A large-deviations approach to gelation

A large-deviations principle (LDP) is derived for the state at fixed time, of the multiplicative coalescent in the large particle number limit. The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic. In particular, it clearly captures the well known gelation phase transition given by the formation of a particle containing a positive fraction of the system mass. Via a standard map of the multiplicative coalescent onto a time-dependent version of the Erdős-Rényi random graph, our results can also be rephrased as an LDP for the component sizes in that graph. The proofs rely on estimates and asymptotics for the probability that smaller Erdős-Rényi graphs are connected

A large-deviations principle for all the cluster sizes of a sparse Erdős–Rényi graph

Let (Formula presented.) be the Erdős–Rényi graph with connection probability (Formula presented.) as N → ∞ for a fixed t ∈ (0, ∞). We derive a large-deviations principle for the empirical measure of the sizes of all the connected components of (Formula presented.), registered according to microscopic sizes (i.e., of finite order), macroscopic ones (i.e., of order N), and mesoscopic ones (everything in between). The rate function explicitly describes the microscopic and macroscopic components and the fraction of vertices in components of mesoscopic sizes. Moreover, it clearly captures the well known phase transition at t = 1 as part of a comprehensive picture. The proofs rely on elementary combinatorics and on known estimates and asymptotics for the probability that subgraphs are connected. We also draw conclusions for the strongly related model of the multiplicative coalescent, the Marcus–Lushnikov coagulation model with monodisperse initial condition, and its gelation phase transition

Petrología del Grupo Eodevónico de Lolén, Sierras Australes (Provincia de Buenos Aires)

La composición mineralógica y petrología del Grupo de Lolén, el más alto de la Serie eodevónica de la Ventana, es descripta con cierto detalle, en un perfil paralelo a la ruta 76. El grupo está constituido por psamitas (grauvacas cuarzosas, cuarcitas y cuarcitas feldespáticas) y pelitas, con algunos conglomerados finos lenticulares y otros de naturaleza intraformacional intercalados. El intenso plegamiento ha afectado todo el grupo, de tal manera que todas las sedimentitas han sido re- cristalizadas con intensidad variable, más marcada hacia las zonas básales. Del análisis microscópico (texturas y composición) se infiere que tres han sido las etapas que caracterizan los procesos metamórficos : cristalización sintectónica (responsable del clivaje de flujo), cristalización postectónica (crecimiento cristalino) y deformación postcristalina (fenómenos cataclásticos). A pesar del carácter metamòrfico de esta serie sedimentaria, es posible inferir con cuidado, la naturaleza primitiva de las sedimentitas y su ambiente de sedimentación

Estudio de la zona con braquiópodos del Grupo de Lolén (Sierra de la Ventana, prov. Buenos Aires)

En el transcurso de los trabajos geológicos efectuados con el auspicio y medios otorgados por la Comisión de Investigación Científica de la provincia de Buenos Aires, en las Sierras Australes durante el período noviembre 1961 - mayo 1963 he tenido la oportunidad de recorrer y observar minuciosamente la porción inferior del grupo de Lolén. Ello me permitió conocer los pormenores de la distribución y contenido faunístico, como asimismo formular en base a nuevos hallazgos de evidente valor estratigráfico, una interpretación de la sucesión de elementos faunísticos, distinta de las precedentemente sugeridas en el caso al presente. En general, desde los primeros hallazgos reconocidos por Keidel en 1910 (Keidel, 1916), la investigación abarcó sectores de mejor acceso y en éstos, obviamente son los que he practicado en primer lugar mis observaciones, a la vez por tener a disposición un mayor número de datos geológicos. Como resultado de una primera visita al tramo fosilífero cerro Colorado al ex Club Hotel Ventana, luego prolongada hasta el abra de la Ventana y finalmente al área del abra del Chaco, en particular esta última, surgió el problema pertinente bajo una nueva faz de carácter geológico y estratigráfico

Petrografía de las sedimentitas psefíticas paleozoicas de las Sierras Australes bonaerenses

En este trabajo se estudian la composición mineralógica esencial y la fábrica de las sedimentitas psefíticas que integran, en parte, los grupos de La Lola (Silúrico) y Bravard (Eodevónico), y la serie de Sauce Grande (Carbónico superior), en las Sierras Australes de la provincia de Buenos Aires. Estos depósitos son considerados como ortoconglomerados (La Lola y Bravard) y paraconglomerados (Sauce Grande), reconociéndose la naturaleza cuarzosa de los primeros y cuarzo-feldespática de los segundos. La deformación tectónica observada varía en sus características, según la intensidad de la misma y la competencia de las sedimentitas afectadas y ha modificado parcialmente la fábrica sedimentaria, especialmente en los conglomerados de La Lola y Bravard. Como complemento, se analizan la génesis, condiciones ambientales y, en el caso de Sauce Grande, la procedencia del material lítico. Se señala además la posible existencia de una discordancia angular entre el grupo eodevónico de Lolén y la serie de Sauce Grande, y se sugiere la unión de la serie de Piedra Azul con la de Sauce Grande.This paper deais with essential mineralogical composition and fabric of the psephitic rocks which partially make up the La Lola (Siluriana and Bravard (Eodevonian) Groups and the Sauce Grande Series (Upper Carboniferous), all in the Sierra de la Ventana range in Southern Buenos Aires Province. The La Lola and Bravard psephites are shown to be orthoconglo- merates on the basis of their quartzose nature, whilst the Sauce Grande ones, on the main quartz-felspathic, are classified as paraconglomerates. Depending on the intensity of deformation and competence of the sedi- ments, the tectonic deformation has partially altered the original depo- sition fabric and imposed a grain orientation, specially in the La Lola and Bravard conglomerates. The study also ineludes provenance of lithic fragments (Sauce Grande Series), enviromental conditions and génesis of the rocks. The presence of a probable angular unconformity between the Lolén Group (Eodevonian) and Sauce Gande Series is mentioned, and the reunión of the Piedra Azul Series to Sauce Grande is suggested

Large deviations for Markov jump processes with uniformly diminishing rates

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the optimality of our assumptions on the decay of the jump rates. As a direct application of this work we relax the assumptions needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise naturally particularly the context of mass action kinetics

A REDUCED KINETIC MECHANISM FOR PROPANE FLAMES

Propane is one of the simplest hydrocarbons that can be a representative of higher hydrocarbons used in many applications. Therefore, this work develops a ten-step reduced kinetic mechanism among 14 reactive species for the propane combustion. The model is based on the solution of the flamelet equations. The equations are discretized using the second-order space finite difference method, using LES (Large-Eddy Simulation). Obtained results compare favorably with data in the literature for a propane jet diffusion flame. The main advantage of this strategy is the decrease of the work needed to solve the system of governing equations

Large deviations for Markov jump processes with uniformly diminishing rates

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further show that our assumptions on the decay of the jump rates are optimal. As a direct application of this work we relax the assumptions needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise naturally particularly the context of Mass action kinetics

The growth and superconducting properties of RE–Ba–Cu–O single grains with combined RE elements (RE = Gd and Y)

Abstract: The superconducting properties, melting temperatures and crystal growth rates of single grain, RE–Ba–Cu–O [(RE)BCO] bulk superconductors (where RE = a rare earth element or yttrium) decrease with the RE-element sequence of Nd, Sm, Eu, Gd, Dy and Y. The mechanical properties of these technologically important materials, on the other hand, however, improve in the same sequence. Consequently, one promising approach for optimising the balance between mechanical and superconducting properties of bulk (RE)BCO superconductors, or for adjusting growth rate, is the use of combinations of different rare earth elements. In this study, we explore combinations of Gd and Y in the formation of (Gd–Y)–Ba–Cu–O single grains. We describe the optimisation of the growth process for this multi-RE element system and use optical and scanning electron microscopy to study the microstructure of both non-superconducting (Gd–Y)2BaCuO5 [(Y–Gd)-211] phase inclusions and the (Y–Gd)Ba2Cu3O7-δ [(Y–Gd)-123] phase matrix itself. We demonstrate that (Gd–Y)–Ba–Cu–O single grains can be fabricated reliably and that they exhibit reasonably good superconducting properties. We observe that there is an increase in RE-211 particle size in this mixed rare earth system, which, ultimately, limits sample performance, and conclude that this may be a general disadvantage of this approach to the synthesis of single grains for high field engineering applications