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A numerical study of the thermodynamic properties of a superconducting quantum cylinder in a longitudinal magnetic field is carried out. Closed-form expressions for the critical temperature, the free energy, the heat capacity jump, and the magnetization difference between the superconducting and normal phases as functions of the nanotube parameters are obtained in limit cases.

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Abstract  

The two-point scaling approach is introduced by the assumption that the thermodynamic potentials are generalized homogeneous functions with respect to the reduced temperature variable and to the fields conjugated to the order parameters, however, the singularities are related to the stability points in contrast to the conventional scaling where the fixed point is identified with the phase transition temperature. The extended scaling theory is illustrated in the case of the pyroelectric function behaviour in the neighbourhood of ferro-paraelectric phase transitions. The method is successfully applied to the description of the melting and surface melting phenomena. Applications to liquid crystals and mixtures of solvents can be predicted as fruitful but they still remain open for considerations.

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. From the aspect of chemical reaction, nano ZnO and bulk ZnO can be considered as the different substances but with the same chemical composition. Therefore, according to thermodynamic potential function method [ 18 ], the thermochemical cycle shown in

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split of the deformation gradient in a mechanical and thermochemical part The free energy is chosen as thermodynamic potential and is additively split into a mechanical and a thermochemical part. 11

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individual stages of the studied process mechanism; (2) transforming right-hand sides of kinetic equations, i.e., making a transition from the space of sought variables of the problem to the space of thermodynamic potentials; (3) imposing constraints on the

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the excess solute concentration Δ c is the driving force for crystallization. The quantity Δ c is related to the chemical potential difference Δ μ as well as to the thermodynamic potential difference Δ F (Kashchiev 2000 ). Both of these quantities

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