Author
B.H. Shah
Bio: B.H. Shah is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Population & Coalescence (physics). The author has an hindex of 5, co-authored 5 publications receiving 233 citations.
Papers
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TL;DR: A simulation procedure is presented in this work which can analyze the behavior of any dispersed phase system consisting of particles whose random behavior is specified in terms of probability functions, and is an efficient alternative to the modeling of such systems.
Abstract: A simulation procedure is presented in this work which can analyze the behavior of any dispersed phase system consisting of particles whose random behavior is specified in terms of probability functions. The procedure distinguishes itself from its predecessors in being free from arbitrary discretization of time or any other parameter along which the system evolves, and its ability to predict the behavior of randomly behaving small populations. Where population balance equations, which describe the behavior of particulate systems, cannot be readily solved, the simulation technique presented herein represents an efficient alternative to the modeling of such systems. Tables and a flow chart are given which would enable the use of the method for any system with specified particle behavior.
118 citations
TL;DR: An early technique by Kendall for simulating the behavior of populations which obey the birth-and-death model has been extended to include the factor of variation in individual cellular state and behavior, and the resulting algorithm is probabilistically exact.
Abstract: Mathematical models of cell populations which recognize them to be segregated into individual cells differing from one another in state and behavior lead to complicated integro-differential equations. Analysis of fluctuations in small populations leads to the even more complex situation of coupled integro-differential equations. An early technique by Kendall for simulating the behavior of populations which obey the birth-and-death model has been extended in this work to include the factor of variation in individual cellular state and behavior. The resulting algorithm is probabilistically exact in the sense that the random variables to be generated have exactly derived distribution functions, and involves no arbitrary discretization of the time interval, characteristic of simulation techniques in general. The simulated systems include populations distributed according to their age in a birth-and-death process and a batch culture of cells distributed according to their mass which grow and reproduce by binary fission.
50 citations
TL;DR: In this article, a population balance model is considered for the description of mass transfer in liquid-liquid dispersions in a mechanically agitated vessel operated continuously, where the dispersions considered are of low dispersed phase fraction in which coalescence processes may be assumed to be negligible.
30 citations
TL;DR: In this paper, the adequacy of the standard population balance equation hinges on the largeness of the population which depends on the nature of the agglomeration kernel, and the complete set of product density equations for an aggregating system has been identified and analytical results have been obtained from some ultra-simplified situations.
25 citations
TL;DR: In this article, the dynamics of bubble populations in a gas fluidized bed have been analyzed using a simulation technique due to the authors [11,12] and it was shown that small bubble populations arising from progressive coalescence may lead to inherent fluctuations which may be considerable.
16 citations
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TL;DR: The Handbook of Statistical Tables (HNT) as mentioned in this paper is a collection of tables from B.D. Owen's "Handbook of Statistical Table Tables" (1962).
Abstract: D. B. Owen: Handbook of Statistical Tables. London: Pergamon Press; Reading, Massachusetts: Addison‐Wesley, 1962. Pp. xii+580. 70s.
635 citations
382 citations
TL;DR: In this paper, a Monte Carlo method for the simulation of growth processes is presented, in which the number of particles is kept constant, regardless of whether the actual process results in a net loss (as in coagulation) or net increase of particles.
326 citations
TL;DR: In this article, high-resolution finite volume methods developed for compressible gas dynamics have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur.
Abstract: Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. Rather than developing new algorithms specific to population balance equations, it is proposed to adapt the high-resolution finite volume methods developed for compressible gas dynamics, which have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur. High-resolution algorithms are presented for simulating multidimensional population balance equations with nucleation and size-dependent growth rates. For sharp distributions, these high-resolution algorithms can achieve improved numerical accuracy with orders-of-magnitude lower computational cost than other finite difference and finite volume algorithms. The algorithms are implemented in the ParticleSolver software package, which is applied to batch and continuous processes with one and multiple internal coordinates. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2738 –2749, 2004
262 citations
TL;DR: An overview of recent developments in the control of crystallization processes, including activities in sensor technologies, model identification, experimental design, process simulation, robustness analysis, and optimal control are provided.
233 citations