1,721,112 research outputs found
A power-law model for nonlinear phonon hydrodynamics
No full textThe Guyer-Krumhansl equation for the heat flux is a phenomenological bridge between Fourier heat transport (for size of the system much bigger than the mean free path of heat carriers) and hydrodynamic heat transport (for size of the system comparable to the mean free path of heat carriers). The corresponding phonon hydrodynamics is analogous to Newtonian hydrodynamics, but with the velocity replaced by the heat flux, the pressure gradient replaced by the temperature gradient and the shear viscosity replaced by the square of the mean-free path divided by the thermal conductivity. In this paper, we propose a nonlinear generalization of the Guyer-Krumhansl equation and phonon hydrodynamics based on an analogy with the power-law model of non-Newtonian fluids leading to a non-diffusive behaviour of heat transport. On the basis of this model, we obtain the corresponding nonlinear effective thermal conductivity of the model, depending on the radius of the channel and on the temperature gradient. The present proposal could be useful in the light of recent analyses of Poiseuille phonon hydrodynamics which suggest a non-Newtonian behaviour
Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States
Full text linkIn 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
Nonlinear Guyer–Krumhansl equation and its boundary conditions in nanolayers
Full text linkThis paper deals with nonlinear effects in the Guyer-Krumhansl equation for nonlocal heat transport, both from the perspective of the boundary conditions (phonon-wall collisions) and of the bulk equation (phonon-phonon collisions) and explores their consequences on the effective thermal conductivity of nanosystems between two parallel layers or in two-dimensional ribbons. The nonlinearity arises from a dependence of the respective mean free paths on the values of the heat flux. The boundary conditions refer to slip heat flow along the limiting walls of the system, analogous to velocity slip flow along the walls in rarefied fluid dynamics. The effective thermal conductivity turns out to depend on the Knudsen numbers related to both mean free paths and on the temperature gradient
A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence
Full text linkWe 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
Nonlocal effects in superfluid turbulence: Application to the low-density-to high-density-state transition and to vortex decay
No full textNonequilibrium effective temperature of superfluid vortex tangle
No full textAn effective nonequilibrium temperature in counterflow superfluid turbulence is proposed, as a parameter characterizing a canonical probability distribution function of vortex orientation, and relating the diffusion coefficient of vortex lines to the vortex friction through an Einstein relation
Description and evolution of anisotropy in superfluid vortex tangles with counterflow and rotation
No full textWe examine several vectorial and tensorial descriptions of the geometry of turbulent vortex tangles. We study the anisotropy in rotating counterflow experiments, in which the geometry of the tangle is especially interesting because of the opposite effects of rotation, which orients the vortices, and counterflow, which
randomizes them. We propose to describe the anisotropy and the polarization of the vortex tangle through a tensor, which contains the first and second moments of the distribution of the unit vector s locally tangent to the vortex lines. We use an analogy with paramagnetism to estimate the anisotropy, the average polarization, the polarization fluctuations, and the geometrical contribution to the entropy of the tangle in terms of angular velocity and counterflow. We explore the influence of the geometry on the evolution of the vortex line density and propose evolution equations for the geometry of the tangle
Non-equilibrium temperature of well-developed quantum turbulence
No full textA non-equilibrium effective temperature of quantum vortex tangles is defined as the average energy of closed vortex loops. The resulting thermodynamic expressions for the entropy and the energy in terms of the temperature of the tangle are confirmed
by a microscopic analysis based on a potential distribution function for the length of vortex loops. Furthermore, these
expressions for the entropy and energy in terms of temperature are analogous to those of black holes: this may be of interest for
establishing further connections between topological defects in superfluids and cosmology
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