Dynamos driven by weak thermal convection and heterogeneous outer boundary heat flux

We use numerical dynamo models with heterogeneous core-mantle boundary (CMB) heat flux to show that lower mantle lateral thermal variability may help support a dynamo under weak thermal convection. In our reference models with homogeneous CMB heat flux, convection is either marginally supercritical or absent, always below the threshold for dynamo onset. We find that lateral CMB heat flux variations organize the flow in the core into patterns that favour the growth of an early magnetic field. Heat flux patterns symmetric about the equator produce non-reversing magnetic fields, whereas anti-symmetric patterns produce polarity reversals. Our results may explain the existence of the geodynamo prior to inner core nucleation under a tight energy budget. Furthermore, in order to sustain a strong geomagnetic field, the lower mantle thermal distribution was likely dominantly symmetric about the equator. (C) 2015 Elsevier B.V. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Anomalous reduction in domain wall displacement at the morphotropic phase boundary of the piezoelectric alloy system PbTiO3-BiScO3

A comparative study of field-induced domain switching and lattice strain was carried out by in situ electric-field-dependent high-energy synchrotron x-ray diffraction on a morphotropic phase boundary (MPB) and a near-MPB rhombohedral/pseudomonoclinic composition of a high-performance piezoelectric alloy (1-x) PbTiO3-(x)BiScO3. It is demonstrated that the MPB composition showing large d(33) similar to 425 pC/N exhibits significantly reduced propensity of field-induced domain switching as compared to the non-MPB rhombohedral composition (d(33) similar to 260 pC/N). These experimental observations contradict the basic premise of the martensitic-theory-based explanation which emphasizes on enhanced domain wall motion as the primary factor for the anomalous piezoelectric response in MPB piezoelectrics. Our results favor field-induced structural transformation to be the primary mechanism contributing to the large piezoresponse of the critical MPB composition of this system.

COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.