Entanglement between Demand and Supply in Markets with Bandwagon Goods

Whenever customers' choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T C Schelling in the 70's.Comment: Updated version, accepted for publication, Journal of Statistical Physics, online Dec 201

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Diversity trapped in cages: Revision of Blumenavia Möller (Clathraceae, Basidiomycota) reveals three hidden species

Basidiomata of Phallales have a diversified morphology with adhesive gleba that exudes an odor, usually unpleasant that attracts mainly insects, which disperse the basidiospores. The genus Blumenavia belongs to the family Clathraceae and, based on morphological features, only two species are currently recognized: B. rhacodes and B. angolensis. However, the morphological characters adopted in species delimitations within this genus are inconsistent, and molecular data are scarce. The present study aimed to review and identify informative characters that contribute to the delimitation of Blumenavia species. Exsiccates from America and Africa were analyzed morphologically, and molecularly, using ITS, LSU, ATP6, RPB2 and TEF-1α markers for Maximum Parsimony, Bayesian and Maximum likelihood analyses, and also for coalescent based species delimitations (BP&P), as well as for bPTP, PhyloMap, Topo-phylogenetic and Geophylogenetic reconstructions. According to our studies, seven species can be considered in the genus: B. rhacodes and B. angolensis are maintained, B. usambarensis and B. toribiotalpaensis are reassessed, and three new species are proposed, B. baturitensis Melanda, M.P. Martín & Baseia, sp. nov., B. crucis-hellenicae G. Coelho, Sulzbacher, Grebenc & Cortez, sp. nov., and B. heroica Melanda, Baseia & M.P. Martín, sp. nov. Blumenavia rhacodes is typified by selecting a lectotype and an epitype. Macromorphological characters considered informative to segregate and delimit the species through integrative taxonomy include length of the basidiomata, color, width and presence of grooves on each arm as well as the glebifer position and shape. These must be clearly observed while the basidiomata are still fresh. Since most materials are usually analyzed after dehydration and deposit in collections, field techniques and protocols to describe fugacious characters from fresh specimen are demanded, as well as the use of molecular analysis, in order to better assess recognition and delimitation of species in Blumenavia