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1. Bouncing phase variations in pilot-wave hydrodynamics and the stability of droplet pairs

   https://doi.org/10.1017/jfm.2019.293  

   Couchman, Miles M. ; Turton, Sam E. ; Bush, John W. ( July 2019 , Journal of Fluid Mechanics)

   We present the results of an integrated experimental and theoretical investigation of the vertical motion of millimetric droplets bouncing on a vibrating fluid bath. We characterize experimentally the dependence of the phase of impact and contact force between a drop and the bath on the drop’s size and the bath’s vibrational acceleration. This characterization guides the development of a new theoretical model for the coupling between a drop’s vertical and horizontal motion. Our model allows us to relax the assumption of constant impact phase made in models based on the time-averaged trajectory equation of Moláček and Bush ( J. Fluid Mech. , vol. 727, 2013b, pp. 612–647) and obtain a robust horizontal trajectory equation for a bouncing drop that accounts for modulations in the drop’s vertical dynamics as may arise when it interacts with boundaries or other drops. We demonstrate that such modulations have a critical influence on the stability and dynamics of interacting droplet pairs. As the bath’s vibrational acceleration is increased progressively, initially stationary pairs destabilize into a variety of dynamical states including rectilinear oscillations, circular orbits and side-by-side promenading motion. The theoretical predictions of our variable-impact-phase model rationalize our observations and underscore the critical importance of accounting for variability in the vertical motion when modelling droplet–droplet interactions. 

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2. The Stability of a Hydrodynamic Bravais Lattice

   https://doi.org/10.3390/sym14081524  

   Couchman, Miles M. ; Evans, Davis J. ; Bush, John W. ( August 2022 , Symmetry)

   We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart. 

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3. The Rocks That Did Not Fall: A Multidisciplinary Analysis of Near‐Source Ground Motions From an Active Normal Fault

   https://doi.org/10.1029/2023AV000885  

   Trugman, D. T. ; Brune, J. ; Smith, K. D. ; Louie, J. N. ; Kent, G. M. ( April 2023 , AGU Advances)

   On 8 July 2021 a M6.0 normal faulting earthquake rocked the community of Walker and the surrounding region near the California‐Nevada border. In the 1990s, field surveys of nearby Meadowcliff Canyon identified numerous precarious rocks deemed likely to topple in the event of strong shaking. Despite their proximity (∼6 km) to the 2021 earthquake, the precarious rocks still remain standing. In this work, we combine advanced source and ground motion characterization techniques to help unravel this mystery. High‐precision hypocentral locations reveal a clear north/south‐striking, east‐dipping rupture plane along the southern extension of the Slinkard Valley fault. The mainshock nucleated near the base of the fault, triggering thousands of aftershocks. Bayesian source spectral analyses indicate that the mainshock had a moderately‐high stress drop (∼17 MPa), and that aftershocks with deeper hypocenters have higher stress drops. Peak Ground Acceleration (PGA) recordings at regional stations agree well with existing ground motion models, predicting PGA of ∼0.3 g in Meadowcliff Canyon, a level sufficient to topple precarious rocks based on PGA‐derived stability criteria. We demonstrate that despite these large ground accelerations, the pulse duration in Meadowcliff Canyon is too short to supply the impulse necessary to damage these features, observations which support the application of dynamic toppling models that account for the joint effects of pulse amplitude and duration when assessing rock fragility. This study provides a unique vantage point from which to interpret rarely‐observed strong‐motion recordings from close to an active normal fault, one of many that dominate hazard along the eastern Sierra.

    

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4. Walking droplets interacting with single and double slits

   https://doi.org/10.1017/jfm.2017.790  

   Pucci, Giuseppe ; Harris, Daniel M. ; Faria, Luiz M. ; Bush, John W. ( January 2018 , Journal of Fluid Mechanics)

   Couder & Fort ( Phys. Rev. Lett. , vol. 97, 2006, 154101) demonstrated that when a droplet walking on the surface of a vibrating bath passes through a single or a double slit, it is deflected due to the distortion of its guiding wave field. Moreover, they suggested the build-up of statistical diffraction and interference patterns similar to those arising for quantum particles. Recently, these results have been revisited (Andersen et al. , Phys. Rev.  E, vol. 92 (1), 2015, 013006; Batelaan et al. , J. Phys.: Conf. Ser. , vol. 701 (1), 2016, 012007) and contested (Andersen et al.  2015; Bohr, Andersen & Lautrup, Recent Advances in Fluid Dynamics with Environmental Applications , 2016, Springer, pp. 335–349). We revisit these experiments with a refined experimental set-up that allows us to systematically characterize the dependence of the dynamical and statistical behaviour on the system parameters. The system behaviour is shown to depend strongly on the amplitude of the vibrational forcing: as this forcing increases, a transition from repeatable to unpredictable trajectories arises. In all cases considered, the system behaviour is dominated by a wall effect, specifically the tendency for a drop to walk along a path that makes a fixed angle relative to the plane of the slits. While the three dominant central peaks apparent in the histograms of the deflection angle reported by Couder & Fort (2006) are evident in some of the parameter regimes considered in our study, the Fraunhofer-like dependence of the number of peaks on the slit width is not recovered. In the double-slit geometry, the droplet is influenced by both slits by virtue of the spatial extent of its guiding wave field. The experimental behaviour is well captured by a recently developed theoretical model that allows for a robust treatment of walking droplets interacting with boundaries. Our study underscores the importance of experimental precision in obtaining reproducible data. 

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5. A systematic investigation of piercing-point-dependent seismic azimuthal anisotropy

   https://doi.org/10.1093/gji/ggab285  

   Jia, Yan ; Liu, Kelly H ; Kong, Fansheng ; Liu, Lin ; Gao, Stephen S ( August 2021 , Geophysical Journal International)

   SUMMARY The vast majority of teleseismic XKS (including SKS, SKKS and PKS) shear wave splitting studies interpret the observed splitting parameters (fast orientation and splitting time) based on the assumption of a spatially invariant anisotropy structure in the vicinity of a recording station. For such anisotropy structures the observed splitting parameters are either independent of the arriving azimuth of the seismic ray paths if the medium traversed by the ray paths can be represented by a single layer of anisotropy with a horizontal axis of symmetry (i.e. simple anisotropy), or demonstrate a periodic variation with respect to the arriving azimuth for a more complicated structure of anisotropy (e.g. multiple layers with a horizontal axis of symmetry, or a single layer with a dipping axis). When a recording station is located near the boundary of two or more regions with different anisotropy characteristics, the observed splitting parameters are dependent on the location of the ray piercing points. Such a piercing-point dependence is clearly observed using a total of 360 pairs of XKS splitting parameters at three stations situated near the northeastern edge of the Sichuan Basin in central China. For a given station, the fast orientations differ as much as 90°, and the azimuthal variation of the fast orientations lacks a 90° or 180° periodicity which is expected for double-layered or dipping axis anisotropy. The observed splitting parameters from the three stations are spatially most consistent when they are projected at a depth of ∼250 km, and can be explained by shear strain associated with the absolute plate motion and mantle flow deflected by the cone-shaped lithospheric root of the Sichuan Basin. 

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