Skinner-Rusk approach to time-dependent mechanics

The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent framework

Land Use Influence on the Characteristics of Groundwater Inputs to the Great Bay Estuary, New Hampshire

This research examines the sources and factors affecting nutrient-laden groundwater discharge to the Great Bay Estuary. To further understand this relationship, examination of groundwater residence time, a review of historic land uses, and nitrate source tracking strategies were used. Seven submarine groundwater discharge (SGD) sites were selected, and groundwater monitoring networks were installed to examine the relationship between land use and groundwater quality at the discharge zones. Field activities were performed in the summer and fall of 2003 and 2004. Estuarine water intrusion in groundwater discharge samples confounded the analyses for major ion chemistry and boron isotopes. CFC-derived and modeled groundwater ages in the study area averaged 23.2 years (±15.0 years). CFC analysis enabled correlation of nitrate concentrations at the SGD sites with the historic land use coverage for the years 1974 (for most of the sites) or 1962 (SGD 58.4). Two types of correlation were made: 1) between the agricultural and residential land use for all observed nitrate concentrations in the recharge areas, and 2) correlation with the nitrate concentrations between developed and undeveloped land uses. Both statistical correlations (Kendall’s Tau and Spearman’s Rho) indicated a connection between the increase of residential land use of the last three decades with the high nitrate-bearing groundwater discharging to the Great Bay (NH). The geochemical composition of the SGD water was also investigated by using simple mixing models that attempted to explain the water chemistry characteristics of the targeted SGD sites. Based on these models it was concluded that overburden groundwater comprises 75% to 95% of the groundwater discharging at the SGD sites. A significant correlation (Tau’s, p=0.021) between nitrate-bearing groundwater and CFCderived groundwater ages was detected supporting the hypothesis that high nitrate bearing groundwater will be discharged to the Great Bay in the near future accounting for the increase of residential land use of 1990’s. Continuous monitoring of SGD sites was suggested to be included as part of the periodic environmental quality monitoring activities of the Great Bay. Long-term step-wise sampling for groundwater dating is required to develop a stronger chronological evolution of groundwater nitrate inputs. Further research should concentrate on detailing the overburden water chemistry, flow paths, and nitrogen loading characteristics

Transforming triangulations on non planar-surfaces

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.Comment: 19 pages, 17 figures. This version has been accepted in the SIAM Journal on Discrete Mathematics. Keywords: Graph of triangulations, triangulations on surfaces, triangulations of polygons, edge fli

Absolute Convergence of Rational Series is Semi-decidable

International audienceWe study \emph{real-valued absolutely convergent rational series}, i.e. functions $r: \Sigma^* \rightarrow {\mathbb R}$, defined over a free monoid $\Sigma^*$, that can be computed by a multiplicity automaton $A$ and such that $\sum_{w\in \Sigma^*}|r(w)|<\infty$. We prove that any absolutely convergent rational series $r$ can be computed by a multiplicity automaton $A$ which has the property that $r_{|A|}$ is simply convergent, where $r_{|A|}$ is the series computed by the automaton $|A|$ derived from $A$ by taking the absolute values of all its parameters. Then, we prove that the set ${\cal A}^{rat}(\Sigma)$ composed of all absolutely convergent rational series is semi-decidable and we show that the sum $\sum_{w\in \Sigma^*}|r(w)|$ can be estimated to any accuracy rate for any $r\in {\cal A}^{rat}(\Sigma)$. We also introduce a spectral radius-like parameter $\rho_{|r|}$ which satisfies the following property: $r$ is absolutely convergent iff $\rho_{|r|}<1$