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Carnegie Mellon Center for Nonlinear Analysis
The further from the defect the stronger electric and mechanical fields - analysis of a Green's function in piezoelectrics


Konrad Bojar
Warsaw University
Faculty of Mathematics, Informatics and Mechanics

Abstract: Conservation laws guarantee that physical effects are weaker, the further is the source causing these effects, provided that this source is spatially constrained. On the other hand, there exists a Green's function of mechanically free piezoeletric plate with a single defect inducing electric and mechanical fields which diverge to infinity with rising distance to the defect. Thorough analysis shows that this solution is correct. Inconsistency with the above mentioned conservation laws has its roots in the fact that any single defect is in this case neither physically possible, nor can be seen as mathematical idealization of physically possible situation. Therefore it can be said that analysis of Green's functions in physics does not always lead to complete knowledge on linear or linearized theories.