The Parabolic Anderson Model with Acceleration and Deceleration

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.Comment: 19 page

Ginzburg-Landau vortices, Coulomb Gases, and Renormalized Energies

This is a review about a series of results on vortices in the Ginzburg-Landau model of superconductivity on the one hand, and point patterns in Coulomb gases on the other hand, as well as the connections between the two topics.Comment: review paper, submitted to J. Stat. Phy

Corpus approaches to language in the media

The main aim of this chapter is to offer an overview of research that has adopted the methodology of Corpus Linguistics to study aspects of language use in the media. The overview begins by introducing the key principles and analytical tools adopted in corpus research. To demonstrate the contribution of corpus approaches to media linguistics, a selection of recent corpus studies is subsequently discussed. The final section summarises the strengths and limitations of corpus approaches and discusses avenues for further research

The links between gender and poverty are over-simplified and under-problematised: a time of economic crisis is an opportune moment to re-think the ‘feminisation of poverty’ and address the ‘feminisation of responsibility’

Women’s poverty levels are at the centre of political discussions around the world as governments put into place deficit reduction plans. These discussions often fail to take account of the complex relationship between gender and poverty, argues Sylvia Chant, and a renewed focus on the time and labour that women invest in bearing the burden of dealing with poverty is now needed

Tides or dark matter sub-halos: Which ones are more attractive?

Young tidal dwarf galaxies (TDGs) are observed in the tidal debris of gas-rich interacting galaxies. In contrast to what is generally assumed to be the case for isolated dwarf galaxies, TDGs are not embedded in their own dark matter (DM) sub-halo. Hence, they are more sensitive to stellar feedback and could be disrupted on a short time-scale. Detailed numerical and observational studies demonstrate that isolated DM-dominated dwarf galaxies can have lifetimes of more than 10 Gyr. For TDGs that evolve in a tidal field with compressing accelerations equal to the gravitational acceleration within a DM sub-halo typical of an isolated dwarf galaxy, a similar survival time is expected. The tidal acceleration profile depends on the virial mass of the host galaxy and the distance between the TDG and its host. We analytically compare the tidal compression to the gravitational acceleration due to either cuspy or cored DM sub-halos of various virial masses. For example, the tidal field at a distance of 100 kpc to a host halo of 10^13 Msol can be as stabilizing as a 10^9 Msol DM sub-halo. By linking the tidal field to the equivalent gravitational field of a DM sub-halo, we can use existing models of isolated dwarfs to estimate the survivability of TDGs. We show that part of the unexpectedly high dynamical masses inferred from observations of some TDGs can be explained by tidal compression and hence TDGs require to contain less unobservable matter to understand their rotation curves.Comment: 11 pages, 7 figures, accepted for publication in MNRA