Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

FrosPy: A Modular Python Toolbox for Normal Mode Seismology

We present free oscillations Python (FrosPy), a modular Python toolbox for normal mode seismology, incorporating several Python core classes that can easily be used and be included in larger Python programs. FrosPy is freely available and open source online. It provides tools to facilitate pre- and postprocessing of seismic normal mode spectra, including editing large time series and plotting spectra in the frequency domain. It also contains a comprehensive database of center frequencies and quality factor (Q) values based on 1D reference model preliminary reference Earth model for all normal modes up to 10 mHz and a collection of published measurements of center frequencies, Q values, and splitting function (or structure) coefficients. FrosPy provides the tools to visualize and convert different formats of splitting function coefficients and plot these as maps. By giving the means of using and comparing normal mode spectra and splitting function measurements, FrosPy also aims to encourage seismologists and geophysicists to learn about normal mode seismology and the study of the Earth’s free oscillation spectra and to incorporate them into their own research or use them for educational purposes.

Ionospheric Disturbances Observed Following the Ridgecrest Earthquake of 4 July 2019 in California, USA

Earthquakes are known to generate disturbances in the ionosphere. Such disturbances, referred to as co-seismic ionospheric disturbances, or ionoquakes, were previously reported for large earthquakes with magnitudes Mw≥ 6.6. This paper reports ionoquakes associated with the Ridgecrest earthquakes of magnitude (Mw=6.4), that occurred on 4 July 2019 in California, USA. The ionoquakes manifested in total electron content (TEC) in the form of traveling ionospheric disturbances (TIDs) within 1 h from the mainshock onset. These seismic-origin TIDs have unique wave characteristics that distinguish them from TIDs of non-seismic origin arising from a moderate geomagnetic activity on the same day. Moreover, in the space-time domain of the detection of seismic-origin TIDs, TIDs are absent on the day before and day after the earthquake day. Their spectral characteristics relate them to the Earth’s normal modes and atmospheric resonance modes. We found the ground velocity associated with the mainshock, rather than the ground displacement, satisfies the threshold criteria for detectable ionoquakes in TEC measurements. Numerical simulation suggested that the coupled seismo–atmosphere–ionosphere (SAI) dynamics energized by the atmospheric waves are responsible for the generation of ionoquakes. This study’s findings demonstrate the potential of using TEC measurement to detect the ionospheric counterparts of moderate earthquakes.

More on the SW-QNM correspondence

We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of SU(2) $$ \mathcal{N} $$ N = 2 SYM with Nf = 3 flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS4 to SU(2) gauge theory with Nf = 4, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.

Director Fluctuations in Two-Dimensional Liquid Crystal Disclinations

We present analytical calculations of the energies and eigenfunctions of all normal modes of excitation of charge +1 two-dimensional splay (bend) disclinations confined to an annular region with inner radius R1 and outer radius R2 and with perpendicular (tangential) boundary conditions on the region’s inner and outer perimeters. Defects such as these appear in islands in smectic-C films and can in principle be created in bolaamphiphilic nematic films. Under perpendicular boundary conditions on the two surfaces and when the ratio β=Ks/Kb of the splay to bend 2D Frank constants is less than one, the splay configuration is stable for all values μ=R2/R1. When β>1, the splay configuration is stable only for μ less than a critical value μc(β), becoming unstable to a “spiral” mixed splay-bend configuration for μ>μc. The same behavior occurs in trapped bend defects with tangential boundary conditions but with Ks and Kb interchanged. By calculating free energies, we verify that the transition from a splay or bend configuration to a mixed one is continuous. We discuss the differences between our calculations that yield expressions for experimentally observable excitation energies and other calculations that produce the same critical points and spiral configurations as ours but not the same excitation energies. We also calculate measurable correlation functions and associated decay times of angular fluctuations.