The Redner - Ben-Avraham - Kahng cluster system

We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on the occasion of their sixtieth birthday

On the convergence to critical scaling profiles in submonolayer deposition models

In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size $n\geq 2$ for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was studied outside of a critical direction $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi := (x-\tau)/\sqrt{\tau}$, corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau\to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.Comment: Dedicated to the memory of Jack Car

Steps in modular specifications for concurrent modules

© 2015 Published by Elsevier B.V.The specification of a concurrent program module is a difficult problem. The specifications must be strong enough to enable reasoning about the intended clients without reference to the underlying module implementation. We survey a range of verification techniques for specifying concurrent modules, in particular highlighting four key concepts: auxiliary state, interference abstraction, resource ownership and atomicity. We show how these concepts combine to provide powerful approaches to specifying concurrent modules

Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition

We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies in a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in (O. Costin, M. Grinfeld, K.P. O'Neill and H. Park, Long-time behaviour of point islands under fixed rate deposition, Commun. Inf. Syst. 13, (2), (2013), pp.183-200) using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of $j$-clusters. The use of higher order expressions, both for the Stirling expansion and for the monomer evolution at large times allow us to obtain, not only the similarity limit, but also the rate at which it is approached.Comment: Revised according to referee's suggestions; to be published in SIAM J. Math. Ana

The Redner - Ben-Avraham - Kahng coagulation system with constant coefficients: the finite dimensional case

We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established in [4] by means of formal arguments.Comment: 13 pages, 1 figur

Social participation in the context of the urban public space renewal: the case of Lagarteiro neighborhood in Oporto

In 1980, Giancarlo de Carlo wrote in the Perspecta: Yale Journal, “An Architecture of the Participation”. Carlo, proposed a sequence of procedures: the problem definition, the solution and the results evaluation, in all the three steps, the social communities should be integrated in as part of a share and dynamic process. This text corresponds to a new way of understanding the importance of the social communities in the architecture definition. From de Carlo’s text, the main goal of this paper is to present the results of an intervention in public space renewal of the Lagarteiro neighborhood (in Oporto city) and the relation of this process with the participation of the resident population. The urban context of Lagarteiro’s neighborhood presented before the intervention the typical and classic signs of disqualification of environmental and urban peripheral areas of resettlement. The term “disadvantaged areas” is associated with these areas in urban or peri-urban case, was framed in a specific Portuguese policy, called Initiative Critical Neighborhoods. Being a recent intervention, the renewal of the public space in Lagarteiro is a complete case study that allows comprehending the participation phenomenon in nowadays, at the same time that seduces a reflexion about technical and architectural solutions for “critical” neighborhood.info:eu-repo/semantics/publishedVersio

A phenomenological model for magnetoresistance in granular polycrystalline colossal magnetoresistive materials: the role of spin polarised tunnelling at the grain boundaries

It has been observed that in bulk and polycrystalline thin films of collossal magnetoresistive (CMR) materials the magnetoresistance follows a different behaviour compared to single crystals or single crystalline films below the ferromagnetic transition temperature Tc. In this paper we develop a phenomenological model to explain the magnetic field dependence of resistance in granular CMR materials taking into account the spin polarised tunnelling at the grain boundaries. The model has been fitted to two systems, namely, La0.55Ho0.15Sr0.3MnO3 and La1.8Y0.5Ca0.7Mn2O7. From the fitted result we have separated out, in La0.55Ho0.15Sr0.3MnO3, the intrinsic contribution from the intergranular contribution to the magnetoresistance coming from spin polarised tunnelling at the grain boundaries. It is observed that the temperature dependence of the intrinsic contribution to the magnetoresistance in La0.55Ho0.15Sr0.3MnO3 follows the prediction of double exchange model for all values of field.Comment: 14 pages + 5 figures, postscript (to appear in Journal of Applied Physics

Cassiano Branco. Modern visions of an “inconvenient” architect

Cassiano Branco (1897-1970) belonged to the pioneer generation of modern Portuguese architects, which worked during the years of the dictatorship regime. During the 30s, Cassiano produced an anti-conservative and eloquent architecture, contrasting with the guidelines of the regime. The discomfort about his personality came also from his ideological opposition to the government. Among his counterparts he has been considered ‘an exception to the rule’, working, mainly for private investors, on programs for renting house buildings, movie theaters and tourism facilities, which were built over the boulevards outlined in Lisbon or in the natural and intact regional scenarios of Portugal.info:eu-repo/semantics/submittedVersio