A cut finite element method for coupled bulk-surface problems on time-dependent domains

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh

Two-dimensional state sum models and spin structures

The state sum models in two dimensions introduced by Fukuma, Hosono and Kawai are generalised by allowing algebraic data from a non-symmetric Frobenius algebra. Without any further data, this leads to a state sum model on the sphere. When the data is augmented with a crossing map, the partition function is defined for any oriented surface with a spin structure. An algebraic condition that is necessary for the state sum model to be sensitive to spin structure is determined. Some examples of state sum models that distinguish topologically-inequivalent spin structures are calculated.Comment: 43 pages. Mathematica script in ancillary file. v2: nomenclature of models and their properties changed, some proofs simplified, more detailed explanations. v3: extended introduction, presentational improvements; final versio

Inflation Dynamics’ Micro Foundations: How Important is Imperfect Competition Really?

This paper analyzes price formation and dynamics according to the industry structure. It divides manufacturing industries of Mexico into two groups: perfectly and imperfectly competitive. The results show that imperfectly competitive industries predominate. Then this classification is used to build consumer price sub indexes for the goods of both sectors. These sub indexes’ inflation dynamics indicate that the exchange rate pass-through in the perfectly competitive sector is significantly higher than in the imperfectly competitive sector, while wage pass-through only affects the imperfectly competitive sector. Also, that inflation inertia is lower in the former than in the latter; adding up in more volatility of the perfectly competitive inflation rate. For policy makers an interesting feature of the perfectly competitive price index is that the evidence suggests that its variations precede those of the imperfectly competitive price index. For economic theorists these features validate recent macroeconomic models with heterogeneous price setting behaviorPanzar-Rosse, Industry Structure, Inflation, Price Dynamics, Price Indexes

A sequence of nitrogen-rich very red giants in the globular cluster NGC 1851

We present the abundances of N in a sample of 62 stars on the red giant branch (RGB) in the peculiar globular cluster NGC 1851. The values of [N/Fe] ratio were obtained by comparing the flux measured in the observed spectra with that from synthetic spectra for up to about 15 features of CN. This is the first time that N abundances are obtained for such a large sample of RGB stars from medium-resolution spectroscopy in this cluster. With these abundances we provide a chemical tagging of the split red giant branch found from several studies in NGC 1851. The secondary, reddest sequence on the RGB is populated almost exclusively by N-rich stars, confirming our previous suggestion based on Stromgren magnitudes and colours. These giants are also, on average, enriched in s-process elements such as Ba, and are likely the results of pollution from low mass stars that experienced episodes of third dredge-up in the asymptotic giant branch phase.Comment: Version to match the one in press on Astronomy and Astrophysic