Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm

Chemical Engineering Science

Volumn 65, Issue 9, 2010, Pages 2741-2750

  de Souza, L G M ^a   Janiga, G ^a   John, V ^b,c   Thevenin D ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Adaptivity; Distribution reconstruction; Finite moment problem; Particle size distribution; Splines

Indexed keywords

ADAPTIVE CRITERION; ADAPTIVITY; APRIORI; COMPLEX SHAPES; CRYSTALLIZATION PROCESS; DISTRIBUTION RECONSTRUCTION; FINITE MOMENT PROBLEM; FINITE MOMENTS; FINITE NUMBER; NON-SMOOTH; NUMERICAL SIMULATION; ORIGINAL ALGORITHMS; PARTICULATE FLOWS;

COMPUTER SIMULATION; PROBLEM SOLVING; PULSE SHAPING CIRCUITS; REPAIR; SIZE DISTRIBUTION; SPLINES;

ADAPTIVE ALGORITHMS;

EID: 77649179117     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2010.01.007     Document Type: Article

References (27)

1. Abramov R.V. An improved algorithm for the multidimensional moment-constrained maximum entropy problem. Journal of Computational Physics 226 (2007) 621-644
2. Agachi P.S., Nagy Z.K., Cristea M.V., and Imre-Lucaci Á. Model Based Control: Case Studies in Process Engineering (2007), Wiley-VCH, Weinheim
3. Allen T. Particle Size Measurement. Particle Technology Series. fifth ed. (1997), Springer, Berlin
4. Alopaeus V., Laakkonen M., and Aittamaa J. Solution of population balances by high order moment-conserving method of classes: reconstruction of a non-negative density distribution. Chemical Engineering Science 63 (2008) 2741-2751
5. BaŁdyga J., and Orciuch W. Barium sulphate precipitation in a pipe: an experimental study and CFD modelling. Chemical Engineering Science 56 (2001) 2435-2444
6. Bandyopadhyay K., Bhattacharya K., Biswas P., and Drabold D.A. Maximum entropy and the problem of moments: a stable algorithm. Physical Review E 71 (2005) 057701-1-057701-4
7. Diemer R., and Olson J. A moment methodology for coagulation and breakage problems: part 2-moment models and distribution reconstruction. Chemical Engineering Science 57 (2002) 2211-2228
8. Elsner M., Menéndez D.F., Muslera E., and Seidel-Morgenstern A. Experimental study and simplified mathematical description of preferential crystallization. Chirality 17 (2005) 183-195
9. Fan R., Marchisio D., and Fox R. Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds. Powder Technology 139 (2004) 7-20
10. John V., Angelov I., Öncül A.A., and Thévenin D. Techniques for the reconstruction of a distribution from a finite number of its moments. Chemical Engineering Science 62 (2007) 2890-2904
11. Kass R.E., and Wasserman L. Selection of prior distributions by formal rules. Journal of the American Statistical Association 91 (1996) 1343-1370
12. Lorenz H., Perlberg A., Sapoundjiev D., Elsner M., and Seidel-Morgenstern A. Crystallization of enantiomers. Chemical Engineering and Processing 45 (2006) 863-873
13. Marchisio D., Barresi A., and Garbero M. Nucleation, growth and agglomeration in barium sulfate turbulent precipitation. A.I.Ch.E. Journal 48 (2002) 2039-2050
14. Marchisio D., and Fox R. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science 36 1 (2005) 43-73
15. McGraw R., Nemesure S., and Schwatz S. Properties and evolution of aerosols with size distributions having identical moments. Journal of Aerosol Science 29 7 (1998) 761-772
16. Mersmann A. Crystallization Technology Handbook. second ed. (2001), Marcel Dekker, Inc., New York
17. Öncül A.A., Janiga G., and Thévenin D. Comparison of various micromixing approaches for computational fluid dynamics simulation of barium sulfate precipitation in tubular reactors. Industrial & Engineering Chemistry Research 48 (2009) 999-1007
18. Qamar S., Elsner M., Angelov I., Warnecke G., and Seidel-Morgenstern A. A comparative study of high resolution schemes for solving population balances in crystallization. Computers & Chemical Engineering 30 (2006) 1119-1131
19. Rodrigo A., Lorenz H., and Seidel-Morgenstern A. Online monitoring of preferential crystallization of enantiomers. Chirality 16 (2004) 499-508
20. Scales J.A., and Tenorio L. Prior information and uncertainty in inverse problems. Geophysics 66 (2001) 389-397
21. Schwarzer H., Schwertfirm F., Manhart M., Schmidt H.-J., and Peukert W. Predictive simulation of nanoparticle precipitation based on the population balance equation. Chemical Engineering Science 61 (2006) 167-181
22. Strumendo M., and Arastoopour H. Solution of PBE by MOM in finite size domains. Chemical Engineering Science 63 (2008) 2624-2640
23. Sundmacher K., Kienle A., and Seidel-Morgenstern A. Integrated Chemical Processes: Synthesis, Operation, Analysis, and Control (2005), John Wiley & Sons, Weinheim
24. Wei H., Zhou W., and Garside J. Computational fluid dynamics modeling of the precipitation process in a semibatch crystallizer. Industrial and Engineering Chemistry Research 40 (2001) 5255-5261
25. White W. Particle size distributions that cannot be distinguished by their integral moments. Journal of Colloid and Interface Science 135 (1990) 297-299
26. Woodbury A.D. A FORTRAN program to produce minimum relative entropy distributions. Computers and Geosciences 30 (2004) 131-138
27. Wright D.L. Retrieval of optical properties of atmospheric aerosols from moments of the particle size distribution. Journal of Aerosol Sciences 31 (2000) 1-18