The approach proposed in the study is based on the revision of the concept of time as a point on the real axis. It uses the concept of fuzzy time as the set of real numbers with a finite, but not equal to one, functio...The approach proposed in the study is based on the revision of the concept of time as a point on the real axis. It uses the concept of fuzzy time as the set of real numbers with a finite, but not equal to one, function of membership to the time set, i.e. the fuzzy time concept. It is postulated that in fuzzy time t the system dynamics follows from the standard variational principle of the least action and is ordinary Hamilton-Jacobi mechanics. This validates the passage to the limit from fuzzy mechanics to ordinary variational conservative mechanics. The Liouville equation is solved by the method of successive approximations in the time domain of a much larger characteristic scale of fuzziness, using interaction as a small parameter. A standard diagram technique is used. It can be shown that the defuzzification of the Liouville equation inevitably reduces the reversible part in the description to the irreversible evolutionary equation. The latter leads to the second law of thermodynamics. Generalization to the quantum case is possible, i.e. the so-called fuzzy Pauli equation can be drawn.展开更多
Inductively coupled plasmas (ICPs) are used in spectrochemical analyses. The introduction of the sample by means of an aerosol are widely used. The introduction and the total evaporation of the aerosol is required i...Inductively coupled plasmas (ICPs) are used in spectrochemical analyses. The introduction of the sample by means of an aerosol are widely used. The introduction and the total evaporation of the aerosol is required in order to obtain a good repeatability and reproducibility of analyses. To check whether the vaporization of the aerosol droplets inside the plasma is completed, a solution could be used to compare the experimental results of the emission spectral lines with theoretical results. An accurate calculation code to obtain monatomic spectral lines intensities is therefore required, which is the purpose of the present paper. The mixtures of argon, water and nitric acid are widely used in spectrochemical analyses with ICPs. With these mixtures, we calculate the composition, thermodynamic functions and monatomic spectral lines intensities of the plasma at thermodynamic equilibrium and at atmospheric pressure. To obtain a self sufficient paper and also to allow other researchers to compare their results, all required data and a robust accurate algorithm, which is simple and easy to compute, are given.展开更多
Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events...Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of do- main fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrink- ing cylindrical domain in a tube configuration during unload- ing. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclu- sion model. It is demonstrated that the two domain fronts ex- hibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in control- ling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the pro- cess is governed by two nondimensional length scales (the normalized tube length and normalized wall-thickness) and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.展开更多
Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best mode...Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, p, the deceleration parameter, q, the equations of state parameter, wD, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the OSLT of thermodynamics in a fractal cosmology.展开更多
文摘The approach proposed in the study is based on the revision of the concept of time as a point on the real axis. It uses the concept of fuzzy time as the set of real numbers with a finite, but not equal to one, function of membership to the time set, i.e. the fuzzy time concept. It is postulated that in fuzzy time t the system dynamics follows from the standard variational principle of the least action and is ordinary Hamilton-Jacobi mechanics. This validates the passage to the limit from fuzzy mechanics to ordinary variational conservative mechanics. The Liouville equation is solved by the method of successive approximations in the time domain of a much larger characteristic scale of fuzziness, using interaction as a small parameter. A standard diagram technique is used. It can be shown that the defuzzification of the Liouville equation inevitably reduces the reversible part in the description to the irreversible evolutionary equation. The latter leads to the second law of thermodynamics. Generalization to the quantum case is possible, i.e. the so-called fuzzy Pauli equation can be drawn.
文摘Inductively coupled plasmas (ICPs) are used in spectrochemical analyses. The introduction of the sample by means of an aerosol are widely used. The introduction and the total evaporation of the aerosol is required in order to obtain a good repeatability and reproducibility of analyses. To check whether the vaporization of the aerosol droplets inside the plasma is completed, a solution could be used to compare the experimental results of the emission spectral lines with theoretical results. An accurate calculation code to obtain monatomic spectral lines intensities is therefore required, which is the purpose of the present paper. The mixtures of argon, water and nitric acid are widely used in spectrochemical analyses with ICPs. With these mixtures, we calculate the composition, thermodynamic functions and monatomic spectral lines intensities of the plasma at thermodynamic equilibrium and at atmospheric pressure. To obtain a self sufficient paper and also to allow other researchers to compare their results, all required data and a robust accurate algorithm, which is simple and easy to compute, are given.
基金supported by the Hong Kong Research Grants Council (GRF619511)the National Natural Science Foundation of China (11128204)
文摘Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of do- main fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrink- ing cylindrical domain in a tube configuration during unload- ing. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclu- sion model. It is demonstrated that the two domain fronts ex- hibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in control- ling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the pro- cess is governed by two nondimensional length scales (the normalized tube length and normalized wall-thickness) and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.
文摘Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, p, the deceleration parameter, q, the equations of state parameter, wD, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the OSLT of thermodynamics in a fractal cosmology.