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Öğe Comparison of standard statistical thermodynamics with generalized statistical thermodynamics results for ising chain(Polish Acad Sciences Inst Physics, 1997) Tirnakli, U; Demirhan, D; Buyukkilic, FIn this study, the internal energy and the specific heat of the one-dimensional Ising model obtained in the frame of the generalized statistical thermodynamics by Andrade, were somewhat extended and compared with the internal energy and the specific heat which were calculated in the standard (conventional) statistical thermodynamics. In the q --> 1 case, approaching of the generalized internal energy and the specific heat to the standard well-known results, were illustrated by numerical applications. In addition to these, N >> 1 case was also investigated.Öğe The effect of nonextensivity on the time development of quantum systems(Springer, 1997) Tirnakli, U; Ozeren, SF; Buyukkilic, F; Demirhan, DIn this study, the classical evolution operator has been generalized within Tsallis thermostatistics. By using the generalized evolution operator, the q-dependent transition probability of a quantal system, namely Fermi Golden rule, has been introduced as w(n --> m) = \ [U-q(t,t(o))](mn)\(2). In order to make the situation concrete, a simple example from quantum mechanics has been solved in the frame of this formalism and the effect of q-index has been clearly illustrated in the figures.Öğe Effect of YBa2Cu3O7-x thin films on the textures and orientational properties of liquid crystals(Springer-Verlag, 2000) Nesrullajev, A; Tepe, M; Abukay, D; Kazanci, N; Demirhan, D; Buyukkilic, FIn the present work, the effect of thin films of YBa2Cu3O7-x complex compound on the mesomorphic and orientational properties of thermotropic nematic liquid crystals has been studied. Homogeneous, stable and reproducible homeotropic and lilted oriented textures of nematic liquid crystals were obtained. The effect of YBa2Cu3O7-x thin films on the morphologic, orientational and optical properties of thermotropic nematic liquid crystals are discussed.Öğe Exact solutions of the Schrodinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential(Elsevier Science Bv, 2000) Egrifes, H; Demirhan, D; Buyukkilic, FExact solutions of the Schrodinger equation for two 'deformed hyperbolic potentials' that were introduced by Arai [J. Math. Anal. Appl. 158 (1991) 63] have been obtained by using an analytical solution method which has been developed by Nikiforov and Uvarov [Special Functions of Mathematical Physics, Birkhauser, Basel, 1988] for the solutions of the differential equations of hypergeometric type in which the solutions are special functions. (C) 2000 Published by Elsevier Science B.V.Öğe Exact solutions of the Schrodinger equation for two deformed hyperbolic molecular potentials(Royal Swedish Acad Sciences, 1999) Egrifes, H; Demirhan, D; Buyukkilic, FThe bound state energy eigenvalues and the corresponding wave functions of the "deformed" Rosen-Morse and modified Rosen-Morse potentials have been obtained by the Nikiforov-Uvarov method [Buyukkilic et al. Theor. Chim Acta. 98, 192 (1997).* The "deformed hyperbolic functions" that were introduced for the first time by Arai IJ. Math. Anal. Appl. 158, 63 (1991)] have been used. The energy eigenvalues of these "deformed hyperbolic molecular potentials" bring up the criteria for the shape invariance of the potentials according to the deformation parameter q, as well as bringing a bound for the value of the parameter.Öğe A Fractal Approach To Entropy and Distribution-Functions(Elsevier Science Bv, 1993) Buyukkilic, F; Demirhan, DThe spectrum of fractal dimensions D(q) of non-interacting classical and quantum gases in non-equilibrium, whose states are described by the set of occupation number {n1, n2, ..., n(K)}, has been obtained. With this point of departure, the fractal inspired entropies of the related gases have been deduced. The generalized non-exponential forms of the distribution functions have been found by the application of Boltzmann's H-theorem.Öğe Generalization of the Maier-Saupe theory of the nematics within Tsallis thermostatistics(Elsevier Science Bv, 2001) Kayacan, O; Buyukkilic, F; Demirhan, DIn this study, one of the mean-field theories in nematics, the Maier-Saupe theory (MST), is generalized within Tsallis thermostatistics (TT). The variation of the order parameter versus temperature has been investigated and compared with experimental data for p-azoxyanisole (PAA). So far, we believe that this is the first attempt at the application of TT in liquid crystals. It is well known that MST fails to explain the experimental data for some of the nematics, one of which is PAA. However, generalized MST is able to account for the experimental data for a long range of temperatures. Also, in this study, the effect of nonextensivity is shown for various values of the entropic index. (C) 2001 Elsevier Science B.V. All rights reserved.Öğe Generalization of the mean-field Ising model within Tsallis thermostatistics(Elsevier Science Bv, 1997) Buyukkilic, F; Demirhan, D; Tirnakli, UIn this study, the mean-field Ising model, using the Bogolyubov inequality which has been obtained in the framework of the generalized statistical thermodynamics (GST), suitable for non-extensive systems, has been investigated. Generalized expressions for the mean-field magnetization and free energy have been established. These new results have been verified by the fact that they transform to the well-known Boltzmann-Gibbs results in the q-->1 limiting case. For the index q which characterizes the fractal structure of the magnetic system, an interval has been established where the generalized mean-field free energy has a minimum and mean-field magnetization has a corresponding finite value. The interval of q is consistent with paramagnetic free spin systems.Öğe Generalized distribution functions and an alternative approach to generalized Planck radiation law(Elsevier Science Bv, 1997) Tirnakli, U; Buyukkilic, F; Demirhan, DIn this study, recently introduced generalized distribution functions are summarized and by using one of these distribution functions, namely generalized Planck distribution, an alternative approach to the generalized Planck law for the blackbody radiation has been tackled. The expression obtained is compared with the expression given by C. Tsallis et al. [Phys. Rev. E 52 (1995) 1447], and it is found that this approximate scheme provides bounds to the exact result, depending on the values of q-index.Öğe Investigation of hydration effect of the proteins by phenomenological thermostatistical methods(Elsevier Science Bv, 2006) Oylumluoglu, G; Buyukkilic, F; Demirhan, DIn this study variations with respect to temperature of entropy increment AS, arising in the dissolution of proteins in water, have been investigated by the methods of statistical thermodynamics. In this formalism, effective electric field E and total dipole moment M are taken as thermodynamical variables. The partition function given by Bakk et al. [Physica A 304 (2002) 355-361] has been used in a modified form while obtaining the free energy. In the constructed phenomenological theory, experimental data are taken from the Study of Privalov [J. Chem. Thermodyn. 29 (1997) 447-474; J. Mol. Biol. 213 (1990) 385; T.E. Creighton, Protein Folding, W.H. Freeman and Company, New York, 1995, pp. 83-151] and relevant parameters have been found by fitting to experimental curves. The variations of entropy increments AS have been investigated in the temperature range 265-350K. (c) 2005 Elsevier B.V. All rights reserved.Öğe Investigation of the Pseudo-Harmonic Oscillator By Su(1, 1) Spectrum Generating Algebra(Elsevier Science Bv, 1992) Buyukkilic, F; Demirhan, D; Ozeren, SfThe discrete and continuous energy spectra of the pseudo-harmonic oscillator (PHO) have been investigated by the spectrum generating algebra. The PHO potential has been obtained depending on the dimension and the angular momentum. The zero-point energy of the two-dimensional PHO is found to be a minimum. The results are consistent with those obtained by other methods.Öğe Landau diamagnetism within nonextensive statistical thermodynamics(Pergamon-Elsevier Science Ltd, 2002) Sokmen, I; Buyukkilic, F; Demirhan, DIn this paper, Landau diamagnetism is revisited in the context of nonextensive statistical thermodynamics. Exact as well as approximate expressions for partition function, magnetization and susceptibility are obtained by using Hilhorst integral transformation which provides exact solutions in the framework of Tsallis statistics. The results have been reassessed with the standard results to illustrate the effect of nonextensivity. (C) 2002 Published by Elsevier Science Ltd.Öğe Landau diamagnetism within Tsallis thermostatistics and quantum groups(Springer, 1998) Ozeren, SF; Tirnakli, U; Buyukkilic, F; Demirhan, DIn this study, using the base of coherent states, Landau diamagnetism has been generalized within Tsallis Thermostatistics. As far as we know, this is the first attempt to introduce coherent states in this formalism. The magnetization and the susceptibility of the system have been obtained and compared with the standard result to illustrate the effect of nonextensivity. Then, adding a perturbation term to the Hamiltonian of the system, nonextensive effects on diamagnetic susceptibility have been investigated. In addition to this, making use of the q(G)-deformed partition function of the q(G)-oscillator system, the magnetization for q(G)-deformed Landau diamagnetism has been derived, with the aim of comparing the results obtained within both formalisms.Öğe Large-N Expansion For a Nucleon-Nucleon Potential(Verlag Z Naturforsch, 1989) Buyukkilic, F; Demirhan, DÖğe Nonextensive thermo statistical investigation of the blackbody radiation(Pergamon-Elsevier Science Ltd, 2002) Buyukkilic, F; Sokmen, I; Demirhan, DThermodynamical quantities of the blackbody radiation such as free energy, entropy, total radiation energy, specific heat are calculated within the Tsallis thermostatistics where factorization method is incorporated. It is shown that basic thermodynamical relation of the blackbody radiation is form invariant with respect to the nonextensivity entropic index q. Furthermore, the nonextensive thermodynamical quantities related to the blackbody radiation are separately obtained in terms of q and the standard thermodynamical quantities of the blackbody radiation. It is indicated that the formulation may give a way to determine q which determines the degree of the nonextensivity that is one of the aims of the present study. (C) 2001 Published by Elsevier Science Ltd.Öğe On a Variable of the Quasi-Particle Transformation of the Hamiltonian of An Odd-Nucleus(Verlag Z Naturforsch, 1989) Demirhan, D; Buyukkilic, FÖğe Polynomial solutions of the Schrodinger equation for the "deformed" hyperbolic potentials by Nikiforov-Uvarov method(Royal Swedish Acad Sciences, 1999) Egrifes, H; Demirhan, D; Buyukkilic, FIn this study, the bound state energy eigenvalues and the corresponding wave functions of the deformed Poschl-Teller and Hyperbolic Kratzer-like potentials have been obtained by the Nikiforov-Uvarov method using the deformed hyperbolic functions (sinh(q) (x) equivalent to 1/2(e(x) - qe(-x)), cosh(q) (x) equivalent to 1/2(e(x) + qe(-x)), sech(q) (x) equivalent to 1/cosh(q) (x) and tanh(q) (x) equivalent to sinh(q) (x)/cosh(q) (x)) that were introduced for the first time by Arai [J. Math. Anal. Appl. 158, 63 (1991)]. It is also observed that, the energy eigenvalues of these "new" type deformed hyperbolic potentials bring up the criteria for the shape invariance of the potentials according to the deformation parameter q.Öğe Solution of the Schrodinger equation for two different molecular potentials by the Nikiforov-Uvarov method(Springer, 1997) Buyukilic, F; Egrifes, H; Demirhan, DIn this study, the solution of the Schrodinger equation by a method developed by Nikiforov and Uvarov which is not based on the manipulation of formal power series has been schematically presented. The method gives elegant, easy and exact solutions of the Schrodinger equation. In order to demonstrate the applications of the method, solutions of the Schrodinger equation for the well-known pseudo-harmonic oscillator and a new symmetrical potential proposed by the authors are given. The concrete energy spectra and corresponding wave functions are obtained. The superiority and the limitations of the method compared to other methods have also been emphasized.Öğe Some bounds upon the nonextensivity parameter using the approximate generalized distribution functions(Elsevier Science Bv, 1998) Tirnakli, U; Buyukkilic, F; Demirhan, DIn this study, the approximate generalized quantal distribution functions and their applications which appeared in the literature so far, have been summarized. Making use of the generalized Planck radiation law, which has been obtained by us [Physica A 240 (1997) 657], some alternative bounds for the nonextensivity parameter q have been estimated. It has been shown that these results are similar to those obtained by Tsallis et al. [Phys. Rev. E 52 (1995) 1447] and by Plastino et al. [Phys. Lett. A 207 (1995) 42]. (C) 1998 Elsevier Science B.V.Öğe A Statistical Mechanical Investigation of the Pseudo-Harmonic Oscillator(Elsevier Science Bv, 1990) Buyukkilic, F; Demirhan, D
