TY - JOUR
T1 - A wavelet based algorithm for pattern analysis
AU - Bowman, Chris
AU - Passot, Thierry
AU - Assenheimer, Michel
AU - Newell, Alan C.
N1 - Funding Information:
We are grateful for support for AFOSR Contract No. F496209410144-DEF and NSF Grant No. DMS-9302013. One of us (TP) wants to specifically thank Ph. Tchamitchian and B. Torresani who were responsible for introducing us to many of the ideas used in this paper. MA is grateful to the hospitality of the University of Arizona. He further acknowledges support from a European Community Human Capital and Mobility Fellowship.
PY - 1998
Y1 - 1998
N2 - Patterns with a local roll structure arise in many diverse physical systems which have little in common at the microscopic level. In this paper we construct an algorithm based on the wavelet transform that can be used as a diagnostic tool to extract from such patterns macroscopic information like the local director field, the local amplitude away from defects, and slowly varying fields, such as mean drift, which may be soft modes of pattern. It allows a precise detection of phase grain boundaries and point defects. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. Finally, the algorithm is applied to actual experimental convection patterns, allowing us to draw several conclusions about the nature of the wave director field in such patterns.
AB - Patterns with a local roll structure arise in many diverse physical systems which have little in common at the microscopic level. In this paper we construct an algorithm based on the wavelet transform that can be used as a diagnostic tool to extract from such patterns macroscopic information like the local director field, the local amplitude away from defects, and slowly varying fields, such as mean drift, which may be soft modes of pattern. It allows a precise detection of phase grain boundaries and point defects. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. Finally, the algorithm is applied to actual experimental convection patterns, allowing us to draw several conclusions about the nature of the wave director field in such patterns.
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U2 - 10.1016/S0167-2789(98)00039-6
DO - 10.1016/S0167-2789(98)00039-6
M3 - Article
AN - SCOPUS:0013258966
SN - 0167-2789
VL - 119
SP - 250
EP - 282
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -