Results 1 - 10 of 2,507

SOME CRITICAL ISSUES FOR THE “EQUATION-FREE” APPROACH TO MULTISCALE MODELING

by Weinan E, Eric Vanden-eijnden
"... The “equation-free” approach has been proposed in recent years as a general framework for developing multiscale methods for efficiently capturing the macroscale behavior of a system using only the microscale models. In this paper, we take a close look at some of the algorithms proposed under the “eq ..."
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The “equation-free” approach has been proposed in recent years as a general framework for developing multiscale methods for efficiently capturing the macroscale behavior of a system using only the microscale models. In this paper, we take a close look at some of the algorithms proposed under

An equation-free approach to coupled oscillator dynamics: the Kuramoto model example

by Sung Joon Moon, Ioannis G. Kevrekidis , 2005
"... We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, Springer-Verlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space of ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, Springer-Verlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space

An equation-free approach to nonlinear control: feedback linearization with poleplacement

by Constantinos I. Siettos, Ioannis G. Kevrekidis, Nikolaos Kazantzis - International Journal of Bifurcations and Chaos , 2005
"... We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the solution of a functional equation involving the macroscopic (coarse ..."
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We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the solution of a functional equation involving the macroscopic

Multiscale analysis of reentrant production lines: An equation-free approach, Phys

by Y Zou , I G Kevrekidis , D Armbruster - A: Statist. Mech. Appl , 2008
"... Abstract The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to competition for processing capacity among the items produ ..."
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advantage of the time scale separation to directly solve such coarse-grained equations, even when we cannot derive them explicitly, through an equation-free computational approach. Short bursts of appropriately initialized stochastic fine-scale simulation are used to perform coarse projective integration

Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation

by Radek Erban, Ioannis G. Kevrekidis, David Adalsteinsson, Timothy C. Elston - J. Chem. Phys , 2006
"... Abstract: We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to ..."
Abstract - Cited by 24 (10 self) - Add to MetaCart
. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarsegrained behavior of certain classes of complex stochastic models of gene regulatory networks

unknown title

by Y. Zou, I. G. Kevrekidis, D. Armbruster , 2005
"... Multiscale analysis of re-entrant production lines: An equation-free approach ..."
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Multiscale analysis of re-entrant production lines: An equation-free approach

Equation-free, multiscale computation for unsteady random diffusion. Multiscale Model

by Dongbin Xiu, Ioannis, G. Kevrekidis - Simul , 2005
"... Abstract. We present an “equation-free ” multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast in the form of stochastic differential equations. A ..."
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Abstract. We present an “equation-free ” multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast in the form of stochastic differential equations. A

A Signal Processing Approach To Fair Surface Design

by Gabriel Taubin , 1995
"... In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fai ..."
Abstract - Cited by 654 (15 self) - Add to MetaCart
In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing

Micro to Macro Equation-Free Bifurcation Analysis of Neuronal Random Graphs: Symmetry Breaking of Majority Rule Dynamics

by Konstantinos Spiliotis, Lucia Russo, Constantinos I. Siettos
"... We address how the Equation-Free approach can be exploited to bridge in a computational rigorous way the micro to macro scales of the dynamics of stochastic individualistic neuronal models evolving on complex random graphs. In particular, we show how bifurcation analysis can be performed bypassing t ..."
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We address how the Equation-Free approach can be exploited to bridge in a computational rigorous way the micro to macro scales of the dynamics of stochastic individualistic neuronal models evolving on complex random graphs. In particular, we show how bifurcation analysis can be performed bypassing

Practical animation of liquids

by Nick Foster, Dimitri Metaxas - Graphical Models and Image Processing , 1996
"... We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier-Stokes equations which couple momentum and mass con ..."
Abstract - Cited by 445 (26 self) - Add to MetaCart
We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier-Stokes equations which couple momentum and mass
Results 1 - 10 of 2,507