Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well

Filling a silo with a mixture of grains: Friction-induced segregation

We study the filling process of a two-dimensional silo with inelastic particles by simulation of a granular media lattice gas (GMLG) model. We calculate the surface shape and flow profiles for a monodisperse system and we introduce a novel generalization of the GMLG model for a binary mixture of particles of different friction properties where, for the first time, we measure the segregation process on the surface. The results are in good agreement with a recent theory, and we explain the observed small deviations by the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as wel

Poster: Continual Network Learning

We make a case for in-network Continual Learning as a solution for seamless adaptation to evolving network conditions without forgetting past experiences. We propose implementing Active Learning-based selective data filtering in the data plane, allowing for data-efficient continual updates. We explore relevant challenges and propose future research directions

Granular Elasticity without the Coulomb Condition

An self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.Comment: 4pages, 2 figure

Consteel© EAF and conventional EAF: a comparison in maintenance practices

The present paper highlights the main differences between Consteel® and conventional EAF technologiesregarding scheduled and unscheduled maintenance practices. The study has been made on the basis of datacollected in plants with high maintenance standards and more than 10 years of operational experience.These data have been analyzed and organized in a comparison table where they have been associated with therelevant maintenance costs. The comparison shows that the Consteel® technology achieves a significantreduction in the overall maintenance costs compared to a conventional EAF