Nonlinear stochastic model for bacterial disinfection: Analytical solution and Monte Carlo simulation

Industrial and Engineering Chemistry Research

Volumn 51, Issue 4, 2012, Pages 1697-1702

  Fan, L T ^a   Argoti, Andres ^a   Maghirang, Ronaldo G ^a   Chou, Song Tien ^b  

^a Kansas State University   (United States)

^b KUN SHAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; ANALYTICAL SOLUTIONS; COEFFICIENT OF VARIATION; CONTACT TIME; CURRENT MODELS; DISINFECTING AGENTS; DISINFECTION PROCESS; EXPERIMENTAL DATA; INTENSITY FUNCTIONS; MASTER EQUATIONS; MONTE CARLO SIMULATION; NONLINEAR STOCHASTIC MODEL; PROCESS MEAN; STANDARD DEVIATION;

COMPUTER SIMULATION; DISINFECTION; MONTE CARLO METHODS; NUMERICAL METHODS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 84856537859     PISSN: 08885885     EISSN: 15205045     Source Type: Journal    
DOI: 10.1021/ie200890p     Document Type: Article

References (20)

1. Argoti, A.; Fan, L. T.; Chou, S. T. Monte Carlo Simulation of Bacterial Disinfection: Nonlinear and Time-Explicit Intensity of Transition Biotechnol. Prog. 2010, 26, 1486-1493
2. Li, Q.; Li, Y. W.; Wu, P.; Xie, R.; Shang, J. K. Palladium Oxide Nanoparticles on Nitrogen-Doped Titanium Oxide: Accelerated Photocatalytic Disinfection and Post-Illumination Catalytic Memory Adv. Mater. 2008, 20, 3717-3723
3. Argoti, A.; Fan, L. T.; Cruz, J.; Chou, S. T. Introducing the Stochastic Simulation of Chemical Reactions using the Gillespie Algorithm and MATLAB: Revisited and Augmented Chem. Eng. Educ. 2008, 42, 35
4. Harper, J. C.; Christensen, P. A.; Egerton, T. A.; Curtis, T. P.; Gunlazuardi, J. Effect of Catalyst Type on the Kinetics of the Photoelectrochemical Disinfection of Water Inoculated with E. Coli J. Appl. Electrochem. 2001, 31, 623-628 (Pubitemid 32657876)
5. van Kampen, N. G. Stochastic Processes in Physics and Chemistry; North-Holland: Amsterdam, 1992.
6. Oppenheim, I.; Shuler, K. E.; Weiss, G. H. Stochastic Processes in Chemical Physics: The Master Equation; The MIT Press: Cambridge, MA, 1977.
7. Clarke, A. B.; Disney, R. L. Probability and Random Processes for Engineers and Scientists; John Wiley & Sons Inc.: New York, 1970.
8. Gardiner, C. W. Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences; Springer: Berlin, 1985.
9. Casella, G.; Berger, R. L. Statistical Inference; Duxbury: Pacific Grove, CA, 2002.
10. Gillespie, D. T. Markov Processes-An Introduction for Physical Scientists; Academic Press: San Diego, CA, 1992.
11. Chiang, C. L. An Introduction to Stochastic Processes and Their Applications; Robert E. Krieger Publishing Company: Huntington, NY, 1980.
12. Gillespie, D. T. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions J. Comput. Phys. 1976, 22, 403-434
13. Gillespie, D. T. Stochastic Simulation of Chemical Kinetics Annu. Rev. Phys. Chem. 2007, 58, 35-55 (Pubitemid 46877584)
14. Shah, B. H.; Borwanker, J. D.; Ramkrishna, D. Monte Carlo Simulation of Microbial Population Growth Math. Biosci. 1976, 31, 1-23
15. Rajamani, K.; Pate, W. T.; Kinneberg, D. J. Time-Driven and Event-Driven Monte Carlo Simulations of Liquid-Liquid Dispersions: A Comparison Ind. Eng. Chem. Fund. 1986, 25, 746-752 (Pubitemid 17479853)
16. Ullah, M.; Schmidt, H.; Cho, K. H.; Wolkenhauer, O. Deterministic Modelling and Stochastic Simulation of Biochemical Pathways using MATLAB IEE Proc. Syst. Biol. 2006, 153, 53-60
17. Rao, C. V.; Arkin, A. P. Stochastic Chemical Kinetics and the Quasi-Steady-State Assumption: Application to the Gillespie Algorithm J. Chem. Phys. 2003, 118, 4999-5010
18. Cao, Y.; Gillespie, D. T.; Petzold, L. R. Efficient Step Size Selection for the Tau-Leaping Simulation Method J. Chem. Phys. 2006, 124, 044109
19. Ramaswamy, R.; González-Segredo, N.; Sbalzarini, F. A New Class of Highly Efficient Exact Stochastic Simulation Algorithms for Chemical Reaction Networks J. Chem. Phys. 2009, 130, 244104
20. Fan, L. T.; Chen, H. T.; Aldis, D. An adaptive random search procedure for large scale industrial and process systems synthesis. Proceedings of Symposium on Computers in Design and Erection of Chemical Plants, Karlovy Vary, 31 Aug.-4 Sept., 1975; pp 279-291.