Vortex line density in plane Couette flow in superfluid helium

Alternative Vinen's equation and its extension to counterflow rotational superfluid turbulence

A Mathematical Model of Counterflow Superfluid Turbulence in Presence of Combined Rotation and Counterflow

Onde di densità di vortici nella turbolenza superfluida

Transition to superfluidity in liquid 4He

In this work the transition from normal liquid helium I to superfluid liquid helium II, controlled by temperature and pressure, is studied in the simplified assumption of absence of viscosity. A macroscopic thermodynamical model is presented, which chooses as new independent fields the heat flux q and a phase field function f. For the heat flux a modification of Cattaneo equation is written, while for the function f a time dependent Ginzburg-Landau equation is proposed.

Extended Thermodynamics of liquid helium II: laminar and turbulent flows

Onde di calore e onde di densità di vortici nella turbolenza superfluida

Nonlinear Kelvin waves on a quantized vortex line in superfluid helium

In this paper we show an exact solution (Kelvin wave) of an approximated dynamical equation for a quantized vortex line in helium superfluid at finite temperature. It is shown that the applied heat flux interacts with the vortex line, and the amplitude of the Kelvin wave can grow (the so-called Donnelly instability) or decrease according with the mutual direction between heat flux and wave vector.

Attenuation of the Fourth Sound in Liquid Helium II via Extended Thermodymamics

METABOLIC SYNDROME IN CHILDHOOD AND CARDIOVASCULAR RISK

Study of the anisotropy in turbulent superfluids

In this review we are interested on the anisotropy and polarity of superfluid turbulence in helium II, a still open problem which needs more details. Though some of the results presented here have already been published in different papers, this short review aims to put the main results together and to extend them when necessary. From the mesoscopic viewpoint, an evolution equation for the vortex line density was proposed in rotating counterflow (heat flux without mass flux) by means of dimensional analysis. Then, starting from the microscopic viewpoint this evolution equation was further extended to include situations where turbulence is not homogeneously distributed. Indeed, microscopical…

Entropy Flux far from equilibrium in solids and in non-viscous gases

Studies in thermal and dynamical duality

Evolution equations in superfluid turbulence

Phenomenological description of the vortex density in rotating BEC superfluids

The close analogy of a purely magnetic excitation scheme, used in the experiments on Bose-Einstein condensate by Hodby et al., and the rotating bucket experiments with liquid helium 4 has suggested us to apply a phenomenological equation for the vortex line density, previously proposed for rotating superfluid helium 4, to describe the vortex density in a rotating Bose-Einstein condensate as a function of the angular speed. In both systems, the phenomenological equation provides a reasonable description of the observed data.

Flow of turbulent superfluid helium inside a porous medium

The work deals with further developments of a study previously initiated, in which a macroscopic model of inhomogeneous superfluid turbulence, based on extended thermodynamics, has been formulated. The model choose as fundamental fields, beside the traditional fields, two extra variables: the averaged vortex line length per unit volume and the heat flux. Using this model the propagation of the fourth sound inside a superleak is investigated: it is shown that, if the configuration of the vortex tangle inside the superleak are not altered -on the average- by the presence of the walls, when the fourth sound is propagated, vibrations in the vortex line density are present, too.

Statistical mechanics and thermodynamics of turbulent quantum vortex tangles

In this paper we present some phenomenological ideas about the thermodynamics of quantized vortex loops arising in superfluid turbulence. The system of vortex loops may be seen as a dissipative structure, not existing on its own but only under the influence of an external heat flux. Starting from a simple definition of the temperature of the vortex tangle and from the relation between energy and vortex length, we obtain the entropy of the system, as well as the caloric and thermal equations of state, relating internal energy and pressure to temperature and volume. We discuss the connection between our macroscopic results and microscopic results on vortex length distribution function having …

Extended thermodynamics of polymers and superfluids

Stability in the plane Couette flow of superfluid helium

An hydrodynamical model previously proposed to describe the presence of vortices in counterflow superfluid turbulence and in rotating containers is used to discuss plane Couette flow and the stability of the stationary solution.

Vortex temperature in turbulent superfluids

Hydrodynamics of superfluid 4He without dissipative effects

This review paper is the first of a series of papers focusing on the singular behavior of superfluids. Here, we will consider the laminar flow of superfluid $^4$He. It is shown that the properties of helium II can be explained both considering it as a two-fluid mixture or as a single fluid with extremely high thermal conductivity and extremely small viscosity. More specifically, in this paper is shown that the anomalous effects in helium II are, in a large measure, a consequence of entropy conservation. Indeed, it will be shown that these effects can be explained imposing entropy conservation in a two-fluid mixture as well as in a single fluid described by extended thermodynamics. Firstly, …

Nonlocal and rotational effects in superfluid turbulence

We discuss phenomenological equations for the evolution of vortex tangle in counterflow superfluid turbulence, which takes into account the influence of the non local effects, both in absence and in the presence of rotation.

Duality-invariant dispersion relations for electromagnetic and gravitational waves at Planck scales

In this paper we explore some mathematical aspects of a duality-invariant Einstein-Planck relation on electromagnetic waves and gravitational waves at a Planckian scale. We explore a generalized version of Maxwell's equations leading to the proposed duality-invariant dispersion relation for electromagnetic waves. We also study the analogous aspects of duality in a post-Newtonian description of gravitational waves.

Generalization of the Alternative Vinen's Equation Describing the Superfluid Turbulence in Rotating Container

Phase transition and lambda-line in liquid helium

A hydrodynamical model describing the superfluid phase transition of 4He close to $\lambda$-line is presented. In the work, which generalizes a phase field model of lambda transition previously formulated by the same authors, the independent fields are the density, the temperature, the velocity, the heat flux and a scalar function $f$, linked to the modulus of the wave-function $\psi$, solution of the Ginzburg-Landau equation. In this framework, the heat flux is given by a modified Maxwell-Cattaneo equation. The restrictions on the constitutive quantities are obtained from the entropy principle, using the Liu method of Lagrange multipliers. A maximum theorem is proved that allows the model …