Nonlinear breathing modes at a defect

Recent molecular dynamics (MD) simulations of Cubero et al (1999) of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond timescale, whereas breathing events in a normal DNA duplex take place on the microsecond timescale. The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice model of the DNA duplex including both nonlinear interactions between opposing bases and a defect in the interaction at one lattice site; each of which can cause localisation of energy. Solutions for a breather mode either side of the defect are derived using multiple-scales asymptotics and are pieced together across the defect to form a solution which includes the effects of the nonlinearity and the defect. We consider defects in the inter-chain interactions and in the along chain interactions. In most cases we find in-phase breather modes and/or out-of-phase breather modes, with one case displaying a shifted mode.

Nonlinear development of matrix-converter instabilities

Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an instability, whose behaviour is examined herein. The desired “steady-state” mode of operation of the matrix converter becomes unstable in a Hopf bifurcation as the output/input voltage transfer ratio, q, is increased through some threshold value, qc. Through weakly nonlinear analysis and direct numerical simulation of an averaged model, we show that this bifurcation is subcritical for typical parameter values, leading to hysteresis in the transition to the oscillatory state: there may thus be undesirable large-amplitude oscillations in the output voltages even when q is below the linear stability threshold value qc.