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    On Nörlund–Voronoi Summability and Instability of Rational Maps
    (Springer, 2020-12-01)
    We investigate the connection between the instability of rational maps and summability methods applied to the spectrum of a critical point belonging to the Julia set of a rational map.
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    On New Two-Dimensional UHF Radar Observations of Equatorial Spread F at the Jicamarca Radio Observatory
    (Springer Science and Business Media Deutschland GmbH, 2023-12-01)
    We describe a mode for two-dimensional UHF (445 MHz) radar observations of F-region irregularities using the 14-panel version of the advanced modular incoherent scatter radar (AMISR-14). We also present and discuss examples of observations made by this mode. AMISR-14 is installed at the Jicamarca Radio Observatory (JRO, 11.95°S, 76.87°W, ~ 0.5° dip latitude) in Peru and, therefore, allows studies of ionospheric irregularities at the magnetic equator. The new mode takes advantage of the electronic beam-steering capability of the system to scan the equatorial F-region in the east–west direction. Therefore, it produces two-dimensional views of the spatial distribution of sub-meter field-aligned density irregularities in the magnetic equatorial plane. The scans have a temporal resolution of 20 s and allow observations over a zonal distance of approximately 400 km at main F-region heights. While the system has a lower angular and range resolution than interferometric in-beam VHF radar imaging observations available at Jicamarca, it allows a wider field-of-view than that allowed with the VHF system. Here, we describe the mode, and present and discuss examples of observations made with the system. We also discuss implications of these observations for studies of ESF at the JRO. Graphical abstract: [Figure not available: see fulltext.].
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    Stability of periodic traveling waves for the hydroelastic Whitham equation
    (Elsevier BV, 2026-01-01)
    In this work, we investigate the stability of hydroelastic periodic traveling waves within a Whitham-type equation framework. The Whitham equation is well known in the literature as a relatively simple model that nevertheless captures rich nonlinear phenomena such as short waves and breaking. Periodic traveling waves are computed numerically, and their stability is analyzed by evaluating the spectrum via the Fourier–Floquet–Hill method. We show that for small values of the flexural rigidity coefficient, small-amplitude periodic traveling waves are unstable; however, as the amplitude increases beyond a critical threshold, we first observe stabilization (not complete); subsequently, the spectrum bifurcates, and the traveling waves become increasingly unstable. In contrast, when the flexural rigidity coefficient is large, periodic traveling waves remain stable for all amplitudes. For moderate elasticity, two scenarios may occur: either (i) the maximal instability growth rate exhibits a monotonic dependence on the wave height, or (ii) complete stabilization is achieved for sufficiently large heights within numerical tolerance.