salts were studied using photon transmission technique. Here, KCl and CaCl2 were chosen as the proper salts for the carrageenan mixtures. Coil-to-double helix (c-h) and double helix-to-dimer (h-d) phase transitions of carrageenan mixtures in monovalent and bivalent cation solutions were studied upon heating and cooling by using photon transmission technique. Photon transmission intensity, It, was monitored against temperature to determine the (c-h) and (h-d) transition temperatures (T-ch and T-nd). Two distinct transition regions were observed in both heating and cooling of the carrageenan-bivatent CaCl2 salt system. At the first step of heating process dimers decompose into double helices by making (d-h) transition. At the high temperature region (h-c) transition takes place. Carrageenan-monovalent KCl salt system presented only (c-h) and (h-c) transitions upon cooling and heating processes. Transition temperatures at the heating and cooling processes were obtained. A hysteresis was observed between (h-c)-(c-h) and (d-h)-(h-d) transitions for the monovalent and bivalent cations respectively.Yayın On extensions, Lie-Poisson systems, and dissipation(Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, SerkanLie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.Yayın Matched pair analysis of the Vlasov plasma(American Institute of Mathematical Sciences-AIMS, 2021-06) Esen, Oğul; Sütlü, SerkanWe present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order >= 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.
