Abstract-A novel approach for developing the electromagnetic fields from a lightning return stroke which follows a tortuous path will be presented. The proposed model is unique in that it recognizes that the symmetrical tortuosity of lightning directly impacts the observable distance r, which in turn, alters the resulting electromagnetic fields. In the literature, lightning return stroke models typically employ the assumption that the cloud-to-ground path is straight. Although this assumption yields fairly consistent results across an array of varying approaches, it does not account for lightning's natural physical appearance. Furthermore, straight-line models only account for the cloud-to-ground discharges and do not address branching and/or cloudto-cloud discharges which are far more common. In reality, the "steps" which make up the lightning channel's initial descent are staggered or tortuous with respect to each other. Given this fact, the upward traveling current wavefront which follows this prescribed path will exhibit the same characteristics. In doing so, each current segment, which forms along its respective step, induces electromagnetic fields with angular aggregates that propagate outward from their origin. This, in turn, will generate spatial points where there are fields of higher and lower intensities. The results presented in this paper will show how the effective observable distance due to symmetrical tortuosity alters the resulting electromagnetic fields. Furthermore, it will be shown that as the observable distance r is increased, results from the proposed model closely resemble the straight-line model which strongly suggests that symmetrical tortuosity is only influential at relatively close distances.

This paper presents a user-centric and application-specific QoS assessment methodology for cellular communication networks. Specifically, it uses the Analytic Hierarchy Process (AHP) to evaluate QoS as a multi-criteria decision problem that represents how well cellular networks' data services are perceived given particular sets of application classes and relative to other networks servicing in the same area. As part of the methodology, drive testing is performed to collect objective measurements associated with identified QoS criteria for data services. Once drive testing is performed and data collected, multiple networks are compared to determine the network that provides higher QoS based on users' perception of quality. The selection of the best performing network is based on the output provided by the AHP approach, which is used as unified measurement of the perceived QoS by users on different networks.In order to determine application-specific priorities, the approach presented uses three different application classes, including Emergency, Business, and Personal. For each class, the relative importance of each quality evaluation criteria is adjusted in the AHP procedure to reflect the priorities of the services expected. Through several case studies, the approach is proven successful in providing a way for analyzing user-centric QoS for application-specific scenarios.

Problem statement:Modify the equations associated with image theory in order to account for perfect and imperfect conductors. Approach: A novel approach for describing the application of image theory for an imperfect conductive surface was presented. The method presented here purposely downplays the physics of how image theory was employed to account for a charge which is in the presence of an imperfect conductive surface. In turn, it adopted an approach which focused on the geometry that existed between the charged particle and surface ground. In doing so, the proposed method formulated a solution that had minimized the complexity of the original problem while providing an approximation founded upon a geometric relationship. Results: The equations derived had elicited the concept of using plane geometry to augment image theory. Conclusion: A method for evaluating image theory for the imperfect conductor had been presented. As the results had shown, the equations derived had provided an augmented approach to account for surfaces which were both perfect and imperfect.

Problem statement: Develop a new formula which describes the magnetic field induced by a lightning strike's indirect effect double exponential current waveform. Approach: A novel approach for developing a closed-form solution for the magnetic field from the indirect effect double exponential current waveform will be presented. In the literature, models typically employ the pulse waveform to derive the corresponding electromagnetic fields. However, given the Department of Defense (DoD) has incorporated the double exponential current waveform as part of their "Electromagnetic Environmental Effects Requirements For Systems", we felt it important to develop a solution for the magnetic field which utilized this waveform. In order to facilitate the integration required for deriving the field, Taylor series expansion was used for all variable dependent exponential terms. In many publications, the dipole and monopole techniques have been used when solving for the magnetic field. However, for this study the dipole technique was deemed the preferred method for evaluating the field. A derivation of the magnetic field will be presented along with a graphical illustration of the field's distribution over time. Results: The equation presented utilized Taylor series to augment the integration required to solve for the magnetic field. Conclusion: A new method for deriving the magnetic field induced by a lightning strike's indirect effect double exponential has been presented. By approximating the variable dependent exponential terms, we were able to minimize the complexity of the mathematics required to solve for the magnetic field in closed-form.

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