Showing papers by "Kurt E. Shuler published in 1972"
TL;DR: In this article, the problem of the derivation of linear macroscopic laws from microscopic laws which are nonlinear in the dynamical variables has been discussed in the context of their results.
Abstract: We have investigated the conditions which must be imposed on the microscopic equations of motion to obtain exact linear laws for macroscopic (phase averaged) variables. The starting point in this study has been the lowest order master equation (Pauli equation) which is a linear microscopic equation in the state probabilities with a time‐independent transition matrix. Discrete and continuous variable master equations as well as their multivariate generalizations have been considered. In the case of continuum state variables, we have used various Fokker‐Planck equations and their corresponding Langevin equations as our starting microscopic equation of motion. In each case the conditions which must be imposed to obtain linear macroscopic transport equations have been derived and discussed. The problem of the derivation of linear macroscopic laws from microscopic laws which are nonlinear in the dynamical variables has been discussed in the context of our results. We find that exact linear macroscopic laws can...
27 citations
TL;DR: In this paper, an exponential relaxation of the momentum autocorrelation function of the mass defect particle was obtained for chains with finite number n of mass points and for nonzero values of n/M.
Abstract: Starting with the Hamiltonian for a linear harmonic chain of 2N particles of massm and one of massM, we have carried out numerical calculations for the momentum autocorrelation function of the mass defect particle for chains with finite numberN of mass points and for nonzero values of the mass ratioμ=m/M. These results have been compared with the well-known exponential relaxation of the momentum autocorrelation function which is found to be the rigorous result when passing to the thermodynamic and weak-coupling limit. In these limits, the dynamics of the mass defect particle is exactly described by a Fokker-Planck equation, i.e., a stochastic equation of motion. We have shown that, to an excellent approximation, an exponential relaxation of the momentum autocorrelation function is obtained for mass ratios as high asμ=0.1 and for chains with only 50 particles. Thus, for the harmonic chain considered here, the stochastic equations of motion can be applied to a very good approximation far outside the usually imposed thermodynamic and weak-coupling limits.
11 citations
TL;DR: In this article, a random walk model of interstitial diffusion of light impurity atoms in a host lattice of heavy atoms in the presence of a thermal gradient was developed to take account of the effect of the thermal gradient on the flux of impurity agents.
Abstract: We have developed a random walk model of interstitial diffusion of light impurity atoms in a host lattice of heavy atoms in the presence of a thermal gradient. To take account of the effect of the thermal gradient on the flux of impurity atoms we introduce a bias in the jump direction of the interstitial impurity. We assume that this bias is due to the temperature dependence of the excluded volume effects which arise during the jump of the impurity atom between interstitial sites. The resulting random walk equation for thermal diffusion is consistent with both positive and negative heats of transport in agreement with experimental data. Using a cell model approach and the assumption of local equilibrium, we then develop equations which permit the calculation of the bias in jump direction. The theory of interstitial diffusion developed here clarifies and supports the classic Wirtz model for interstitial thermal diffusion.
11 citations