Physics – Mathematical Physics
Scientific paper
2010-10-23
Physics
Mathematical Physics
19 pages, 11 figures
Scientific paper
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the balance equations for spatial averages obtained earlier by a number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum balance equation contains a flux (stress), which is given by an exact function of particle positions and velocities. We propose a method for approximating this function by a sequence of operators applied to average density and momentum. The resulting approximate mesoscopic models are systems in closed form. The closed from property allows one to work directly with the mesoscale equaitons without the need to calculate underlying particle trajectories, which is useful for modeling and simulation of large particle systems. The proposed closure method utilizes the theory of ill-posed problems, in particular iterative regularization methods for solving first order linear integral equations. The closed from approximations are obtained in two steps. First, we use Landweber regularization to (approximately) reconstruct the interpolants of relevant microscale quantitites from the average density and momentum. Second, these reconstructions are substituted into the exact formulas for stress. The developed general theory is then applied to non-linear oscillator chains. We conduct a detailed study of the simplest zero-order approximation, and show numerically that it works well as long as fluctuations of velocity are nearly constant.
Barannyk Lyudmyla L.
Gilbert Robert P.
Panchenko Alexander
No associations
LandOfFree
Closure method for spatially averaged dynamics of particle chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Closure method for spatially averaged dynamics of particle chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Closure method for spatially averaged dynamics of particle chains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-115515