91 research outputs found
On the variational limits of lattice energies on prestrained elastic bodies
We study the asymptotic behaviour of the discrete elastic energies in
presence of the prestrain metric , assigned on the continuum reference
configuration . When the mesh size of the discrete lattice in
goes to zero, we obtain the variational bounds on the limiting (in the sense of
-limit) energy. In case of the nearest-neighbour and
next-to-nearest-neibghour interactions, we derive a precise asymptotic formula,
and compare it with the non-Euclidean model energy relative to
Micromechanics of Smart Composite Plates with Periodically Embedded Actuators and Rapidly Varying Thickness
The effect of uncertain material properties on free vibrations of thin periodic plates
Planck 2015 results. XVIII. Background geometry and topology of the Universe
Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance Ïrec), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius âi of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Îlnâ > â5 relative to a simply-connected flat Planck best-fit model) are: âi > 0.97 Ïrec for the T3 cubic torus; and âi > 0.56 Ïrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, âi > 0.97 Ïrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of â0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. In the physically motivated setting, where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (Ï/H)0 < 7.6 Ă 10-10 (95% CL)
Dynamics of medium thickness plates interacting with a periodic Winklerâs foundation: non-asymptotic tolerance modelling
Platonic topology and CMB fluctuations: homotopy, anisotropy and multipole selection rules
Hillâs Lemma of Homogeneity for Granular Materials and Discrete Media
International audienc
Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis
Ătude de la conduction stationnaire dans un domaine comportant une rĂ©partition pĂ©riodique d'inclusions minces de grande conductivitĂ©
Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis
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