Several-temperature systems: extended irreversible thermodynamics and thermal wavefront propagation

Two-dimensional nonlinear nonequilibrium kinetic theory under steady heat conduction

“…[37,38,39,40,41,42,43,44] This model can be derived explicitly using a collision law of hardcore molecules, and the diameter of hard-core molecules is regarded as a distance between centers of monatomic molecules at contact. [37,38,42] In equilibrium states, experimental results including the temperature dependency can be fitted by the results from the line-ofcenters model.…”

“…[37,40,41] Under nonequilibrium situations such as gases under a heat flux or a shear flow, their pure nonequilibrium contributions to the rate of chemical reaction have also attracted much attention. [39,43,44,45,46,47,48,49] Since nonequilibrium correction terms of the chemical reaction rate are quadratic functions of nonequilibrium fluxes, the explicit nonequilibrium velocity distribution function of the Boltzmann equation for hard-core molecules to second order is needed to derive it based on the line-of-centers model. [39,43,45,46] The pure effect of a heat flux on the chemical reaction rate has been recently calculated using the second-order velocity distribution function of the Boltzmann equation for hard-core molecules.…”

“…[55,56,57,58] There are also several applications of information theory to chemically reacting gases. [39,43] However, some qualitative differences between information theory and the Boltzmann equation have been recently reported, and the invalidity of information theory as universal nonlinear nonequilibrium statistical mechanics has been demonstrated. [59] There have been no efforts to solve two-dimensional kinetic models to second order and discuss the two-dimensional second-order nonequilibrium phenomena, though twodimensional transport phenomena have created great interest.…”

Reaction–diffusion pulses: a combustion model

“…(b) F = −b(n − n 0 ) + A e −E/Rn , with b, k, E, R > 0. This term has been used in some combustion models [8][9][10][11], n being the temperature of the system. The linear term concerns the heat lost by convection, while the second one comes from the Arrhenius law [8,12].…”

A formula for the generalized Sato-Levine invariant

“…They appear in combustion [1], crystallization [2], superconductors [3], etc, and also have many biophysical applications (for a recent review, see [4]). Usually, one assumes that the reaction and diffusion parameters are uniform and steady.…”