The adjoint group of an Alexander quandle

We show that the adjoint group of the Alexander quandle associated to an abelian group M and an automorphism T has a nice description in terms of M and T

The algebra of rack and quandle cohomology

In this paper we describe methods for computing rack and quandle cohomology. We illustrate these methods by completely determining the cohomology of prime dihedral quandles

Goldstone bosons and a dynamical Higgs field

Higgs inflation uses the gauge variant Higgs field as the inflaton. During inflation the Higgs field is displaced from its minimum, which results in associated Goldstone bosons that are apparently massive. Working in a minimally coupled U(1) toy model, we use the closed-time-path formalism to show that these Goldstone bosons do contribute to the one-loop effective action. Therefore the computation in unitary gauge gives incorrect results. Our expression for the effective action is gauge invariant upon using the background equations of motion.Comment: 27 pages, 2 figures, published version with minor correction

The three phases of galaxy formation

We investigate the origin of the Hubble sequence by analysing the evolution of the kinematic morphologies of central galaxies in the EAGLE cosmological simulation. By separating each galaxy into disc and spheroidal stellar components and tracing their evolution along the merger tree, we find that the morphology of galaxies follows a common evolutionary trend. We distinguish three phases of galaxy formation. These phases are determined primarily by mass, rather than redshift. For M∗≲109.5M⊙ galaxies grow in a disorganized way, resulting in a morphology that is dominated by random stellar motions. This phase is dominated by in situ star formation, partly triggered by mergers. In the mass range 109.5M⊙≲M∗≲1010.5M⊙ , galaxies evolve towards a disc-dominated morphology, driven by in situ star formation. The central spheroid (i.e. the bulge) at z = 0 consists mostly of stars that formed in situ, yet the formation of the bulge is to a large degree associated with mergers. Finally, at M∗≳1010.5M⊙ growth through in situ star formation slows down considerably and galaxies transform towards a more spheroidal morphology. This transformation is driven more by the build-up of spheroids than by the destruction of discs. Spheroid formation in these galaxies happens mostly by accretion at large radii of stars formed ex situ (i.e. the halo rather than the bulge)

Mathematical properties of the

Context. In the SimpleX radiative transfer algorithm, photons are transported on an unstructured Delaunay triangulation. This approach is non-standard, requiring a thorough analysis of possible systematic effects. Aims. We verify whether the SimpleX radiative transfer algorithm conforms to mathematical expectations and develop both an error analysis and improvements to earlier versions of the code. Methods. We use numerical simulations and classical statistics to obtain quantitative descriptions of the systematics of the SimpleX algorithm. Results. We present a quantitative description of the error properties of SimpleX , numerical validation of the method and verification of the analytical results. Furthermore we describe improvements in accuracy and speed of the method. Conclusions. It is possible to transport particles such as photons in a physically correct manner with the SimpleX algorithm. This requires the use of weighting schemes or the modification of the point process underlying the transport grid. We explore and apply several possibilities