Nonlocal and rotational effects in quantum 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

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

In this work, a generalization for the alternative Vinen’s equation in counterflow rotational superfluid turbulence is proposed. It is compared with the equation proposed in Phys. Rev. B, 69, 094513 (2004) and with the experimental results. We consider not only steady-states but also unsteady situations. From this analysis follows that the solutions of the alternative Vinen’s equation tend significantly faster to the corresponding final steady state values than the solutions of the usual Vinen’s equation. [DOI: 10.1685 / CSC06099] About DO

Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles

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 thin cylinders towed across a superfluid, because in these situations polarization is expected to play a relevant role.Comment: 21 page

A note on the modeling of immune-cancer competition in the homogeneous systems

This work deals with the model focuses on the study of the early stage of the immune cancer competition. The approach used in this model is based on the kinetic theory of active particles (KTAP), which has been developed to modeling systems constituted by a large number of interacting particles (active particles), whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity) but also biological functions called activities related to the intrinsic biological function of particles. The model consider a scalar activity variable u ∈ (0,∞). The overall system is divided into six (M = 6) different populations (functional subsystems), the first three subsystems contain epithelial (subsystem 1) and cancer cells (subsystems 2,3), the other functional subsystems contain cells of the immune system. After some reasonable assumptions, we obtain for the cancer cells and immune cells of the last hallmark a Lotka-Volterra system that allows us to describe the dynamics of the biological system in a very simple way

Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes

We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed

Fractal dimension of superfluid turbulence : A random-walk toy model

This paper deals with the fractal dimension of a superuid vortex tangle. It extends a previous model [1] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent proposals in the bibliography. The range between 1.35 and 1.75 seems the most consistent one

A mathematical description of glitches in neutron stars

In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the absence of information about the physics of the matter of the star. This has motivated several authors to suggest dynamical models that interpret most of the astronomical data. Many predictions are based on the assumption that the inner part is analogous to the structure of matter of superfluids. Here, we illustrate a new mathematical model, partially inspired by the dynamics of superfluid helium. We obtain two evolution equations for the angular velocities (of the crust and of superfluid), which are supported by another evolution equation for the average vortex line length per unit volume. This third equation is more delicate from an analytical perspective and is probably at the origin of glitches. We identify two stationary solutions, corresponding to the straight vortex regime and the turbulent regime

Non-equilibrium Thermodynamical Description of Superfluid Transition in Liquid Helium

In previous papers a phase field model for λ-transition in 4He was proposed, which is able to describe the influence of the heat flux on the temperature transition. The model presented here generalizes previous results taking into account of a homogeneous presence of quantized vortices below the λ-transition. As parameter that controls the transition, a dimensionless field f linked to the modulus of the condensate wave function is used. In addition to the field f , the resulting model chooses the following field variables: Density, velocity, temperature and heat flux. Nonlocal terms to describe inhomogeneities in the field variables and dissipative effects of mechanical and thermal origin are also taken into account. Under the hypothesis that the liquid is at rest, the second sound propagation near the superfluid transition is studied. It is seen that the order parameter modifies the speed and the attenuation of the second sound, as well as the presence of a small tangle of vortices. This shows that the influence of the order parameter is not restricted to the description of the lambda transition, but its presence influences also other features, as the second sound speed and attenuation. In addition to the second sound a new mode is present, corresponding to a perturbation in the order parameter f , which is attenuated within a short number of wavelengths.