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EN
The paper presents some mechanical models of gauge theories, i.e. gauge fields transposed in a space with a finite number of degree of freedom. The main focus is on how a global symmetry as the BRST one could be transferred in this context. The mechanical Yang-Mills model modified by taking the ghost type variables into account will be considered as an example of nonlinear dynamical systems.
EN
Normally polymer electrolyte membranes are prepared and studied for applications in electrochemical devices. In this work, polymer electrolyte membranes have been used as the media to culture fractals. In order to simulate the growth patterns and stages of the fractals, a model has been identified based on the Brownian motion theory. A computer coding has been developed for the model to simulate and visualize the fractal growth. This computer program has been successful in simulating the growth of the fractal and in calculating the fractal dimension of each of the simulated fractal patterns. The fractal dimensions of the simulated fractals are comparable with the values obtained in the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.
EN
Polyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.
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