Search results for "value"
showing 10 items of 5321 documents
ÉQUATIONS DIFFÉRENTIELLES À COEFFICIENTS DANS DES CORPS DE SÉRIES GÉNÉRALISÉES.
2007
We express the connection between the support of some equations and those of generalized series solutions. On the one hand we prove that any real power series solution of a sub-analytic differential equation belong to a lattice (i.e. an additive sub semi-group of positive reals). On the other hand we consider the field Mr of series with well-ordered support included in the Hahn product Hr with finite rank r (i.e. the lexicographic product of r copies of the reals). We equip Mr with a "Hardy type" derivation and define some well-ordered sets T1, ..., Tr such that : for all equation F(y,...,y(n))=0 with F in Mr[[Y0,...,Yn]] and whose support Supp F is a well-ordered subset of Hr, and for all …
Optimal control of the atmospheric arc of a space shuttle and numerical simulations with multiple-shooting method
2005
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the thermal flux, the normal acceleration and the dynamic pressure. Our analysis is based on the evaluation of the reachable set using the maximum principle and direct computations with the boundary conditions according to the CNES research project\footnote{The project is partially supported by the Centre National d'Etude Spatiales.}. The optimal solution is approximated by a concatenat…
Optimal control of an ensemble of Bloch equations with applications in MRI
2016
International audience; The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal control and the dynamics is analyzed in the framework of geometric optimal control. This lead to numerical implementations or suboptimal controls using averaging principle.
Minimum fuel control of the planar circular restricted three-body problem
2012
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point bound…
$PT$-symmetry and Schrödinger operators. The double well case
2016
International audience; We study a class of $PT$-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size $O(1)$. We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condi…
Recent changes in measured wind in the NE Atlantic and variability of correlation with NAO
2010
The paper deals with wind measurements, recorded since the 1950s, at twelve meteorological stations along a transect near the westernmost European border, between 64° and 44° N. Extreme wind speed tends to decrease sharply near the northern boundary (at Reykjavick), near the middle of the study area (at Shannon and Valentia) and near the southern boundary (at Brest and Cap Ferret), to increase at Thorshavn, with less significant trends at the other stations. Average wind speeds confirm the above tendencies, with an additional increasing speed at Lerwick, Kirkwall, Malin Head, Belle-Ile and Cap Ferret. To compare changes in wind activity, the data have been subdivided into three periods: unt…
Functional ecology for evaluating and predicting the aptitude of permanent grassland to provide services
2013
National audience; Applying the principles of functional ecology helps better predict the services which can be provided by permanent grassland. Farming practices and environmental characteristics influence the functional composition of grassland. Functional plant types have a generic effect on forage services which can be assessed. 13 types of grassland composed of distinct functional types were defined based on 1,283 sample grassland fields located on 8 sites. This approach was validated by checking 8 Ellenberg indicator values (used to evaluate environmental characteristics and farming practices) against climatic data and descriptive data for farming practices. The interest of a function…
Hemispheric asymmetry in the visual contribution to postural control in healthy adults.
1997
International audience; This study was carried out in order to test the hypothesis of a right hemisphere dominance in the visual control of body balance. Eight healthy adults were subjected to a self-regulated lateral balance task, performed while sitting on a rocking platform. Four visual conditions were tested: open eyes with normal vision, closed eyes in the dark, left visual field-right hemisphere and right visual field-left hemisphere. Head and support displacements in the roll plane were recorded by means of an optoelectronic system. Two main results emerged from this study: (1) head stabilization in space was much more efficient in the left visual field-right hemisphere condition tha…
Scheduling independent stochastic tasks under deadline and budget constraints
2018
This article discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow independent and identically distributed probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an ef…
Transition dynamics in optical fiber amplifiers operating in the normal dispersion regime
2011
Over the past decade there has been large interest in ultrafast optical fiber amplifiers operating in the normal dispersion regime because of the discovery that, high-energy pulses with a parabolic intensity profile and linear frequency chirp are the asymptotic solution to the system for arbitrary initial conditions [1]. These so-called “similariton” solutions propagate in a self-similar manner, holding certain relations (scaling) between pulse power, duration, and chirp parameter. While the asymptotic similariton features seem now well understood [1], the physics of the transition to this solution from arbitrary initial pulses has not been fully explored yet (most of the previous attempts …