(Table S1) Diatom abundance in coastal upwelling systems

Coastal upwelling systems account for approximately half of global ocean primary production and contribute disproportionately to biologically driven carbon sequestration. Diatoms, silica-precipitating microalgae, constitute the dominant phytoplankton in these productive regions, and their abundance and assemblage composition in the sedimentary record is considered one of the best proxies for primary production. The study of the sedimentary diatom abundance (SDA) and total organic carbon content (TOC) in the five most important coastal upwelling systems of the modern ocean (Iberia-Canary, Benguela, Peru-Humboldt, California and Somalia-Oman) reveals a global-scale positive relationship between diatom production and organic carbon burial. The analysis of SDA in conjunction with environmental variables of coastal upwelling systems such as upwelling strength, satellite-derived net primary production and surface water nutrient concentrations shows different relations between SDA and primary production on the regional scale. At the global-scale, SDA appears modulated by the capacity of diatoms to take up silicic acid, which ultimately sets an upper limit to global export production in these ocean regions.

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Viability study of sailing propulsion combined with a conventional system

For many years now, sails have been used as a propulsion system. At present, they are restricted to recreational/sport crafts since the appearance of the first steam vessels in the beginning of the 19 th century. But in the last years, due to the increase of fuel price and the pollution of the environment, it is being studied the possibility to introduce again the sail as a propulsive method combined with other conventional systems. In this paper, it is studied the viability of using a sail as a propellant with other conventional systems of propulsion. After considering the concept of apparent wind, the range of use of this complementary propulsion is presented. The calculation methodology, the numerical simulations and the wind inputs from a specific route are also included.