Search results for "equation"
showing 10 items of 4219 documents
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.
Computation of conjugate times in smooth optimal control: the COTCOT algorithm
2006
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this setting: the so-called regular ones, and the minimum time singular single-input affine systems. Conjugate point theory is recalled in these two cases, and two applications are presented: the minimum time control of the Kepler and Euler equations.
Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation
2008
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.
Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to…
2017
The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.
A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with NuStar
2017
We present $\emph{NuSTAR}$ observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, $F_{\mathrm{Edd}}$, of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K$_{\alpha}$ line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be $R_{in}=1.03\pm0.03$ ISCO (innermost stable circular orbit) assuming a dimensionless spin parameter $a_{*}=cJ/GM^{2}=0.0$, and $R_{in}=1.08\pm0.06$ ISCO for $a_{*}=0.3$ (errors quoted at 1 $\sig…
Experimental and numerical enhancement of Vibrational Resonance in a neural circuit
2012
International audience; A neural circuit exactly ruled by the FitzHugh-Nagumo equations is excited by a biharmonic signal of frequencies f and F with respective amplitudes A and B. The magnitude spectrum of the circuit response is estimated at the low frequency driving f and presents a resonant behaviour versus the amplitude B of the high frequency. For the first time, it is shown experimentally that this Vibrational Resonance effect is much more pronounced when the two frequencies are multiple. This novel enhancement is also confirmed by numerical predictions. Applications of this nonlinear effect to the detection of weak stimuli are finally discussed.
A physical-based constitutive model for surface integrity prediction in machining of OFHC copper
2017
International audience; Due to the rising interest in predicting machined surface integrity and sustainability, various models for metal cutting simulation have been developed. However, their accuracy depends deeply on the physical description of the machining process. This study aims to develop an orthogonal cutting model for surface integrity prediction, which includes a physical-based constitutive model of Oxygen Free High Conductivity (OFHC) copper. This constitutive model incorporates the effects of the state of stress and microstructure on the work material behavior, as well as a dislocation density-based model for surface integrity prediction. The coefficients of the constitutive mod…
Orthogonal cutting simulation of OFHC copper using a new constitutive model considering the state of stress and the microstructure effects
2016
International audience; This work aims to develop an orthogonal cutting model for surface integrity prediction, which incorporates a new constitutive model of Oxygen Free High Conductivity (OFHC) copper. It accounts for the effects of the state of stress on the flow stress evolution up to fracture. Moreover, since surface integrity parameters are sensitive to the microstructure of the work material, this constitutive model highlights also the recrystallization effects on the flow stress. Orthogonal cutting model is validated using experimental designed cutting tests. More accurate predictions were obtained using this new constitutive model comparing to the classical Johnson-Cook model.
An alternative space-time meshless method for solving transient heat transfer problems with high discontinuous moving sources
2016
International audience; The aim of this work is the development of a space-time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space-time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.
Ultra-short pulse propagation in birefringent fibers-the projection operator method
2008
International audience; We examine the propagation of ultra-short optical light pulses in dispersion-managed birefringent fiber transmission systems, in which the pulse dynamics is governed by the coupled higher-order nonlinear Schrödinger equations with higher-order linear and nonlinear optical effects. We derive the equations of motion in terms of pulse parameters such as amplitude, temporal position, width, chirp, frequency and phase, using a projection operator method, and we obtain the spatial dynamical behavior of picosecond and femtosecond pulse parameters. From our detailed analysis, we show that the stimulated Raman scattering has a strong impact on the pulse dynamics.