2018, Exner, Pavel, Kostenko, Aleksey, Malamud, Mark, Neidhardt, Hagen

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.

2020, Cornford, Stephen L., Seroussi, Helene, Asay-Davis, Xylar S., Gudmundsson, G. Hilmar, Arthern, Rob, Borstad, Chris, Christmann, Julia, dos Santos, Thiago Dias, Feldmann, Johannes, Goldberg, Daniel, Hoffman, Matthew J., Humbert, Angelika, Kleiner, Thomas, Leguy, Gunter, Lipscomb, William H., Merino, Nacho, Durand, Gaël, Morlighem, Mathieu, Pollard, David, Rückamp, Martin, Williams, C. Rosie, Yu, Hongju

We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions - notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods - taking a secondary role. © 2020 Wolters Kluwer Medknow Publications. All rights reserved.