In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to… (More)

By Jaime Cisternas1,2†, C. William Gear2,3, Simon Levin4 and Ioannis G. Kevrekidis1,2 1Program in Applied and Computational Mathematics and 2Department of Chemical Engineering, Princeton University,… (More)

We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A… (More)

Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which… (More)

In the context of the recently developed “equation-free” approach to the computerassisted analysis of complex systems, we illustrate the computation of coarsely selfsimilar solutions. Dynamic… (More)

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by… (More)

In “equation-free” multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations… (More)

We describe and implement a computer-assisted approach for accelerating the exploration of uncharted effective free-energy surfaces (FESs). More generally, the aim is the extraction of… (More)

In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which… (More)

This note reports on a scheme for interpolating the boundary conditions between non-adjacent modeling regions when the model is based on Monte-Carlo computations of a collection of particles. The… (More)