title: Modeling Evolution: An Introduction to Numerical Methods
author:  Derek A. Roff 
description: <br>"This textbook provides both an introduction to a wide range of models relevant in evolutionary biology as well as to the analytical, numerical, and computational methods for studying them. A further useful point is that the coding is available at the author's <br>website, making implementation much easier." -- Reinhard Burger, <em>Mathematics</em>, University of Vienna, Vienna, Austria
zlib_text: Population Balances
   
  2 
   
  Contents
  1 
  Modelling Batch Fluid Bed Granulation Processes Using Population Balances 
  1.1 
  The nature and framework of population balances
  1.2 
  One-dimensional population balances for ﬂ uid bed batch systems
  1.2.1 
  One-dimensional growth and aggregation balances 
  1.2.2 
  Modiﬁ cation of the one-dimensional PB – inclusion of breakage functions 
  1.2.3 
  Review of coalescence kernels for one-dimensional balances
  1.2.4 
  About one-dimensional balances 
  1.3 
  Multi-dimensional population balances 
  1.4 
  Solving one-dimensional population balances 
  1.4.1 
  Analytical solution to the pure growth by coating (layering) situation 
  1.4.2 
  Analytical solution to the pure growth by agglomeration situation 
  1.4.3 
  Numerical solutions to one-dimensional population balances 
  1.4.3.1 Hounslow’s discretisation method and the Litster expansion
  1.4.3.2 Other methods for numerical solution of population balances 
  1.5 
  Inverse problems in population balances 
   
  Summary
   
  Table of symbo