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Abstract Gravitational wave memory and its electromagnetic analog are shown to be straightforward consequences of the wave equation. From Maxwell’s equations one can derive a wave equation for the electric field, while from the Bianchi identity one can derive a wave equation for the Riemann tensor in linearized gravity. Memory in both cases is derived from the structure of the source of those wave equations.
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The dimensions of scatterers in the lower mantle using USArray recordings of S-wave to P-wave conversions
- Award ID(s):
- 1644829
- PAR ID:
- 10215603
- Date Published:
- Journal Name:
- Physics of the Earth and Planetary Interiors
- Volume:
- 306
- Issue:
- C
- ISSN:
- 0031-9201
- Page Range / eLocation ID:
- 106541
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A millimetric droplet may bounce and self-propel across the surface of a vertically vibrating liquid bath, guided by the slope of its accompanying Faraday wave field. The ‘walker’, consisting of a droplet dressed in a quasi-monochromatic wave form, is a spatially extended object that exhibits many phenomena previously thought exclusive to the quantum realm. While the walker dynamics can be remarkably complex, steady and periodic states arise in which the energy added by the bath vibration necessarily balances that dissipated by viscous effects. The system energetics may then be characterised in terms of the exchange between the bouncing droplet and its guiding or ‘pilot’ wave. We here characterise this energy exchange by means of a theoretical investigation into the dynamics of the pilot-wave system when time-averaged over one bouncing period. Specifically, we derive simple formulae characterising the dependence of the droplet’s gravitational potential energy and wave energy on the droplet speed. Doing so makes clear the partitioning between the gravitational, wave and kinetic energies of walking droplets in a number of steady, periodic and statistically steady dynamical states. We demonstrate that this partitioning depends exclusively on the ratio of the droplet speed to its speed limit.more » « less
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This paper discusses wave-by-wave near-optimal control of a wave energy device in irregular waves. A deterministic propagation model is used to predict the wave elevation several seconds into the future at the device location. Two prediction approaches are considered. The first is based on a time series being measured over an advancing time window at a particular up-wave location. This approach is here utilized in long-crested irregular waves. The second approach uses successive snapshots of wave elevation measurements over an up-wave area. This approach is found more convenient for multi-directional waves, and is here applied in a bi-directional wave irregular wave field. A small, heaving vertical cylinder reacting against a deeply submerged (i.e. assumed to undergo negligible oscillations) mass is studied under wave-by-wave control. The non-causal feedforward control force required for optimum velocity under a swept-volume constraint is based on the past, current, and predicted wave elevation at the device. Results for time-averaged converted power and displacement/force maxima are obtained for a range of irregular wave conditions. Also presented in addition are energy conversion results with a feedback-alone control force using a multi-resonant control technique.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.pepi.2020.106541
