The big problem of small change

Western Europe was plagued with currency shortages from the 14th century, at which a 'standard formula' had been devised to cure the problem. We use a cash-in-advance model of commodity money to define a currency shortage, show that they could develop and persist under commodity money regime, and analyze the role played by each ingredient in the standard formula. A companion paper documents the evolution of monetary theory, monetary experiments and minting technology over the course of six hundred years.Monetary theory ; Money ; Money theory

An ab initio study of the C3(+) cation using multireference methods

The energy difference between the linear 2 sigma(sup +, sub u) and cyclic 2B(sub 2) structures of C3(+) has been investigated using large (5s3p2d1f) basis sets and multireference electron correlation treatments, including complete active space self consistent fields (CASSCF), multireference configuration interaction (MRCI), and averaged coupled-pair functional (ACPF) methods, as well as the single-reference quadratic configuration interaction (QCISD(T)) method. Our best estimate, including a correction for basis set incompleteness, is that the linear form lies above the cyclic from by 5.2(+1.5 to -1.0) kcal/mol. The 2 sigma(sup +, sub u) state is probably not a transition state, but a local minimum. Reliable computation of the cyclic/linear energy difference in C3(+) is extremely demanding of the electron correlation treatment used: of the single-reference methods previously considered, CCSD(T) and QCISD(T) perform best. The MRCI + Q(0.01)/(4s2p1d) energy separation of 1.68 kcal/mol should provide a comparison standard for other electron correlation methods applied to this system

Predicting Dust Distribution in Protoplanetary Discs

We present the results of three-dimensional numerical simulations that include the effects of hydrodynamical forces and gas drag upon an evolving dusty gas disk. We briefly describe a new parallel, two phase numerical code based upon the smoothed particle hydrodynamics (SPH) technique in which the gas and dust phases are represented by two distinct types of particles. We use the code to follow the dynamical evolution of a population of grains in a gaseous protoplanetary disk in order to understand the distribution of grains of different sizes within the disk. Our ``grains'' range from metre to submillimetre in size.Comment: 2 pages, LaTeX with 1 ps figure embedded, using newpasp.sty (supplied). To appear in the proceedings of the XIXth IAP colloquium "Extrasolar Planets: Today and Tomorrow" held in Paris, France, 2003, June 30 -- July 4, ASP Conf. Se

Sulfur reduction in sediments of marine and evaporite environments

Transformations of sulfur in sediments of ponds ranging in salinities from that of normal seawater to those of brines saturated with sodium chloride were examined. The chemistry of the sediment and pore waters were focused on with emphasis on the fate of sulfate reduction. The effects of increasing salinity on both forms of sulfur and microbial activity were determined. A unique set of chemical profiles and sulfate-reducing activity was found for the sediments of each of the sites examined. The quantity of organic matter in the salt pond sediments was significantly greater than that occurring in the adjacent intertidal site. The total quantitative and qualitative distribution of volatile fatty acids was also greater in the salt ponds. Volatile fatty acids increased with salinity

Joint density-functional theory for electronic structure of solvated systems

We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. A simple approximate functional predicts, without any fitting of parameters to solvation data, solvation energies as well as state-of-the-art quantum-chemical cavity approaches, which require such fitting.Comment: Fixed typos and minor updates to tex

The Earliest Phases of Galaxy Evolution

In this paper we study the very early phases of the evolution of our Galaxy by means of a chemical evolution model which reproduces most of the observational constraints in the solar vicinity and in the disk. We have restricted our analysis to the solar neighborhood and present the predicted abundances of several elements (C, N, O, Mg, Si, S, Ca, Fe) over an extended range of metallicities $[Fe/H] = -4.0$ to $[Fe/H] = 0.0$ compared to previous models. We adopted the most recent yield calculations for massive stars taken from different authors (Woosley & Weaver 1995 and Thielemann et al. 1996) and compared the results with a very large sample of data, one of the largest ever used to this purpose. These data have been analysed with a new and powerful statistical method which allows us to quantify the observational spread in measured elemental abundances and obtain a more meaningful comparison with the predictions from our chemical evolution model. Our analysis shows that the ``plateau'' observed for the [$\alpha$/Fe] ratios at low metallicities ($-3.0< [Fe/H] <-1.0$) is not perfectly constant but it shows a slope, especially for oxygen. This slope is very well reproduced by our model with both sets of yields. This is not surprising since realistic chemical evolution models, taking into account in detail stellar lifetimes, never predicted a completely flat plateau. This is due either to the fact that massive stars of different mass produce a slightly different O/Fe ratio or to the often forgotten fact that supernovae of type Ia, originating from white dwarfs, start appearing already at a galactic age of 30 million years and reach their maximum at 1 Gyr.Comment: 32 pages, 9 figures, to be published in Ap