Related papers: Coarse Stability and Bifurcation Analysis Using St…
Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for…
We present a computer-assisted approach to locating approximate coarse optimal switching policies between stationary states of chemically reacting systems described by microscopic/stochastic evolution rules. The ``coarse time-stepper"…
Over the past few years it has been demonstrated that "coarse timesteppers" establish a link between traditional numerical analysis and microscopic/ stochastic simulation. The underlying assumption of the associated…
We address an iterative procedure that can be used to detect coarse-grained hyperbolic unstable equilibria (saddle points) of microscopic simulators when no equations at the macroscopic level are available. The scheme is based on the…
We present a computer-assisted approach to approximating coarse optimal switching policies for systems described by microscopic/stochastic evolution rules. The coarse timestepper constitutes a bridge between the underlying kinetic Monte…
We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain…
We demonstrate how time-integration of stochastic differential equations (i.e. Brownian dynamics simulations) can be combined with continuum numerical bifurcation analysis techniques to analyze the dynamics of liquid crystalline polymers…
The arc-length continuation framework is used for the design of state feedback control laws that enable a microscopic simulator trace its own open-loop coarse bifurcation diagram. The steering of the system along solution branches is…
If a stochastic system during some periods of its evolution can be divided into non-interacting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
The parametric behavior of regular periodic arrays of rising bubbles is investigated with the aid of 2-dimensional BGK Lattice-Boltzmann (LB) simulators. The Recursive Projection Method is implemented and coupled to the LB simulators,…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…
Kinetic approaches are routinely employed to simulate the dynamics of systems that are too rarified to be described by the Navier-Stokes equations. However, generally they are far too computationally expensive to be applied for systems that…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of…
We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…