Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective
and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical
pseudodifferential operator on $M$. In this note, we strengthen asymptotics for
the equivariant (or reduced) spectral function of $P_0$ derived previously,
which are already sharp in the eigenvalue aspect, to become almost sharp in the
isotypic aspect. In particular, this leads to hybrid equivariant $L^p$-bounds
for eigenfunctions that are almost sharp in the eigenvalue and isotypic aspect.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1512.0219

Arnould, Olivier

Bardet, Sandrine

Chrysochoos, Andre

Yadav, Pankaj

English

arXiv

International audienceAnalysis of the thermo-mechanical behaviour of the polymers has been and still is the subject of many rheological studies both experimentally and theoretically. For small deformations, the modelling framework retained by rheologists is often of linear viscoelasticity which led us to the definition of complex moduli and to the rules of the renowned time-temperature superposition principle (TTSP). In this context, the effect of time (i.e., rate dependence) is almost unanimously associated with viscous effects. It has however been observed that the dissipative effects associated with viscous effects may be superimposed with thermo-elastic coupling effects, indicating a high sensitivity of polymeric materials to temperature variations (thermodilatability). Indeed, because of heat diffusion, it was also noticed that these strong thermo-mechanical couplings may induce a time dependence of the material behaviour. Using traditional experimental methods of visco-analysis i.e., dynamic mechanical thermal analysis (DMTA) and via an experimental energy analysis of the behaviour using quantitive infrared techniques, the relative importance of thermoelastic heat sources compared to viscous dissipation was analysed with the increasing frequency of monochromatic cyclic tensile tests made at different ambient temperatures

Hal-Diderot

Effect of thermomechanical couplings on viscoelastic behaviour of polystyrene

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