Reconstruction of material losses by perimeter penalization and phase-field methods

We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type. The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem.We justify the proposed approach by a convergence result, as the error on the measurement goes to zero.Comment: 28 page

Postreproductive killer whale grandmothers improve the survival of their grandoffspring

Abstract under embarg

Patterns of winter occurrence of three sympatric killer whale populations off eastern Vancouver Island, Canada, based on passive acoustic monitoring

Understanding habitat use patterns of animal populations across space and time is fundamental to identifying ecological requirements, and informing threat mitigation and conservation strategies. Persistent data gaps tend to occur with cryptic species in difficult-to-access environments, where the use of appropriate monitoring tools is indispensable for detection. Three populations of threatened and endangered killer whales occur year-round in waters off British Columbia, Canada; however, their winter habitat use patterns are not well known. Here we quantify wintertime use of the northern Strait of Georgia by these sympatric killer whale populations, revealing the importance of this previously understudied region. Using a network of passive acoustic monitoring devices deployed over three winter periods, we examine site-specific and regional patterns of occurrence of Bigg’s, and Southern and Northern Resident killer whales. All three populations frequented these waters in nearly every month from November to April, and across all study years. Bigg’s killer whales were detected most frequently, followed by Southern Residents, then Northern Residents. Population-specific differences in site use was apparent, with Southern Resident detections occurring more often than expected off the southwest side of Texada Island, while Northern Residents appeared to favor the east side of Texada Island. Remarkably, the patterns of winter use we observe in this region by Resident killer whale populations have seemingly persisted for at least 50 years. Additionally, we evaluate and discuss the effect of using multiple simultaneous recorders to characterize habitat use patterns. Lastly, we present a data-driven approach for estimating acoustic residence time, describe inter-population differences in winter residency in the northern Strait of Georgia, and discuss implications for critical habitat designation. This study fills important knowledge gaps related to killer whale winter occurrence off western Canada, highlighting the significance of the northern Strait of Georgia for these at-risk populations

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs