System In Local Equilibrium Research Articles

Heat conduction across 1D nano film: Local thermal conductivity and extrapolation length

We analyze the short scale effects on the 1D steady-state heat conduction across a nano film using discrete variable model (DVM). The DVM allows for both diffusive and ballistic components of energy transport and can be used to study far from local equilibrium systems when the characteristic space and time scales of interest are of the order of or even smaller than the mean free path and mean free time of energy carriers, respectively. This is particularly important for the performance evaluation of modern thermal nano systems and microdevices, which usually operate on an extremely short space scale. Thermal extrapolation length and local (position-dependant) thermal conductivity are introduced to virtually eliminate the temperature jump at the boundaries with thermal baths. We also analyze the effects of the film thickness on the bulk effective thermal conductivities and effective boundary conductance to describe the transition from diffusive to ballistic heat transfer. The results are compared with other theories and available experimental data.

A derivation of Maxwell's equations using the Heaviside notation.

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E-fields and B-fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism.This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

Clausius' entropy revisited

Conventional nonequilibrium thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper, fluids will be considered in a state of local equilibrium. We argue that the main feature of such systems is not the entropy production, but the organization of the flowing currents in such systems. These currents do not only have entropy production, but must also have an organization needed to flow in a certain direction. It is the latter, which is the source of the equilibrium entropy, when the fluid goes from a local equilibrium state to an equilibrium state. This implies a transmutation of the local equilibrium currents' organization into the equilibrium entropy. Alternatively, when a fluid goes from an equilibrium state to a local equilibrium state, its entropy transmutes into the organization of the currents of that state.

Transfer coefficients for the liquid–vapor interface of a two-component mixture

We present the excess entropy production for heat and mass transport across an interface of a non-ideal two-component mixture, using as interface variables the excess densities proposed by Gibbs. With the help of these variables we define the interface as an autonomous system in local equilibrium and study its transport properties. The entropy production determines the conjugate fluxes and forces, and equivalent forms are given. The forms contain finite differences of intensive variables into and across the surface as driving forces. These expressions for the fluxes serve as boundary conditions for integration across heterogeneous systems that are far from global equilibrium. The resistivities to heat transfer and the coupling coefficients for heat and mass transfer were determined using non-equilibrium molecular dynamics (NEMD) simulations in a system of Lennard-Jones spline particles of the same diameter and mass, but with potential depths that differ by a factor 0.8. The coupling coefficients for heat and mass transfer are significant. A relation of the coupling coefficients and the partial molar enthalpy of evaporation is verified for each component. As a consequence, it is not sufficient to use for instance Fourier's law for transport of heat across surfaces. Support is presented for a new method to find coefficients from integral relations. The method was verified using one of the NEMD coefficients, and used to calculate contributions to the remaining resistivities. One would expect kinetic theory to predict the resistivities at low vapor densities, but this is found to be correct only for the thermal resistivity. The interfacial heat and mass transfer coefficients are found to differ widely from kinetic theory predictions. Estimates of the resistivities to mass transfer differ by more than an order of magnitude. These results will have a bearing on the dynamic modeling of evaporation/condensation and desorption/adsorption.

Glass does not play dice: observation of non-random organization of atomic bond tensions in glasses

Self-organization of normal forces under various external stresses (compression, shear) has been extensively studied for granular materials and recently also for liquids and glasses. In order to address this self-organization on an atomic level, we introduced a new parameter, the atomic bond tension (ABT) tensor, that takes into account the magnitudes and the directions associated with “bonds” between an atom and its neighbors. Simulations of four different glassy systems in local equilibrium show that the eigenvalues of ABT tensor belonging to the same atom are correlated on average, favoring local isotropy of normal forces. The strength of these correlations increases with the tendency of the system to be a good glass former.

Photon intensity interferometry for expanding sources

Using Quantum Field Theory we derive a general formula for the double inclusive spectra of photons radiated by a system in local equilibrium. The derived expression differs significantly from the one mostly used up to now in photon intensity interferometry of heavy-ion collisions. We present a covariant expression for double inclusive spectra adapted for usage in numerical simulations. Application to a schematic model with a Bjørken-type expansion gives strong evidence for the need of reinvestigating photonphoton correlations for expanding sources.