English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Dripping water from a faucet is a typical example exhibiting rich nonlinearphenomena. For such a system, the time stamps at which water drops separatefrom the faucet can be directly observed in real experiments, and the timeseries of intervals \tau_n between drop separations becomes a subject ofanalysis. 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-valuedfunction, i.e., not a deterministic dynamical system. In this paper, we proposea method to construct a nonlinear coordinate which provides a "surrogate" ofthe internal state m_n from the time series of \tau_n. Here, a key of theproposed approach is to use ISOMAP, which is a well-known method of manifoldlearning. We first apply it to the time series of $\tau_n$ generated from thenumerical simulation of a phenomenological mass-spring model for the drippingfaucet system. It is shown that a clear one-dimensional map is obtained by theproposed approach, whose characteristic quantities such as the Lyapunovexponent, the topological entropy, and the time correlation function coincidewith the original dripping faucet system. Furthermore, we also analyze dataobtained from real dripping faucet experiments which also provides promisingresults.

Manifold Learning Approach for Chaos in the Dripping Faucet