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…

Studies in thermal and dynamical duality

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 …

Vortex temperature in turbulent superfluids

Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States

Abstract In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons.

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.