28 citations · 44 across the 10 of their papers we have counts for
4 papers · 1 filter
Optimizing performance of the deconvolution model reduction for large ODE systems
Lyudmyla L. Barannyk, Alexander Panchenko
We investigate the numerical performance of the regularized deconvolution closure introduced recently by the authors. The purpose of the closure is to furnish constitutive equation…
Deconvolution closure for mesoscopic continuum models of particle systems
Alexander Panchenko, Lyudmyla L. Barannyk, Kevin Cooper
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages s…
Closure method for spatially averaged dynamics of particle chains
Alexander Panchenko, Lyudmyla L. Barannyk, Robert P. Gilbert
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 equati…
Still states of bistable lattices, compatibility, and phase transition
Andrej Cherkaev, Andrei Kouznetsov, Alexander Panchenko
A two-dimensional bistable lattice is a periodic triangular network of non-linear bi-stable rods. The energy of each rod is piecewise quadratic and has two minima. Consequently, a…