1,958 research outputs found
Bound Pairs of Fronts in a Real Ginzburg-Landau Equation Coupled to a Mean Field
Motivated by the observation of localized traveling-wave states (`pulses') in
convection in binary liquid mixtures, the interaction of fronts is investigated
in a real Ginzburg-Landau equation which is coupled to a mean field. In that
system the Ginzburg-Landau equation describes the traveling-wave amplitude and
the mean field corrsponds to a concentration mode which arises due to the
slowness of mass diffusion. For single fronts the mean field can lead to a
hysteretic transition between slow and fast fronts. Its contribution to the
interaction between fronts can be attractive as well as repulsive and depends
strongly on their direction of propagation. Thus, the concentration mode leads
to a new localization mechanism, which does not require any dispersion in
contrast to that operating in the nonlinear Schr\"odinger equation. Based on
this mechanism alone, pairs of fronts in binary-mixture convection are expected
to form {\it stable} pulses if they travel {\it backward}, i.e. opposite to the
phase velocity. For positive velocities the interaction becomes attractive and
destabilizes the pulses. These results are in qualitative agreement with recent
experiments. Since the new mechanism is very robust it is expected to be
relevant in other systems as well in which a wave is coupled to a mean field.Comment: 9 pages (RevTex), 9 figures (postscript
Exponential stability to localized type III thermoelasticity
This paper investigates the system proposed by a wave equation and a heat equation of type III in one part of the domain; a wave equation and a heat equation of type II in another part of the domain, coupled in a certain pattern. In this paper we prove the exponential stability of the solutions under suitable conditions for the thermal conductivity and coupling term.Peer ReviewedPostprint (author's final draft
Qualitative results for a mixture of Green-Lindsay thermoelastic solids
We study qualitative properties of the solutions of the system of partial
differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity e ects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of
the solutions over the time. We use the semigroup arguments to establish our resultsPeer ReviewedPostprint (author's final draft
Granular Matter: a wonderful world of clusters in far-from-equilibrium systems
In this paper, we recall various features of non equilibrium granular
systems. Clusters with specific properties are found depending on the packing
density, going from loose (a granular gas) to sintered (though brittle)
polycrystalline materials. The phase space available can be quite different.
Unexpected features, with respect to standard or expected ones in classical
fluids or solids, are observed, - like slow relaxation processes or anomalous
electrical and thermoelectrical transport property dependences. The cases of
various pile structures and the interplay between classical phase transitions
and self-organized criticality for avalanches are also outlined.Comment: 7 figures, 37 refs., to be published in Physica
Decay of solutions for strain gradient mixtures
We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin-Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different cases, each at a time. For each case we prove existence and uniqueness of solutions. We obtain the exponential decay of the solutions in the hyperviscosity and viscosity cases. Exponential decay is also expected when the dissipation is generated by the relative velocity (in the generic case, although a particular combination of the constitutive parameters leads to slow decay). These results are proved with the help of the theory of semigroupsPeer ReviewedPostprint (published version
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