Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materials represent a composition of mineralogies or solute species. Minerals are composed of structured relationships between cations and anions which, through atomic and molecular forces, keep the elements bound in specific configurations. The chemical compositions of minerals have specific relationships that are governed by these molecular controls. In the case of olivine, there is a well-defined relationship between Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition and other significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linear relationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe), which is typically described but poorly illustrated in the simplex. The present contribution corresponds to ongoing research, which attempts to relate stoichiometry and geochemical data using compositional geometry. We describe here the approach by which stoichiometric relationships based on mineralogical constraints can be accounted for in the space of simplicial coordinates using olivines as an example. Further examples for other mineral types (plagioclases and more complex minerals such as clays) are needed. Issues that remain to be dealt with include the reduction of a bulk chemical composition of a rock comprised of several minerals from which appropriate balances can be used to describe the composition in a realistic mineralogical framework. The overall objective of our research is to answer the question: In the cases where the mineralogy is unknown, are there suitable proxies that can be substituted? Kew words: Aitchison geometry, balances, mineral composition, oxides

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

La catedral i Girona: l' entrada del complex episcopal dins murs entre els segles X-XI

Fins a la darreria del segle VIII, el complex episcopal gironí se situava fora murs, al voltant de l'església martirial de Sant Feliu; a principis del segle IX, el complex es desdoblà amb la consagració d'una segona església episcopal, Santa Maria, dins murs, raó per la qual la seu fou coneguda, al llarg d'aquella centúria, amb la doble advocació de Santa Maria i Sant Feliu. Al llarg del segle X, s'afermà la preeminència de Santa Maria fins al punt que, en l'últim terç del segle. Sant Feliu ja no és esmentada com a seu episcopal, encara que hi continuà vinculada com a una església dependent, sense personalitat ni administració pròpia. Des de final del segle, el procés s'accelerà amb la construcció d'una nova església catedral a Santa Maria, que complementà l'aixecament d'un nou complex episcopal dins murs, en gran part culminat a mitjan segle XI i format per xenodoquium, catedral, palau episcopal i conjunt canonical, a banda de noves residències de canonges i altres clergues en el seu entorn. Aquests fets significaren la consolidació de Santa Maria com a seu única, però també la profunda remodelació urbanística d'un sector significatiu de la ciutat, prop d'un 20% del total, expressió del nou domini del bisbe i dels clergues sobre la 'seva ciutat'