Current challenges in the design and control of multiscale systems

Canadian Journal of Chemical Engineering

Volumn 89, Issue 6, 2011, Pages 1324-1341

  Ricardez Sandoval, Luis A ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Mathematical modelling; Modelling and simulation studies; Process systems engineering

Indexed keywords

ACROSS TIME; COMPUTATIONAL LIMITATIONS; CONTINUUM MODEL; DESIGN AND CONTROL; IN-PROCESS; LENGTH SCALE; MATHEMATICAL MODELLING; MODELLING AND SIMULATIONS; MODELLING METHOD; MULTI-SCALE MODELLING; MULTI-SCALE SYSTEM; MULTISCALE PROCESS; NUMERICAL SOLUTION; PROCESS SYSTEMS ENGINEERING;

COMPUTER SIMULATION; CONTINUUM MECHANICS; MODELS; NUMERICAL METHODS; SYSTEMS ENGINEERING;

PROCESS CONTROL;

EID: 81155131044     PISSN: 00084034     EISSN: 1939019X     Source Type: Journal    
DOI: 10.1002/cjce.20607     Document Type: Article

References (103)

1. Adalsteinsson, H., B. J. Debusschere, K. L. Long and H. N. Najm, " Components for Atomistic to Continuum Multiscale Modelling of Flow in Micro and Nanofluidic Systems, " Sci. Progr. 16, 297-313 (2008).
2. Allen, M. P. and D. J. Tildesley, "Computer Simulation of Liquids, " Oxford, New York (1987).
3. Armaou, A., I. G. Kevrekidis and C. Theodoropoulos, " Equation-Free Gap Tooth-Based Controller Design for Distributed Complex/Multiscale Processes, " Comp. Chem. Eng. 29, 731-740 (2005).
4. Behrens, C. M. and A. Armaou, " Optimal Design and Operation of Spatially Distributed Multiscale Process With Regard to Layered Heterostructure Growth, " Ind. Eng. Chem. Res. 49, 7891-7900 (2010).
5. Bortz, A. B., M. H. Kalos and J. L. Lebowitz, " A New Algorithm for Monte Carlo Simulation of King Spin Systems, " J. Comp. Phys. 17, 10-18 (1975).
6. Braatz, R. D., R. C. Alkire, E. Seebauer, E. Rusli, R. Gunawan, T. O. Drews, X. Li and Y. He, " Perspectives on the Design and Control of Multiscale Systems, " J. Process Control 16, 193-204 (2006a).
7. Braatz, R. D., R. C. Alkire, E. Seebauer, T. O. Drews, E. Rusli, M. Karulkar, F. Xue, M. Y. L. Jung and R. Gunawan, " A Multiscale Systems Approach to Microelectronic Processes, " Comp. Chem. Eng. 30, 1643-1656 (2006b).
8. Brenan, K. E., S. L. Campbell and L. R. Petzold, "Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, " SIAM, North-Holland, NY (1996).
9. Buzea, C. and K. Robbie, " State of the Art in Thin Film Thickness and Deposition Rate Monitoring Sensors, " Rep. Prog. Phys. 68, 385-409 (2005).
10. Cao, Y. and L. Petzold, " Slow-Scale tau-Leaping Method, " Compt. Methods Appl. Mech. Eng. 197, 3472-3479 (2008).
11. Cao, Y., D. T. Gillespie and L. R. Petzold, " Adaptive Explicit-Implicit tau-Leaping Method With Automatic tau Selection, " J. Chem. Phys. 126, 224101 (2007).
12. Cavallotti, C., M. Nemirovskaya and K. F. Jensen, " A Multiscale Study of the Selective MOVPE of AlxGa1-xAs in the Presence of HCl, " J. Cryst. Growth 248, 411-416 (2003).
13. Chapra, S. C. and R. P. Canale, "Numerical Methods for Engineers, " 5th ed., McGraw Hill, New York, NY (2006).
14. Chatterjee, A. and D. G. Vlachos, " Multiscale Spatial Monte Carlo Simulations: Multigriding, Computational Singular Perturbation, and Hierarchical Stochastic Closures, " J. Chem. Phys. 124, 064110 (2006).
15. Chatterjee, A., M. A. Snyder and D. G. Vlachos, " Mesoscopic Modelling of Chemical Reactivity, " Chem. Eng. Sci. 59, 5559-5567 (2004).
16. Christofides, P. D., A. Armaou, Y. Lou and A. Varshney, "Control and Optimisation of Multiscale Process Systems, " Springer, New York, NY (2009).
17. Collins, S. D., A. Chatterjee and D. G. Vlachos, " Coarse-Grained Kinetic Monte Carlo Models: Complex Lattices, Multicomponent Systems, and Homogenisation at the Stochastic Level, " J. Chem. Phys. 129, 184101 (2008).
18. Dollet, A., " Multiscale Modelling of CVD Film Growth-A Review of Recent Works, " Surf. Coat. Technol. 177-178, 245-251 (2004).
19. Drews, T. O., R. D. Braatz and R. C. Alkire, " Parameter Sensitivity Analysis of Monte Carlo Simulations of Copper Electrodeposition With Multiple Additives, " J. Electrochem. Soc. 150(11), 807-812 (2003).
20. Drews, T. O., E. G. Webb, D. L. Ma, J. Alameda, R. D. Braatz and R. C. Alkire, " Coupled Mesoscale-Continuum Simulations of Copper Electrodeposition in a Trench, " AIChE J. 50(1), 226-240 (2004).
21. Ferreira, M. A. R. and H. K. H. Lee, "Multiscale Modelling: A Bayesian Perspective, " Springer, New York, NY (2007).
22. Frenkel, D. and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications, " 2nd ed., Academic Press, San Diego, CA (2002).
23. Gallivan, M. A. and H. A. Atwater, " Design of a Film Surface Roughness-Minimising Molecular Beam Epitaxy Process by Reduced-Order Modelling of Epitaxial Growth, " J. Appl. Phys. 95(2), 483-489 (2004).
24. Gallivan, M. A. and R. M. Murray, " Reduction and Identification Methods for Markovian Control Systems, With Application to Thin Film Deposition, " Int. J. Robust Nonlin. Control 14, 113-132 (2004).
25. Garcia, A. L., J. B. Bell, W. Y. Crutchfield and B. J. Alder, " Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo, " J. Comput. Phys. 154, 134-155 (1999).
26. Gear, C. W., J. Li and I. G. Kevrekidis, " The Gap-Tooth Method in Particle Simulations, " Phys. Lett. A 316, 190-195 (2003).
27. Ghosal, S., R. L. Kosut, J. L. Ebert and L. L. Porter, II, "Multiscale Modelling and Control of RF Diode Sputter Deposition and GMR Thin Films, " in "Proceedings of the 2004 American Control Conference, " Boston, MA, June 30-July 2, 2004, International Federation of Automatic Control (2004), pp. 3930-3941.
28. Gillespie, D. T., " A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions, " J. Comput. Phys. 2, 403-434 (1976).
29. Gillespie, D. T., " A Rigorous Derivation of the Chemical Master Equation, " Physica A 188, 404-425 (1992).
30. Gillespie, D. T., " Approximate Accelerated Stochastic Simulation of Chemically Reacting Systems, " J. Chem. Phys. 115(4), 1716-1733 (2001).
31. Gubbins, K. E. and J. D. Moore, " Molecular Modelling of Matter: Impact and Prospects in Engineering, " Ind. Eng. Chem. Res. 49, 3026-3046 (2010).
32. Gummalla, M., M. Tsapatsis, J. J. Watkins and D. G. Vlachos, " Multiscale Hybrid Modelling of Film Deposition Within Porous Substrates, " AIChE J. 50(3), 684-695 (2004).
33. Gunawan, R., M. Y. L. Jung, R. D. Braatz and E. G. Seebauerz, " Parameter Sensitivity Analysis Applied to Modelling Transient Enhanced Diffusion and Activation of Boron in Silicon, " J. Electrochem. Soc. 150(12), G758-G765 (2003).
34. Gunawan, R., Y. Cao, L. Petzold and F. J. Doyle, III, " Sensitivity Analysis of Discrete Stochastic Systems, " Biophys. J. 88, 2530-2540 (2005).
35. Gungor, M. R., L. J. Gray, S. J. Zhou and D. Maroudas, " Modelling of Failure in Methalic Thin Films Induced by Stress and Electromigration: A Multiscale Computational Analysis, " Mater. Res. Soc. Symp. Proc. 538, 263-268 (1999).
36. Haseltine, E. L., "Systems Analysis of Stochastic and Population Balance Models for Chemically Reacting Systems, " PhD thesis Dissertation, University of Wisconsin, Madison (2005).
37. Haseltine, E. L. and J. B. Rawlings, " Critical Evalation of Extended Kalman Filtering and Moving-Horizon Estimation, " Ind. Eng. Chem. Res. 44, 2451-2460 (2005).
38. Hu, G., G. Orkoulas and P. D. Christofides, " Modelling and Control of Film Porosity in Thin Film Deposition, " Chem. Eng. Sci. 64, 3668-3682 (2009).
39. Ingalls, B., " Sensitivity Analysis: From Model Parameters to System Behaviour, " Essays Biochem. Syst. Biol. 45, 177-193 (2008).
40. Katsoulakis, M. A. and D. G. Vlachos, " Coarse-Grained Stochastic Processes and Kinetic Monte Carlo Simulators for the Diffusion of Interacting Particles, " J. Chem. Phys. 119(18), 9412-9427 (2003).
41. Katsoulakis, M. A., A. J. Majda and D. G. Vlachos, " Corase-Grained Stochastic Processes and Monte Carlo Simulations in Lattice Systems, " J. Comput. Phys. 186, 250-278 (2003).
42. Katsoulakis, M. A., A. J. Majda and A. Sopasakis, " Multiscale Couplings in Prototype Hybrid Deterministic/Stochastic Systems Part I, Deterministic Closures, " Comm. Math. Sci. 2(2), 255-294 (2004).
43. Kevrekidis, I. G., C. W. Gear and G. Hummer, " Equation-Free: The Computer-Aided Analysis of Complex Multiscale Systems, " AIChE J. 40(7), 1346-1355 (2004).
44. Kiparissides, A., S. S. Kucherenko, A. Mantalaris and E. N. Pistikopoulos, " Global Sensitivity Analysis Challenges in Biological Systems Modelling, " Ind. Eng. Chem. Res. 48, 7168-7180 (2009).
45. Kreyszig, E., "Advanced Engineering Mathematics, " 9th ed., Wiley, United States (2006).
46. Lam, R. and D. G. Vlachos, " Multiscale Model for Epitaxial Growth of Films: Growth Mode Transition, " Phys. Rev. B 64, 035401-035410 (2001).
47. Leach, A. R., "Molecular Modelling: Principles and Applications, " 2nd ed., Pearson Prentice Hall, Great Britain (2001).
48. Lombardo, S. J. and A. T. Bell, " A Review of Theorical Models of Adsorption, Diffusion Desorption, and Reaction of Gases on Metal-Surfaces, " Surf. Sci. Rep. 31(1-2), 1-72 (1991).
49. Lou, Y. and P. D. Christofides, " Estimation and Control of Surface Roughness in Thin Film Growth Using Kinetic Monte-Carlo Methods, " Chem. Eng. Sci. 58, 3115-3129 (2003).
50. Lou, Y. and P. D. Christofides, " Feedback Control of Surface Roughness of GaAs (001) Thin Films Using Kinetic Monte Carlo Models, " Comp. Chem. Eng. 29(1), 225-241 (2004).
51. Lou, Y. and P. D. Christofides, " Feedback Control of Surface Roughness Using Stochastic PDEs, " AIChE J. 51(1), 345-352 (2005).
52. Majumder, D. and L. J. Broadbelt, " A Multiscale Scheme for Modelling Catalytic Flow Reactors, " AICHE J. 52(12), 4214-4228 (2006).
53. Marder, M. P., "Condensed Matter Physics, " Wiley, New York, NY (2000).
54. Maroudas, D., " Multiscale Modelling of Hard Materials: Challenges and Opportunities for Chemical Engineering, " AIChE J. 46(5), 878-882 (2000).
55. Metropolis, N. and S. Ulam, " The Monte Carlo Method, " J. Am. Stat. Assoc. 44(247), 335-341 (1949).
56. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth and A. H. Teller, " Equation of State Calculations by Fast Computing Machines, " J. Chem. Phys. 21(6), 1087-1091 (1953).
57. Montgomery, D. C. and G. C. Runger, "Applied Statistics and Probability for Engineers, " 4th ed., Wiley, USA (2007).
58. Moscatelli, D., A. Veneroni, C. Cavallotti, M. Masi, M. Bosi, G. Attolini and C. Pelosi, " Designing a Large Scale CVD Reactor for GaAs Growth on Ge Substrates by Multi-Hierachy Modelling, " Cryst. Res. Technol. 40(10-11), 987-992 (2005).
59. Muller-Plathe, F., " Coarse-Graining in Polymer Simulation: From the Atomistic to the Mesoscopic Scale and Back, " Chem. Phys. Chem. 3(9), 754-769 (2002).
60. Nielsen, S. O., C. F. Lopez, G. Srinivas and M. L. Klein, " Coarse Grain Models and the Computer Simulation of Soft Materials, " J. Phys. Condens. Matter 16, 481-512 (2004).
61. Plyasunov, S. and A. P. Arkin, " Efficient Stochastic Sensitivity Analysis of Discrete Event Systems, " J. Comput. Phys. 221, 724-738 (2007).
62. Poovathingal, S. K. and R. Gunawan, " Global Parameter Estimation Methods for Stochastic Biochemical Systems, " BMC Bioinform. 11, 414-426 (2010).
63. Prasad, V. and D. G. Vlachos, " Multiscale Model and Informatics-Based Optimal Design of Experiments: Application to the Catalytic Decomposition of Ammonia on Ruthenium, " Ind. Eng. Chem. Res. 47, 6555-6567 (2008).
64. Prasad, V., A. M. Karim, Z. Ulissi, M. Zagrobelny and D. G. Vlachos, " High Through Put Multiscale Modelling for Design of Experiments, Catalysts, and Reactors: Application to Hydrogen Production From Ammonia, " Chem. Eng. Sci. 65, 240-246 (2010).
65. Pricer, T. J., M. J. Kushner and R. C. Alkire, " Monte Carlo Simulation of the Electrodeposition of Copper I. Additive-Free Acidic Sulfate Solution, " J. Electrochem. Soc. 149(8), 396-405 (2002).
66. Raimondeau, S. and D. G. Vlachos, " Recent Developments on Multiscale, Hierarchical Modelling of Chemical Reactors, " Chem. Eng. J. 90, 3-23 (2002).
67. Raimondeau, S., P. Aghalayam, A. B. Mhadeshwar and D. G. Vlachos, " Parameter Optimisation of Molecular Models: Application to Surface Kinetics, " Ind. Eng. Chem. Res. 42, 1174-1183 (2003).
68. Ramesh, K. T., "Nanomaterials, " Springer, New York, NY (2009).
69. Rao, C. V., D. M. Wolf and A. P. Arkin, " Control, Exploitation and Tolerance of Intracellular Noise, " Nature 420(6912), 231-237 (2002).
70. Rathinam, M., C. Yang and D. T. Gillespie, " Stiffness in Stochastic Chemically Reacting Systems: The Implicit tau-Leaping Method, " J. Chem. Phys. 119(24), 12784-12794 (2003).
71. Rathinam, M., P. W. Sheppard and M. Khammash, " Efficient Computation of Parameter Sensitivities of Discrete Stochastic Chemical Reaction Networks, " J. Chem. Phys. 132, 034103 (2010).
72. Resat, H., H. S. Wiley and D. A. Dixon, " Probability-Weighted Dynamic Monte Carlo Method for Reaction Kinetics Simulations, " J. Phys. Chem. B 105(44), 11026-11034 (2001).
73. Rodgers, S. T. and K. F. Jensen, " Multiscale Modelling of Chemical Vapour Deposition, " J. Appl. Phys. 83(1), 524-530 (1998).
74. Rondanini, M., C. Cavallotti, D. Mocatelli, M. Masi and S. J. Carra, " A Combined Fluid Dynamic and 3D Kinetic Monte Carlo Investigation of the Selective Deposition of GaAs and InP, " J. Cryst. Growth 272, 52-58 (2004).
75. Rudd, R. E. and J. Q. Broughton, " Coarse-Grained Molecular Dynamics and the Atomic Limit of Finite Elements, " Phys. Rev. B 58(10), R5893-R5896 (1998).
76. Rudd, R. E. and J. Q. Broughton, " Concurrent Coupling of Length Scales in Solid State Systems, " Phys. Status Sol. B 217(1), 251-291 (2000).
77. Rudd, R. E. and J. Q. Broughton, " Coarse-Grained Molecular Dynamics: Nonlinear Finite Elements and Finite Temperature, " Phys. Rev. B 72(14), 144104 (2005).
78. Rundorg, O., C. Theodoropoulos and I. G. Kevrekidis, " Effective Bifurcation Analysis: A Time-Stepper-Based Approach, " Nonlinearity 15, 491-511 (2002).
79. Rusli, E., T. O. Drews, D. L. Ma, R. C. Alkire and R. D. Braatz, " Robust Nonlinear Feedback-Feedfoward Control of a Coupled Kinetic Monte Carlo-Finite Difference Simulation, " J. Process Control 16, 409-417 (2006).
80. Rusli, E., F. Xue, T. O. Drews, P. M. Vereecken, P. Andricacos, H. Deligianni, R. D. Braatz and R. C. Alkire, " Effect of Additives on Shape Evolution During Electrodeposition II. Parameter Estimation From Roughness Evolution Experiments, " J. Electrochem. Soc. 154, 584-597 (2007).
81. Santiso, E. E. and K. E. Gubbins, " Multi-Scale Molecular Modelling of Chemical Reactivity, " Mol. Simulat. 30, 699-748 (2004).
82. Sherwood, P., B. R. Brooks and M. S. P. Sansom, " Multiscale Methods for Macromolecular Simulations, " Curr. Opin. Struct. Biol. 18, 630-640 (2008).
83. Sholl, D. S. and J. A. Steckel, "Density Functional Theory: A Practical Introduction, " John Wiley & Sons, Inc., Hoboken, New Jersey (2009).
84. Siettos, C. I., A. Armaou, G. Makeev and I. G. Kevrekidis, " Microscopic/Stochastic Timesteppers and "Coarse" Control: A KMC Example, " AIChE J. 49(7), 192-196 (2003a).
85. Siettos, C. I., M. D. Graham and I. G. Kevrekidis, " Coarse Brownian Dynamics for Nematic Liquid Crystals: Bifurcation, Projective Integration, and Control Via Stochastic Simulation, " J. Chem. Phys. 118(22), 10149-10156 (2003b).
86. Sinno, T. and R. A. Brown, " Modelling Microdefect Formation in Czochralski Silicon, " J. Electrochem. Soc. 146(6), 2300-2312 (1999).
87. Snyder, M. A. and D. G. Vlachos, " Rational, Hierarchical Parameterisation of Complex Zeolite-Guest Molecular Models, " Mol. Simulat. 30(9), 561-577 (2004).
88. Snyder, M. A., A. Chatterjee and D. G. Vlachos, " Net-Event Kinetic Monte Carlo for Overcoming Stiffness in Spatially Homogeneous and Distributed Systems, " Comp. Chem. Eng. 29(4), 701-712 (2005).
89. Tammaro, M., M. Sabella and J. W. Evans, " Hybrid Treatment of Saptio-Temporal Behaviour in Surface Reactions With Coexisting Immobile and Highly Mobile Reactants, " J. Chem. Phys. 102(23), 10277-10285 (1995).
90. Tee, K. P., S. S. Ge and F. E. H. Tay, " Adaptive Control of Electrostatic Microactuators With Bidirectional Drive, " IEEE Trans. Control Syst. Technol. 17(2), 340-352 (2009).
91. Tian, T. and K. Burrage, " Binomial Leap Methods for Simulating Stochastic Chemical Kinetics, " J. Chem. Phys. 121(21), 10356-10364 (2004).
92. Varshney, A. and A. Armaou, " Identification of Macroscopic Variables for Low Order Modelling of Thin-Film Growth, " Ind. Eng. Chem. Res. 45(25), 8290-8298 (2006).
93. Vlachos, D. G., " Multiscale Integration Hybrid Algorithms for Homogeneous-Heterogeneous Reactors, " AIChE J. 43(11), 3031-3041 (1997).
94. Vlachos, D. G., " A Review of Multiscale Analysis: Examples From Systems Biology, Materials Engineering, and other Fluid-Surface Interacting Systems, " Adv. Chem. Eng. 30, 1-61 (2005).
95. Vlachos, D. G., " Temporal Coarse-Graining of Microscopic-Lattice Kinetic Monte Carlo Simulations Via τ Leaping, " Phys. Rev. E 78, 046713 (2008).
96. Vlachos, D. G., L. D. Schmidt and R. Aris, " The Effect of Phase Transitions, Surface Diffusion, and Defects on Heterogeneous Reactions: Multiplicities and Fluctuations, " Surf. Sci. 249, 248-264 (1991).
97. Weinan, E. and B. Engquist, " Multiscale Modelling and Computation, " Notices AMS 50(9), 1062-1070 (2003).
98. Weinan, E., B. Engquist and Z. Huang, " Heterogeneous Multiscale Method: A General Methodology for Multiscale Modelling, " Phys. Rev. B 67, 092101 (2003).
99. Weinan, E., B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden, " The Heterogeneous Multiscale Method: A Review, " Commun. Comput. Phys. 2, 367 (2007).
100. Xiong, R. and M. A. Grover, " A Modified Moving Horizon Estimator for In Situ Sensing of a Chemical Vapor Deposition Process, " IEEE Trans. Control Syst. Technol. 17(5), 1228-1235 (2009).
101. Yang, A. and W. Marquardt, " An Ontological Conceptualisation of Multiscale Models, " Comput. Chem. Eng. 33, 822-837 (2009).
102. Zhang, X., G. Hu, G. Orkoulas and P. D. Christofides, " Controller and Estimator Design for Regulation of Film Thickness, Surface Roughness, and Porosity in a Multiscale Thin Film Growth Process, " Ind. Eng. Chem. Res. 49, 7795-7806 (2010).
103. Zienkiewicz, O. C., R. L. Taylor and J. Z. Zhu, "The Finite Element Method: Its Basis & Fundamentals, " 6th ed., Elsevier, Burlington, MA (2005).