Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank–Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time

Undoing the market : corporate sponsorship and activist protests at Tate Galleries

This article focuses on activist group Liberate Tate’s online performance-based protests against BP’s (Beyond Petroleum) sponsorship of Tate Galleries in London. Their life protests took place at one of London’s Tate Galleries, either Tate Britain or Tate Modern (2010-2016), and were recorded, edited and posted online on the group’s website. The article conceptualises the protests as interaction rituals (Collins, 2001); collective gatherings characterised by their group assembly, a shared focus of attention including an object/symbol and the creation of barriers to outsiders. If successful, they can lead to the production of group identity, and emotional energy, feelings of confidence, of enthusiasm, that translate into a desire for action, and collective, group symbols (Collins, 2001). The article draws upon and critiques Collins’ perspective, arguing for the importance of embodiment and the online environment of protests in understanding their ability to produce emotional energy and collective identity

Exploring sizable triple Higgs couplings in the 2HDM

An important task at future colliders is the measurement of the triple Higgs coupling. Depending on its size relative to the Standard Model (SM) value, certain collider options result in a higher experimental accuracy. Within the framework of Two Higgs Doublet Models (2HDM) type I and II we investigate the allowed ranges for all triple Higgs couplings involving at least one light, SM-like Higgs boson. We take into account theoretical constraints (unitarity, stability), experimental constraints from direct Higgs-boson searches, measurements of the SM-like Higgs-boson properties, flavor observables and electroweak precision data. We find that the SM-type triple Higgs coupling w.r.t. its SM value, $\lambda_{hhh}/\lambda_{\rm SM}$, can range between $\sim -0.5$ and $\sim 1.5$. Depending on which value is realized, the HL-LHC can compete with, or is clearly inferior to the ILC. We find the coupling $\lambda_{hhH}$ between $\sim -1.5$ and $\sim 1.5$. Triple Higgs couplings involving two heavy Higgs bosons, $\lambda_{hHH}$, $\lambda_{hAA}$ and $\lambda_{hH^+H^-}$ can reach values up to ${\cal O}(10)$, roughly independent of the 2HDM type. This can lead to potentially strongly enhanced production of two Higgs-bosons at the HL-LHC or high-energy $e^+e^-$ colliders.Comment: 44 pages, 16 figure