Solution of population balance equations using the direct quadrature method of moments

Matrix Computations

Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505 · see citing works

The Fractal Geometry of Nature.

Sparrow, C. T., & Mandelbrot, B. B. (1984) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981858 · Cited by 14,732 · see citing works

Numerical Recipes: FORTRAN

Press, W. H., Teukolsky, S. L. A., Flannery, B. P., & Vetterling, W. T. (1990) · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · Cited by 6,980 · see citing works

Mathematical Methods for Physicists

(1985) · Elsevier eBooks · doi:10.1016/c2013-0-10310-8 · Cited by 2,776 · see citing works

Mathematical Methods for Physicists

Arfken, G. B., & Mullin, A. A. (1967) · American Journal of Physics · doi:10.1119/1.1973757 · Cited by 2,708 · see citing works

Some problems in particle technology

Hulburt, H. M., & Katz, S. (1964) · Chemical Engineering Science · doi:10.1016/0009-2509(64)85047-8 · Cited by 1,670 · see citing works

MFIX documentation theory guide

Syamlal, M., USDOE, W., Rogers, W., et al. (1993) · doi:10.2172/10145548 · Cited by 1,160 · see citing works

Description of aerosol dynamics by the quadrature method of moments

McGraw, R. (1997) · Aerosol Science and Technology · doi:10.1080/02786829708965471 · Cited by 1,128 · see citing works

Computational Models for Turbulent Reacting Flows

Fox, R. O. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610103 · Cited by 922 · see citing works

Theory of Particulate Processes

(1988) · Elsevier eBooks · doi:10.1016/b978-0-12-579652-1.x5001-7 · Cited by 760 · see citing works

Matrices with Applications in Statistics.

Thomas, G. E., & Graybill, F. A. (1984) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981752 · Cited by 744 · see citing works

Quadrature method of moments for aggregation-breakage processes

Marchisio, D. L., Vigil, R. D., & Fox, R. O. (2003) · Journal of Colloid and Interface Science · doi:10.1016/s0021-9797(02)00054-1 · Cited by 524 · see citing works

Quadrature method of moments for population-balance equations

Marchisio, D. L., Pikturna, J. T., Fox, R. O., Vigil, R. D., & Barresi, A. A. (2003) · AIChE Journal · doi:10.1002/aic.690490517 · Cited by 461 · see citing works

Error Bounds in Equilibrium Statistical Mechanics

Gordon, R. G. (1968) · Journal of Mathematical Physics · doi:10.1063/1.1664624 · Cited by 453 · see citing works

Aerosol dynamics modeling using the method of moments

Frenklach, M., & Harris, S. J. (1987) · Journal of Colloid and Interface Science · doi:10.1016/0021-9797(87)90454-1 · Cited by 420 · see citing works

Spray Combustion and Atomization

Williams, F. A. (1958) · The Physics of Fluids · doi:10.1063/1.1724379 · Cited by 380 · see citing works

Application of the direct quadrature method of moments to polydisperse gas–solid fluidized beds

Fan, R., Marchisio, D. L., & Fox, R. O. (2003) · Powder Technology · doi:10.1016/j.powtec.2003.10.005 · Cited by 293 · see citing works

Implementation of the quadrature method of moments in CFD codes for aggregation–breakage problems

Marchisio, D. L., Vigil, R. D., & Fox, R. O. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(03)00211-2 · Cited by 268 · see citing works

Approximate Population Balance Equations for Aggregation–Breakage Processes

Vanni, M. (2000) · Journal of Colloid and Interface Science · doi:10.1006/jcis.1999.6571 · Cited by 244 · see citing works

The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis

Rukhin, A. L., Dette, H., & Studden, W. J. (1998) · Journal of the American Statistical Association · doi:10.2307/2670071 · Cited by 239 · see citing works

Digestive Ripening, Nanophase Segregation and Superlattice Formation in Gold Nanocrystal Colloids

Lin, X., SORENSEN, C. M., & Klabunde, K. J. (2000) · Journal of Nanoparticle Research · doi:10.1023/a:1010078521951 · Cited by 209 · see citing works

Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods

Laurent, F., & Massot, M. (2001) · Combustion Theory and Modelling · doi:10.1088/1364-7830/5/4/303 · Cited by 165 · see citing works

Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations

Wright, D. L., McGraw, R., & Rosner, D. E. (2001) · Journal of Colloid and Interface Science · doi:10.1006/jcis.2000.7409 · Cited by 160 · see citing works

Implementation of the population balance equation in CFD codes for modelling soot formation in turbulent flames

Zucca, A., Marchisio, D. L., Barresi, A., et al. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.11.061 · Cited by 121 · see citing works

A comparison of some approximate methods for solving the aerosol general dynamic equation

Barrett, J. C., & Webb, N. A. (1998) · Journal of Aerosol Science · doi:10.1016/s0021-8502(97)00455-2 · Cited by 119 · see citing works

Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments

McGraw, R., & Wright, D. L. (2002) · Journal of Aerosol Science · doi:10.1016/s0021-8502(02)00157-x · Cited by 91 · see citing works

Comparison of micromixing models for CFD simulation of nanoparticle formation

Wang, L., & Fox, R. O. (2004) · AIChE Journal · doi:10.1002/aic.10173 · Cited by 82 · see citing works

Multivariate Population Balances via Moment and Monte Carlo Simulation Methods: An Important Sol Reaction Engineering Bivariate Example and “Mixed” Moments for the Estimation of Deposition, Scavenging, and Optical Properties for Populations of Nonspherical Suspended Particles

Rosner, D. E., McGraw, R., & Tandon, P. (2003) · Industrial & Engineering Chemistry Research · doi:10.1021/ie020627l · Cited by 70 · see citing works

Bivariate moment simulation of coagulating and sintering nanoparticles in flames

Rosner, D. E., & Pyykönen, J. (2002) · AIChE Journal · doi:10.1002/aic.690480307 · Cited by 60 · see citing works

Representation of generally mixed multivariate aerosols by the quadrature method of moments: I. Statistical foundation

Yoon, C., & McGraw, R. (2004) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2003.11.003 · Cited by 58 · see citing works

Using discrete distributions to analyze CSD data from MSMPR crystallizers

Jones, C. M. (2002) · AIChE Journal · doi:10.1002/aic.690480709 · Cited by 6 · see citing works

Implementation of the population balance equation in CFD codes for modelling soot formation in flames

Zucca, A., Marchisio, D. L., Barresi, A., et al. (2004) · PORTO@Iris · Cited by 2 · see citing works

Conditional quadrature method of moments for kinetic equations

Yuan, C., & Fox, R. O. (2011) · Journal of Computational Physics · doi:10.1016/j.jcp.2011.07.020 · Cited by 232 · see citing works

An extended quadrature method of moments for population balance equations

Yuan, C., Laurent, F., & Fox, R. O. (2012) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2012.04.003 · Cited by 225 · see citing works

Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

Attarakih, M. M., Drumm, C., & Bart, H.-J. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2008.05.006 · Cited by 141 · see citing works

Euler-Euler simulation of bubbly flow in a rectangular bubble column: Experimental validation with Radioactive Particle Tracking

Gupta, A., & Roy, S. (2013) · Chemical Engineering Journal · doi:10.1016/j.cej.2012.11.012 · Cited by 125 · see citing works

Multivariate Quadrature-Based Moments Methods for turbulent polydisperse gas-liquid systems

Buffo, A., Vanni, M., Marchisio, D. L., & Fox, R. O. (2013) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2012.09.005 · Cited by 96 · see citing works

Simulation of coalescence, break-up and mass transfer in a gas-liquid stirred tank with CQMOM

Petitti, M., Vanni, M., Marchisio, D. L., Buffo, A., & Podenzani, F. (2013) · Chemical Engineering Journal · doi:10.1016/j.cej.2013.05.047 · Cited by 90 · see citing works

Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review

Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works

On the representation of QMOM as a weighted-residual method-The dual-quadrature method of generalized moments

Lage, P. L. C. (2011) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2011.05.017 · Cited by 43 · see citing works

Integral formulation of the population balance equation: Application to particulate systems with particle growth

Attarakih, M. (2013) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2012.08.001 · Cited by 25 · see citing works

Application of extended quadrature method of moments for simulation of bubbly flow and mass transfer in gas-liquid stirred tanks

Askari, E., St‐Pierre Lemieux, G., & Proulx, P. (2019) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.23470 · Cited by 24 · see citing works

The quadrature method of moments and its relationship with the method of weighted residuals

Dorao, C. A., & Jakobsen, H. A. (2006) · Chemical Engineering Science · doi:10.1016/j.ces.2006.09.014 · Cited by 18 · see citing works

Flow Simulation in a 2D Bubble Column with the Euler-lagrange and Euler-euler Method

Weber, A., & Bart, H.-J. (2018) · The Open Chemical Engineering Journal · doi:10.2174/1874123101812010001 · Cited by 15 · see citing works

New scheme for implementing the method of moments with interpolative closure

Yu, M., & Lin, J. (2017) · Aerosol Science and Technology · doi:10.1080/02786826.2017.1319566 · Cited by 7 · see citing works

Advances in numerical methods for the solution of population balance equations for disperse phase systems

Su, J., Gu, Z., & Xu, X. Y. (2009) · Science China Chemistry · doi:10.1007/s11426-009-0164-2 · Cited by 27 · see citing works

Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM)

Haftchenari, H., Darvizeh, M., Darvizeh, A., et al. (2005) · Composite Structures · doi:10.1016/j.compstruct.2005.10.003 · Cited by 49 · see citing works

Free vibration analysis of laminated composite cylindrical shells by DQM

Shu, C., & Du, H. (1997) · Composites Part B Engineering · doi:10.1016/s1359-8368(96)00052-2 · Cited by 94 · see citing works

Solution of population balance equation using quadrature method of moments with an adjustable factor

Su, J., Gu, Z., Li, Y., Feng, S., & Xu, X. Y. (2007) · Chemical Engineering Science · doi:10.1016/j.ces.2007.06.016 · Cited by 65 · see citing works

Free Vibration Analysis of Thin Cylindrical Shells by the Differential Quadrature Method

Bert, C. W., & Malik, M. (1996) · Journal of Pressure Vessel Technology · doi:10.1115/1.2842156 · Cited by 76 · see citing works