Manifold Learning Approach for Chaos in the Dripping Faucet

Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of intervals \tau_n between drop separations becomes a subject of analysis. Even if the mass m_n of a drop at the onset of the n-th separation, which cannot be observed directly, exhibits perfectly deterministic dynamics, it sometimes fails to obtain important information from time series of \tau_n. This is because the return plot \tau_n-1 vs. \tau_n may become a multi-valued function, i.e., not a deterministic dynamical system. In this paper, we propose a method to construct a nonlinear coordinate which provides a "surrogate" of the internal state m_n from the time series of \tau_n. Here, a key of the proposed approach is to use ISOMAP, which is a well-known method of manifold learning. We first apply it to the time series of $\tau_n$ generated from the numerical simulation of a phenomenological mass-spring model for the dripping faucet system. It is shown that a clear one-dimensional map is obtained by the proposed approach, whose characteristic quantities such as the Lyapunov exponent, the topological entropy, and the time correlation function coincide with the original dripping faucet system. Furthermore, we also analyze data obtained from real dripping faucet experiments which also provides promising results.Comment: 9 pages, 10 figure

Photometric Studies of a WZ Sge-Type Dwarf Nova Candidate, ASAS160048-4846.2

We report on our time-resolved CCD photometry during the 2005 June superoutburst of a WZ Sge-type dwarf nova candidate, ASAS 160048-4846.2. The ordinary superhumps underwent a complex evolution during the superoutburst. The superhump amplitude experienced a regrowth, and had two peaks. The superhump period decreased when the superhump amplitude reached to the first maximum, successively gradually increased until the second maximum of the amplitude, and finally decreased again. Investigating other SU UMa-type dwarf novae which show an increase of the superhump period, we found the same trend of the superhump evolution in superoutbursts of them. We speculate that the superhump regrowth in the amplitude has a close relation to the increase of the superhump period, and all of SU UMa-type dwarf novae with a superhump regrowth follow the same evolution of the ordinary superhumps as that of ASAS 160048-4846.2.Comment: 7 pages, 4 figure