A study on the shallow water effect on a ship's pivot point

Information on the pivot point of a turning ship is collected, taking into account practical notes and manuals on ship maneuvering as well as experimental data and simulated results which all together reveal a consistent behavior when varying water depth or some ship particulars. Results from the studies already carried out on the Riverine Support Patrol Vessel (RSPV) of the Colombian Navy are included in this one, in order to estimate the pivot point’s position and to contrast those results with theory and available empirical observations. Linear manoeuvrability theory is tested and its results show poor approximation with respect to the kinematic equations. As to the depth variation effect, by means of fullscale experiments it is confirmed that the pivot point’s position, when going to shallow water, always varies in the same way, proving to be coherent with the available information on this phenomenon.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.