Search results for "Matematica"

Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion

2016

In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709–743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary…

Hydrodynamic Equations of Anisotropic, Polarized, Turbulent Superfluids

2009

HYDRODYNAMICAL MODELS OF SUPERFLUID TURBULENCE

2011

This review paper puts together some of our results concerning the application of non equilibrium Thermodynamics to superfluid liquid helium. Two of the most important situations of this quantum fluid are rotating superfluid and superfluid turbulence, both characterized by the presence of quantized vortices (vortex lines whose core is about 1 Angstrom and the quantum of circulation is $h/m$, $h$ being the Plank's constant and $m$ the mass of helium atom). In the first part of the work a non-standard model of superfluid helium, which considers heat flux as independent variable, is briefly recalled, and compared with the well known two-fluid model, in absence of vortices, proposed by Tisza an…

Propagation of fourth sound in turbulent superfluids via extended thermodynamics

2011

The work deals with further developments of a study previously initiated, in which a macroscopic one-fluid model of inhomogeneous turbulent superfluids, based on extended thermodynamics, had been formulated. In this work the study is carried on. First the influence of the remnant vortices on the propagation of the first and second sound is studied. Then a boundary condition able to explain the reversible flow of superfluid flowing through a thin capillary is postulated and two vector fields, which have the dimensions of velocity and can be interpreted as the velocities of normal and superfluid components, are introduced. By using these new fields, a comparison between this model and the Hal…

Model pseudofermionic systems: Connections with exceptional points

2014

We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection with the validity of the extended anti-commutation rules which define the pseudo-fermionic structure.

QUANTUM MODELING OF LOVE AFFAIRS

2010

We adopt the so-called number representation, originally used in quantum me- chanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relation. We present a simple model, involv- ing two actors (Alice and Bob), and we consider either a linear model or a nonlinear model.

D pseudo-bosons in quantum models

2013

Abstract We show how some recent models of PT-quantum mechanics perfectly fit into the settings of D pseudo-bosons, as introduced by one of us. Among the others, we also consider a model of non-commutative quantum mechanics, and we show that this model too can be described in terms of D pseudo-bosons.

A thermodynamical model of inhomogeneous superfluid turbulence

2007

In this paper we perform a thermodynamical derivation of a nonlinear hydrodynamical model of inhomogeneous superfluid turbulence. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux and the averaged vortex line length per unit volume. The restrictions on the constitutive quantities are derived from the entropy principle, using the Liu method of Lagrange multipliers. The mathematical and physical consequences deduced by the theory are analyzed both in the linear and in the nonlinear regime. Field equations are written and the wave propagation is studied with the aim to describe the mutual interactions between the second sound and the vortex t…

Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component

2013

In this paper, the velocity profile of the normal component in the stationary flow of turbulent superfluid helium inside a cylindrical channel is determined, making use of a one-fluid model with internal variables derived from Extended Thermodynamics. In the hypothesis of null barycentric velocity of the fluid (the so-called counterflow situation) it is seen that, in the presence of a sufficiently high vortex length density, the velocity profile of the normal component becomes very flat in the central region of the channel. Thus, a central flat profile of the normal fluid does not necessarily imply that the flow of the normal component is turbulent.

Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles

2008

We include the effects of anisotropy and polarization in the hydrodynamics of inhomogeneous vortex tangles, thus generalizing the well known Hall-Vinen-Bekarevich-Khalatnikov equations, which do not take them in consideration. These effects contribute to the mutual friction force ${\bf F}_{ns}$ between normal and superfluid components and to the vortex tension force $\rho_s{\bf T}$. These equations are complemented by an evolution equation for the vortex line density $L$, which takes into account these contributions. These equations are expected to be more suitable than the usual ones for rotating counterflows, or turbulence behind a cylinder, or turbulence produced by a grid of parallel th…