Courant

Etude et realisation de sondes pour la caracterisation non destructive par courants de Foucault de couches de cementation des aciers. Les proprietes electromagnetiques des aciers dependent de leur composition, de leurs microstructures et des contraintes appliquees. II est done naturel d essayer d utiliser les parametres electriques et magnetiques des aciers pour evaluer leur microstructure. 

Les experimentations realisees ont montre les larges possibilites d analyse par la methodes des courants de Foucault, de I evolution des divers caracteristiques metallurgiques. 11 permettent, outre la verification du revetement et la determination de son epaisseur, de dormer par un... 

CECCO, Manuel du controle par courants de Foucault Cours avances. Office des normes generates du Canada, Ottawa, 1986. 

STOSSEL (A.), Caracterisation de I etat metallurgique des alliages fer-carbone par la methode des courants de Foucault, Doctorate Thesis, University of sciences of Aix-Marseille, 1980,2. 

WATCHE (G.), LASNIER (J.), MANSIR (M.), BURAIS (N.), NICOLAS (A.), Definition d un logiciel adapte au calcul de I impedance d un capteur a courants de Foucault, CEDRAT recherche, 1985. 

FISET (M.), CHOUINARD (G.), Caracterisation des revetements nitrures et cementes sur Lacier par courants de Foucault, University of Laval, 1992. 

N Madaoui, D Premel, and D Placko. Description et modelisation d un dispositif cx-perimetal 4, courants induits tournants pour la tomographie 3d a courants de foucault. In COFREND Congress on Non Destructive Testing, Nantes, 1997. 

Tors du controle par courants de Foucault, on explode I information foumie a distance par la variation d impedance d un solenoi de au voisinage d un materiau conducteur. Elle est I indice d un transfert d energie a distance entre le solenoi de et le materiau conducteur. 

CECCO, V.S AL manuel du contiole par courants de Foucault-cours avance OTTAWA, office des normes generales du CANADA, 1986, 207p. 

MICHEL F1SET GUY CHOUINARD caracterisation des revetements nitrures et cementer sur I acier par courants de Foucault , universite LAVAL, avril 1992. 

Department of Chemistry and Courant Institute of Mathematical Sciences, New York University and The Howard Hughes Medical Institute, 251 Mercer Street, New York, NY 10012, U.S.A. 

Acknowledgments. Folkmar Bornemann greatfully acknowledges the hospitality of the Courant Institute of Mathematical Sciences, New York University, where he spent the academic year 96/97. His work was supported in part by the U.S. Department of Energy under contract DE-FG02-92ER25127. 

Courant, R., and D. Hilhert. Methods of Mathematical Fhysics, Interscience, New York (1953, 1962). 

To reiterate, the development of these relations, (2.1)-(2.3), expresses conservation of mass, momentum, and energy across a planar shock discontinuity between an initial and a final uniform state. They are frequently called the jump conditions" because the initial values jump to the final values as the idealized shock wave passes by. It should be pointed out that the assumption of a discontinuity was not required to derive them. They are equally valid for any steady compression wave, connecting two uniform states, whose profile does not change with time. It is important to note that the initial and final states achieved through the shock transition must be states of mechanical equilibrium for these relations to be valid. The time required to reach such equilibrium is arbitrary, providing the transition wave is steady. For a more rigorous discussion of steady compression waves, see Courant and Friedrichs (1948). 

R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves Interscience, New York, 1948. 

This implies that, at constant k, the line integral of the differential form s de, parametrized by time t, taken over the closed curve h) zero. This is the integrability condition for the existence of a scalar function tj/ e) such that s = d j//de (see, e.g., Courant and John [13], Vol. 2, 1.10). This holds for an elastic closed cycle at any constant values of the internal state variables k. Therefore, in general, there exists a function ij/... 

Courant, R. and John, F., Introduction to Calculus and Analysis, Wiley, New York, 1974. 

Lax, P.D., Hyperbolic Difference Equations A Review of the Courant-Friedrichs-Lewy Paper in the Light of Recent Developments, IBM J., 235-238 (1967). 

Courant R. Friedrichs K. O., Supersonic fiow and shock waves, I-nterscience, New York, i948. [PycCKHfl nepeBoa , KypanT P., Opnapnxc K., CeepxaByKOBoe TeqeHHe h yaap- Hue BOAHU, HJI, M., 1950.]... 

Often this stability condition is named the Courant condition because it has been proved for the first time by R. Courant, C. Friedrichs and G. Levy in 1928. 

Courant, R. and Hilbert, D. (1953) Methods of Mathematical Physics. Volume 1. Wiley New York. 

Saltzman, J. A Variational Method for Generating Multidimensional Adaptive Grids Courant Mathematics and Computing Laboratory, New York University, 1982. 

An alternative approach to the finite element approach is one, introduced as a concept by Courant as early as 1943 [197], in which the total energy functional, implicit in the finite element method, is directly minimized with respect to all nodal positions. The approach is conjugate to the finite element method and merely differs in its procedural approach. It parallels, however, methods often used in atomistic modeling schemes where the potential energy functional of a system (e. g., given by the force field ) is minimized with respect to the position of all (or at least many) atoms of the system. A simple example of this emerging technique is given below. 

Mendez, D., Warner, K.E., Courant, P.N. Has smoking cessation ceased Expected trends in the prevalence of smoking in the United States. Am. J. Epidemiol. 148 249, 1998. 

These equations are integrated from some initial conditions. For a specified value of s, the value of x and y shows the location where the solution is u. The equation is semilinear if a and b depend just on x and y (and not u), and the equation is linear if a, b, and/all depend on x and y, but not u. Such equations give rise to shock propagation, and conditions have been derived to deduce the presence of shocks. Courant and Hilbert (1953, 1962) Rhee, H. K., R. Aris, and N. R. Amundson, First-Order Partial Differential Equations, vol. I, Theory and Applications of Single Equations, Prentice-Hall, Englewood Cliffs, N.J. (1986) and LeVeque (1992), ibid. 

References Courant, R., and D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience, New York (1953) Linz, P., Analytical and Numerical Methods for Volterra Equations, SIAM Publications, Philadelphia (1985) Porter, D., and D. S. G. Stirling, Integral Equations A Practical Treatment from Spectral Theory to Applications, Cambridge University Press (1990) Statgold, I., Greens Functions and Boundary Value Problems, 2d ed., Interscience, New York (1997). 

All the methods have a limit to the time step that is set by the convection term. Essentially, the time step should not be so big as to take the material farther than it can go at its velocity. This is usually expressed as a Courant number limitation. 

In a backwards-in-distance solution for advective transport in the absence of dispersion or diffusion, the Courant criterion limits the time step. In one dimension, the grid Courant number is the number of nodal blocks the fluid traverses over a time step. By the Courant criterion, the Courant number Co must not exceed one, or... 

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