Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques

This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding - or approximating as closely as possible - the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. Exclusion tests rely on the ability to bound the solution set of the dynamic system for a given parameter subset and the tightness of these bounds is therefore paramount. Equally important is the time required to compute the bounds, thereby defining a trade-off. It is the objective of this paper to investigate this trade-off by comparing various bounding techniques based on interval arithmetic, Taylor model arithmetic and ellipsoidal calculus. When applied to a simple case study, ellipsoidal and Taylor model approaches are found to reduce the number of iterations significantly compared to interval analysis, yet the overall computational time is only reduced for tight approximation levels due to the computational overhead. © 2013 EUCA

The golden ratio in Schwarzschild-Kottler black holes

In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio $\Phi = (\sqrt{5}-1)/2$. This is a general result which is independent of the value and sign of the cosmological constant $\Lambda$

Lagoon water-level oscillations driven by rainfall and wave climate

Barrier breaching and subsequent inlet formation represent critical processes that ensure the temporary or permanent connection and transference of water, nutrients, or living organisms between a lagoon and the open sea. Here, we investigate the conditions inducing natural barrier breaching through a 34 months monitoring program of water-level oscillations within a shallow lagoon and the adjacent nearshore, at the Northern coast of the Iberian Peninsula, Louro lagoon. Seven natural openings were identified to have occurred during the three monitored wet seasons, from the 2009 to 2012, (Wet1, Wet2 and Wet3); four in the Wetl, two in the Wet2 and one in. the Wet3. The openings were grouped in three types depending on the observed relation between the lagoon water-level (L-wl), the estimated berm height (B-h) and the water-level at the beach (B-wl): (i) openings by lagoon outflow, which include those characterized by L-wl higher than B-h and lower B-wl; (ii) openings by wave inundation, including those induced by B-wl higher than B-h, and (iii) mixed openings, which result from a combination of the two previous conditions. We observed that L-wl is modulated by the rainfall regime (R-f) and can be explained by the accumulated precipitation. We estimated applying runup equations to obtain B-h and B-wl which depend on the wave climate and tidal level. The inlet lifespan was found to be regulated by the wave climate and rainfall regime; in particular barrier sealing was associated with a sudden increase in wave period and a reduction in precipitation. This work proves that the natural openings could be predicted successfully with support to medium term water-level monitoring programs, which in turn may significantly contribute to strategic decision making for management and conservation purposes.Xunta de Galicia [08MDS036000PR, PlanI2C-ED481B 2014/132-0]MICINN [CTM2012-39599-C03-01]Portuguese Science Foundation [IF/01047/2014]info:eu-repo/semantics/publishedVersio