Search results for " Matematica"
showing 10 items of 1345 documents
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
Dynamics of Confined Crowd Modelled Using Fermionic Operators
2014
An operatorial method based on fermionic operators is used to describe the dynamics of a crowd made of different kind of populations mutually interacting and moving in a two–dimensional bounded closed region. The densities of the populations are recovered through the Heisenberg equation and the diffusion process is driven by the Hamiltonian operator defined by requiring that the populations move along optimal paths. We apply the model obtained in a concrete situation and we discuss the effect of the interaction between the populations during their motion.
Large-scale normal fluid circulation in helium superflows
2017
We perform fully-coupled numerical simulations of helium II pure superflows in a channel, with vortex- line density typical of experiments. Peculiar to our model is the computation of the back-reaction of the superfluid vortex motion on the normal fluid and the presence of solid boundaries. We recover the uniform vortex-line density experimentally measured employing second sound resonators and we show that pure superflow in helium II is associated with a large-scale circulation of the normal fluid which can be detected using existing particle-tracking visualization techniques.
Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence
2007
Two alternative Vinen's evolution equations for the vortex line density L in counterflow superfluid turbulence, are physically admissible and lead to analogous results in steady states. In Phys. Rev. B, 69, 094513 (2004) the most used of them was generalized to counterflow superfluid turbulence in rotating containers. Here, the analogous generalization for the alternative Vinen's equation is proposed. Both generalized Vinen's equations are compared with the experimental results, not only in steady-states but also in some unsteady situations. From this analysis follows that the solutions of the alternative Vinen's equation tend significantly faster to the corresponding final steady state val…
Effective temperature and scaling laws of polarized quantum vortex bundles
2011
Abstract An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A ∝ k − 1 / 2 , follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.
Refrigeration of an Array of Cylindrical Nanosystems by Flowing Superfluid Helium
2016
We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simplified model of computer refrigeration. We explore the use of He II as cooling fluid, taking into account forced convection and heat conduction. The main conceptual and practical difficulties arise in the calculation of the effective thermal conductivity. Since He II does not follow Fourier’s law, the effective geometry-dependent conductivity must be extracted from a more general equation for heat transfer. Furthermore, we impose the restrictions that the maximum temperature along the array should be less than (Formula presented.) transition temperature and that quantum turbulence is avoided, in o…
Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes
2014
The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we disc…
Contribution of the normal component to the thermal resistance of turbulent liquid helium
2015
Previous results for the velocity profile of the normal component of helium II in counterflow are used to evaluate the viscous contribution to the effective thermal resistance. It turns out that such a contribution becomes considerably higher than the usual Landau estimate, because in the presence of vortices, the velocity profile is appreciably different from the Poiseuille parabolic profile. Thus, a marked increase in the contribution of the normal component to the thermal resistance with respect to the viscous Landau estimate does not necessarily imply that the normal component is turbulent. Furthermore, we examine the influence of a possible slip flow along the walls when the radius of …
Vortex diffusion and vortex-line hysteresis in radial quantum turbulence
2014
Abstract We study the influence of vortex diffusion on the evolution of inhomogeneous quantized vortex tangles. A simple hydrodynamical model to describe inhomogeneous counterflow superfluid turbulence is used. As an illustration, we obtain solutions for these effects in radial counterflow of helium II between two concentric cylinders at different temperatures. The vortex diffusion from the inner hotter cylinder to the outer colder cylinder increases the vortex length density everywhere as compared with the non-diffusive situation. The possibility of hysteresis in the vortex line density under cyclical variations of the heat flow is explored.
A non self-adjoint model on a two dimensional noncommutative space with unbound metric
2013
We demonstrate that a non self-adjoint Hamiltonian of harmonic oscillator type defined on a two-dimensional noncommutative space can be diagonalized exactly by making use of pseudo-bosonic operators. The model admits an antilinear symmetry and is of the type studied in the context of PT-symmetric quantum mechanics. Its eigenvalues are computed to be real for the entire range of the coupling constants and the biorthogonal sets of eigenstates for the Hamiltonian and its adjoint are explicitly constructed. We show that despite the fact that these sets are complete and biorthogonal, they involve an unbounded metric operator and therefore do not constitute (Riesz) bases for the Hilbert space $\L…