Lian-Gang Li | Searcharxiv

arXiv2012

The Analysis of Rotated Vector Field for the Pendulum

The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $β$ and the periodic solution, and a conclusion that the critical value of $β$ is a fixed one in the over damping situation. These results are of practical significance in the study of charge-density waves in physics.

math.DS↗

arXiv2008

The analysis on the single particle model of CDW

Gruner put forward a single particle model of charge-density wave, which is a typical nonlinear differential equation, and also a mathematical model of pendulum. This Letter analyzes the solution of equation by the rotated vector fields theory, providing the relation between the applied field E and the periodic solution, and the conclusion that the critical value of E for the periodic solution is fixed in the over-damped situation. With these conclusions, it derives the formulae of nonlinear conductivity, narrow-band noise, which are consistent with the empirical ones given by Fleming.

cond-mat.str-el↗