Browsing by Author "Kayacan O."
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Item The effects of the nonextensivity on the dimerization process and nematic ordering(2003) Kayacan O.The influence of the dimerization process on the nematic ordering is investigated by using a nonextensive thermostatistics, namely Tsallis thermostatistics (TT). A theoretical model taking into account the dimerization influence on the nematic scalar order parameter has been recently presented (Phys. Lett. A 256 (1999) 309). Our study considers this model and the theoretical predictions for the nematic order parameter are improved by using TT. © 2003 Elsevier B.V. All rights reserved.Item Nonextensive thermostatistical approach to the thermoluminescence decay(2004) Kayacan O.; Can N.In this study, thermoluminescence decay is investigated within Tsallis thermostatistics (TT). We believe that this is the first attempt to handle the thermoluminescence decay process within TT. The generalized form of glow intensity vs temperature is examined and the effect of the nonextensitivity is shown for various values of the entropic index q. The results are interpreted in terms of the entropic index q and the occupied trap density n. © 2003 Elsevier B.V. All rights reserved.Item Mean-field theory of anisotropic potential of rank L=4 and nonextensive formalism(Elsevier, 2004) Kayacan O.In this study, we employ the potential Uij=-f(r ij)PL(cosθij) with rank L=4 to study on the nematic-isotropic phase transition, using generalized mean-field theory. We use a mean-field theory (P4 model) with this potential and generalize it using a nonextensive thermostatistics, namely Tsallis thermostatistics (TT). It is well known that mean-field theories have some insufficiencies. So we could expect similar insufficiencies from the P 4 model. Therefore to improve the P4 model, if necessary, one could use TT. In this study, we give the possible contributions of TT to the nematic-isotropic transition. TT includes a parameter which is called the entropy index and it is a measure of the nonextensivity of the system. In this framework, the variations of P̄4 and P̄2 vs. temperature have been showed for various values of the entropic index q. The entropy changes with respect to the entropic index have been also reported. © 2003 Elsevier B.V. All rights reserved.Item Orientational ordering in the nematic phase of a thermotropic liquid crystal: A nonextensive approach(2004) Kayacan O.In this study, the dependence of fourth-rank order parameter on second-rank order parameter for para-azoxyanisole is investigated by using Tsallis statistics. Also, orientational distribution function is studied within Tsallis thermostatistics using the maximum entropy method, and the generalized distribution function is plotted for various values of the entropic index. The effects of the nonextensivity are illustrated for various values of the entropic index. © 2004 Elsevier B.V. All rights reserved.Item A generalized method for handling first- and second-order thermal desorption and thermoluminescence(Elsevier, 2004) Kayacan O.; Can N.The influence of the nonextensivity on first- and second-order thermal desorption is investigated. A theoretical model for analyzing first- and second-order desorption spectra and glow curves were been presented [J. Appl. Phys. 51 (1980) 2594]. In addition, thermoluminescence decay has been recently investigated within Tsallis thermostatistics (TT). In this manner, our study considers this model and the effect of the nonextensivity is shown for various values of the entropic index q. © 2003 Elsevier B.V. All rights reserved.Item Generalized mean-field theory relating helix tilt in a bilayer to lipid disorder(2004) Kayacan O.We present a generalized theory relating the helix tilt angle in a bilayer to lipid disorder. In doing so, we consider a theory performed earlier [Biophys. Chem., 86 (2000) 79] and generalize it within a nonextensive formalism. The generalized theory provides a method to compare the rotational barriers for different helices in lipid bilayers, accounting for long-range interactions via a parameter which is called "entropic index". The results obtained could lead to point out future experiments which might shed light on lipid-protein interactions. © 2004 Published by Elsevier B.V.Item A nonextensive statistical approach to the kinetics of phase transformation(2005) Kayacan O.; Cetinel H.Some limitations of Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, which is used widely for describing kinetics of phase transformation, were demonstrated using probabilistic analysis and Monte Carlo simulations [Acta Mater. 48 (2000) 4217]. As well-known, JMAK equation predicts correctly the real transformed fraction only if the number of the growing nuclei in the controlled volume is large. However JMAK equation seems to fail, if the number of growing nuclei is small, no matter how large the volume of the controlled volume is. In this study, we propose a different equation for describing kinetics of phase transformation, using a nonextensive formalism, namely Tsallis thermostatistics which has been commonly employed to study the various physical systems for a decade. © 2004 Elsevier B.V. All rights reserved.Item Free energies and specific heats of the nematics within nonextensive thermostatistics(Association for Scientific Research, 2005) Afsar O.; Kayacan O.In this study, the free energies and specific heats of the nematic liquid crystals are studied within Tsallis thermostatistics. In equilibrium, free energy of PAA (para-azoxyanisole) vs the order parameter is plotted, as well as its the specific heat vs temperature. The effect of the nonextensivity is illustrated for some values of the entropic index q. © Association for Scientific Research.Item Application for Tsallis thermostatistics to half-width method used in thermoluminescence glow peaks in analysis of thermal desorption spectra(Elsevier, 2005) Kayacan O.; Can N.; Karabulut Y.; Afsar O.Several methods have been developed in the analysis of the thermoluminescence glow peaks, and in particular when applied to thermoluminescence (TL) dosimetry and TL dating of archaeological and geological minerals. Some of these methods are identical to those developed for the study of thermal desorption. Such a method is called half-width method where a shape factor is introduced. Recently TL decay and thermal desorption process have been studied using a nonextensive formalism, namely Tsallis thermostatistics. In the present work, we consider the half-width method because it is the easiest one to estimate the activation energy. Importantly, we give the generalized form of the activation energy for all order of kinetics. We also investigate the influence of the nonextensivity on the shape factor parameter and on the activation energy. © 2004 Elsevier B.V. All rights reserved.Item The influence of nonextensivity on orientational ordering in liquid crystal systems with variable molecular shape(2005) Kayacan O.A generalized model taking into account the photoisomerization influence on the nematic ordering is presented. This generalized theory is used to investigate the effect of the nonextensivity on the concentration dependence of the long-range order parameter. The q-dependent variation of the concentration of cis-trans isomers and of the order parameter with the time of exposure to the illumination is investigated within nonextensivity. It is also shown that for sufficiently long exposition of the mesophase to the illumination the nematic phase cannot disappear for some value of the entropic index, coming from Tsallis statistics. Moreover it is shown that long range interactions or the fractal structure in the liquid crystalline system might affect the characteristics of the phase transition in the physical system. We think therefore that this conclusion might shed light on the interaction potential energy terms in the similar system in future possible experiments, even to be performed on new objects with different symmetries. © 2005 Elsevier B.V. All rights reserved.Item Nonextensive mean-field theory for ferroelectric nematic liquid crystal phases(2005) Kayacan O.Ferroelectric ordering in a nematic liquid crystal system is described using nonextensive thermostatistics. We use a mean-field potential, including effective potentials for both axial and polar interactions. By using a self-consistent numerical analysis, a complete q-dependent phase diagram is obtained as a function of the axial and polar interaction potential strengths. The phase transition behaviours and the generalized angular orientational distribution function of the molecules were investigated by studying the dependence of the polar and the axial order parameters on the reduced temperature for various values of the entropic index. This study can provide basic information to further detailed theoretical studies of molecular interactions.Item Investigation of the phase transition at the nematic liquid crystal-wall interface with P4-interaction(2006) Kayacan O.The nematic-isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, using a self-consistent model. The interacting potential is given by a sum of the direct interaction of a given nematic molecule with the substrate and of one with the other nematic molecules due to the presence of the limiting surface. The variation of second- and fourth-rank long-range order parameters with temperature is investigated. To describe the behaviour of second- and fourth-rank order parameters at the surfaces and its profile inside the sample, a model based on the Maier-Saupe model including P4 interaction is used. In conclusion, we show the existence of a boundary layer in which the second- and fourth-rank order parameters can be greater or smaller than the one in the bulk. © 2006 Elsevier B.V. All rights reserved.Item Generalized cluster variation theory for the isotropic-nematic phase transition(2006) Afsar O.; Kayacan O.In this study, a cluster variation theory for the Maier-Saupe model of the nematic-isotropic phase transition is generalized by using non-extensive thermostatistics. The variation of long-range order parameter with temperature is investigated and the effect of the possible generalization is shown for some values of the entropic index. The critical value of the long-range order parameter at the nematic-isotropic transition temperature versus the entropic index is also compared with Monte Carlo simulation values and experimental data. © 2006 The Royal Swedish Academy of Sciences.Item A new nonlinear quantizer for image processing within nonextensive statistics(2007) Kilic I.; Kayacan O.In this study, we introduce a new nonlinear quantizer for image processing by using Tsallis entropy. Lloyd-Max quantizer is commonly used in minimizing the quantization errors. We report that the new introduced technique works better than Lloyd-Max one for selected standard images and could be an alternative way to minimize the quantization errors for image processing. We, therefore, hopefully expect that the new quantizer could be a useful tool for all the remaining process after image quantization, such as coding (lossy and lossless compression). © 2007 Elsevier B.V. All rights reserved.Item Investigation of the phase transition at the nematic liquid crystal-wall interface within nonextensivity(2007) Kayacan O.In this study, the nematic-isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, using nonextensive formalism. The interaction potential is written as the sum of the direct interaction of a given nematic molecule with the substrate and of its incomplete interaction with the other nematic molecules due to the presence of the limiting surface. In this framework, we show the effects of the nonextensivity on the nematic-isotropic transition at the nematic-wall interface. The generalized model can shed light on the properties of nematic liquid crystal confined in small-scale structures. © 2007 Elsevier B.V. All rights reserved.Item Temperature dependency of phase transitions in polymer-dispersed nematic liquid crystal mediums(2007) Kayacan O.; Eren San S.; Okutan M.In this work, electrical measurements were performed on a polymer-dispersed LC sample so that we could demonstrate the temperature dependent molecular behavior, determined according to the electrical response of the system. Experimental results are found to be in favorable accordance with the molecular theory in several aspects. Critical temperatures, order parameters and entropy of transition are acquired for the studied system. © 2006 Elsevier B.V. All rights reserved.Item Nonextensive treatment of nucleation and growth in a thin layer(2007) Cetinel H.; Kayacan O.In this study, a generalized method based upon nonextensive statistics is presented for nucleation and growth processes in a thin layer between two interfaces. It is shown that the presented mathematical model, which uses an index called the entropic index that measures the nonextensivity of the physical system, successfully deals with the nucleation and growth processes, and works better than Johnson-Mehl-Avrami-Kolmogorov model. The presented model also contains Austin-Rickett model as a special case. © 2006.Item Generalized statistical mechanics for nucleus(Association for Scientific Research, 2008) Babacan H.; Kayacan O.; Atici R.In this study, we derived the grand partition function and some thermodynamical quantities of the nucleus in the high temperature limit by adopting the ideal Fermi gas partition function of generalized Tsallis thermostatistics. The behaviour of number of neutron and internal energy are depicted as a function of temperature. Sensitivity of q entropy index to the number neutron are also analyzed. © Association for Scientific Research.Item Calculation of generalized level densities for nuclei in mass region 20 < A < 50(Association for Scientific Research, 2010) Babacan H.; Kayacan O.In this study, a relation between generalized level density and standard level density is derived. Using this relation and Bethe formula of Fermi gas model for standart level density we obtained a generalized nuclear level density formula for nucleus. Generalized level densities were calculated for some nuclei in mass region between 20 and 50 for different q values close to 1 . Our results explain experimental data better than those of Gilbert-Cameron (GC) and Rohr, which are two of the leading compilations in evaluating nuclear level density. © Association for Scientific Research.Item A study for boronizing process within nonextensive thermostatistics(Association for Scientific Research, 2010) Kayacan O.; Şahin S.; Taştan F.In this study, diffusion mechanism of the boronizing process of AISI 1040 has been investigated. A nonlinear diffusion equation, which was proposed earlier, has been employed and compared with the experimental data. An interesting property of the diffusion equation used here is that it establishes a connection between the diffusion process and nonextensivity. The theoretical model also exhibits a possible connection between the exponents appeared in the differential equation and the entropic index. In this manner, the possible effects of nonextensivity on the boronizing process have been shown theoretically. We believe that a diffusion equation based on the nonextensive formalism is first applied to the boronizing process in literature. © Association for Scientific Research.