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The article presents a summarised history of the equations governing fluid motion, known as the Navier–Stokes equations. It starts with the work of Castelli, who established the continuity equation in 1628. The determination of fluid flow resistance was a topic that involved the brightest minds of the 17th and 18th centuries. Navier's contribution consisted of the incorporation of molecular attraction effects into Euler's equation, giving rise to an additional term associated with resistance. However, his analysis was not the only one. This continued until 1850, when Stokes firmly established the boundary conditions that must be applied to the differential equations of motion, specifically stating the non-slip condition of the fluid in contact with a solid surface. With this article, the author wants to commemorate the bicentennial of the publication of "Sur les Lois du Mouvement des Fluides" by Navier in the Mémoires de l'Académie Royale des Sciences de l'Institut de France. [ABSTRACT FROM AUTHOR]

Summary: A theoretical framework for minimum streamflow is developed. It grasps over the whole spectrum of the problem from the tail-behaviour of the parent distribution via the asymptotic theory of extreme value distributions to the derived distribution approach allowing a physical interpretation of its parameters. It is shown how the power parameter and also the moments of the Weibull distribution depend on the statistical properties of the parent and especially its coefficient of variation. For the application of the threshold method – Pit Under Threshold (PUT) – a mean deficit function is defined. It is a useful tool to analyse the tail towards minima and directs to the formulation of a generalised Pareto distribution for minima. A derived distribution function approach based on a linear recession leads to the same principal distribution but with a physical interpretation of its parameters. It is further generalised to include also a non-linear recession. The theoretical findings are tested in an exploratory manner against streamflow data from 35 sites in the Moselle drainage basin, France. Parameters estimated from PUT data describing distribution type and form show very stable behaviour with an appropriate determination of the threshold. Parameters estimated from annual minima show larger uncertainty due to existence of high outliers. Location parameters, the mean minimum streamflow and the threshold value, vary significantly between series. Only for large downstream basins common values appear. For small and medium sized basins low flow statistic are controlled by very local factors. In lack of very detailed information the link to parent statistics can be used for regionalisation purposes. The developed distributions are parsimonious with only one or two parameters besides the threshold value. Anyhow the hypothesis that the regional sample follows these distributions cannot be rejected. The distributions can be kept simple and give good results due to the good foundation in theory and process understanding. [Copyright &y& Elsevier]

Using an asymptotic methodology, including an expansion in inverse powers of , where ω is the frequency, we derive a solution for flow in a medium with pressure dependent properties. The solution is valid for a heterogeneous medium with smoothly varying properties. That is, the scale length of the heterogeneity must be significantly larger then the scale length over which the pressure increases from it initial value to its peak value. The solution is in the form of a travelling disturbance and is defined along a trajectory through the medium, similar to a ray. The expression for pseudo-phase, which is related to the ‘traveltime’ of the transient pressure disturbance, and the expression for pressure amplitude contain modifications due to the pressure dependence of the medium. We apply the method to synthetic and observed pressure variations in a deforming medium. In the synthetic test we model 1-D propagation in a pressure-dependent medium. Comparisons with both an analytic self-similar solution and the results of a numerical simulation indicate general agreement. Furthermore, we are able to match pressure variations observed during a pulse test at the Coaraze Laboratory site in France. [ABSTRACT FROM AUTHOR]

The original paper (Baggs and Freedman, 1990) gave a model of the interaction of a bilingual with a unilingual population. This paper examines the original in an exhaustive fashion and identifies four possible scenarios in the long-term future of the bilingual population. Equilibrium points are found in a manner conducive to practical interpretation, and their stability is investigated. The original model is then applied to the situation in modern Wales and more briefly to that in Scotland, Ireland and Brittany. In conclusion the capacity of the model to inform policy is considered, and an amended model is suggested. [ABSTRACT FROM AUTHOR]

The empirical Green's functions (EGF) technique is used to investigate two methods for predicting ground motion in a sedimentary basin for a future earthquake, including variability assessment. This study focuses on the Grenoble basin (French Alps). The basic principle of both methods is to generate a variety of source parameter sets based on a grid testing approach. Next, these sets are used to compute a population of ground motions by means of a kinematic EGF method and to estimate ground-motion variability. The first method tried, called the direct-parameter-input approach, selects input parameter combinations from assumed source parameter probability density functions. It is demonstrated that this approach leads to overestimated variability. Moreover, these simulation results are not calibrated. A new (screened-parameter-input) procedure is therefore proposed: (1) reference rock site response spectra are simulated for fractiles of several orders using empirical ground-motion prediction equations; (2) a large population of rock site response spectra is generated by means of the EGF method with varying rupture parameter combinations; (3) the spectra that do not fit the empirical motion for the chosen fractiles are screened out and sets of permissible source parameter combinations are thus obtained; (4) sediment site response spectra are computed with this EGF procedure and with these permissible parameter combinations; and (5) for each frequency median spectral acceleration and standard-deviation values are derived. [ABSTRACT FROM AUTHOR]

In the second half of the nineteenth century, a new interest in explosive chemical reactions, sudden release of energy in living beings, physical instabilities, and bifurcations in the solutions of differential equations drew the attention of some scholars. New concepts like triggering actions and guiding principles also emerged. Mathematicians, physicists, physiologists, and philosophers were attracted by this kind of phenomena since they raised a question about the actual existence of a strict determinism in science. In 1878 the mathematical physicist Joseph Boussinesq pointed out a structural analogy among physical instabilities, some essential features of living beings, and singular solutions of differential equations. These developments revived long-lasting philosophical debates on the problematic link between deterministic physical laws and free will. We find in Boussinesq an original and almost isolated attempt to merge mathematical, physical, biological, and philosophical issues into a complex intellectual framework. In the last decades, some philosophers of science rediscovered the connection between physical instabilities and determinism, both in the context of chaos theory, and in the debates on the Norton dome. I put forward a consistent historical reconstruction of the main issues and characters involved., (Copyright © 2014 Elsevier Ltd. All rights reserved.)