We have constructed a semi-analytical model of the energetic-ion foreshock of a CME-driven coronal/interplanetary shock wave responsible for the acceleration of large solar energetic particle (SEP) events. The model is based on the analytical model of diffusive shock acceleration of Bell (1978), appended with a temporal dependence of the cut-off momentum of the energetic particles accelerated at the shock, derived from the theory. Parameters of the model are re-calibrated using a fully time-dependent self-consistent simulation model of the coupled particle acceleration and Alfvén-wave generation upstream of the shock. Our results show that analytical estimates of the cut-off energy resulting from the simplified theory and frequently used in SEP modelling are overestimating the cut-off momentum at the shock by one order magnitude. We show also that the cut-off momentum observed remotely far upstream of the shock (e.g., at 1 AU) can be used to infer the properties of the foreshock and the resulting energetic storm particle (ESP) event, when the shock is still at small distances from the Sun, unaccessible to the in-situ observations. Our results can be used in ESP event modelling for future missions to the inner heliosphere, like the Solar Orbiter and Solar Probe Plus as well as in developing acceleration models for SEP events in the solar corona.

We consider the holographic candidate for the entanglement of purification E P , given by the minimal cross sectional area of an entanglement wedge E W . The E P is generally very complicated quantity to obtain in field theories, thus to establish the conjectured relationship one needs to test if E W and E P share common features. In this paper the entangling regions we consider are slabs, concentric spheres, and creases in field theories in Minkowski space. The latter two can be mapped to regions in field theories defined on spheres, thus corresponding to entangled caps and orange slices, respectively. We work in general dimensions and for slabs we also consider field theories at finite temperature and confining theories. We find that E W is neither a monotonic nor continuous function of a scale. We also study a full ten-dimensional string theory geometry dual to a non-trivial RG flow of a three-dimensional Chern-Simons matter theory coupled to fundamentals. We show that also in this case E W behaves non-trivially, which if connected to E P , lends further support that the system can undergo purification simply by expansion or reduction in scale. * niko.jokela@helsinki.fi † arttu.ponni@helsinki.fi

The DC resistivity of charge density waves weakly-pinned by disorder is controlled by diffusive, incoherent processes rather than slow momentum relaxation. The corresponding incoherent conductivity can be computed in the limit of zero disorder. We compute this transport coefficient in holographic spatially modulated breaking translations spontaneously. As a by-product of our analysis, we clarify how the boundary heat current is obtained from a conserved bulk current, defined as a suitable generalization of the Iyer-Wald Noether current of the appropriate Killing vector.