Prony Series Representation for the Lightning Channel Base Current

2012 ◽  
Vol 54 (2) ◽  
pp. 308-315 ◽  
Author(s):  
Federico Delfino ◽  
Renato Procopio ◽  
Mansueto Rossi ◽  
Farhad Rachidi
2008 ◽  
Vol 2 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Federico Delfino ◽  
Renato Procopio ◽  
Mansueto Rossi

In this paper, a novel procedure to reconstruct the lightning channel-base current starting from the measurement of the induction field generated by it is presented. The procedure is based on a suitable mathematical manipulation of the equation expressing the induction field in the time domain, in order to transform it into a Volterra-like integral equation. Such kind of equations can be easily numerically solved without resorting to any sort of regularization techniques as they are not affected by the typical ill-conditioning of the inverse problems. The developed algorithm has been validated by means of several numerical simulations, which have shown its effectiveness also in presence of measurement noise on the induction field values.


Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4201
Author(s):  
Grzegorz Karnas

A method for computation of the lightning channel base current from the corresponding vertical component of lightning electric field was presented. The algorithm was developed by applying Laplace transform. The lightning current was estimated from its deconvolution with a special transfer function. The transfer function includes information about geometry and physical properties of entire lightning impulse generation system. The method was verified for a Heidler-type base current and a MTLL model of its propagation within the lightning channel. Research was done for close, middle, and far distance to the lightning strike point. Optimum performance was obtained for the middle distance of several kilometers where the electrostatic, induction, and radiation components of the transfer function were of the same range. An analysis was done for input electric field with and without noise superimposed on its time domain waveform. Relative uncertainties for the electric field and calculated lightning channel base current were similar each other. The presented approach can substantially increase a number of lightning current parameters which can be identified on the basis of its electric field signature. This method can be applied by the lightning location systems using preprocessing which increases the timing efficiency of the transfer function estimation.


2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Benjamin S. Elkin ◽  
Ashok Ilankova ◽  
Barclay Morrison

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ∼10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.


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