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Volumn 30, Issue 10-12, 2006, Pages 1632-1642

A systems-based approach to multiscale computation: Equation-free detection of coarse-grained bifurcations

Author keywords

Bifurcation; Equation free; Multiscale

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); CATALYSIS; COMPUTATION THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; REACTION KINETICS;

EID: 33747887361     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2006.05.019     Document Type: Article
Times cited : (17)

References (50)
  • 1
    • 0001795886 scopus 로고
    • An efficient algorithm for the determination of certain bifurcation points
    • Abbot P.J. An efficient algorithm for the determination of certain bifurcation points. Journal of Computational and Applied Mathematics 4 (1978) 19-26
    • (1978) Journal of Computational and Applied Mathematics , vol.4 , pp. 19-26
    • Abbot, P.J.1
  • 2
    • 0022661079 scopus 로고
    • Local feedback stabilization and bifurcation control. I. Hopf bifurcation
    • Abed E.H., and Fu J.H. Local feedback stabilization and bifurcation control. I. Hopf bifurcation. Systems and Control Letters 7 (1986) 11-17
    • (1986) Systems and Control Letters , vol.7 , pp. 11-17
    • Abed, E.H.1    Fu, J.H.2
  • 3
    • 0023346390 scopus 로고
    • Local feedback stabilization and bifurcation control. II. Stationary bifurcation
    • Abed E.H., and Fu J.H. Local feedback stabilization and bifurcation control. II. Stationary bifurcation. Systems and Control Letters 8 (1986) 467-473
    • (1986) Systems and Control Letters , vol.8 , pp. 467-473
    • Abed, E.H.1    Fu, J.H.2
  • 5
    • 27444435456 scopus 로고    scopus 로고
    • Equation-free optimal switching policies for bistable reacting systems using coarse time-steppers
    • Armaou A., and Kevrekidis I.G. Equation-free optimal switching policies for bistable reacting systems using coarse time-steppers. International Journal of Robust and Nonlinear Control 15 (2005) 713-726
    • (2005) International Journal of Robust and Nonlinear Control , vol.15 , pp. 713-726
    • Armaou, A.1    Kevrekidis, I.G.2
  • 6
    • 15944420251 scopus 로고    scopus 로고
    • Equation-free gaptooth-based controller design for distributed complex/multiscale systems
    • Armaou A., Kevrekidis I.G., and Theodoropoulos C. Equation-free gaptooth-based controller design for distributed complex/multiscale systems. Computers & Chemical Engineering 29 (2005) 731-740
    • (2005) Computers & Chemical Engineering , vol.29 , pp. 731-740
    • Armaou, A.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 9
    • 0039523241 scopus 로고
    • Stability and multiplicity of solutions to discretizations of nonlinear ordinary-differential equations
    • Beyn W.J., and Doedel E.J. Stability and multiplicity of solutions to discretizations of nonlinear ordinary-differential equations. SIAM Journal on Scientific and Statistical Computing 2 (1981) 107-120
    • (1981) SIAM Journal on Scientific and Statistical Computing , vol.2 , pp. 107-120
    • Beyn, W.J.1    Doedel, E.J.2
  • 12
    • 0003180233 scopus 로고    scopus 로고
    • Just in time learning and estimation
    • Bittani S., and Picci G. (Eds), Springer
    • Cybenko G. Just in time learning and estimation. In: Bittani S., and Picci G. (Eds). Identification, adaptation, learning (NATO ASI) (1996), Springer 423-434
    • (1996) Identification, adaptation, learning (NATO ASI) , pp. 423-434
    • Cybenko, G.1
  • 14
  • 15
    • 0346685924 scopus 로고    scopus 로고
    • Reduction and identification methods for Markovian control systems, with application to thin film deposition
    • Gallivan M.A., and Murray R.M. Reduction and identification methods for Markovian control systems, with application to thin film deposition. International Journal of Robust and Nonlinear Control 14 (2004) 113-132
    • (2004) International Journal of Robust and Nonlinear Control , vol.14 , pp. 113-132
    • Gallivan, M.A.1    Murray, R.M.2
  • 16
    • 0037104864 scopus 로고    scopus 로고
    • Coarse integration/bifurcation analysis via microscopic simulators
    • Gear C.W., Kevrekidis I.G., and Theodoropoulos C. Coarse integration/bifurcation analysis via microscopic simulators. Comp. Chem. Eng. 26 (2002) 941-963
    • (2002) Comp. Chem. Eng. , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 17
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • Gillespie D.T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22 (1976) 403-434
    • (1976) Journal of Computational Physics , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 18
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81 (1977) 2340-2361
    • (1977) Journal of Physical Chemistry , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 21
    • 0033707050 scopus 로고    scopus 로고
    • Bifurcation control via state feedback for systems with a single uncontrollable mode
    • Kang W. Bifurcation control via state feedback for systems with a single uncontrollable mode. SIAM Journal on Control and Optimization 38 (2000) 1428-1452
    • (2000) SIAM Journal on Control and Optimization , vol.38 , pp. 1428-1452
    • Kang, W.1
  • 22
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and non-linear eigenvalue problems
    • Rabinowitz P.H. (Ed), Academic Press, New York
    • Keller H.B. Numerical solution of bifurcation and non-linear eigenvalue problems. In: Rabinowitz P.H. (Ed). Applications of bifurcation theory (1977), Academic Press, New York 359-384
    • (1977) Applications of bifurcation theory , pp. 359-384
    • Keller, H.B.1
  • 26
    • 0032290723 scopus 로고    scopus 로고
    • Useful nonlinearities and global stabilization of bifurcations in a model of jet engine surge and stall
    • Krstić M., Fontaine D., Kokotović P.V., and Paduano J.D. Useful nonlinearities and global stabilization of bifurcations in a model of jet engine surge and stall. IEEE Transactions on Automatic Control 43 (1998) 1739-1745
    • (1998) IEEE Transactions on Automatic Control , vol.43 , pp. 1739-1745
    • Krstić, M.1    Fontaine, D.2    Kokotović, P.V.3    Paduano, J.D.4
  • 27
    • 0033906528 scopus 로고    scopus 로고
    • Stability of extremum seeking feedback for general nonlinear dynamic systems
    • Krstić M., and Wang H.H. Stability of extremum seeking feedback for general nonlinear dynamic systems. Automatica 36 (2000) 595-601
    • (2000) Automatica , vol.36 , pp. 595-601
    • Krstić, M.1    Wang, H.H.2
  • 29
    • 33747886866 scopus 로고    scopus 로고
    • Lee, H-C. (1991). Robust control of bifurcating nonlinear systems with applications. Ph.D. thesis, University of Maryland.
  • 30
    • 0035279015 scopus 로고    scopus 로고
    • Recursive least squares and accelerated convergence in stochastic approximation schemes
    • Ljung L. Recursive least squares and accelerated convergence in stochastic approximation schemes. International Journal of Adaptive Control and Signal Processing 15 (2001) 169-178
    • (2001) International Journal of Adaptive Control and Signal Processing , vol.15 , pp. 169-178
    • Ljung, L.1
  • 31
    • 13444304351 scopus 로고    scopus 로고
    • Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation
    • Lou Y.M., and Christofides P.D. Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation. Computers & Chemical Engineering 29 (2005) 741-759
    • (2005) Computers & Chemical Engineering , vol.29 , pp. 741-759
    • Lou, Y.M.1    Christofides, P.D.2
  • 33
    • 0037162264 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples
    • Makeev A.G., Maroudas D., and Kevrekidis I.G. Coarse stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples. Journal of Chemical Physics 116 (2002) 10083-10091
    • (2002) Journal of Chemical Physics , vol.116 , pp. 10083-10091
    • Makeev, A.G.1    Maroudas, D.2    Kevrekidis, I.G.3
  • 34
    • 33745342032 scopus 로고    scopus 로고
    • Nadler, B., Lafon, S., Coifman, R. C., & Kevrekidis, I. G. (2006). Diffusion maps, spectral clustering and the reaction coordinates of dynamical systems. Applied and Computational Harmonic Analysis, in press.
  • 35
    • 0141527410 scopus 로고    scopus 로고
    • Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems
    • Nagy Z.K., and Braatz R.D. Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems. IEEE Transactions on Control Systems Technology 11 (2003) 494-504
    • (2003) IEEE Transactions on Control Systems Technology , vol.11 , pp. 494-504
    • Nagy, Z.K.1    Braatz, R.D.2
  • 36
    • 13444263244 scopus 로고    scopus 로고
    • Dynamics and control of thin film surface microstructure in a complex deposition process
    • Ni D., and Christofides P.D. Dynamics and control of thin film surface microstructure in a complex deposition process. Chemical Engineering Science 60 (2005) 1603-1617
    • (2005) Chemical Engineering Science , vol.60 , pp. 1603-1617
    • Ni, D.1    Christofides, P.D.2
  • 37
    • 13444249983 scopus 로고    scopus 로고
    • Multivariable predictive control of thin film deposition using a stochastic PDE model
    • Ni D., and Christofides P.D. Multivariable predictive control of thin film deposition using a stochastic PDE model. Industrial and Engineering Chemistry Research 44 (2005) 2416-2427
    • (2005) Industrial and Engineering Chemistry Research , vol.44 , pp. 2416-2427
    • Ni, D.1    Christofides, P.D.2
  • 40
    • 0000015457 scopus 로고    scopus 로고
    • Effective bifurcation analysis: A time-stepper-based approach
    • Runborg O., Theodoropoulos C., and Kevrekidis I.G. Effective bifurcation analysis: A time-stepper-based approach. Nonlinearity 15 (2002) 491-511
    • (2002) Nonlinearity , vol.15 , pp. 491-511
    • Runborg, O.1    Theodoropoulos, C.2    Kevrekidis, I.G.3
  • 42
    • 0027641824 scopus 로고
    • Stabilization of unstable procedures-The recursive projection method
    • Shroff G.M., and Keller H.B. Stabilization of unstable procedures-The recursive projection method. SIAM Journal on Numerical Analysis 30 (1993) 1099-1120
    • (1993) SIAM Journal on Numerical Analysis , vol.30 , pp. 1099-1120
    • Shroff, G.M.1    Keller, H.B.2
  • 43
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and coarse control: A kinetic Monte Carlo example
    • Siettos C.I., Armaou A., Makeev A.G., and Kevrekidis I.G. Microscopic/stochastic timesteppers and coarse control: A kinetic Monte Carlo example. AIChE Journal 49 (2003) 1922-1926
    • (2003) AIChE Journal , vol.49 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 44
    • 0038608279 scopus 로고    scopus 로고
    • Coarse Brownian dynamics for nematic liquid crystals: Bifurcation diagrams via stochastic simulation
    • Siettos C.I., Graham M., and Kevrekidis I.G. Coarse Brownian dynamics for nematic liquid crystals: Bifurcation diagrams via stochastic simulation. Journal of Chemical Physics 118 (2003) 10149-10156
    • (2003) Journal of Chemical Physics , vol.118 , pp. 10149-10156
    • Siettos, C.I.1    Graham, M.2    Kevrekidis, I.G.3
  • 45
  • 46
    • 0346816494 scopus 로고    scopus 로고
    • Enabling dynamic process simulators to perform alternative tasks: Time-stepper based toolkit for computer-aided analysis
    • Siettos C.I., Pantelides C.C., and Kevrekidis I.G. Enabling dynamic process simulators to perform alternative tasks: Time-stepper based toolkit for computer-aided analysis. Industrial Chemistry & Industrial Research 42 (2004) 6795-6801
    • (2004) Industrial Chemistry & Industrial Research , vol.42 , pp. 6795-6801
    • Siettos, C.I.1    Pantelides, C.C.2    Kevrekidis, I.G.3
  • 47
    • 2342652956 scopus 로고    scopus 로고
    • Theory of inexact Krylov subspace methods and applications to scientific computing
    • Simoncini V., and Szyld D.B. Theory of inexact Krylov subspace methods and applications to scientific computing. SIAM Journal on Scientific Computing 25 (2003) 454-477
    • (2003) SIAM Journal on Scientific Computing , vol.25 , pp. 454-477
    • Simoncini, V.1    Szyld, D.B.2
  • 48
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using timesteppers: A reaction-diffusion example
    • Theodoropoulos C., Qian Y.H., and Kevrekidis I.G. Coarse stability and bifurcation analysis using timesteppers: A reaction-diffusion example. PNAS 97 (2000) 9840-9843
    • (2000) PNAS , vol.97 , pp. 9840-9843
    • Theodoropoulos, C.1    Qian, Y.H.2    Kevrekidis, I.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.