Kinetic Analysis of Nonisothermal Crystallization

1995 ◽  
Vol 398 ◽  
Author(s):  
K. F. Kelton
Keyword(s):  
Computer Model ◽  
Fine Particles ◽  
Finite Sample ◽  
Nucleation Behavior ◽  
Structured Materials ◽  
Size Dependent ◽  
Model Predictions ◽  
Finite Sample Size ◽  
Dependent Growth ◽  
Calorimetric Studies

ABSTRACTA realistic computer model for polymorphic crystallization under isothermal and nonisothermal conditions, which takes proper account of time-dependent nucleation behavior and cluster-size-dependent growth, is presented. A new correction to the standard Johnson-Mehl-Avrami-Kolmogorov (JMAK) statistical analysis that takes account of finite sample size is incorporated to simulate data taken from fine particles and nano-structured materials. Model predictions compare well with experimental data obtained from calorimetric studies of the polymorphic crystallization of lithium disilicate glass. The computer model is employed to evaluate commonly used methods of analysis for calorimetric data and to suggest new approaches for extracting kinetic parameters.

scholarly journals THRESHOLD SIZE FOR FLOWERING IN DIFFERENT HABITATS: EFFECTS OF SIZE-DEPENDENT GROWTH AND SURVIVAL

Ecology ◽  
1997 ◽  
Vol 78 (7) ◽  
pp. 2118-2132 ◽  
Author(s):  
Renate A. Wesselingh ◽  
Peter G. L. Klinkhamer ◽  
Tom J. de Jong ◽  
Laurence A. Boorman
Keyword(s):  
Growth And Survival ◽  
Threshold Size ◽  
Size Dependent ◽  
Dependent Growth

Apparent size-dependent growth in aggregating crystallizers

1996 ◽  
Vol 51 (14) ◽  
pp. 3685-3695 ◽  
Author(s):  
David M. Ginter ◽  
Sudarshan K. Loyalka
Keyword(s):  
Apparent Size ◽  
Size Dependent ◽  
Dependent Growth

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bahador Abolpour ◽  
M. Mehdi Afsahi ◽  
Ataallah Soltani Goharrizi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fine Particles ◽  
Direct Reduction ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Dynamic Motion ◽  
Magnetite Ore ◽  
Model Predictions ◽  
Kinetics Of

Abstract In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust
Keyword(s):  
Unit Root ◽  
Sufficient Conditions ◽  
Unit Root Test ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Test Procedures ◽  
Asymptotic Size ◽  
Finite Sample Size ◽  
Topological Sense

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

Size-dependent growth responses to competition and environment in Nothofagus menziesii

2012 ◽  
Vol 270 ◽  
pp. 223-231 ◽  
Author(s):  
Tomás A. Easdale ◽  
Robert B. Allen ◽  
Duane A. Peltzer ◽  
Jennifer M. Hurst
Keyword(s):  
Growth Responses ◽  
Size Dependent ◽  
Dependent Growth

scholarly journals On the variance parameter estimator in general linear models

Metrika ◽  
2019 ◽  
Vol 83 (2) ◽  
pp. 243-254
Author(s):  
Mathias Lindholm ◽  
Felix Wahl
Keyword(s):  
Sample Size ◽  
Linear Models ◽  
General Linear ◽  
Finite Sample ◽  
Parameter Estimator ◽  
General Linear Models ◽  
Vector Autoregressive ◽  
Finite Sample Size ◽  
Error Terms ◽  
Variance Parameter

Abstract In the present note we consider general linear models where the covariates may be both random and non-random, and where the only restrictions on the error terms are that they are independent and have finite fourth moments. For this class of models we analyse the variance parameter estimator. In particular we obtain finite sample size bounds for the variance of the variance parameter estimator which are independent of covariate information regardless of whether the covariates are random or not. For the case with random covariates this immediately yields bounds on the unconditional variance of the variance estimator—a situation which in general is analytically intractable. The situation with random covariates is illustrated in an example where a certain vector autoregressive model which appears naturally within the area of insurance mathematics is analysed. Further, the obtained bounds are sharp in the sense that both the lower and upper bound will converge to the same asymptotic limit when scaled with the sample size. By using the derived bounds it is simple to show convergence in mean square of the variance parameter estimator for both random and non-random covariates. Moreover, the derivation of the bounds for the above general linear model is based on a lemma which applies in greater generality. This is illustrated by applying the used techniques to a class of mixed effects models.

The expected population size in a cell-size-dependent branching process

1981 ◽  
Vol 18 (01) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Exponential Growth ◽  
Branching Process ◽  
Expected Number ◽  
Size Dependent ◽  
Daughter Cells ◽  
Rate Of Increase ◽  
A Cell ◽  
Dependent Growth ◽  
Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

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