Gestion optimale d'un réservoir en avenir déterminé

Massé, dans ses deux volumes (1946), discute le problème de la gestion optimale des lâchures dans le cas d'un seul réservoir quand le bénéfice est dérivé de la production d'énergie hydroélectrique. Massé obtint ses résultats à la fois par un raisonnement économique et par une généralisation du Calcul des Variations. Sa méthode lui permit de fournir la preuve rigoureuse de la méthode graphique de Varlet (1923), dite du "fil tendu". Dans cet article on généralise la procédure de Massé au cas où (1) le bénéfice est réalisé bien en aval du point de lâchure, et (2) il y a plusieurs "point-cibles" (points où un certain objectif doit être assuré). Massé avait trouvé que la gestion optimale est celle qui maintient la valeur marginale du bénéfice constante dans le temps, pourvu que la gestion soit en régime libre, c' est à dire tant que le réservoir ne fonctionne ni à plein ni à vide. Par contre si le réservoir fonctionne par exemple à plein, Massé montra que la stratégie qui consiste à garder le réservoir plein ne peut être optimale que si la valeur marginale du bénéfice croît constamment avec le temps durant la période où le réservoir reste plein. On montre de manière rigoureuse dans le cas général que pour une gestion optimale ce qui doit rester constant c' est la valeur marginale future du bénéfice. Dans un article ultérieur on fournira la généralisation pour plusieurs réservoirs.The problem for operations of reservoirs is to choose on a day to day basis the value of the release at the dam location. The choice of the value of that discharge is conditioned by a criterion of satisfaction of one or several objectives. These objectives are defined in one or several points in the system on the river, or the rivers, downstream from the point, or the points, of release. Typical objectives may be to maximize electric production, or to minimize damage due to flooding downstream from the dams or due to shortages of water in the rivers at diversion points for municipal water supply or other uses, etc.adapted to the concerns of the managers, and relatively intuitive. The approach described in this article pursues the reasoning of Massé (1946) but generalizes it and therefore makes it more applicable. At first we look at the case of a single reservoir, located directly on the stream for the production of electric energy. In this case the target-point (the point where an objective function is to be evaluated) coincides with the point of release. This was precisely the problem studied by Massé (1946) in his classical two volumes on "Reserves and the Regulation of the Future". We pursue his reasoning but we use a more appropriate mathematical procedure which will allow us to obtain more general results. The same results are derived using two different approaches. The first one is more intuitive and uses the concept of marginal value to secure the necessary condition of optimality to be satisfied by the releases. The second procedure is more mathematical and uses, basically, the method of Calculus of Variations, generalized to the case where there are inequality constraints that must be satisfied. In the case of a single reservoir one shows that the optimality condition provides the rigorous proof of the graphical method of Varlet (1923). The results of Massé are generalized to the case where the objective function is evaluated downstream from the point of release and the management strategy must account for the phenomenon of propagation of discharges in the streams. Again in this case the results are obtained in two ways, (1) by the economic reasoning on the marginal values and (2) with the Constrained Calculus of Variations. Massé had found that the optimal policy for the releases was the one that maintained the marginal benefit constant in time. That applied for the case of a single reservoir and where the target-point coincides with the point of release. If B{x(t),t} is the instantaneous benefit obtained from making the release at the dam at a rate x(t) at time t, then the optimality condition is mathematically: b{x(t),t}=L=constant with timewhere b{x(t),t} is the marginal benefit, i.e. the partial derivative of B{x(t),t} with respect to the argument x. L is a constant, which in the mathematical formulation of the problem is the Lagrange multiplier associated with the mass balance constraint to be satisfied over the selected horizon of operations. In other words the cumulative volume of releases over the time horizon must be equal to the cumulative volume of inflows plus the drop in reservoir storage between the initial and final times. Economically the marginal benefit is the incremental benefit realized by making an extra release of one unit of water, given that the rate of release was x(t). Typically the marginal benefit decreases as the rate of release increases and that is often referred to as the "law of decreasing returns". For the case of electric production the marginal benefit will depend on the amount of releases made through the turbines but also on the season of year or day of week or hour of day. The price of electricity is higher in winter than it is in summer. It is higher during peak hours during the week than it is on weekends, etc. If on the other hand the marginal benefit is only a function of the release, and not a function of time, then the constancy of the marginal benefit with time is equivalent to the constancy of the release with time. Optimality becomes synonymous with regulation, i.e. releasing at a constant rate. It is only under these conditions that the graphical method of Varlet is applicable. In the graphical domain of cumulative volume of releases versus time, the optimal "trajectory" is a straight line where such a strategy is feasible i.e. does not make the reservoir more than full nor less than empty. When the objective is evaluated at a point downstream from the point of release and the marginal benefit (or cost) has a seasonal character, neither the graphical procedure of Varlet nor the mathematical result of Massé apply. For this more general case the derived optimality condition states that it is no longer an instantaneous marginal benefit that must remain constant in time. What must remain constant in time is a time integrated and weighted value of the marginal benefit (or damage) between the time the release is made and a later time. That later time is the release time plus the memory of the propagation system. The memory time is the time that must lapse before an upstream release is no longer felt at the target point downstream. The longer the distance between the release point and the target-point the longer is the memory of the propagation system. At the downstream point the damage depends on the discharge at that point, which is of course related to the release rate but also to the lateral inflows in between from tributaries and on the amount of attenuation that happens between the point of release and the target-point downstream. The integrand at dummy integration time t' is the marginal damage at that time multiplied by the instantaneous unit hydrograph at that time. Mathematically the integrand is: f{q(t'),t'}*k(t'-t) where f is marginal damage, q(t') is discharge at target point and k(.) is instantaneous unit hydrograph of propagation between release and target points. This integrand is to be integrated between time t of the release and time t + M, where M is the memory of the system. It is that integral that we have called the "Integrated Marginal Future" (or IMF for short) value that must remain constant in time. That optimality condition applies as long as the trajectory remains in the feasible domain bounded by the constraints of the problem, the "interior domain". When on a bound, the IMF value does not remain constant but must vary monotonically in a given direction, i.e. increases or decreases with time, depending on the constraint on which the solution rests

Seismic study of stellar convective cores

It has been shown that a discontinuity in the derivatives of the sound speed at the edge of the convective regions inside a star gives rise to a characteristic oscillatory signal in the frequencies of stellar oscillations. This oscillatory signal has been suggested as a means to study the base of the outer convection zone in low mass stars and possibly the outer edge of the convective core in high mass stars. Using stellar models we show that because of a phenomenon similar to aliasing in Fourier transform, it may not be possible to use this signal to detect the convective core. Nevertheless, it may be possible to determine the size of convective cores using the frequency separation \nu_{n+1,l}-\nu_{n,l}.Comment: Accepted for publication in A &

Pathways to Engagement: The Natural and Historic Environment in England

This article sets out to address what lessons can be learnt from conservation and management efforts across both the natural and cultural heritage environments by highlighting how approaches which separate the two environments are worked into policies and bureaucracies of activities. The authors discuss issues related to the natural and historic environment, the complexities in English legislation, and the organisational structures which make it difficult to work towards an integrated approach which enhances, protects and conserves both the natural and cultural heritage. These complexities are looked at through the 2018 revision of the National Planning Policy Framework, the introduction of the Environment Bill and the Net Gain concept. The authors suggest that working coordination and cooperation across the sectors may result in more effective lobbying and more substantive improvements

Small angle neutron scattering contrast variation reveals heterogeneities of interactions in protein gels

The structure of model gluten protein gels prepared in ethanol/water is investigated by small angle X-ray (SAXS) and neutrons (SANS) scattering. We show that gluten gels display radically different SAXS and SANS profiles when the solvent is (at least partially) deuterated. The detailed analysis of the SANS signal as a function of the solvent deuteration demonstrates heterogeneities of sample deuteration at different length scales. The progressive exchange between the protons (H) of the proteins and the deuteriums (D) of the solvent is inhomogeneous and 60 nm large zones that are enriched in H are evidenced. In addition, at low protein concentration, in the sol state, solvent deuteration induces a liquid/liquid phase separation. Complementary biochemical and structure analyses show that the denser protein phase is more protonated and specifically enriched in glutenin, the polymeric fraction of gluten proteins. These findings suggest that the presence of H-rich zones in gluten gels would arise from the preferential interaction of glutenin polymers through a tight network of non-exchangeable intermolecular hydrogen bonds.Comment: Soft Matter, Royal Society of Chemistry, 201

Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds

This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the material but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent $\zeta = 0.59 \pm 0.07$ over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, $D$, which evolves with the distance from the crack tip. For large distances, $D$ is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack

Topography of supplementary eye field afferents to frontal eye field in macaque: Implications for mapping between saccade coordinate systems

Two discrete areas in frontal cortex are involved in generating saccadic eye movements—the frontal eye field (FEF) and the supplementary eye field (SEF). Whereas FEF represents saccades in a topographic retinotopic map, recent evidence indicates that saccades may be represented craniotopically in SEF. To further investigate the relationship between these areas, the topographic organization of afferents to FEF from SEF in Macaco mulatto was examined by placing injections of distinct retrograde tracers into different parts of FEF that represented saccades of different amplitudes. Central FEF (lateral area 8A), which represents saccades of intermediate amplitudes, received afferents from a larger portion of SEF than did lateral FEF (area 45), which represents shorter saccades, or medial FEF (medial area 8A), which represents the longest saccades in addition to pinna movements. Moreover, in every case the zone in SEF that innervated lateral FEF (area 45) also projected to medial FEF (area 8A). In one case, a zone in rostral SEF projected to both lateral area 8A from which eye movements were evoked by microstimulation as well as medial area 8A from which pinna movements were elicited by microstimulation. This pattern of afferent convergence and divergence from SEF onto the retinotopic saccade map in FEF is indicative of some sort of map transformation between SEF and FEF. Such a transformation would be necessary to interconnect a topographic craniotopic saccade representation in SEF with a topographic retinotopic saccade representation in FE

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

First orbital solution for the non-thermal emitter Cyg OB2 #9

After the first detection of its binary nature, the spectroscopic monitoring of the non-thermal radio emitter Cyg OB2 #9 (P=2.4yrs) has continued, doubling the number of available spectra of the star. Since the discovery paper of 2008, a second periastron passage has occurred in February 2009. Using a variety of techniques, the radial velocities could be estimated and a first, preliminary orbital solution was derived from the HeI5876 line. The mass ratio appears close to unity and the eccentricity is large, 0.7--0.75. X-ray data from 2004 and 2007 are also analyzed in quest of peculiarities linked to binarity. The observations reveal no large overluminosity nor strong hardness, but it must be noted that the high-energy data were taken after the periastron passage, at a time where colliding wind emission may be low. Some unusual X-ray variability is however detected, with a 10% flux decrease between 2004 and 2007. To clarify their origin and find a more obvious signature of the wind-wind collision, additional data, taken at periastron and close to it, are needed.Comment: 15 pages, 4 figures, accepted by Ap

Policy and Practice of London’s Historic Environment

An original approach to understanding London – one of the world’s most prominent global cities – and its constant reform and modernisation of governance, planning and the historic environment through the first broad collection of social history. The past 40 to 50 years have seen successive governments attempt to resolve issues of governance, institutional structures and planning. The city, both in government and its institutions, is in a continuous state of flux – like many other global cities – and struggles with shifting boundaries of power as it attempts to strategically govern a range of social, economic, political and environmental challenges. The following paper evidences significant events that have influenced the shaping of planning and archaeology in London, and the organisations and legislation relevant to the practice of London archaeology in a unique way, enriching the basic skeletal history of legal frameworks and changing institutions with historical narratives offered by London archaeologists from a series of 55 in-depth interviews conducted between 2012 and 2013