메뉴 건너뛰기




Volumn 14, Issue 2, 2004, Pages 89-111

Time-steppers and 'coarse' control of distributed microscopic processes

Author keywords

Coarse control; Distributed systems; Multiscale modelling; Time stepper

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; CONTROL EQUIPMENT; DIFFUSION; DISCRETE TIME CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; KINETIC THEORY; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; MONTE CARLO METHODS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PREDICTIVE CONTROL SYSTEMS;

EID: 0346685925     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.865     Document Type: Article
Times cited : (58)

References (36)
  • 1
    • 0034616305 scopus 로고    scopus 로고
    • Wave suppression by nonlinear finite-dimensional control
    • Armaou A, Christofides PD. Wave suppression by nonlinear finite-dimensional control. Chemical Engineering Science 2000; 55:2627-2640.
    • (2000) Chemical Engineering Science , vol.55 , pp. 2627-2640
    • Armaou, A.1    Christofides, P.D.2
  • 2
    • 0142225973 scopus 로고    scopus 로고
    • Finite-dimensional control of nonlinear parabolic PDEs with time-dependent spatial domains using empirical eigenfunctions
    • Armaou A, Christofides PD. Finite-dimensional control of nonlinear parabolic PDEs with time-dependent spatial domains using empirical eigenfunctions. International Journal of Applied Mathematics and Computer Science 2001; 11:287-317.
    • (2001) International Journal of Applied Mathematics and Computer Science , vol.11 , pp. 287-317
    • Armaou, A.1    Christofides, P.D.2
  • 4
    • 84896552867 scopus 로고    scopus 로고
    • Nonlinear model reduction for control of distributed parameter systems
    • Shvartsman S, Kevrekidis IG. Nonlinear model reduction for control of distributed parameter systems. AIChE Journal 1998; 44:1579-1595.
    • (1998) AIChE Journal , vol.44 , pp. 1579-1595
    • Shvartsman, S.1    Kevrekidis, I.G.2
  • 5
    • 0029732249 scopus 로고    scopus 로고
    • The use of the Karhunen-Loeve decomposition for the modeling of distributed parameter systems
    • Park HM, Cho DH. The use of the Karhunen-Loeve decomposition for the modeling of distributed parameter systems. Chemical Engineering Science 1996; 51:81-98.
    • (1996) Chemical Engineering Science , vol.51 , pp. 81-98
    • Park, H.M.1    Cho, D.H.2
  • 7
    • 0037050975 scopus 로고    scopus 로고
    • Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method
    • Sankaranarayanan K, Shan X, Kevrekidis IG, Sundaresan S. Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. Journal of Fluid Mechanics 2002; 452: 61-96.
    • (2002) Journal of Fluid Mechanics , vol.452 , pp. 61-96
    • Sankaranarayanan, K.1    Shan, X.2    Kevrekidis, I.G.3    Sundaresan, S.4
  • 8
    • 0037104864 scopus 로고    scopus 로고
    • 'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods
    • Gear CW, Kevrekidis IG, Theodoropoulos C. 'Coarse' integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engineering 2002; 26:941-963.
    • (2002) Computers and Chemical Engineering , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 9
    • 0037162264 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using stochastic simulator: Kinetic Monte Carlo examples
    • Makeev AG, Maroudas D, Kevrekidis IG. Coarse stability and bifurcation analysis using stochastic simulator: kinetic Monte Carlo examples. Journal of Chemical Physics 2002; 116:10083-10091.
    • (2002) Journal of Chemical Physics , vol.116 , pp. 10083-10091
    • Makeev, A.G.1    Maroudas, D.2    Kevrekidis, I.G.3
  • 10
    • 0041428215 scopus 로고    scopus 로고
    • Protective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum
    • Gear CW, Kevrekidis IG. Protective methods for stiff differential equations: problems with gaps in their eigenvalue spectrum. SIAM Journal on Scientific Computing 2003; 24:1091-1106, also NEC Technical Report NECI-TR, 2001; 029.
    • (2003) SIAM Journal on Scientific Computing , vol.24 , pp. 1091-1106
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 11
    • 85140868060 scopus 로고    scopus 로고
    • Gear CW, Kevrekidis IG. Protective methods for stiff differential equations: problems with gaps in their eigenvalue spectrum. SIAM Journal on Scientific Computing 2003; 24:1091-1106, also NEC Technical Report NECI-TR, 2001; 029.
    • (2001) NEC Technical Report , vol.NECI-TR , pp. 029
  • 12
    • 0037408148 scopus 로고    scopus 로고
    • Telescopic projective integrators for stiff differential equations
    • Gear CW, Kevrekidis IG. Telescopic projective integrators for stiff differential equations. Journal on Computational Physics 2003; 187:95-109, also NEC Technical Report, November 2001.
    • (2003) Journal on Computational Physics , vol.187 , pp. 95-109
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 13
    • 85140868060 scopus 로고    scopus 로고
    • November
    • Gear CW, Kevrekidis IG. Telescopic projective integrators for stiff differential equations. Journal on Computational Physics 2003; 187:95-109, also NEC Technical Report, November 2001.
    • (2001) NEC Technical Report
  • 14
    • 0027641824 scopus 로고
    • Stabilization of unstable procedures: The recursive projection method
    • Shroff GM, Keller HB. Stabilization of unstable procedures: the recursive projection method. SIAM Journal on Numerical Analysis 1993; 30:1099-1120.
    • (1993) SIAM Journal on Numerical Analysis , vol.30 , pp. 1099-1120
    • Shroff, G.M.1    Keller, H.B.2
  • 15
    • 49149143501 scopus 로고
    • Variations of Arnoldi's method for computing eigenelements of large unsymmetric matrices
    • Saad Y. Variations of Arnoldi's method for computing eigenelements of large unsymmetric matrices. Linear Algebra and Applications 1980; 34:269-295.
    • (1980) Linear Algebra and Applications , vol.34 , pp. 269-295
    • Saad, Y.1
  • 16
    • 0001524578 scopus 로고
    • Finding leading modes of a viscous free surface flow: An assymmetric generalized eigenproblem
    • Christodoulou KN, Scriven LE. Finding leading modes of a viscous free surface flow: an assymmetric generalized eigenproblem. Journal of Scientific Computing 1988; 3:355-405.
    • (1988) Journal of Scientific Computing , vol.3 , pp. 355-405
    • Christodoulou, K.N.1    Scriven, L.E.2
  • 17
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and coarse control: Kinetic Monte Carlo example
    • Siettos CI, Armaou A, Makeev AG, Kevrekidis IG. Microscopic/stochastic timesteppers and coarse control: kinetic Monte Carlo example. AIChE Journal 2003; 49:1922-1926.
    • (2003) AIChE Journal , vol.49 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 18
    • 0346816494 scopus 로고    scopus 로고
    • Enabling dynamic process simulators to perform alternative tasks: A time-stepper based toolkit for computer-aided analysis
    • accepted, Can be obtained as math.OC/0302040 at arXiv.org
    • Siettos CI, Pantelides CC, Kevrekidis IG. Enabling dynamic process simulators to perform alternative tasks: a time-stepper based toolkit for computer-aided analysis. Industrial Engineering and Chemical Research, accepted, 2003. Can be obtained as math.OC/0302040 at arXiv.org.
    • (2003) Industrial Engineering and Chemical Research
    • Siettos, C.I.1    Pantelides, C.C.2    Kevrekidis, I.G.3
  • 21
    • 0037962061 scopus 로고    scopus 로고
    • Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models
    • Lou Y, Christofides PD. Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models. Chemical Engineering Science 2003; 58:3115-3129.
    • (2003) Chemical Engineering Science , vol.58 , pp. 3115-3129
    • Lou, Y.1    Christofides, P.D.2
  • 22
    • 0038068807 scopus 로고    scopus 로고
    • Feedback control of growth rate and surface roughness in thin film growth
    • Lou Y. Christofides PD. Feedback control of growth rate and surface roughness in thin film growth. AIChE Journal 2003; 49:2099-2113.
    • (2003) AIChE Journal , vol.49 , pp. 2099-2113
    • Lou, Y.1    Christofides, P.D.2
  • 23
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y, Schultz MH, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986; 7:856-869.
    • (1986) SIAM Journal on Scientific and Statistical Computing , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 24
    • 0002914778 scopus 로고
    • Iterative methods for linear and nonlinear equations
    • SIAM: Philadelphia, USA
    • Kelley CT. Iterative methods for linear and nonlinear equations. In Frontiers in Applied Mathematics, vol. 16. SIAM: Philadelphia, USA, 1995.
    • (1995) Frontiers in Applied Mathematics , vol.16
    • Kelley, C.T.1
  • 27
    • 26344468007 scopus 로고
    • A model for collisional processes in gases I: Small amplitude processes in charged and neutral one-component systems
    • Bhatnagar PL, Gross EP, Krook M. A model for collisional processes in gases I: small amplitude processes in charged and neutral one-component systems. Physical Review 1954; 94:511-525.
    • (1954) Physical Review , vol.94 , pp. 511-525
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, M.3
  • 30
    • 0003983878 scopus 로고
    • Integral manifolds and inertial manifolds for dissipative partial differential equations
    • Springer: New York, NY
    • Nicolaenko C, Foias B, Temam R, Constantin P. Integral manifolds and inertial manifolds for dissipative partial differential equations. Applied Mathematical Sciences, vol. 70. Springer: New York, NY, 1989.
    • (1989) Applied Mathematical Sciences , vol.70
    • Nicolaenko, C.1    Foias, B.2    Temam, R.3    Constantin, P.4
  • 31
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer Verlag: New York, NY
    • Temam R. Infinite-dimensional dynamical systems in mechanics and physics. In Applied Mathematical Sciences, vol. 68. Springer Verlag: New York, NY, 1988.
    • (1988) Applied Mathematical Sciences , vol.68
    • Temam, R.1
  • 32
    • 21844509237 scopus 로고
    • Scalings in diffusion driven reaction A + B → C simulations by Lattice BGK models
    • Qian Y-H, Orszag SA. Scalings in diffusion driven reaction A + B → C simulations by Lattice BGK models. Journal of Statistical Physics 1995; 81:237-253.
    • (1995) Journal of Statistical Physics , vol.81 , pp. 237-253
    • Qian, Y.-H.1    Orszag, S.A.2
  • 33
    • 0002246664 scopus 로고    scopus 로고
    • Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator
    • Li J, Liao D, Yip S. Coupling continuum to molecular-dynamics simulation: reflecting particle method and the field estimator. Physical Review E 1998; 57:7259-7267.
    • (1998) Physical Review E , vol.57 , pp. 7259-7267
    • Li, J.1    Liao, D.2    Yip, S.3
  • 34
    • 53349102813 scopus 로고
    • Impulse and physiological states in models of nerve membrane
    • FitzHugh. R. Impulse and physiological states in models of nerve membrane. Biophysics Journal 1961; 1:445-466.
    • (1961) Biophysics Journal , vol.1 , pp. 445-466
    • Fitzhugh, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.