[1] We report observations and analysis of 30 kHz radio emissions (sferics) from lightning discharges associated with 26 terrestrial gamma ray flashes (TGFs) recorded by the RHESSI satellite over the Caribbean and Americas, between 1500 and 4000 km away from the magnetic field sensors located at Duke University. Thirteen of the TGFs are found to occur within À3/+1 ms of lightning discharges of positive polarity from the direction of the RHESSI subsatellite point, strongly indicating that the TGFs are linked to these discharges. The event timing and sferic direction finding reveals that the discharges occur within a $300 km radius circle around the RHESSI subsatellite point. Although the positive polarity of all 13 discharges is consistent with runaway breakdown, the lightning charge moment changes are approximately two orders of magnitude smaller than present high altitude runaway breakdown theory predicts. Implications of these measurements are discussed. Citation: Cummer, S. A.,

[1] The transient ELF ($50 -5000 Hz) magnetic field radiated by lightning discharges across North America was continuously measured at Duke University during the summer of 2000. In total, 881 sprite-associated lightning discharges over 17 days were analyzed. We report in detail on 76 sprites for which we could reliably determine the lightning charge moment change from the ELF data at the time of sprite onset. The charge moment change for the initiation of a sprite is found to be as low as 120 C km. By folding together the charge moment distributions of spriteproducing lightning and all positive lightning, we find that the probability of sprite generation for lightning with >1000 C km charge moment change in <6 ms is >90%, while the sprite probability for lightning with <600 C km charge moment change in <6 ms is <10%.

We report on the measurement of topological invariants in an electromagnetic topological insulator analog formed by a microwave network, consisting of the winding numbers of scattering matrix eigenvalues. The experiment can be regarded as a variant of a topological pump, with non-zero winding implying the existence of topological edge states. In microwave networks, unlike most other systems exhibiting topological insulator physics, the winding can be directly observed. The effects of loss on the experimental results, and on the topological edge states, is discussed.

[1] Previous research has shown that the statistical measurements of charge moment changes in sprite-producing lightning are in general agreement with the predictions based on the conventional breakdown theory for sprite initiation in the mesosphere. Measurements have progressed to the point where a detailed, event-level quantitative comparison between the measurements and predictions could more rigorously test the existing theories by estimating the electric fields above the thunderstorm clouds responsible for sprite initiation. We selected for this analysis a set of sprite events from the summer of 2004 whose initiation times are well bounded. Then we measured the current moments and charge moment changes of the parent lightning discharges using the radiated electromagnetic fields recorded by our extremely low frequency/ultra low frequency lightning remote sensing systems. The measured current moments were then used as the input of a two-dimensional cylindrical full-wave finite-difference time-domain model for lightning-generated electromagnetic field simulations. We compared the simulated mesospheric electric fields to the threshold electric field for conventional breakdown to see whether, according to theory, conventional breakdown (and thus a sprite) would be initiated by that electric field and at what altitude. By analyzing sprites that are both short and long delayed from the source lightning strokes, we compared measurements and theory across a wide range of timescales. The results show that for bright, short-delayed sprites, the measurement-inferred mesospheric electric field agrees within 20% with the threshold electric field for conventional breakdown. However, for long delayed sprite events and dimmer sprites, the measurement-inferred mesospheric electric field for sprite initiation is somewhat below the threshold for conventional breakdown.

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We investigate the effects of non-Hermiticity on topological pumping, and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear. We show that this can be understood in terms of the effects of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally, in a non-Hermitian microwave network containing variable gain amplifiers.

We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium.

We present a simultaneous multifrequency inversion approach for seismic data interpretation. This algorithm inverts all frequency data components simultaneously. A dataweighting scheme balances the contributions from different frequency data components so the inversion process does not become dominated by high-frequency data components, which produce a velocity image with many artifacts. A Gauss-Newton minimization approach achieves a high convergence rate and an accurate reconstructed velocity image. By introducing a modified adjoint formulation, we can calculate the Jacobian matrix efficiently, allowing the material properties in the perfectly matched layers ͑PMLs͒ to be updated automatically during the inversion process. This feature ensures the correct behavior of the inversion and implies that the algorithm is appropriate for realistic applications where a priori information of the background medium is unavailable. Two different regularization schemes, an L 2 -norm and a weighted L 2 -norm function, are used in this algorithm for smooth profiles and profiles with sharp boundaries, respectively. The regularization parameter is determined automatically and adaptively by the so-called multiplicative regularization technique. To test the algorithm, we implement the inversion to reconstruct the Marmousi velocity model using synthetic data generated by the finite-difference time-domain code. These numerical simulation results indicate that this inversion algorithm is robust in terms of starting model and noise suppression. Under some circumstances, it is more robust than a traditional sequential inversion approach.