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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 Photon transmission study on conformational ordering of iota-carrageenan in CaCl2 solution(Taylor & Francis Inc, 2005-06) Kara, Selim; Pekcan, Mehmet ÖnderCoil-to-double helix (c-h) and double helix-to-dimer (h-d) phase transitions of iota-carrageenan in CaCl2 solution upon cooling were studied using photon transmission technique. Photon transmission intensity, I-iota r was monitored against temperature to determine the (c-h) and (h-d) transition temperatures (T-ch and T-hd) and activation energies (Delta E-ch and Delta E-hd). An extra dimer-to-dimer (d-d) transition was also observed during cooling at low temperature region. However, upon heating dimers disappear to double helices by making dimer-to-double helix (d-h) transition. Further heating resulted double helix-to-coil (h-c) transition at high temperature region. T-dh and T-ch temperatures and Delta E-dh and Delta E-hc activation energies were also determined. It was observed that T-hc and T-ch temperatures and Delta E-dh and Delta E-hd activation energies do not effected by carrageenan content. However, T-hd, T-dh and T-dd temperatures and Delta E-ch and Delta E-hc activation energies were found to be strongly correlated to the carrageenan content in the system.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 Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations(Academic Press Inc Elsevier Science, 2011-02-01) Duruk, Nilay; Erbay, Hüsnü Ata; Erkip, AlbertWe study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite-time blow-up and as well as global existence of solutions of the problem.Yayın Swelling of iota-carrageenan gels prepared with various CaCl2 content: A fluorescence study(European Polymer Federation, 2008-01-05) Tarı İlgin, Özlem; Pekcan, Mehmet ÖnderIota carrageenan gels prepared with various CaCl2 content were completely dried and then swelled in water vapor. Steady-state fluorescence ( SSF) technique was used to monitor the swelling process of each iota carrageenan gels at various temperatures. Pyranine was used as a fluorescence probe. Apparent fluorescence intensity, I increased as swelling time increased for all gel samples. The increase in I was modelled using Li-Tanaka equation from which the swelling time constants, tau(1) and cooperative diffusion coefficients, D-c were determined. It was observed that D-c increased as the swelling temperature was increased. On the other hand at each temperature, it was seen that D-c decreased as CaCl2 content was increased. Activation energies for swelling were obtained and found to be 60.5, 61.0, 61.5 and 62.8 kJmol(-1) for the gels prepared with increasing amount of CaCl2 content.Yayın Small molecule diffusion into swelling Iota-Carrageenan gels: A fluorescence study(Taylor & Francis Group, 2007-04) Ataman, Evren; Pekcan, Mehmet ÖnderSmall molecule diffusion into Iota-Carrageenan gel was studied by using steady-state fluorescence (SSF) technique. Pyranine, dissolved in water was used as fluorescence probe. Fluorescence emission intensity, I-p, and scattered light intensity, I-sc, were monitored to study diffusion and swelling processes at various temperatures respectively. Fickian and Li-Tanaka models were elaborated to produce diffusion, D, and collective diffusion, D-0, coefficients. Diffusion and swelling activation energies were also obtained and found to be 20.5 kj mol(-1) and 28.2 kj mol(-1). 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 Monitoring of a laboratory-scale inland-delta formation using a structured-light system(Blackwell Publishing Ltd, 2016-06) Akça, Mehmet Devrim; Seybold, Hansjörg J.A reduced complexity model, which simulates the process of fluvial inland-delta formation, has been developed in a previous study. The results have been compared and validated with a laboratory experiment. This work elaborates the laboratory investigation in which an experimental inland delta is generated and its eroding topography is measured using a structured-light 3D scanner. The least squares 3D (LS3D) co-registration and comparison method is used for alignment as well as for comparing data epochs both spatially and temporally. A spatial precision value of around ±50 ?m (1/20 000) is achieved. A series of high-quality digital elevation models (DEMs) are generated and the space-time evolution of the inland delta is monitored and analysed, in terms of slope and topography dynamics, in the consecutive DEM layers. The combination of high-resolution scanning together with high-precision co-registration techniques allows investigation of the details of the space-time variability of the sedimentation-deposition patterns to be used for geomorphological analysis.Yayın Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows(Springer, 2014-06) Delale, Can Fuat; Pasinlioğlu, Şenay; Başkaya, Zafer; Schnerr, Günter H.Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300-311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.
