Volume 41, Number 3, May-June 2007
|Page(s)||447 - 459|
|Published online||02 August 2007|
Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices
Department of Mathematics, Yonsei University,
2 Department of Mathematics, Yonsei University and National Institute for Mathematical Science, Korea. firstname.lastname@example.org
3 College of Electronics and Information, Kyung Hee University, Korea. email@example.com
Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational model providing a quantitative and reliable analysis about the distribution of J. In this paper, we set up a mathematical model of a typical EMD shock, bearing in mind that we are aiming to compute the current density distribution inside the human body with a pair of inserted darts. The safety issue of TASER is directly related to the magnitude of |J| at the region of the darts where the current density J is highly concentrated. Hence, fine computation of J near the dart is essential. For such numerical simulations, serious computational difficulties are encountered in dealing with the darts having two different very sharp corners, tip of needle and tip of barb. The boundary of a small fishhook-shaped dart inside a large computational domain and the presence of corner singularities require a very fine mesh leading to a formidable amount of numerical computations. To circumvent these difficulties, we developed a multiple point source method of computing J. It has a potential to provide effective analysis and more accurate estimate of J near fishhook-shaped darts. Numerical experiments show that the MPSM is just fit for the study of EMD shocks.
Mathematics Subject Classification: 93A30 / 32S05 / 92C55 / 33K28 / 35M10 / 35R30
Key words: Electro-muscular disruption (EMD) device / electrical current density / Maxwell equations / non-smooth boundary / elliptic partial differential equations / corner singularity.
© EDP Sciences, SMAI, 2007
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