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Abstract The cores of pulsars are expected to become superconducting soon after birth. The transition to type-II superconductivity is associated with the bunching of magnetic field lines into discrete superconducting flux tubes which possess enormous tension. The coupling of the crust to the flux tubes implies the existence of huge tangential magnetic fields at the crust–core interface. We show that the transition to superconductivity triggers a highly nonlinear response in the Hall drift of the crustal magnetic field, an effect which was neglected in previous numerical modeling. We argue that at the time of the phase transition giant Hall waves are launched from the crust–core interface toward the surface. Our models show that if the crust contains a multipolar magnetic field ∼1013G, the amplitude of the Hall waves is ∼1015G. The elastic deformation of the lattice is included in our models, which allows us to track the time-dependent shear stresses everywhere in the crust. The simulations indicate that the Hall waves may be strong enough to break the crust, and could cause star quakes which trigger rotation glitches and changes in the radio pulse profile. The Hall waves also couple to slow magnetospheric changes, which cause anomalous braking indices. The emission of the giant Hall waves from the crust–core interface facilitates fast flux expulsion from the superconducting core, provided that the flux tubes in the core are themselves sufficiently mobile. For all of the flux tube mobility prescriptions implemented in this work, the core approaches the Meissner state withB= 0 at late times.
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On the ground states of the Ostrovskyi equation and their stability
Abstract The Ostrovskyi (Ostrovskyi‐Vakhnenko/short pulse) equations are ubiquitous models in mathematical physics. They describe water waves under the action of a Coriolis force as well as the amplitude of a “short” pulse in an optical fiber. In this paper, we rigorously construct ground traveling waves for these models as minimizers of the Hamiltonian functional for any fixedL2norm. The existence argument proceeds via the method of compensated compactness, but it requires surprisingly detailed Fourier analysis arguments to rule out the nonvanishing of the limits of the minimizing sequences. We show that all of these waves are weakly nondegenerate and spectrally stable.
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- Award ID(s):
- 1908626
- PAR ID:
- 10457826
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 144
- Issue:
- 4
- ISSN:
- 0022-2526
- Page Range / eLocation ID:
- p. 548-575
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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