Robin-type boundary control problems for the nonlinear Boussinesq type equations

In this paper, we study a linear and a nonlinear boundary control problems arising from viscous flows. The equations are of nonlinear Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the temperature and the salinity. The essential difficulties are due to the nonlinear nature of a part of the boundary conditions and to the nature of the equations: time-dependent, coupled and nonlinear. The existence and the conditions of the uniqueness of the solution, for the variational problem, are studied. The control is of linear or nonlinear Robin-type and acts on a part of the boundary during a time T. The cost function measures the distance between the observed and the computed vorticity. The existence of an optimal control in the admissible set of states and controls is proved. A first order necessary conditions of optimality are obtained.     

Determination of trace zinc in seawater by coupling solid phase extraction and fluorescence detection in the Lab-On-Valve format

By virtue of their compactness, long-term stability, minimal reagent consumption and robustness, miniaturized sequential injection instruments are well suited for automation of assays onboard research ships. However, in order to reach the sensitivity and limit of detection required for open-ocean determinations of trace elements, it is necessary to preconcentrate the analyte prior its derivatization and subsequent detection by fluorescence. In this work, a novel method for the determination of dissolved zinc (Zn) at subnanomolar levels in seawater is described. The proposed method combines, for the first time, automated matrix removal, extraction of the target element, and fluorescence detection within a miniaturized flow manifold, based on the Lab-On-Valve (LOV) concept. The key feature of the microfluidic manipulation of the sample is flow programming, designed to pass sample through a mini-column where the target analyte and other complexable cations are retained, while the seawater matrix is washed out. Next, zinc is eluted and merged with a Zn selective fluorescent probe (FluoZin-3) at the confluence point of the LOV central channel using two high-precision stepper motor driven pumps that are operated in concert. Finally, the thus formed Zn complex is transported to the LOV flow cell for selective fluorescence measurement. This work describes the characterization and optimization of the method including Solid Phase Extraction using the Toyopearl AF-Chelate-650M resin, and detailed assay protocol controlled by a commercially available software and instrument. The proposed method features a LOD of 0.02 nM, high precision (<3% at 0.1 and 2 nM Zn levels), an assay cycle of 13 min and a reagent consumption of 150 μL FluoZin-3 per sample, which makes the method highly suitable for oceanographic shipboard analysis. The accuracy of the method has been validated through the analysis of seawater reference standards and comparison with ICP-MS determinations on seawater samples collected in the upper 1300 m of the subtropical south Indian Ocean. This work confirms that integration of sample pretreatment with optical detection in the LOV format offers a widely applicable approach to trace analysis of seawater.     

Applied thermodynamics of the real gas with respect to the thermodynamic zeros of the entropy and internal energy

Gibbs's work on the thermodynamic properties of substances [1] presented a complete thermodynamic theory. The formulations of the entropy S and internal energy U as extensive quantities allow the zeros of the real gas to be given: S=0 at absolute zero (Nernst, Planck) and U=0 at the critical point. Consequently, every thermodynamic function is unique and absolutely specified. Interdependences among quantities such as temperature, vapor pressure, chemical potential, volume, entropy, internal energy, and heat capacity are likewise unique and numerically well defined. This is shown for the saturated fluid, water, in the region between absolute zero and the critical point. As a consequence of the calculation of the chemical potential, it follows that the free particle flow in an inhomogeneous system is essentially governed by the difference in chemical potential, and not through the difference in pressure, this effect being of importance for meteorology and oceanography.     

Modelling of extreme wave heights and periods through copulas

Optimal design of coastal or offshore structures requires the estimation of extreme quantiles of oceanographic data such as wave heights and wave periods. Since there are strong correlations between oceanographic variables, it is necessary to use multivariate models in order to capture its dependencies. To achieve this, an approach based on copulas is proposed and is compared to a model based on the physical behaviour of waves.     

On solvability of a parabolic system arising in physical oceanography

As many equations in fluid mechanics, the thermocline equations, in standard notation, are composed of quasi-linear, first-order partial differential equations. The aim of this paper is to establish an existence, uniqueness result for the solution of such a problem.