On the stochastic simulation of particulate systems

Haseltine, Eric L.; Patience, Daniel B.; Rawlings, James B.

doi:10.1016/j.ces.2004.05.038

Cited by 30 publications

(30 citation statements)

References 23 publications

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“…While the method is highly efficient when the physics are simple, the approach does not generalize to complex physics. Monte Carlo simulations track the histories of individual particles, each of which exhibits random behaviour according to a probabilistic model [122,123]. Monte Carlo simulations are most suitable for stochastic PB equations, especially for complex systems, but typically very computationally expensive.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…Therefore, various numerical algorithms have been developed for solving PB equations such as method of moment [114][115][116][117], method of characteristics [108,[118][119][120][121], Monte Carlo techniques [122,123], and discretization methods including finite element technique [119,124,125], cell average methods [107], hierarchical solution strategy based on multilevel discretization [126], method of classes [82,95], fixed and moving pivot method [127,128], and finite difference/volume methods [90,119,[129][130][131]. Table 1 summarises these numerical solution methods with the further reviews below.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

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Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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“…Hence, representative values for these classes need to be determined because equation (6) only provides the aggregation rate for two distinct sizes. Accordingly, an averaging of the rates over each size class interval is performed:…”

Section: Monte Carlo Schemementioning

confidence: 99%

“…As an alternative to deterministic population balance models, stochastic or so-called Monte Carlo methods have gained increasing popularity for the simulation of par ticulate processes [2][3][4][5][6] . There, the evolution of a set of representative, discrete particles is tracked.…”

Section: Introductionmentioning

confidence: 99%

Aggregate Structure Evolution for Size-Dependent Aggregation by Means of Monte Carlo Simulations

Briesen

2007

KONA

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Aggregation during crystallization and precipitation processes often leads to complex-shaped particle aggregates. As an alternative to low-dimensional deterministic population balance models, where assumptions on the particle shape must be made, stochastic or so-called Monte Carlo methods can be employed. In previous work a hierarchical characterization of aggregates has been proposed (Briesen, AIChE J., 52, 2436-2446, 2006

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“…[5] It has diverse applications including polymerization, crystallization, precipitation, and several other chemical industrial processes. [6,7] In the biological sciences, PBM has been employed heavily due to vast applications of population dynamics in the modelling of continuous variation in the microbial populations, [2,8,9] phenomena such as cell growth, [10] intracellular reactions and division with stochastic partitioning, [11][12][13] and gene regulatory processes by population mediated signalling. [14] Mathematical modelling for the concentrations of multi proteins in a given T-cell has been investigated by several researchers.…”

Section: Introductionmentioning

confidence: 99%

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Ali

Elkamel

Gruy³

et al. 2016

Can J Chem Eng

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The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, mass, and protein concentration) is typically modelled by a population balance equation, a first-order linear hyperbolic partial differential equation that is shared by all T-cells is involved. At these crossing points, the linear advection equation is not possible by using the hyperbolic conservation laws in a classical way. Therefore, a new transport method is introduced in this article that is able to find the population density function for such processes. A multi-scale mathematical modelling framework is employed. At the first scale, two processes, which are termed as the activation and reaction terms (assimilated as nucleation and growth in chemical processes), are studied as independent processes. At the second scale, the dynamic variation in the population density of activated T-cells is investigated in the presence of activation and reaction terms. The newly-developed transport method is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.2

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On the stochastic simulation of particulate systems

Cited by 30 publications

References 23 publications

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Aggregate Structure Evolution for Size-Dependent Aggregation by Means of Monte Carlo Simulations

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

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