Localized modes in resonant circuit array consisting of circular coils and capacitors are analytically investigated. First, an appropriate approximation of magnetic couplings between the coils is introduced. Then, analytical solutions are successfully derived by solving simultaneous polynomials for two different positions of the external coil. These solutions are evaluated by comparing with numerically exact solutions in the original problem. It is confirmed that the obtained solutions fit well the exact solutions when the overlapping and the diameter of the external coil are not too large.
Abstract:We model the Fermi-Pasta-Ulam lattice, in which masses move in a twodimensional plane, and identify different types of intrinsic localized modes (ILMs): longitudinal and transverse. The stability of the ILMs is evaluated by using characteristic multipliers. Longitudinal ILMs tend to be unstable because of the buckling effect of the chain. In contrast, transverse ILMs become stable if the chain is initially stretched. This difference between the longitudinal and the transverse ILMs is revealed by computing existence regions with respect to the angular frequency and the initial extension of the chain. The results show that the longitudinal ILMs tend to be stable in low-frequency and low-extension areas whereas the transverse ILMs become stable upon strongly stretching the chain.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.