Crystal growth rate models and similarity of population balances for size-dependent growth rate and for constant growth rate dispersion

AbstractKinetic parameters describing continuous reaction crystallization of struvite from aqueous solutions containing also calcium ions (from 100 to 2000 mg Ca2+/kg) were estimated. Test results were compared with kinetic data of struvite manufactured from real cattle liquid manure. Kinetic model for ideal MSMPR (Mixed Suspension Mixed Product Removal) crystallizer was used assuming dependence of crystal growth rate G on its size L (size-dependent growth, SDG MSMPR model). Based on nonlinear regression and statistical analysis, one from within five considered G(L) models was selected – Rojkowski exponential (RE) model – rendering the experimental population density distributions the best. It was concluded, that calcium ions influenced all components of struvite manufacturing process disadvantageously. A rise of Ca2+ concentration in a feed from 100 to 2000 mg/kg increased nucleation rate ca. 160-time, whereas growth rate of nuclei up to macroscopic size G0 decreased more than 10-time. Linear (larger) crystal growth rate G¥ was nearly two-times smaller: 1.71·10–8 m/s (100 mg Ca2+/kg) – 9.10·10–9 m/s (2000 mg Ca2+/kg). Resulting in a product with deteriorated quality. Mean size of the crystals decreased nearly two-times (to 18.4 μm), non-homogeneity within product population enlarged and calcium fraction in the product increased. The product, beside struvite MgNH4PO4·6H2O, also contained hydrated amorphous calcium phosphate(V) Ca3(PO4)2·nH2O (ACP). It was observed, that 5-times smaller concentration of phosphate(V) ions in a feed and magnesium ions excess in relation to phosphate(V) and ammonium ions (1.2 : 1 : 1) influenced all kinetic parameters of continuous struvite reaction crystallization advantageously.

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Hybrid systems approach to modeling stochastic dynamics of cell size

10.1101/044131 ◽

2016 ◽

Cited By ~ 1

Author(s):

Cesar Augusto Vargas-Garcia ◽

Abhyudai Singh

Keyword(s):

Growth Rate ◽

Cell Size ◽

Size Variation ◽

Model Parameters ◽

Constant Growth Rate ◽

Division Rate ◽

Size Dependent ◽

Daughter Cells ◽

Constant Growth ◽

Over Time

A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider three different classes of models: i) a size-dependent growth rate and timer-dependent division rate; ii) a constant growth rate and size-dependent division rate and iii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

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An Appraisal of the Size-Dependent Mortality Hypothesis for Larval Fish: Comparison of a Multispecies Study with an Empirical Review

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f93-242 ◽

1993 ◽

Vol 50 (10) ◽

pp. 2166-2174 ◽

Cited By ~ 39

Author(s):

Pierre Pepin

Keyword(s):

Growth Rate ◽

Larval Fish ◽

Mortality Rates ◽

Accurate Information ◽

Constant Growth Rate ◽

Size Dependent ◽

Conception Bay ◽

Biased Estimates ◽

Constant Growth ◽

Dependent Mortality

This study presents an assessment of the size-dependent mortality hypothesis for larval fish from a multispecies survey of Conception Bay, Newfoundland, Canada. Mortality rates are estimated using a length-based method (per millimetre). The results from this survey are consistent with previous studies which indicate that losses decrease with increasing size of fish. However, for each species within this survey, mortality rates are constant. Comparison of mortality rates within species among surveys indicates that as the range of size categories sampled increases, the estimated mortality rates decrease, despite evidence of adequate fit to the length-based model. The findings indicate that previous relationships between size or stage and mortality of larval fish should be reevaluated. Length-based methodology used to estimate mortality rates of larval fish appears to provide biased estimates of this vital characteristic. It is suggested that using size as a proxy for biological age (i.e., assuming a constant growth rate) may be an invalid assumption. Future surveys will need to provide accurate information about the age structure of larvae sampled in order to properly estimate mortality rates.

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Crystal Growth Rate Dispersion versus Size-Dependent Crystal Growth: Appropriate Modeling for Crystallization Processes

Crystal Growth & Design ◽

10.1021/acs.cgd.5b00126 ◽

2015 ◽

Vol 15 (5) ◽

pp. 2330-2336 ◽

Cited By ~ 17

Author(s):

Sukanya Srisanga ◽

Adrian E. Flood ◽

Shaun C. Galbraith ◽

Supagorn Rugmai ◽

Siriwat Soontaranon ◽

...

Keyword(s):

Growth Rate ◽

Crystal Growth ◽

Crystal Growth Rate ◽

Size Dependent

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Empirical Size-Dependent Growth Rate Models

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19920309 ◽

1992 ◽

Vol 57 (2) ◽

pp. 309-325 ◽

Cited By ~ 1

Author(s):

Jerzy Mydlarz

Keyword(s):

Growth Rate ◽

Crystal Size ◽

Size Range ◽

Growth Models ◽

Crystal Growth Rate ◽

Size Distributions ◽

Large Crystal ◽

Size Dependent ◽

Dependent Growth ◽

Empirical Size

A comparison of well known size-dependent crystal growth rate models has been presented. The models have been verified for crystal size distributions which have been recently presented in the literature. It is shown that for large crystal size range both the Abegg-Stevenson-Larson (ASL) model and the Canning-Randolph (C-R) model can be reduced to the simplest Bransom model. Two another kinetics size-dependent growth rate models have been presented and tested for size distributions which were recently presented by Mydlarz and Jones. Application of the proposed size-dependent growth models gives much better estimation of growth rate than other size-dependent models tested as well as Sikdar and White-Bendig-Larson methods.

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Bulk SiC Crystal Growth at Constant Growth Rate Utilizing a New Design of Resistive Furnace

Materials Science Forum ◽

10.4028/www.scientific.net/msf.600-603.27 ◽

2008 ◽

Vol 600-603 ◽

pp. 27-30 ◽

Cited By ~ 3

Author(s):

Eugene Y. Tupitsyn ◽

Alexander Galyukov ◽

Maxim V. Bogdanov ◽

Alexey Kulik ◽

Mark S. Ramm ◽

...

Keyword(s):

Growth Rate ◽

Crystal Growth ◽

Growth Parameters ◽

Constant Growth Rate ◽

Growth Profiles ◽

Constant Growth

In this work the problem of growth rate decaying during growth is considered. A new design and growth profiles are suggested in order to reduce deviations of growth parameters during the process of growth.

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Outbreaks in care homes may lead to substantial disease burden if not mitigated

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2020.0269 ◽

2021 ◽

Vol 376 (1829) ◽

pp. 20200269

Author(s):

Ian Hall ◽

Hugo Lewkowicz ◽

Luke Webb ◽

Thomas House ◽

Lorenzo Pellis ◽

...

Keyword(s):

Growth Rate ◽

Care Home ◽

Additive Model ◽

Care Homes ◽

Constant Growth Rate ◽

Worst Case ◽

Sis Model ◽

Dependent Growth ◽

The Uk ◽

Constant Growth

The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

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