Papers by Michele Sciacca
Zeitschrift für angewandte Mathematik und Physik, Apr 1, 2024
Physics Reports, 2018
This review paper puts together some results concerning non equilibrium thermodynamics and heat t... more This review paper puts together some results concerning non equilibrium thermodynamics and heat transport properties of superfluid He II. A one-fluid extended model of superfluid helium, which considers heat flux as an additional independent variable, is presented, its microscopic bases are analized, and compared with the well known two-fluid model. In laminar situations, the fundamental fields are density, velocity, absolute temperature, and heat flux. Such a theory is able to describe the termomechanical phenomena, the propagation of two sounds in liquid helium, and of fourth sound in superleak. It also leads in a natural way to a two-fluid model on purely macroscopical grounds and allows a small amount of entropy associated with the superfluid component. Other important features of liquid He II arise in rotating situations and in superfluid turbulence, both characterized by the presence of quantized vortices (thin vortex lines whose circulation is restricted by a quantum condition). Such vortices have a deep influence on the transport properties of superfluid helium, as they increase very much its thermal resistance. Thus, heat flux influences the vortices which, in turn, modify the heat flux. The dynamics of vortex lines is the central topic in turbulent superfluid helium. The model is generalized to take into account the vortices in different cases of physical interest: rotating superfluids, counterflow superfluid turbulence, combined counterflow and rotation, and mass flow in addition to heat flow. To do this, the averaged vortex line density per unit volume L, is introduced and its dynamical equations are considered. Linear and non-linear evolution equations for L are written for homogeneous and inhomogeneous, isotropic and anisotropic situations. Several physical experiments are analyzed and the influence of vortices on the effective thermal conductivity of turbulent superfluid helium is found. Transitions from laminar to turbulent flows, from diffusive to ballistic regimes, from isotropic to anisotropic situations, are analyzed, thus providing a wide range of practical applications. Besides the steady-state effective thermal conductivity, the propagation of harmonic waves is also studied, motivated by the fact that vortex line density is experimentally detected via the attenuation of second sound and because it provides dynamical information on heat transport and thermal waves which complement the static information of the thermal conductivity.
DOAJ (DOAJ: Directory of Open Access Journals), May 1, 2019
In this paper we go ahead in our studies on refrigeration of nanosystems by superfluid helium, as... more In this paper we go ahead in our studies on refrigeration of nanosystems by superfluid helium, as an appealing subject for future applications to computers or astronautical precision nanodevices. We first recall the effective thermal conductivity in laminar counterflow superfluid helium through arrays of mutually parallel cylinders and we discuss the conditions for the appearance of quantum turbulence around the heatproducing cylinders. We then consider the cooling of an array of heat-producing cylindrical nanosystems by means of superfluid-helium counterflow. We discuss the upper bound on heat removal set by avoidance of quantum turbulence and avoidance of phase transition to normal He I, for arrays of cylinders placed between two infinite insulating plates and with heat flowing in the two dimensions parallel to such plates.
In this paper we show an exact solution (Kelvin wave) of an approximated dynamical equation for a... more 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
Monthly Notices of the Royal Astronomical Society, May 25, 2017
In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the ... more 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.
arXiv (Cornell University), Oct 22, 2013
The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled wi... more 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.
Physica D: Nonlinear Phenomena, Jun 1, 2020
We generalize the K − model of classical turbulence to superfluid helium. In a classical viscous ... more We generalize the K − model of classical turbulence to superfluid helium. In a classical viscous fluid the phenomenological eddy viscosity characterizing the effects of turbulence depends on the turbulent kinetic energy K and the dissipation function , which are mainly related to the fluctuations of the velocity field and of its gradient. In superfluid helium, instead, we consider the necessary coefficients for describing the effects of classical and quantum turbulence, involving fluctuations of the velocity, the heat flux, and the vortex line density of the quantized vortex lines. By splitting the several fields into a timeaverage part and a fluctuating part, some expressions involving the second moments of the turbulent fluctuations appear in the evolution equations for the average quantities. As in the K − model, a practical way of closing such equations is to tentatively express such fluctuating terms as a function of the average quantities. In this context we propose how the turbulent coefficients so introduced could depend on the second moments of the fluctuations of v, q and L (respectively denoted as K, K q and K L), and on their respective dissipation functions (related to the second moments of their gradients) , q and L .
Journal of Non-Equilibrium Thermodynamics, Mar 31, 2022
In a series of papers we have obtained results for nonlinear heat transport when thin wires excha... more 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.
arXiv (Cornell University), Jun 11, 2008
We include the effects of anisotropy and polarization in the hydrodynamics of inhomogeneous vorte... more 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 F ns between normal and superfluid components and to the vortex tension force ρ s 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.
Waves and Stability in Continuous Media, Apr 1, 2010
The aim of this work is to propose a simple mathematical model which is able to capture the pecul... more The aim of this work is to propose a simple mathematical model which is able to capture the peculiar behaviour of the rotating neutron star: glitches. This is made by using the knowledge on helium superfluid and particularly on rotating superfluid helium, which has interested many researchers over the years.
Journal of Mathematical Physics, Oct 1, 2021
We obtain some exact solutions in the context of solitons, for heat conduction with inertia along... more We obtain some exact solutions in the context of solitons, for heat conduction with inertia along a cylinder whose heat exchange with the environment is a non-linear function of the difference of temperatures of the cylinder and the environment, due to a flux-limiter behavior of the exchange. We study the consequences of heat transfer and information transfer along the wire, and we compare the situation with analogous solitons found in nonlinear lateral radiative exchange studied in some previous papers. We also find further exact solutions in terms of Weierstrass elliptic functions for the sake of completeness.
International Journal of Heat and Mass Transfer, Jul 1, 2020
The aim of this paper is to consider soliton propagation of heat signals along a cylinder whose h... more The aim of this paper is to consider soliton propagation of heat signals along a cylinder whose heat exchange with the environment is a non-linear function of the difference of temperatures of the cylinder and the environment and whose heat transfer along the system is described by the Maxwell-Cattaneo equation. To find the soliton solutions we use the auxiliary equation method. Our motivation is to obtain and compare the speed of propagation, the maximum rate of information transfer, and the energy necessary for the transfer of one bit of information for different solitons, by assuming that a localized soliton may carry a bit of information. It is shown that a given total power (energy/time) may be used either to send a few bits in a fast way, or many bits in a slower way. This may be controlled by choosing the initial condition imposed at one end of the wire.
Physics Letters, Aug 1, 2007
In this paper we show that a recent hydrodynamical model of superfluid turbulence describes vorte... more In this paper we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.
Acta Applicandae Mathematicae, Apr 1, 2023
We propose a mathematical interpolation between several regimes of energy cascade in quantum turb... more We propose a mathematical interpolation between several regimes of energy cascade in quantum turbulence in He II. On the basis of a physical interpretation of such mathematical expression we discuss in which conditions it is expected to appear an intermediate k 2 regime (equipartition regime) in the transition region between the hydrodynamic regime and the Kelvin wave regime (namely, between the k −5/3 and k −1 regions in coflow situations and between the k −3 and k −1 regions in counterflow situations). It is seen that if the energy rate transfer from the hydrodynamic region to the Kelvin wave region is sufficiently slow, such equipartition region will be present, but for higher values of such energy rate transfer it will disappear. For high rates of the energy rate transfer, the transition regime between the hydrodynamic and the Kelvin wave regimes will be monotonous, characterized by a negative exponent of k between −5/3 and −1 (or between −3 and −1), instead of the positive 2 exponent of the equipartition regime.
An hydrodynamical model previously proposed to describe the presence of vortices in counterflow s... more 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
Zeitschrift für Angewandte Mathematik und Physik, Jul 15, 2019
We analyze the stability of the temperature profile of an array of computing nanodevices refriger... more We analyze the stability of the temperature profile of an array of computing nanodevices refrigerated by flowing superfluid helium, under variations of temperature, computing rate, and barycentric velocity of helium. It turns out that if the variation of dissipated energy per bit with respect to temperature variations is higher than some critical values, proportional to the effective thermal conductivity of the array, then the steady-state temperature profiles become unstable and refrigeration efficiency is lost. Furthermore, a restriction on the maximum rate of variation of the local computation rate is found.
International Journal of Modern Physics D, Sep 6, 2015
Journal of Low Temperature Physics, Dec 1, 2016
We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simpli... more 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 T λ transition temperature and that quantum turbulence is avoided, in order not to have too high heat resistance.
International Journal of Heat and Mass Transfer, 2017
We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simpli... more 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 T λ transition temperature and that quantum turbulence is avoided, in order not to have too high heat resistance.
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Papers by Michele Sciacca