The motion of a system consisting of three coupled oscillators of three masses attached together by four springs is studied analytically. The system is used as a model to describe the interactions between atoms in a one dimensional crystal with spring-like forces under white noise excitations.  Two different cases are considered and the frequencies of oscillations are obtained as well as the equations of motion.  The equations of motions are used to determine the power flow in the systems. The power flow determined is used to describe the effects of substitution impurities in a crystal. The power flow of the two systems studied decreases exponentially with increase in frequency to an asymptotic value.

In this research, DFT+U approach was used to investigate the performance of Iridium (Ir) and Boron (B) co-doped armchair (8, 8) Single-walled Carbon Nanotube (SWCNT). Calculations of the structural electronic and optical spectra analysis of the system under study were carried out using the ab’initio quantum simulations implemented in Quantum ESPRESSO and thermo_pw codes within the popular density functional theory. In the doping process, carbon atoms have been replaced by Ir and B atoms in the SWCNT, the investigations were done on the basis of distance of H2 (d) from the co-doped SWCNT at intervals of 6.12 Å, 6.45 Å and 6.77Å, variations of temperature, variations of external electric field, band gaps, optical adsorptions and binding energy variations were all taken in to account. It is found that Ir/B co-doping in pristine SWCNT significantly enhanced the H2 adsorption capacity of the SWCNT. Furthermore, an increase in temperature decrease the performance ability of the co-doped SWCNT, negative adsorptions intensities were recorded by temperature increase by 650, 700 and 750 0C, this can be termed as exothermic adsorption. Therefore it can be demonstrated that H2 by co-doped SWCNT undergoes endothermic adsorption under ambient temperature and shows exothermic adsorption under higher temperatures.

No abstract