Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author

Inexact spectral deferred corrections

Implicit integration methods based on collocation are attractive for a number of reasons, e.g. their ideal (for Gauss-Legendre nodes) or near ideal (Gauss-Radau or Gauss-Lobatto nodes) order and stability properties. However, straightforward application of a collocation formula with M nodes to an initial value problem with dimension d requires the solution of one large Md × Md system of nonlinear equations

Adaptive Macro Finite Elements for the Numerical Solution of Monodomain Equations in Cardiac Electrophysiology

[EN] Many problems in Biology and Engineering are governed by anisotropic reaction diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.Heidenreich, E.; Ferrero De Loma-Osorio, JM.; Doblaré Castellano, M.; Rodríguez Matas, JF. (2010). 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Sinterização de cerâmicas em microondas. Parte III: Sinterização de zircônia, mulita e alumina Microwave sintering of ceramics. Part III: Sintering of zirconia, mullite and alumina

O aquecimento utilizando microondas possui muitas vantagens com relação aos métodos convencionais de aquecimento, como redução no tempo de processamento, economia de energia e melhora na uniformidade microestrutural dos corpos cerâmicos. Assim esse trabalho tem por objetivo a utilização da sinterização híbrida com microondas na queima rápida de materiais cerâmicos. Foram utilizados materiais que requerem altas temperaturas para densificação. Foram sinterizados materiais que apresentam bruscas e acentuadas mudanças nas suas propriedades dielétricas com a elevação da temperatura, zircônia, e materiais com baixas perdas dielétricas na temperatura ambiente, que apresentam dificuldades de aquecimento com microondas em baixas temperaturas, alumina e mulita. Foi utilizando material susceptor como agente auxiliar de aquecimento. Com base nos resultados obtidos pode-se concluir que o sistema de sinterização híbrida desenvolvido pode ser utilizado com sucesso na sinterização rápida e uniforme dos materiais estudados, sendo possível a sinterização de zircônia em ciclos de 20 min, mulita em ciclos de 16 min e alumina em ciclos de 40 min.<br>Thermal processing by microwaves offers several advantages over conventional heating methods, such as shorter processing times, energy savings and improved microstructural homogeneity of ceramic bodies. Thus, this work focused on the fast hybrid microwave sintering of ceramic materials that require high sintering temperatures for densification. The materials studied here were zirconia, which displays abrupt and severe increases in dielectric loss with rising temperature, and alumina and mullite, which show low dielectric losses at ambient temperature and are difficult to microwave at low temperatures. A susceptor was used as an auxiliary heating agent. The results indicate that the sintering system developed here can be used efficiently for the rapid, homogeneous sintering of all the ceramics in question. Zirconia was sintered in 20 min, mullite in 16 min and alumina in 40 min heating cycles