27,030 research outputs found
Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions
We consider the first order differential equation with a sinusoidal
nonlinearity and periodic time dependence, that is, the periodically driven
overdamped pendulum. The problem is studied in the case that the explicit
time-dependence has symmetries common to pure ac-driven systems. The only
bifurcation that exists in the system is a degenerate pitchfork bifurcation,
which describes an exchange of stability between two symmetric nonlinear modes.
Using a type of Prufer transform to a pair of linear differential equations, we
derive an approximate condition of the bifurcation. This approximation is in
very good agreement with our numerical data. In particular, it works well in
the limit of large drive amplitudes and low external frequencies. We
demonstrate the usefulness of the theory applying it to the models of pure
ac-driven semiconductor superlattices and Josephson junctions. We show how the
knowledge of bifurcations in the overdamped pendulum model can be utilized to
describe effects of rectification and amplification of electric fields in these
microstructures.Comment: 15 pages, 7 figures, Revtex 4.1. Revised and expanded following
referee's report. Submitted to journal Chaos
Slowly modulated oscillations in nonlinear diffusion processes
It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion
From Low Thrust to Solar Sailing: A Homotopic Approach
This paper describes a novel method to solve solar-sail minimum-time-of-flight optimal control problems starting from a low-thrust solution. The method is based on a homotopic continuation. This technique allows to link the low-thrust with the solar-sail acceleration, so that the solar-sail solution can be computed starting from the usually easier low-thrust one by means of a numerical iterative approach. Earth-to-Mars transfers have been studied in order to validate the proposed method. A comparison is presented with a conventional solution approach, based on the use of a genetic algorithm. The results show that the novel technique has advantages, in terms of accuracy of the solution and computational time
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