Ivana Bochicchio

A mathematical model for phase separation: a generalized Cahn-Hilliard equation

In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced for an incompressible fluid, so the resulting differential system couples a generalized Cahn–Hilliard equation with the Navier–Stokes equation. Its consistency with the second law of thermodynamics in the classical Clausius–Duhem form is finally proved. Copyright

Simplicial Approach to Fractal Structures

A fractal lattice is defined by iterative maps on a simplex. In particular, Sierpinski gasket and von Koch flake are explicitly obtained by simplex transformations.

On the mechanical analogy between the relativistic evolution of a spherical dust universe and the classical motion of falling bodies

Abstract Using the analogy between the einsteinian evolution of the shells of a spherical dust universe and the newtonian motion of the bodies freely falling toward or from a Newtonian center of attraction, we have qualitatively studied the relativistic evolution of a spherically symmetric dust universe by means of the classical Weierstrass method.

THE WEIERSTRASS CRITERION AND THE LEMAÎTRE–TOLMAN–BONDI MODELS WITH COSMOLOGICAL CONSTANT Λ

We analyze Lemaitre-Tolman-Bondi models in presence of the cosmological constant Lambda through the classical Weierstrass criterion. Precisely, we show that the Weierstrass approach allows us to classify the dynamics of these inhomogeneous spherically symmetric Universes taking into account their relationship with the sign of Lambda.

Wavelet Analysis of Bifurcation in a Competition Model

A nonlinear dynamical system which describes two interacting and competing populations (tumor and immune cells) is studied through the analysis of the wavelet coefficients. The wavelet coefficients (also called detail coefficients) are able to reproduce the behaviour of the function, and, being sensible to local changes, are strictly related to the differentiable properties of the function, which cannot be easily derived from the numerical interpolation. So the main features of the dynamical system will be given in terms of detail coefficients that are more adapted to the description of a nonlinear problem.

On the evolution of dust shells in Lemaître-Tolman-Bondi models

Abstract In this work some geometric properties of Lemaître-Tolman-Bondi Universes are analyzed. More precisely, the curvature properties of the initial spatial hypersurface are investigated to show as they determinate the sub-sequent evolution of the Universe.

A REVIEW ON THE GEOMETRIC FORMULATION OF TOLMAN–BONDI EQUATIONS IN GENERAL RELATIVITY

This work is focused on spherically symmetric space-times. More precisely, geometric and structural properties of spatially spherical shells of a dust universe are analyzed in detail considering recent results of our research. Moreover, exact solutions, obtained for constant Ricci principal curvatures, are inferred and qualitatively analyzed through suitable classic analogies.

Sulla sesta distorsione elementare di Volterra per un cilindro cavo omogeneo e isotropo di altezza finita con carico alla Saint Venant

In this work we consider the sixth elementary Volterras distortion for a circular hollow, homogeneous, elastic, isotropic cylinder, to analyze the load acting on the bases as a Saint Venant characteristic external stress. In this way we are able to prove that the specific load connected to the sixth distortion and examined as external stress, is equivalent (in Saint Venants theory) to a right combined compressive and bending stress (or to a right combined tensile and bending stress).

Global and exponential attractors for a Ginzburg-Landau model of superfluidity

The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4 He by means of a non-linear differential system, where the concentration of the superfluid phase satisfies a non-isothermal Ginzburg-Landau equation. This system, which turns out to be consistent with thermodynamical principles and whose well-posedness has been recently proved, has been shown to admit a Lyapunov functional. This allows to prove existence of the global attractor which consists of the unstable manifold of the stationary solutions. nFinally, by exploiting recent techinques of semigroups theory, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.

Transition and separation process in brine channels formation

In this paper, we discuss the formation of brine channels in sea ice. The model includes a time-dependent Ginzburg-Landau equation for the solid-liquid phase change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics, and the heat equation for the temperature change. The macroscopic motion of the fluid is also considered, so the resulting differential system couples with the Navier-Stokes equation. The compatibility of this system with the thermodynamic laws and a maximum theorem is proved.