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A new dual approach for a class of phase transitions with memory : existence and long-time behaviour of solutions
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Attractors for a three-dimensional thermo-mechanical model of shape memory alloys
No full textIn this note, we consider a Fremond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor
A model for shape memory alloys with the possibility of voids
Full text linkThe paper is devoted to the study of a mathematical model for the
thermomechanical evolution of metallic shape memory alloys. The
main novelty of our approach consists in the fact that we include
the possibility for these materials to exhibit voids during the
phase change process. Indeed, in the engineering paper
\cite{allvoids} has been recently proved that voids may appear
when the mixture is produced by the aggregations of powder. Hence,
the composition of the mixture varies (under either thermal or
mechanical actions) in this way: the martensites and the austenite
transform into one another whereas the voids volume fraction
evolves. The first goal
of this contribution is hence to state a PDE system capturing all these modelling
aspects in order then to establish the well-posedness of the
associated initial-boundary value problem
Solid-liquid phase changes with different densities
Full text linkIn this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container Omega when we freeze the container. Since the density rho(2) of ice with volume fraction beta(2) is lower than the density rho(1) of water with volume fraction beta(1), experiments, for instance the freezing of a glass bottle filled with water, show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing play produce a nonhomogeneous material, for instance water, ice or sorbet. Here we describe a general class of phase transition processes, including this example as a particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint, recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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