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Studies on population balance equation involving aggregation and growth terms via symmetries

  • Zehra Pinar ORCID logo EMAIL logo
Published/Copyright: March 31, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 22 Issue 3-4

Abstract

The population balance equation (PBE) is one of the most popular integro-differential equations modeled for several industrial processes. The solution to this equation is usually solved using a numerical approach as the analytical solutions of such equations are not obtained easily. Typically, the available analytical solutions are limited and are based on momentous Laplace transform. In this study, the reduced equations of the PBE are obtained via the group analysis method. Two particulate cases involving aggregation, growth and nucleation are selected, the determining equations are solved and the reduced equations are solved via approximate methods. The approximate method involves the target solution of the nonlinear evolution equation, here the PBE, to be expressed as a polynomial in an elementary function which satisfies a particular ordinary differential equation termed as an auxiliary equation.

Keywords: aggregation; auxiliary equation method; growth; Lie groups; population balance equation
Corresponding author: Zehra Pinar, Department of Mathematics, Faculty of Arts and Science, Tekirdağ Namık Kemal University, 59030 Merkez-Tekirdağ, Turkey, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/ijnsns-2018-0389).

Received: 2018-12-28
Revised: 2021-03-01
Accepted: 2021-03-11
Published Online: 2021-03-31
Published in Print: 2021-06-25

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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  2. Original Research Articles
  3. Numerical analysis of geometrical nonlinear aeroelasticity with CFD/CSD method
  4. Application of moving least squares algorithm for solving systems of Volterra integral equations
  5. Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative
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https://doi.org/10.1515/ijnsns-2018-0389
Keywords for this article
aggregation; auxiliary equation method; growth; Lie groups; population balance equation

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Numerical analysis of geometrical nonlinear aeroelasticity with CFD/CSD method
  4. Application of moving least squares algorithm for solving systems of Volterra integral equations
  5. Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative
  6. Stochastic models with multiplicative noise for economic inequality and mobility
  7. Fast interaction of Cu2+ with S2O3 2− in aqueous solution
  8. Rotorcraft fuselage/main rotor coupling dynamics modelling and analysis
  9. Modeling and fault identification of the gear tooth surface wear failure system
  10. Wavelet-optimized compact finite difference method for convection–diffusion equations
  11. A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint
  12. Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps
  13. The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations
  14. Distributed consensus of multi-agent systems with increased convergence rate
  15. Studies on population balance equation involving aggregation and growth terms via symmetries
  16. Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines
  17. Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation
  18. Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator
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