Modelling and simulation of photosynthetic microorganism growth: Random walk vs. finite difference method

Mathematics and Computers in Simulation

Volumn 82, Issue 10, 2012, Pages 2022-2032

  Papáček, Štěpán ^a   Matonoha, Ctirad ^b   Štumbauer, Václav ^a   Štys, Dalibor ^a  

^a UNIVERSITY OF SOUTH BOHEMIA   (Czech Republic)

^b INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

Author keywords

Boundary value problem; Distributed parameter system; Multi scale modelling; Photosynthetic factory; Random walk

Indexed keywords

ALTERNATIVE APPROACH; DIFFUSION SYSTEMS; DISTRIBUTED PARAMETER SYSTEMS; LUMPED PARAMETER MODELS; MICRO-ALGAE; MICROBIAL CULTURE; MODELING FRAMEWORKS; MODELLING AND SIMULATIONS; MULTI-SCALE MODELLING; MULTISCALES; PHOTOSYNTHETIC MICROORGANISMS; PSF MODEL; RANDOM WALK; RANDOM WALK MODELS; TURBULENT DIFFUSION;

ATMOSPHERIC TURBULENCE; BOUNDARY VALUE PROBLEMS; DIFFUSION; FINITE DIFFERENCE METHOD;

RANDOM PROCESSES;

EID: 84865762394     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2011.07.006     Document Type: Conference Paper

References (25)

1. Beek W.J., Muttzall K.M.K., and van Heuven J.W. Transport Phenomena 2000 Wiley & Sons
2. Bohl E., and Marek I. Input-output systems in biology and chemistry and a class of mathematical models describing them Applications of Mathematics 50 2005 219 245
3. Čelikovský S. On the continuous dependence of trajectories of bilinear systems on controls and its applications Kybernetika 24 1988 278 292
4. Čelikovský S., Papáček Š., Cervantes-Herrera A., and Ruiz-León J. Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis TAC IEEE 55 3 2010 767 772
5. Dunn I.J., Heinzle E., Ingham J., and Přenosil J.E. Biological Reaction Engineering 1992 VCH Weinheim, New York, Basel, Cambridge
6. Eilers P.H.C., and Peeters J.C.H. A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton Ecological Modelling 42 1988 199 215
7. Eilers P.H.C., and Peeters J.C.H. Dynamic behaviour of a model for photosynthesis and photoinhibition Ecological Modelling 69 1993 113 133
8. Janssen M., Tramper J., Mur L.R., and Wijffels R.H. Enclosed outdoor photobioreactors: light regime, photosynthetic efficiency, scale-up, and future prospects Biotechnology and Bioengineering 81 2003 193 210
9. Kmeť T., Straškraba M., and Mauersberger P. A mechanistic model of the adaptation of phytoplankton photosynthesis Bulletin of Mathematical Biology 55 1993 259 275
10. Luo H.P., Kemoun A., Al-Dahhan M.H., Fernández Sevilla J.M., García Sánchez J.L., García Camacho F., and Molina Grima E. Analysis of photobioreactors for culturing high-value microalgae and cyanobacteria via an advanced diagnostic technique: CARPT Chemical Engineering Science 58 12 2003 2519 2527
11. Masojídek J., Papáček Š., Jirka V., Červený J., Kunc J., Korečko J., Sergejevová M., Verbovikova O., Kopecký J., Štys D., and Torzillo G. A closed solar photobioreactor for cultivation of microalgae under supra-high irradiances: basic design and performance of pilot plant Journal of Applied Phycology 15 2003 239 248
12. Molina E., Acien F.G., Garcia F., Camacho F., and Chisti Y. Scale-up of tubular photobioreactors Journal of Biotechnology 92 2000 113 131
13. Muller-Feuga A., Le Guédes R., and Pruvost J. Benefits and limitations of modeling for optimization of Porphyridium cruentum cultures in an annular photobioreactor Journal of Biotechnology 103 2003 153 163
14. Nedbal L., Tichý V., Xiong F., and Grobbelaar J.U. Microscopic green algae and cyanobacteria in high-frequency intermittent light Journal of Applied Phycology 8 1996 325 333
15. Papáček Š., Čelikovský S., Štys D., and Ruiz-León J. Bilinear System as Modelling Framework for Analysis of Microalgal Growth Kybernetika 43 2007 1 20
16. Papáček Š., Čelikovský S., and Ruiz-León J. Optimal feedback control of microalgal growth based on the slow reduction Proc. IFAC World Congress 2008 Seoul, Korea July 2008 14588 14593
17. Papáček Š., Čelikovský S., Rehák B., and Štys D. Experimental design for parameter estimation of two time-scale model of photosynthesis and photoinhibition in microalgae Mathematics and Computers in Simulation 80 2010 1302 1309
18. Pruvost J., Legrand J., Legentilhomme P., and Muller-Feuga A. Lagrangian trajectory model for turbulent swirling flow in an annular cell: comparison with residence time distribution measurements Chemical Engineering Science 57 2002 205 1215
19. 2 response measurement Joint Special Issue of TAC IEEE and TCAS IEEE 2008 101 108
20. Rektorys K. Přehled užité matematiky, Nakladatelství Prometheus 1995 Praha
21. Schugerl K., and Bellgardt K.H. Bioreaction Engineering, Modeling and Control 2000 Springer-Verlag Berlin, Heidelberg
22. Terry K.L. Photosynthesis in modulated light: quantitative dependence of photosynthetic enhancement on flashing rate Biotechnology and Bioengineering 28 1986 988 995
23. Tichonov A.N., Vasil'eva A.B., and Sveshnikov A.G. Differential Equations 1980 Nauka Moscow (in Russian)
24. Vitásek E. Numerické metody, Nakladatelství technické literatury 1987 Praha
25. Wu X., and Merchuk J.C. A model integrating fluid dynamics in photosynthesis and photoinhibition processes Chemical Engineering Science 56 2001 3527 3538