D. Jou
Universitat Autònoma de Barcelona, Departament de Fisica, Faculty Member
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ABSTRACT 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... more
ABSTRACT 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 the tube becomes comparable with the phonon mean free path; this implies a reduction of the thermal resistance with respect to that obtained for nonslip boundary conditions.
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... The direct influence of the viscous pressure tensor and other fluxes, such as heat flux or diffusion flux, on the thermodyn-amic potentials clearly opens a way towardsthermodynamics under flow. 2.1 Basic Rheological Quantities ...
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The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We propose a... more
The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We propose a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means that the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.
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ABSTRACT In Chap. 2 , we postulated the existence of a generalised entropy which is compatible with some classes of evolution equations for the fluxes. Otherwise stated, our formalism aims to describe the class of processes which are... more
ABSTRACT In Chap. 2 , we postulated the existence of a generalised entropy which is compatible with some classes of evolution equations for the fluxes. Otherwise stated, our formalism aims to describe the class of processes which are compatible with the existence of a non-equilibrium entropy whose rate of production is non-negative. Once the expression of the entropy is known, there is no difficulty in deriving the corresponding equations of state, which are directly obtained as the first derivatives of the entropy with respect to the basic variables. A natural question concerns the physical meaning of these equations of state, which, of course, depend on the fluxes and therefore differ from their analogous local-equilibrium expressions. In classical thermodynamics, it is known that the derivative of the entropy with respect to the internal energy (by keeping fixed the volume and the composition of the system) is the reciprocal of the absolute temperature; the derivatives with respect to the volume and to the number of moles yield the equilibrium pressure and (with a minus sign) the chemical potentials respectively (divided by the absolute temperature). It may then be asked whether the derivatives of the generalised entropy introduced in extended irreversible thermodynamics (EIT) still allow an absolute temperature to be defined, as well as a non-equilibrium pressure and a non-equilibrium chemical potential. Another important problem is to determine whether the non-equilibrium temperature and pressure are measurable by a thermometer and a manometer. These are subtle and unsolved problems which have however received partial answers during the last years stimulated by recent developments in glasses, granular matter, flowing suspensions, nuclear collisions, nano-systems, molecular dynamics and computer simulations, or in the analysis of fluctuations. The objective of the present chapter is to better apprehend the physical meaning of the generalised entropy and to pay detailed attention to the nature of the corresponding equations of state.
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We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat... more
We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat conduction in nanowires of different cross sections and in thin layers is analyzed, and the dependence of the thermal conductivity on the geometry, as well as on the roughness is pointed out. We also analyze the effects of the roughness of the surface of the pores on the thermal conductivity of porous silicon. Thermoelectric effects are considered as well.In memory of Professor Carlo Cercignani
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In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions–each of them at different temperatures–and there are only few collisions, in such a way that... more
In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions–each of them at different temperatures–and there are only few collisions, in such a way that equilibrium between the different populations will be reached very slowly. Here, we tentatively approach the local distribution function by a superposition of local-equilibrium distribution functions with different temperatures, corresponding to the different starting positions of the particles. In a second-order expansion, we find a distribution function which depends not only on the Hamiltonian H but also on H2, and we study the additional contribution to energy fluctuations.
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The influence of a flow on the transfer of a polymer solution from a porous matrix to a flowing fluid is analysed. Since the flow modifies the free energy of the solution, through stretching and orientation of the macromolecules, the... more
The influence of a flow on the transfer of a polymer solution from a porous matrix to a flowing fluid is analysed. Since the flow modifies the free energy of the solution, through stretching and orientation of the macromolecules, the thermodynamic driving force for polymer transport is modified with respect to that of a quiescent fluid. The consequences of this
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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... more
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.
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ABSTRACT The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General... more
ABSTRACT The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General boundary conditions are obtained from the constraint imposed by the second law of thermodynamics expressing that the global entropy production is non-negative. In parallel, evolution equations for the heat flux inside the bulk of the system are also formulated.
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A binary mixture of ideal gases in Couette flow is studied in the framework of information theory. It is shown that if the total shear viscous pressure is imposed as a constraint, there is equipartition of energy between the different... more
A binary mixture of ideal gases in Couette flow is studied in the framework of information theory. It is shown that if the total shear viscous pressure is imposed as a constraint, there is equipartition of energy between the different chemical species but not amongst the different spatial directions. In contrast, if a same shear rate is imposed on both species, there is no equipartition between species neither amongst spatial directions. In both situations, the thermodynamic temperature, defined from the Lagrange multiplier conjugated to the internal energy, is the same for both species, independently of the equality or not of their local-equilibrium temperature.
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Fast phase transitions under lack of local thermalization between successive elementary steps of the physical process are treated analytically. Non-Markovian master equations are derived for fast processes, which do not have enough time... more
Fast phase transitions under lack of local thermalization between successive elementary steps of the physical process are treated analytically. Non-Markovian master equations are derived for fast processes, which do not have enough time to reach energy or momentum thermalization during rapid phase change or freezing of a highly nonequilibrium system. These master equations provide a further physical basis for evolution and transport equations of the phase-field model used previously in the analyses of fast phase transitions.
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We discuss the thermodynamic aspects of a simple model of cosmic string loops, whose energy is nonlinearly related to their lengths. We obtain in a direct way an equation of state having the form p=-(1+α)Ï/3, with Ï the energy density... more
We discuss the thermodynamic aspects of a simple model of cosmic string loops, whose energy is nonlinearly related to their lengths. We obtain in a direct way an equation of state having the form p=-(1+α)Ï/3, with Ï the energy density and 1+α the exponent which relates the energy u{sub l} of a loop with its length l as u{sub l}âl{sup 1+α}. In the linear situation (α=0) one has p=-Ï/3, in the quadratic one (α=1) p=-2Ï/3, and in the cubic case (α=2) p=-Ï. For all values of α the entropy goes as Sâ(2-α)L³² (L being the string length density). The expression of S is useful to explore the behavior of such string loops under adiabatic expansion of the Universe. Thermodynamic stability suggests that the gas of string loops must coexist with several long strings, longer than the horizon radius.
Research Interests: Field Theory, Quantum Physics, Thermodynamics, Quantum Mechanics, High Energy Density Physics, and 10 moreEarly Universe, Dark Energy, Mathematical Model, Thermodynamic Stability, Irreversible Thermodynamics, Cosmic String, Physical Properties, Equation of State, Elementary Particles, and energy density
ABSTRACT We propose a generalized Einstein-Planck relation for photons which is invariant under the change λ/alP to alP/λ, λ being the photon wavelength, lP Planck’s length, and a a numerical constant. This yields a wavelength-dependent... more
ABSTRACT We propose a generalized Einstein-Planck relation for photons which is invariant under the change λ/alP to alP/λ, λ being the photon wavelength, lP Planck’s length, and a a numerical constant. This yields a wavelength-dependent speed of light v(λ)=c/(1+a2(lP/λ)2), with c the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum fluctuations of the space-time, as well as its consequences on Heisenberg’s uncertainty principle up to second order in lP.
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Equations of state and transport equations in viscous cosmological models. ... Phys. (NY) 100, 310 (1973). 1600 48 EQUATIONS OF STATE AND TRANSPORT EQUATIONS IN ... ...
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A heat-transport equation incorporating nonlocal and nonlinear contributions of the heat flux is derived in the framework of weakly nonlocal nonequilibrium thermodynamics. The motivation for these terms arises from applications to... more
A heat-transport equation incorporating nonlocal and nonlinear contributions of the heat flux is derived in the framework of weakly nonlocal nonequilibrium thermodynamics. The motivation for these terms arises from applications to nanosystems, where strong gradients are found, due to the small distance over which changes in temperature and heat flux take place. This equation generalizes to the nonlinear domain previous
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We 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... more
We 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{sup '} 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.
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... Thermodyn. 20 (1995), p. 103. Full Text via CrossRef AS Vasconcellos, R. Luzzi and LS Garcia-Colin, J. Non-Equilib. Thermodyn. 20 (1995), p. 119. ... Phys. (Japan) 33 (1965), p. 423. Full Text via CrossRef. R. Luzzi, AR Vasconcellos,... more
... Thermodyn. 20 (1995), p. 103. Full Text via CrossRef AS Vasconcellos, R. Luzzi and LS Garcia-Colin, J. Non-Equilib. Thermodyn. 20 (1995), p. 119. ... Phys. (Japan) 33 (1965), p. 423. Full Text via CrossRef. R. Luzzi, AR Vasconcellos, D. Jou and J. Casas-Vazquez, Phys. Rev. ...
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ABSTRACT In a recent paper by Gaspard et al. [Physica A 323 (2003) 294] it was shown in detail that the Lorentz diffusive gas is compatible with irreversible thermodynamics at the local-equilibrium level of description. In this short note... more
ABSTRACT In a recent paper by Gaspard et al. [Physica A 323 (2003) 294] it was shown in detail that the Lorentz diffusive gas is compatible with irreversible thermodynamics at the local-equilibrium level of description. In this short note we point out that this compatibility with irreversible thermodynamics remains valid, but with a larger domain of physical situations, when one includes in the entropy second-order terms of the diffusion flux.
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ABSTRACT In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of... more
ABSTRACT In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the Liu method of Lagrange multipliers. The form of the entropy and the entropy flux are compared with those obtained in the maximum-entropy formalism. The several non-local terms are discussed in detail to clarify their physical meaning, and an experiment is proposed to check their actual existence and measure their values.
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A phenomenological generalization of the well known Vinen equation for the evolution of vortex line density in superfluid counterflow turbulence is proposed. This generalization includes nonlinear production terms in the counterflow... more
A phenomenological generalization of the well known Vinen equation for the evolution of vortex line density in superfluid counterflow turbulence is proposed. This generalization includes nonlinear production terms in the counterflow velocity and corrections depending on the diameter of the tube. The equation provides a unified framework for the various phenomena (stationary states and transitions) present in counterflow superfluid turbulence:
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The authors outline an approach to irreversible thermodynamics leading to a covariant evolution equation for the four-flux of heat in a relativistic non-viscous simple fluid. This relation results in a non-trivial generalisation of the... more
The authors outline an approach to irreversible thermodynamics leading to a covariant evolution equation for the four-flux of heat in a relativistic non-viscous simple fluid. This relation results in a non-trivial generalisation of the classical case.
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We study the behaviour of the thermal conductivity for an ideal ultra-relativistic gas far from equilibrium by using information theory and the fluctuation-dissipation theorem in nonequilibrium steady states. We compare two different... more
We study the behaviour of the thermal conductivity for an ideal ultra-relativistic gas far from equilibrium by using information theory and the fluctuation-dissipation theorem in nonequilibrium steady states. We compare two different proposals for the nonlinear generalization of the fluctuation-dissipation theorem to the far-from-equilibrium regime. Both proposals lead to a saturation of the heat flux for high temperature gradients, but
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A new, simple and physically transparent derivation of thermodynamics and hydrodynamics of radiating fluids is presented. The hydrodynamics is then extended to strongly inhomogeneous radiating fluids. The presence of inhomogeneities gives... more
A new, simple and physically transparent derivation of thermodynamics and hydrodynamics of radiating fluids is presented. The hydrodynamics is then extended to strongly inhomogeneous radiating fluids. The presence of inhomogeneities gives rise, among other changes, to new stresses (the stresses that are added to the classical Eddington stresses). The physical basis of the analysis is the requirement that solutions to
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... Rev E 48 (1993), 310-321. [23] Camacho, J., Thermodynamic functions for Taylor dispersion, Phys. ... Phys., 34 (1993), 3012-3029. [29] Chimento, LP, Jakubi, AS, Cosmological solutions of the Einstein equation with a causal viscous... more
... Rev E 48 (1993), 310-321. [23] Camacho, J., Thermodynamic functions for Taylor dispersion, Phys. ... Phys., 34 (1993), 3012-3029. [29] Chimento, LP, Jakubi, AS, Cosmological solutions of the Einstein equation with a causal viscous fluid, Class Quant. ...