A New Approach to Equations with Memory

In this work, we present a novel approach to the mathematical analysis of equations with memory based on the notion of a state, namely, the initial configuration of the system which can be unambiguously determined by the knowledge of the future dynamics. As a model, we discuss the abstract version of an equation arising from linear viscoelasticity. It is worth mentioning that our approach goes back to the heuristic derivation of the state framework, devised by L.Deseri, M.Fabrizio and M.J.Golden in "The concept of minimal state in viscoelasticity: new free energies and applications to PDEs", Arch. Ration. Mech. Anal., vol. 181 (2006) pp.43-96. Starting from their physical motivations, we develop a suitable functional formulation which, as far as we know, is completely new.Comment: 39 pages, no figur

Packaging reconditioned household appliances

This article aims to present a research and design work that focuses on exploring new possible approaches to packaging design as applied to the field of reconditioning and reintroducing old household appliances to the market

Forces Applied on the Ground in Roller Skating

Walking, running, cycling, skating are just some examples of the many possibilities available to man for his own motion. Most of these activities have been widely studied both from a physiological as well as biomechanic viewpoint. On the contrary, few researches and experiments are available as regards skating, particularly roller-skating. In this sport the athlete wears a special pair of shoes fitted with four little wheels, each one of which is able to spin freely on a axis of its own. The analysis of the techniques used in roller-skating (as to how, when and where the propulsive force is applied and of the most appropriate length and frequency of each step) can provide some valuable information for a more thorough development of this sport activity. In order to have the opportunity to study and evaluate at least some of these parameters, some special force transducers were built and applied to each of the wheel fitted on a pair of skates. Furthermore, front and back weight-force detectors were also installed

On a doubly nonlinear phase-field model for first-order transitions with memory

Solid-liquid transitions in thermal insulators and weakly conducting media are modeled through a phase-field system with memory. The evolution of the phase variable $\varphi$ is ruled by a balance law which takes the form of a Ginzburg-Landau equation. A thermodynamic approach is developed starting from a special form of the internal energy and a nonlinear hereditary heat conduction flow of Coleman-Gurtin type. After some approximation of the energy balance, the absolute temperature $\theta$ obeys a doubly nonlinear "heat equation" where a third-order nonlinearity in $\varphi$ appears in place of the (customarily constant) latent-heat. The related initial and boundary value problem is then formulated in a suitable setting and its well--posedness and stability is proved

Well-posedness for solid-liquid phase transitions with a forth-order nonlinearity

A phase-field system which describes the evolution of both the absolute temperature $\theta$ and the phase variable $f$ during first-order transitions in thermal insulators is considered. A thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law. By virtue of the special form of the internal energy, a third-order nonlinearity $G_2^\prime(f)$ appears into the energy balance in place of the (customary constant) latent-heat. As a consequence, the bounds $0\le f\le1$ hold true whenever $\theta$ is positive valued. In addition, a nonlinear Fourier law with conductivity proportional to temperature is assumed. Well-posedness for the resulting initial and boundary value problem are then established in a suitable setting

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 $\chi$

A three-dimensional phase transition model in ferromagnetism: existence and uniqueness

We scrutinize both from the physical and the analytical viewpoint the equations ruling the paramagnetic-ferromagnetic phase transition in a rigid three dimensional body. Starting from the order structure balance, we propose a non-isothermal phase-field model which is thermodynamically consistent and accounts for variations in space and time of all fields (the temperature $\theta$, the magnetic field vector H and the magnetization vector M). In particular, we are able to establish a well-posedness result for the resulting coupled system

Kramers polarization in strongly correlated carbon nanotube quantum dots

Ferromagnetic contacts put in proximity with carbon nanotubes induce spin and orbital polarizations. These polarizations affect dramatically the Kondo correlations occurring in quantum dots formed in a carbon nanotube, inducing effective fields in both spin and orbital sectors. As a consequence, the carbon nanotube quantum dot spectral density shows a four-fold split SU(4) Kondo resonance. Furthermore, the presence of spin-orbit interactions leads to the occurrence of an additional polarization among time-reversal electronic states (polarization in the time-reversal symmetry or Kramers sector). Here, we estimate the magnitude for the Kramer polarization in realistic carbon nanotube samples and find that its contribution is comparable to the spin and orbital polarizations. The Kramers polarization generates a new type of effective field that affects only the time-reversal electronic states. We report new splittings of the Kondo resonance in the dot spectral density which can be understood only if Kramers polarization is taken into account. Importantly, we predict that the existence of Kramers polarization can be experimentally detected by performing nonlinear differential conductance measurements. We also find that, due to the high symmetry required to build SU(4) Kondo correlations, its restoration by applying an external field is not possible in contrast to the compensated SU(2) Kondo state observed in conventional quantum dots.Comment: 8 pages, 4figure

Robustness of different indicators of quantumness in the presence of dissipation

The dynamics of a pair of coupled harmonic oscillators in separate or common thermal environments is studied, focusing on different indicators of quantumness, such as entanglement, twin oscillators correlations and quantum discord. We compare their decay under the effect of dissipation and show, through a phase diagram, that entanglement is more likely to survive asymptotically than twin oscillators correlations