We consider the concept of deformed gauge invariance. The described formalism allows the vector gauge bosons to be massive independently of Higgs mechanism. It also allows the possibility for the variability of gauge coupling constants in spacetime.

The mass spectrum for spinor fields in extra dimensions is considered within the framework of the mass creation mechanism proposed in our previous works (Duc and Giao 2013; Duc and Giao J. Mod. Phys. 4(N7), 991, 2013; Duc et al. J. Phys Sci. Appl. (USA) 4(N1), 60, 2014; Duc and Giao J. Mod. Phys. 5(N6), 2014). It is shown that a single spinor field in the whole space-time with extradimensions corresponds to a set of multiplets of effective spinor fields in ordinary 4-dimensional space-time with masses obeying the sum rule expressed in terms of metric for extradimensions and parameter functions dictated from the periodicity conditions.

The structure and dynamics of liquid lead silicate with a wide range of PbO ratio are done by molecular dynamics methods. The simulated result shows that the pair radial distribution functions (PRDFs) are in good agreement with the results of previous studies. Our calculated data indicates that the system exists regions of fast and slow atoms determined via the mean square displacement (MSD) in the same interval. The exhibition of dynamical heterogeneity (DH) is also found in this paper.

The structural properties of xAl2O3(1-x)SiO2 liquid systems have been investi-gated by molecular dynamics simulation in a wide range of compositions, x = 0.05–0.7 at 3000 K. The structure of liquid aluminosilicate system is clarified by analyzing the simplex and shell-core. The simulated results showed that the liquid consists of a large quantity of void-simplex, O-simplex, T-simplex, and SC-particle. Our simulation reveals that the densification of the liquid is due to the fact that the number of large simplexes and the radii of simplexes and SC-particles decrease. Besides, results also indicated that the distribution of cations in the liquid is not uniform.

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