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We investigate the use of parabolic equation (PE) methods for solving radio-wave propagation in polar ice. PE methods provide an approximate solution to Maxwells equations, in contrast to full-field solutions such as finite-difference-time-domain (FDTD) methods, yet provide a more complete model of propagation than simple geometric ray-tracing (RT) methods that are the current state of the art for simulating in-ice radio detection of neutrino-induced cascades. PE are more computationally efficient than FDTD methods, and more flexible than RT methods, allowing for the inclusion of diffractive effects, and modeling of propagation in regions that cannot be modeled with geometric methods. We present a new PE approximation suited to the in-ice case. We conclude that current ray-tracing methods may be too simplistic in their treatment of ice properties, and their continued use could overestimate experimental sensitivity for in-ice neutrino detection experiments. We discuss the implications for current in-ice Askaryan-type detectors and for the upcoming Radar Echo Telescope; two families of experiments for which these results are most relevant. We suggest that PE methods be investigated further for in-ice radio applications.
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numer
The Askaryan Radio Array (ARA) experiment at the South Pole is designed to detect high-energy neutrinos which, via in-ice interactions, produce coherent radiation at frequencies up to 1000 MHz. In Dec. 2018, a custom high-amplitude radio-frequency tr
In a previous work, we developed the idea to solve Keplers equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Keplers equation usi
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, di
Radiative transfer has a strong impact on the collapse and the fragmentation of prestellar dense cores. We present the radiation-hydrodynamics solver we designed for the RAMSES code. The method is designed for astrophysical purposes, and in particula