Québec, Canada
Québec, Canada

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Desharnais J.,Pavillon Adrien Pouliot | Moller B.,University of Augsburg | Struth G.,University of Sheffield
Logical Methods in Computer Science | Year: 2011

Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, Löb's formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To model infinite behaviours, idempotent semirings are extended to divergence semirings, divergence Kleene algebras and omega algebras. The resulting notions and techniques are used in calculational proofs of classical theorems of rewriting theory. These applications show that modal semirings are powerful tools for reasoning algebraically about the finite and infinite dynamics of programs and transition systems. © J. Desharnais, B. Möller, and G. Struth.


Grellet D.,Pavillon Adrien Pouliot | Dore G.,Pavillon Adrien Pouliot | Bilodeau J.-P.,Pavillon Adrien Pouliot
Canadian Journal of Civil Engineering | Year: 2012

Complex and variable solicitations from climate and traffic greatly impact pavements performance and therefore user's safety and comfort. As the effect of traffic is related to the strains induced in the pavement structures, this study objective is to determine if changing conventional dual tires to wide base single tires may impact significantly strains in flexible pavements. This paper documents an experimental investigation of strain induced close to the edge of the tire and under the tire. Two pavement structures and two climate conditions have been tested. For each test section, optical fiber strain gauges fixed on asphalt concrete cores are installed within the asphalt concrete pavement layer. This is a retrofit technique that allows measuring strains in the upper and lower part of the asphalt layer. The experiment led to the following observations: wide base single tires cause a 14 to 30% increase of the tensile strains at the bottom of the asphalt concrete layer but cause a 20% decrease of the tensile strains at shallow depth near the edge of the tire. A complex extension-contraction phenomenon has been observed at that level. This phenomenon should be taken into account in the analysis of complex strain patterns occurring within the pavement bounded layers.

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