Firms’ Size Distribution and Growth Rates as Determinants of Business Fluctuations

2006 ◽  
pp. 181-186 ◽  
Author(s):  
Domenico Gatti ◽  
Corrado Guilmi ◽  
Edoardo Gaffeo ◽  
Mauro Gallegati ◽  
Gianfranco Giulioni ◽  
...  
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Business Fluctuations

Firms’ Size Distribution and Growth Rates as Determinants of Business Fluctuations

2005 ◽  
pp. 181-186
Author(s):  
Domenico Delli Gatti ◽  
Corrado Di Guilmi ◽  
Edoardo Gaffeo ◽  
Mauro Gallegati ◽  
Gianfranco Giulioni ◽  
...  
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Business Fluctuations

Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

scholarly journals Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function

2019 ◽  
Vol 377 (2143) ◽  
pp. 20180210 ◽  
Author(s):  
Eugenya V. Makoveeva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Growth Rates ◽  
Separation Of Variables ◽  
Size Distribution Function ◽  
Solid Particles ◽  
Supersaturated Solution ◽  
Metastable Liquid ◽  
Differential Model ◽  
Nonlinear Growth

In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

scholarly journals Novel estimation of aerosol processes with particle size distribution measurements: a case study with the TOMAS algorithm v1.0.0

2021 ◽  
Vol 14 (3) ◽  
pp. 1821-1839
Author(s):  
Dana L. McGuffin ◽  
Yuanlong Huang ◽  
Richard C. Flagan ◽  
Tuukka Petäjä ◽  
B. Erik Ydstie ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Growth Rates ◽  
Measurement Bias ◽  
Size Distributions ◽  
Inverse Technique ◽  
Microphysical Processes ◽  
Model Measurement ◽  
Aerosol Properties

Abstract. Atmospheric aerosol microphysical processes are a significant source of uncertainty in predicting climate change. Specifically, aerosol nucleation, emissions, and growth rates, which are simulated in chemical transport models to predict the particle size distribution, are not understood well. However, long-term size distribution measurements made at several ground-based sites across Europe implicitly contain information about the processes that created those size distributions. This work aims to extract that information by developing and applying an inverse technique to constrain aerosol emissions as well as nucleation and growth rates based on hourly size distribution measurements. We developed an inverse method based upon process control theory into an online estimation technique to scale aerosol nucleation, emissions, and growth so that the model–measurement bias in three measured aerosol properties exponentially decays. The properties, which are calculated from the measured and predicted size distributions, used to constrain aerosol nucleation, emission, and growth rates are the number of particles with a diameter between 3 and 6 nm, the number with a diameter greater than 10 nm, and the total dry volume of aerosol (N3–6, N10, Vdry), respectively. In this paper, we focus on developing and applying the estimation methodology in a zero-dimensional “box” model as a proof of concept before applying it to a three-dimensional simulation in subsequent work. The methodology is first tested on a dataset of synthetic and perfect measurements that span diverse environments in which the true particle emissions, growth, and nucleation rates are known. The inverse technique accurately estimates the aerosol microphysical process rates with an average and maximum error of 2 % and 13 %, respectively. Next, we investigate the effect that measurement noise has on the estimated rates. The method is robust to typical instrument noise in the aerosol properties as there is a negligible increase in the bias of the estimated process rates. Finally, the methodology is applied to long-term datasets of in situ size distribution measurements in western Europe from May 2006 through June 2007. At Melpitz, Germany, and Hyytiälä, Finland, the average diurnal profiles of estimated 3 nm particle formation rates are reasonable, having peaks near noon local time with average peak values of 1 and 0.15 cm−3 s−1, respectively. The normalized absolute error in estimated N3–6, N10, and Vdry at three European measurement sites is less than 15 %, showing that the estimation framework developed here has potential to decrease model–measurement bias while constraining uncertain aerosol microphysical processes.

scholarly journals Novel estimation of aerosol processes with particle size distribution measurements: a case study with TOMAS algorithm

2020 ◽  
Author(s):  
Dana L. McGuffin ◽  
Yuanlong Huang ◽  
Richard C. Flagan ◽  
Tuukka Petäjä ◽  
B. Erik Ydstie ◽  
...  
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Measurement Bias ◽  
Size Distributions ◽  
Inverse Technique ◽  
Microphysical Processes ◽  
Aerosol Emissions ◽  
Model Measurement ◽  
Aerosol Properties

Abstract. Atmospheric aerosol microphysical processes are a significant source of uncertainty in predicting climate change. Specifically, aerosol nucleation, emissions, and growth rates, which are simulated in chemical transport models to predict the particle size distribution, are not understood well. However, long-term size distribution measurements made at several ground-based sites across Europe implicitly contain information about the processes that created those size distributions. This work aims to extract that information by developing and applying an inverse technique to constrain aerosol emissions as well as nucleation and growth rates based on hourly size distribution measurements. We developed an inverse method based upon process control theory into an online estimation technique to scale aerosol emissions, growth, and nucleation so that the model-measurement bias in three measured aerosol properties exponentially decays. The properties, which are calculated from the measured and predicted size distributions, used to constrain aerosol nucleation, emission, and growth rates are the number of particles with diameter between 3 nm and 6 nm, the number with diameter greater than 10 nm, and the total dry volume of aerosol (N3-6, N10, Vdry), respectively. In this paper, we focus on developing and applying the estimation methodology in a zero-dimensional "box" model as a proof-of-concept before applying it to a three-dimensional simulation in subsequent work. The methodology is first tested on a dataset of synthetic and perfect measurements that span diverse environments in which the true particle emissions, growth, and nucleation rates are known. The inverse technique accurately estimates the aerosol microphysical process rates with an average and maximum error of 2 % and 13 %, respectively. Next, we investigate the effect that measurement noise has on the estimated rates. The method is robust to typical instrument noise in the aerosol properties as there is a negligible increase in bias of the estimated process rates. Finally, the methodology is applied to long-term datasets of in-situ size distribution measurements in Western Europe from May 2006 through June 2007. At Melpitz, Germany and Hyytiälä, Finland, the average diurnal profiles of estimated 3 nm particle formation rates are reasonable, having peaks near noon local time with average peak values of 1 and 0.15 cm−3 s−1, respectively. The normalized absolute error in estimated N3-6, N10, and Vdry at three European measurement sites is less than 15 %, showing that the estimation framework developed here has potential to decrease model-measurement bias while constraining uncertain aerosol microphysical processes.

scholarly journals On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization

2019 ◽  
Vol 377 (2143) ◽  
pp. 20180214 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Irina G. Nizovtseva
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Growth Rates ◽  
Biomedical Applications ◽  
Size Distribution Function ◽  
Porcine Insulin ◽  
Unsteady State ◽  
State Growth

A generalized theory of nucleation and growth of crystals in a metastable (supercooled or supersaturated) liquid is developed taking into account two principal effects: the diffusion mechanism of the particle-size distribution function in the space of particle radii and the unsteady-state growth rates of individual crystals induced by fluctuations in external temperature or concentration field. A system of the Fokker–Planck and balance integro-differential equations is formulated and analytically solved in a parametric form for arbitrary nucleation kinetics and arbitrary growth rates of individual crystals. The particle-size distribution function and system metastability are found in an explicit form. The Weber–Volmer–Frenkel–Zel'dovich and Meirs kinetic mechanisms, as well as the unsteady-state growth rates of nuclei (Alexandrov & Alexandrova 2019 Phil. Trans. R. Soc. A 377 , 20180209 ( doi:10.1098/rsta.2018.0209 )), are considered as special cases. Some potential biomedical applications of the present theory for crystal growth from supersaturated solutions are discussed. The theory is compared with experimental data on protein and insulin crystallization (growth dynamics of the proteins lysozyme and canavalin as well as of bovine and porcine insulin is considered). The hat-shaped particle-size distribution functions for lysozyme and canavalin crystals as well as for bovine and porcine insulin are found. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

Effects of growth rates in models of size distribution formation in plants and animals

1987 ◽  
Vol 36 (1-2) ◽  
pp. 119-137 ◽  
Author(s):  
D.L. DeAngelis ◽  
M.A. Huston
Keyword(s):  
Size Distribution ◽  
Growth Rates

Particle number size distribution in the eastern Mediterranean: Formation and growth rates of ultrafine airborne atmospheric particles

2013 ◽  
Vol 77 ◽  
pp. 790-802 ◽  
Author(s):  
I. Kopanakis ◽  
S.E. Chatoutsidou ◽  
K. Torseth ◽  
T. Glytsos ◽  
M. Lazaridis
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Particle Number ◽  
Eastern Mediterranean ◽  
Atmospheric Particles ◽  
Number Size Distribution ◽  
Particle Number Size Distribution

scholarly journals A Comparison of the Biology of Echinus esculentus in Different Habitats. Part II

1935 ◽  
Vol 20 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Hilary B. Moore
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Sea Temperature ◽  
Growing Period ◽  
Isle Of Man ◽  
Males And Females

1. Echinus esculentus was studied from four localities in the Isle of Man and from one in the Clyde.2. The inshore races are thicker shelled and natter, and on all grounds the urchins become taller with increasing age.3. Size distribution measurements on the Chickens material showed a rapid growing period in the spring, followed by cessation of growth for the rest of the year. There is a correlation between amount of growth in a given year, and the sea temperature. On the Breakwater the males and females grow at slightly different times of year.4. Concentric pigmented rings are demonstrated in the test, and are shown to be annual. They are used for estimating the growth rates on the different grounds, which are compared.5. The duration of life is four to eight years, and perhaps more in the very large southern urchins.

Estimating atmospheric nucleation rates from size distribution measurements: Analytical equations for the case of size dependent growth rates

2014 ◽  
Vol 69 ◽  
pp. 13-20 ◽  
Author(s):  
Hannele Korhonen ◽  
Veli-Matti Kerminen ◽  
Harri Kokkola ◽  
Kari E.J. Lehtinen
Keyword(s):  
Size Distribution ◽  
Growth Rates ◽  
Size Dependent ◽  
Atmospheric Nucleation ◽  
Dependent Growth
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