Champ

The Champ-Sons model has been developed to quantitatively predict the field radiated by water- or solid wedge- eoupled transdueers into solids. It is required to deal with interfaces of complex geometry, arbitrary transducers and arbitrary excitation pulses. It aims at computing the time-dependent waveform of various acoustical quantities (displacement, velocity, traction, velocity potential) radiated at a (possibly large) number of field-points inside a solid medium. 

The Champ-Sons model is based upon this approximation. It results into a modified Rayleigh integral where specific terms appear. The resulting formula for the refracted field (e.g., displacement vector-field), is given by... 

The Champ-Sons model is a most effieient tool allowing quantitative predictions of the field radiated by arbitrary transducers and possibly complex interfaces. It allows one to easily define the complete set of transducer characteristics (shape of the piezoelectric element, planar or focused lens, contact or immersion, single or multi-element), the excitation pulse (possibly an experimentally measured signal), to define the characteristics of the testing configuration (geometry of the piece, transducer position relatively to the piece, characteristics of both the coupling medium and the piece), and finally to define the calculation to run (field-points position, acoustical quantity considered). 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

Figure I Simulation of a transducer calibration test, a) Calibration configuration T45° transducer and 6 flat bottom holes at various depths b) Predicted field by Champ-Sons c) Simulated Bscan d) Echodynamic curve.

We have presented in this paper the modelling capabilities of the CIVA system. Two main connected softwares, Champ-Sons and Mephisto, allow the prediction of A, B, or Cscans obtained in many conventional and less conventional testing configurations. 

We are currently working on extensions of the two models presented in the present paper. Some concern the Champ-Sons capabilities to deal with more complex propagation... 

Weiss P 1907 L Hypotheese du champ moleculaire et la propriete ferromagnetique J. Phys. Redium Peris 6 661-90... 

Plenary 7 7. P M Champion et al, e-mail address champ neu.edu (TRRRS). Femtosecond impulsive preparation and timing of ground and excited state Raman coherences in heme proteins. Discovery of coherence transfer along a de-ligation coordinate. See above for fiirther connnent. 

C. H. Champness and C. H. Chan, Solar Energy Materials and Solar Cells, to be pubhshed. 

Pauthenier, M. M., and M. Moreau-Hanot. La Charge des Particules Spheriques Dansun Champ Ionise. Journal de Physique et le Radium. 3 (1932), p. 590. 

European champs by PaulJ. Sutton/Duomo line art by J/B Wookey Associates)... 

Quantites calcul6es recuperables dans les conditions economiques et d exploitation actuelles pour les champs de gaz d6couverts, explores au moyen d un ou de plusieurs puits, et delimites avec un degr6 eleve de certitude. 

Quantites calcul es comme indique ci-dessus pour les champs de gaz d couverts, avec un degre raisonnablement elev6 de certitude, qui sugg re leur existence probable. 

Quantit s calculees comme pour les champs decouverts, avec un degre assez faible de certitude. 

Sondage d exploration pour la decouverte d un champ nouveau Q... 

Brillouin, L., ActualiUs sci. et ind. No. 71, La m thode du champ self-consistent." The Brillouin theorem introduced, b. 

Berthier, G., J. chim. phys. 51, 363, Configurations dectroniques incompl tes. I. La m thode du champ mol culaire self-consistent et l tude des tats k couches incompletes. ... 

Pullman, A., and Baudet, J., Compt. rend. 238, 241, "L inter-action des configurations dans le butadiene calculi par la m thode du champ mol culaire self-consistent."... 

LEFfevBRE, R., and Moser, C. M., J. chim. phys. 53, 393, L inter-action des configurations comme m thode de calcul cles orbitales moleculaires du champ self-consistent. I. Etats k couches completes. Cas des hydrocarbures conjugu s alternants paires. ... 

Cerf, R. La dynamique des solutions de macromolecules dans un champ de vitesses. VoL 1, pp. 382-450. 

---