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Identification and stability of small-sized dislocations using a direct algorithm

  • * Corresponding author: Abdellatif El Badia

    * Corresponding author: Abdellatif El Badia 
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  • This paper considers the problem of identifying dislocation lines of curvilinear form in three-dimensional materials from boundary measurements, when the areas surrounded by the dislocation lines are assumed to be small-sized. The objective of this inverse problem is to reconstruct the number, the initial position and certain characteristics of these dislocations and establish, using certain test functions, a Hölder stability of the centers. This paper can be considered as a generalization of [9], where instead of reconstructing point-wise dislocations, as done in the latter paper, our aim is to recover the parameters of line dislocations by employing a direct algebraic algorithm.

    Mathematics Subject Classification: 35R30, 74G75, 74B05, 74B10, 74C10, 35Q70.

    Citation:

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  • Figure 1.  Edge dislocation.

    Figure 2.  The form of the dislocations

    Figure 3.  The form of the dislocations.

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