A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page

Analysis of Coupled Bending-Torsional Vibration of Beams in the Presence of Uncertainties

Several methods are presented for the modeling and analysis of uncertain beams and other structural elements/systems. By representing each uncertain parameter as an interval number, the vibration problem associated with any uncertain system can be expressed in the form of a system of nonlinear interval equations. The resulting equations can be solved using the exact or a truncation-based interval analysis method. An universal grey number-based approach and an interval-discretization method are proposed to obtain more efficient and/or more accurate solutions. Specifically, the problem of the coupled bending-torsional vibration of a beam involving uncertainties is considered. It is found that the range of the solution (response) increases with increasing levels of uncertainty in all the methods. Numerical examples are presented to illustrate the computational aspects of the methods presented and also to indicate the high accuracy of the interval-discretization approach in finding the solution of practical uncertain systems. The results given by the different interval analysis methods (including the universal grey number-based analysis) are compared with those given by the Monte Carlo method (probabilistic approach) and the results are found to be in good agreement with those given by the interval analysis-based methods for similar data

Simulation tools for calculating loss in microstructured optical fibers

We apply the Finite-Difference Time-Domain algorithm to the problem of calculating modal loss in microstructured optical fibers. We use periodic boundary conditions in the longitudinal direction to isolate a mode that decays through transverse perfectly-matched layerboundaries. The loss coefficient is extracted by a direct monitoring of the energy enclosed in the simulation domain. Predictions of the method are compared to results from beam propagation and multipole approaches, and finally the tool is applied to fibers containing elliptical air holes.8 page(s