Uniform attractors for a phase-field model with memory and quadratic nonlinearity

A phase-field system with memory which describes the evolution of both the temperature variation $\theta$ and the phase variable $\chi$ is considered. This thermodynamically consistent model is based on a linear heat conduction law of Coleman-Gurtin type. Moreover, the internal energy linearly depends both on the present value of $\theta$ and on its past history, while the dependence on $\chi$ is represented through a function with quadratic nonlinearity. A Cauchy-Neumann initial and boundary value problem associated with the evolution system is then formulated in a history space setting. This problem is shown to generate a non-autonomous dynamical system which possesses a uniform attractor. In the autonomous case, the attractor has finite Hausdorff and fractal dimensions whenever the internal energy linearly depends on $\chi$

Cahn-Hilliard equations with memory and dynamic boundary conditions

We consider a modified Cahn\u2013Hiliard equation where the velocity of the order parameter u depends on the past history of \u394\u3bc, \u3bc being the chemical potential with an additional viscous term \u3b1ut, \u3b1 650. This type of equation has been proposed by P. Galenko et al. to model phase separation phenomena in special materials (e.g., glasses). In addition, the usual no-flux boundary condition for u is replaced by a nonlinear dynamic boundary condition which accounts for possible interactions with the boundary. The resulting boundary value problem is subject to suitable initial conditions and is reformulated in the so-called past history space. Existence of a variational solution is obtained. Then, in the case \u3b1>0, we can also prove uniqueness and construct a strongly continuous semigroup acting on a suitable phase space. We show that the corresponding dynamical system has a (smooth) global attractor as well as an exponential attractor. In the case \u3b1=0, we only establish the existence of a trajectory attractor

Granular Rheology in Zero Gravity

We present an experimental investigation on the rheological behavior of model granular media made of nearly elastic spherical particles. The experiments are performed in a cylindrical Couette geometry and the experimental device is placed inside an airplane undergoing parabolic flights to cancel the effect of gravity. The corresponding curves, shear stress versus shear rate, are presented and a comparison with existing theories is proposed. The quadratic dependence on the shear rate is clearly shown and the behavior as a function of the solid volume fraction of particles exhibits a power law function. It is shown that theoretical predictions overestimate the experiments. We observe, at intermediate volume fractions, the formation of rings of particles regularly spaced along the height of the cell. The differences observed between experimental results and theoretical predictions are discussed and related to the structures formed in the granular medium submitted to the external shear.Comment: 10 pages, 6 figures to be published in Journal of Physics : Condensed Matte

Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page

Computing Matveev's complexity via crystallization theory: the boundary case

The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove that for each compact irreducible and boundary-irreducible 3-manifold it coincides with the modified Heegaard complexity introduced by Cattabriga, Mulazzani and Vesnin. Moreover, via Gem-Matveev complexity, we obtain an estimation of Matveev's complexity for all Seifert 3-manifolds with base $\mathbb D^2$ and two exceptional fibers and, therefore, for all torus knot complements.Comment: 27 pages, 14 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

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

IR spectroscopic characterization of tetrabasic lead sulphate

The knowledge of the physicochemical properties of the basic lead sulphates is of great interest from the point of view of the technology of lead-acid batteries.Facultad de Ciencias Exacta

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well