The Master Equation and the Pauli Equation in the Fuzzy Time Model

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.

Plasma Formed in Argon,Acid Nitric and Water Used in Industrial ICP Torches

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.

On stability of elastic domain during isothermal solid-solid phase transformationin a tube configuration

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.