De Mello, Fernanda; Oliveira, Carlos A L; Ribeiro, Ricardo P; Resende, Emiko K; Povh, Jayme A; Fornari, Darci C; Barreto, Rogério V; McManus, Concepta; Streit, Danilo
2015-01-01
Was evaluated the pattern of growth among females and males of tambaqui by Gompertz nonlinear regression model. Five traits of economic importance were measured on 145 animals during the three years, totaling 981 morphometric data analyzed. Different curves were adjusted between males and females for body weight, height and head length and only one curve was adjusted to the width and body length. The asymptotic weight (a) and relative growth rate to maturity (k) were different between sexes in animals with ± 5 kg; slaughter weight practiced by a specific niche market, very profitable. However, there was no difference between males and females up to ± 2 kg; slaughter weight established to supply the bigger consumer market. Females showed weight greater than males (± 280 g), which are more suitable for fish farming purposes defined for the niche market to larger animals. In general, males had lower maximum growth rate (8.66 g / day) than females (9.34 g / day), however, reached faster than females, 476 and 486 days growth rate, respectively. The height and length body are the traits that contributed most to the weight at 516 days (P <0.001). PMID:26628036
For prediction of elder survival by a Gompertz model, number dead is preferable to number alive
Hirsch, Henry R.
2008-01-01
The standard Gompertz equation for human survival fits very poorly the survival data of the very old (age 85 and above), who appear to survive better than predicted. An alternative Gompertz model based on the number of individuals who have died, rather than the number that are alive, at each age, tracks the data more accurately. The alternative model is based on the same differential equation as in the usual Gompertz model. The standard model describes the accelerated exponential decay of the number alive, whereas the alternative, heretofore unutilized model describes the decelerated exponential growth of the number dead. The alternative model is complementary to the standard and, together, the two Gompertz formulations allow accurate prediction of survival of the older as well as the younger mature members of the population. PMID:19424855
Nonselective Harvesting of a Prey-Predator Fishery with Gompertz Law of Growth
ERIC Educational Resources Information Center
Purohit, D.; Chaudhuri, K. S.
2002-01-01
This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…
2010-01-01
Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice. PMID:21029411
Nedorezov, L V
2015-01-01
For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation. PMID:26349222
Riggs, J E; Millecchia, R J
1992-09-01
Mortality trends in industrialized countries are characterized by declines in vascular disease (ischemic heart disease and stroke) and rises in cancers and degenerative diseases. These trends are typically analyzed by examining each disorder in isolation using the perspective of genetic and environmental influences. However, longitudinal Gompertzian analysis and the Gompertz-Strehler model of aging and mortality as modified by Lestienne suggest that age-specific mortality rates, for both general and disease-specific mortality, are an interrelated deterministic function of aggregate genetic, environmental and competitive influences. Consequently, evolving mortality trends and patterns appear to be influenced by three factors (with deterministic competition being the third factor), rather than just two factors (genetic and environmental) as commonly depicted. PMID:1434950
Predictive implications of Gompertz's law
NASA Astrophysics Data System (ADS)
Richmond, Peter; Roehner, Bertrand M.
2016-04-01
Gompertz's law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold up to age 106. At that age the death rate is about 50%. Beyond 106 there is so far no convincing statistical evidence available because the number of survivors are too small even in large nations. However, assuming that Gompertz's law continues to hold beyond 106, we conclude that the mortality rate becomes equal to 1 at age 120 (meaning that there are 1000 deaths in a population of one thousand). In other words, the upper bound of human life is near 120. The existence of this fixed-point has interesting implications. It allows us to predict the form of the relationship between death rates at age 35 and the doubling time of Gompertz's law. In order to test this prediction, we first carry out a transversal analysis for a sample of countries comprising both industrialized and developing nations. As further confirmation, we also develop a longitudinal analysis using historical data over a time period of almost two centuries. Another prediction arising from this fixed-point model, is that, above a given population threshold, the lifespan of the oldest persons is independent of the size of their national community. This prediction is also supported by empirical evidence.
Nonlinear Gompertz Curve Models of Achievement Gaps in Mathematics and Reading
ERIC Educational Resources Information Center
Cameron, Claire E.; Grimm, Kevin J.; Steele, Joel S.; Castro-Schilo, Laura; Grissmer, David W.
2015-01-01
This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth--Children and Young Adults and Early Childhood Longitudinal Study--Kindergarten Cohort [ECLS-K]). The S-shaped…
Golubev, A G
2004-01-01
The Gompertz-Makeham law (-dn/dt x l/n(t)=C+lambdae(gammat)) so as other genuine laws of Nature is strictly applicable only to ideal objects (populations and cohorts) analogously to laws of mechanics or thermodynamics, which are exactly true only for such physical abstractions as mass points or ideal gases. Therefore, a biologically meaningful interpretation of the parameters of this law is likely to be more important for understanding the aging process than devising of alternative analytical descriptions of biodemographic processes for the sake of a better fit only. Numerical modeling of ideal cohorts of aging organisms obeying the Gompertz-Makeha law makes it possible to differentiate possible real and apparent changes in mortality patterns that occur in human history and in evolution and are observed in gerontological experiments and to demonstratively show such effects as the dependency of longevity upon population size, the evolutionarily important possibility of reciprocal changes in the mean and maximal longevity, or detection of apparent changes in negatively correlated aging rate and vitality when the Makeham term is ignored, which is usual in demography. The basic difference between the Makeham term Cand Gompertz term lambdae(gammat) is suggested to be not that the former is constant, whereas the latter is age-dependent, but that the former comprises the contributions of inherently irresistible stresses to mortality, whereas the latter comprises the contributions of resistible stresses to mortality and shows how changes in the ability to resist them is translated into changes in mortality. PMID:15754953
Gompertz-Makeham life expectancies: expressions and applications.
Missov, Trifon I; Lenart, Adam
2013-12-01
In a population of individuals, whose mortality is governed by a Gompertz-Makeham hazard, we derive closed-form solutions to the life-expectancy integral, corresponding to the cases of homogeneous and gamma-heterogeneous populations, as well as in the presence/absence of the Makeham term. Derived expressions contain special functions that aid constructing high-accuracy approximations, which can be used to study the elasticity of life expectancy with respect to model parameters. Knowledge of Gompertz-Makeham life expectancies aids constructing life-table exposures. PMID:24084064
Lambe, N R; Navajas, E A; Simm, G; Bünger, L
2006-10-01
This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from linear regression. In both breeds, all nonlinear models fitted the data well, with an average coefficient of determination (R2) of > 0.98. The linear model had a lower average R2 than any of the nonlinear models (< 0.94). The variables used to describe the best 3 models (logistic, Gompertz, and Richards) included estimated final BW (A); maximum ADG (B); age at maximum ADG (C); position of point of inflection in relation to A (D, for Richards only). The Richards and Gompertz models provided the best fit (average R2 = 0.986 to 0.989) in both breeds. Richards estimated an extra variable, allowing increased flexibility in describing individual growth patterns, but the Akaike's information criteria value (which weighs log-likelihood by number of parameters estimated) was similar to that of the Gompertz model. Variables A, B, C, and D were moderately to highly heritable in Texel lambs (h2 = 0.33 to 0.87), and genetic correlations between variables within-model ranged from -0.80 to 0.89, suggesting some flexibility to change the shape of the growth curve when selecting for different variables. In SBF lambs, only variables from the logistic and Gompertz models had moderate heritabilities (0.17 to 0.56), but with high genetic correlations between variables within each model (< -0.88 or > 0.92). Selection on growth variables seems promising (in Texel more than SBF), but high genetic correlations between variables may restrict the possibilities to change the growth curve shape. A random regression model was also fitted to the data to allow predictions of growth rates at relevant time
Evidence for the Gompertz curve in the income distribution of Brazil 1978-2005
NASA Astrophysics Data System (ADS)
Moura, N. J., Jr.; Ribeiro, M. B.
2009-01-01
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)], where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution P(x) = βx-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.
Redfern, Rebecca C.; DeWitte, Sharon N.
2011-01-01
This is the first study of Romanization to use the Siler and Gompertz-Makeham models of mortality in order to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N=518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose 2002) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern 2007; Redfern 2008b; Roberts and Cox 2003). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality were present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for males. The latter finding challenges received wisdom concerning the benefits of Romanization and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of males did not out-weigh underlying sex differences in biology that advantage females. PMID:20925081
Costa, L R F; Barthem, R B; Albernaz, A L; Bittencourt, M M; Villacorta-Corrêa, M A
2013-05-01
The tambaqui, Colossoma macropomum, is one of the most commercially valuable Amazonian fish species, and in the floodplains of the region, they are caught in both rivers and lakes. Most growth studies on this species to date have adjusted only one growth model, the von Bertalanffy, without considering its possible uncertainties. In this study, four different models (von Bertalanffy, Logistic, Gompertz and the general model of Schnüte-Richards) were adjusted to a data set of fish caught within lakes from the middle Solimões River. These models were adjusted by non-linear equations, using the sample size of each age class as its weight. The adjustment evaluation of each model was based on the Akaike Information Criterion (AIC), the variation of AIC between the models (Δi) and the evidence weights (wi). Both the Logistic (Δi = 0.0) and Gompertz (Δi = 1.12) models were supported by the data, but neither of them was clearly superior (wi, respectively 52.44 and 29.95%). Thus, we propose the use of an averaged-model to estimate the asymptotic length (L∞). The averaged-model, based on Logistic and Gompertz models, resulted in an estimate of L∞=90.36, indicating that the tambaqui would take approximately 25 years to reach average size. PMID:23917568
Redfern, Rebecca C; Dewitte, Sharon N
2011-02-01
This is the first study of health in the Roman Empire to use the Siler and Gompertz-Makeham models of mortality to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N = 518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose: The backbone of history: health and nutrition in the western hemisphere (2002)) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern: J Rom Archaeol Supp Series 64 (2007) 171-194; Redfern: Britannia 39 (2008a) 161-191; Roberts and Cox: Health and disease in Britain: from prehistory to the present day (2003)). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality was present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for men. The latter finding challenges received wisdom concerning the benefits of incorporation into the Empire and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet, and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of men did not outweigh underlying sex differences in biology that advantage women. PMID:20925081
Makeham's addition to the Gompertz law re-evaluated.
Hallén, Anund
2009-08-01
The Makeham parameter, a constant mortality rate independent of aging added to the Gompertz law of human mortality, is proposed to be a measure of the impact on mortality rate by extrinsic causes of mortality, with the effect of aging removed. A small intrinsic contribution to mortality, assumed to depend on the components involved in cellular function, is linked to the initial mortality rate of the Gompertz law. To avoid biased results and conclusions, the impact of extrinsic mortality should be eliminated from the Gompertz parameters. PMID:18951143
Belda-Galbis, Clara Miracle; Pina-Pérez, María Consuelo; Espinosa, Josepa; Marco-Celdrán, Aurora; Martínez, Antonio; Rodrigo, Dolores
2014-04-01
In order to assess the antibacterial activity of Stevia rebaudiana Bertoni (Stevia), Listeria innocua growth was characterized at 37 °C, in reference medium supplemented with a leaf infusion, a crude extract, and a steviol glycosides purified extract. Experimental data were fitted to the modified Gompertz model and the antibacterial activity of Stevia was determined based on the lag time (λ) and the maximum growth rate (μmax) reached, depending on the incubation conditions. As the leaf infusion showed the most marked elongation of λ and the most marked μmax reduction, its antimicrobial effect was evaluated at different concentrations, at 37, 22 and 10 °C. According to the results obtained, in general, the lower the temperature or the higher the Stevia concentration, the longer the λ and the lower the μmax, statistically significant being the effect of reducing temperature from 37 or 22 to 10 °C, the effect of increasing Stevia concentration from 0 or 0.5 to 1.5 or 2.5% (w/v), at 37 °C, and the elongation of λ observed in presence of 1.5 and 2.5% (w/v) of Stevia, at 22 °C. These results show that Stevia could be a bacterial growth control measure if a cold chain failure occurs. PMID:24290626
Compound equation developed for postnatal growth of birds and mammals
NASA Technical Reports Server (NTRS)
Laird, A. K.
1968-01-01
Compound growth equation was developed in which the rate of this linear growth process is regarded as proportional to the mass already attained at any instant by an underlying Gompertz process. This compound growth model was fitted to the growth data of a variety of birds and mammals of both sexes.
Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth
Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip
2014-01-01
Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199
Bhowmick, Amiya Ranjan; Bhattacharya, Sabyasachi
2014-08-01
Growth of living organisms is a fundamental biological process. It depicts the physiological development of the species related to the environment. Mathematical development of growth curve models has a long history since its birth. We propose a mathematical model to describe the evolution of relative growth rate as a function of time based on a real life experiment on a major Indian Carp Cirrhinus mrigala. We establish that the proposed model is able to describe the fish growth dynamics more accurately for our experimental data than some existing models e.g. logistic, Gompertz, exponential. Approximate expressions of the points of inflection and the time of achieving the maximum relative growth rate are derived. We study, in detail, the existence of a nonlinear least squares estimator of the model parameters and their consistency properties. Test-statistics is developed to study the equality of points of inflection and equality of the amount of time necessary to achieve the maximum relative growth rate for a species at two different locations. Using the theory of variance stabilizing transformations, we propose a new test statistic to test the effect of the decay parameter for the proposed growth law. The testing procedure is found to be more sensitive in comparison with the test based on nonlinear least squares estimates. Our proposed model provides a general framework to model growth in other disciplines as well. PMID:24933474
[The Gompertz-Makeham function in the description and projection of demographic phenomena].
Ogaz Pierce, H
1991-01-01
"The main aim of this article is to examine the application of [the Gompertz-Makeham mathematical function] in detail, and more specifically, its mathematical formulation and development. Another objective is to test an iterative method for obtaining parameters, by which one may obtain an optimal function best describing the behavior of a population in the face of demographic phenomena. This study was conducted with [Mexican data on] population growth and...structures by age of fertility and the labor force." (SUMMARY IN ENG) PMID:12319427
How could the Gompertz-Makeham law evolve.
Golubev, A
2009-05-01
In line with the origin of life from the chemical world, biological mortality kinetics is suggested to originate from chemical decomposition kinetics described by the Arrhenius equation k = A*exp(-E/RT). Another chemical legacy of living bodies is that, by using the appropriate properties of their constituent molecules, they incorporate all their potencies, including adverse ones. In early evolution, acquiring an ability to use new molecules to increase disintegration barrier E might be associated with new adverse interactions, yielding products that might accumulate in organisms and compromise their viability. Thus, the main variable of the Arrhenius equation changed from T in chemistry to E in biology; mortality turned to rise exponentially as E declined with increasing age; and survivorship patterns turned to feature slow initial and fast late descent making the bulk of each finite cohort to expire within a short final period of its lifespan. Numerical modelling shows that such acquisition of new functions associated with faster functional decline may increase the efficiency of investing resources into progeny, in line with the antagonistic pleiotropy theory of ageing. Any evolved time trajectories of functional changes were translated into changes in mortality through exponent according to the generalised Gompertz-Makeham law mu = C(t)+Lambda*exp[-E(t)], which is reduced to the conventional form when E(t) = E0-gammat and C is constant. The proposed model explains the origin of the linear mid-age functional decline followed by its deceleration at later ages and the positive correlation between the initial vitality and the rate of ageing. PMID:19490880
Lee, Yong Ju; Jung, Byeong Su; Kim, Kee-Tae; Paik, Hyun-Dong
2015-09-01
A predictive model was performed to describe the growth of Staphylococcus aureus in raw pork by using Integrated Pathogen Modeling Program 2013 and a polynomial model as a secondary predictive model. S. aureus requires approximately 180 h to reach 5-6 log CFU/g at 10 °C. At 15 °C and 25 °C, approximately 48 and 20 h, respectively, are required to cause food poisoning. Predicted data using the Gompertz model was the most accurate in this study. For lag time (LT) model, bias factor (Bf) and accuracy factor (Af) values were both 1.014, showing that the predictions were within a reliable range. For specific growth rate (SGR) model, Bf and Af were 1.188 and 1.190, respectively. Additionally, both Bf and Af values of the LT and SGR models were close to 1, indicating that IPMP Gompertz model is more adequate for predicting the growth of S. aureus on raw pork than other models. PMID:25930109
English, Sinéad; Bateman, Andrew W; Clutton-Brock, Tim H
2012-05-01
Lifetime records of changes in individual size or mass in wild animals are scarce and, as such, few studies have attempted to model variation in these traits across the lifespan or to assess the factors that affect them. However, quantifying lifetime growth is essential for understanding trade-offs between growth and other life history parameters, such as reproductive performance or survival. Here, we used model selection based on information theory to measure changes in body mass over the lifespan of wild meerkats, and compared the relative fits of several standard growth models (monomolecular, von Bertalanffy, Gompertz, logistic and Richards). We found that meerkats exhibit monomolecular growth, with the best model incorporating separate growth rates before and after nutritional independence, as well as effects of season and total rainfall in the previous nine months. Our study demonstrates how simple growth curves may be improved by considering life history and environmental factors, which may be particularly relevant when quantifying growth patterns in wild populations. PMID:22108854
NASA Astrophysics Data System (ADS)
McAneney, H.; O'Rourke, S. F. C.
2007-02-01
The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth
[Gompertz-Makeham law or the question of accuracy].
Koschin, F
1981-01-01
The author attempts to use the Gompertz-Makeham curve to smooth age-specific mortality data without methodological errors or simplification. He also calculates an estimate of the inaccuracy of the statistical data used and evaluates the quality of this estimate. The data concern the mortality of Czechoslovak men aged 60-87 during the 1960s. The result of the calculations are compared with the results obtained by Cramer and Wold for Sweden. (summary in ENG, RUS) PMID:12338689
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective of this research was to develop a new kinetic model to describe the isothermal growth of microorganisms. The new model was tested with Listeria monocytogenes in broth and frankfurters, and compared with two commonly used models - Baranyi and modified Gompertz models. Bias factor (BF)...
Technology Transfer Automated Retrieval System (TEKTRAN)
A new concept for estimating the bacterial growth under temperature fluctuations was hypothesized and validated using Clostridium perfringens as a test organism. This new methodology was based on the Gompertz models to calculate the equivalent growth times under different temperatures, and estimate...
Modeling the growth of Listeria monocytogenes in mold-ripened cheeses.
Lobacz, Adriana; Kowalik, Jaroslaw; Tarczynska, Anna
2013-06-01
This study presents possible applications of predictive microbiology to model the safety of mold-ripened cheeses with respect to bacteria of the species Listeria monocytogenes during (1) the ripening of Camembert cheese, (2) cold storage of Camembert cheese at temperatures ranging from 3 to 15°C, and (3) cold storage of blue cheese at temperatures ranging from 3 to 15°C. The primary models used in this study, such as the Baranyi model and modified Gompertz function, were fitted to growth curves. The Baranyi model yielded the most accurate goodness of fit and the growth rates generated by this model were used for secondary modeling (Ratkowsky simple square root and polynomial models). The polynomial model more accurately predicted the influence of temperature on the growth rate, reaching the adjusted coefficients of multiple determination 0.97 and 0.92 for Camembert and blue cheese, respectively. The observed growth rates of L. monocytogenes in mold-ripened cheeses were compared with simulations run with the Pathogen Modeling Program (PMP 7.0, USDA, Wyndmoor, PA) and ComBase Predictor (Institute of Food Research, Norwich, UK). However, the latter predictions proved to be consistently overestimated and contained a significant error level. In addition, a validation process using independent data generated in dairy products from the ComBase database (www.combase.cc) was performed. In conclusion, it was found that L. monocytogenes grows much faster in Camembert than in blue cheese. Both the Baranyi and Gompertz models described this phenomenon accurately, although the Baranyi model contained a smaller error. Secondary modeling and further validation of the generated models highlighted the issue of usability and applicability of predictive models in the food processing industry by elaborating models targeted at a specific product or a group of similar products. PMID:23548297
[The age-related dynamics of mortality and the Gompertz-Makeham law].
Ekonomov, A L; Iarygin, V N
1989-01-01
Using the statistics of mortality of Caucasian population of 48 states of the USA (1969-1971) it was demonstrated that the real age dynamics of human mortality may differ significantly both from the Gompertz law and from the Gompertz-Makeham law. Using of the Gompertz-Makeham formula leads to appearance of negative A value in 77 cases out of 96. This makes it difficult to interpret this parameter as a "background" component of mortality. Using of the Gompertz formula in different age groups leads uncoordinated changes in alpha and R0 values in every state. Hence, it is impossible to plot geographically stable characters for Gompertz parameters alpha for subsequent epidemiological analysis. The "aging rate", estimated by parameter is not stable throughout the life span of 30-92 years, but changes with certain pattern. PMID:2741560
Critical analysis of the applicability of the Gompertz-Makeham law in human populations.
Pakin YuV; Hrisanov, S M
1984-01-01
The adequacy of the Gompertz-Makeham law (Rt = Beat + A) for a description of human mortality was tested. The analysis was based on statistical data of current mortality rates in men and women of 35 countries for 5 calender years. The study tested the justification of the part of the Gompertz-Makeham law postulating that age-associated mortality (i.e. Beat) increases exponentially. It was found that the alpha parameter of the age component of the Gompertz-Makeham law was not a constant value within the age range 35-75 years, but had rather an age-associated shift which was qualitatively different in men and women. The conclusion was made that the Gompertz-Makeham law did not adequately describe the mortality pattern of a modern human population. This should be borne in mind when use is made of mortality indices for the analysis of the human aging process. PMID:6698409
Flexible and fixed mathematical models describing growth patterns of chukar partridges
NASA Astrophysics Data System (ADS)
Aygün, Ali; Narinç, Doǧan
2016-04-01
In animal science, the nonlinear regression models for growth curve analysis ofgrowth patterns are separated into two groups called fixed and flexible according to their point of inflection. The aims of this study were to compare fixed and flexible growth functions and to determine the best fit model for the growth data of chukar partridges. With this aim, the growth data of partridges were modeled with widely used models, such as Gompertz, Logistic, Von Bertalanffy as well as the flexible functions, such as, Richards, Janoschek, Levakovich. So as to evaluate growth functions, the R2 (coefficient of determination), adjusted R2 (adjusted coefficient of determination), MSE (mean square error), AIC (Akaike's information criterion) and BIC (Bayesian information criterion) goodness of fit criteria were used. It has been determined that the best fit model from the point of chukar partridge growth data according to mentioned goodness of fit criteria is Janoschek function which has a flexible structure. The Janoschek model is not only important because it has a higher number of parameters with biological meaning than the other functions (the mature weight and initial weight parameters), but also because it was not previously used in the modeling of the chukar partridge growth.
Kirkwood, Thomas B. L.
2015-01-01
In 1825, the actuary Benjamin Gompertz read a paper, ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’, to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750242
Bardsley, W G; Ackerman, R A; Bukhari, N A; Deeming, D C; Ferguson, M W
1995-01-01
A variety of model-based (growth models) and model-free (cubic splines, exponentials) equations were fitted using weighted-nonlinear least squares regression to embryonic growth data from Alligator mississippiensis eggs incubated at 30 and 33 degrees C. Goodness of fit was estimated using a chi 2 on the sum of squared, weighted residuals, and run and sign tests on the residuals. One of the growth models used (Preece & Baines, 1978) was found to be superior to the classical growth models (exponential, monomolecular, logistic, Gompertz, von Bertalanffy) and gave an adequate fit to all longitudinal measures taken from the embryonic body and embryonic mass. However, measurements taken from the head could not be fitted by growth models but were adequately fitted by weighted least squares cubic splines. Data for the stage of development were best fitted by a sum of 2 exponentials with a transition point. Comparison of the maximum growth rates and parameter values, indicated that the growth data at 30 degrees C could be scaled to 33 degrees C to multiplying the time by a scaling factor of 1.2. This is equivalent to a Q10 of about 1.86 or, after solving the Arrhenius equation, an E++ of 46.9 kJmol-1. This may be interpreted as indicating a common rate-limiting step in development at the 2 temperatures. PMID:7591979
Stochastic ontogenetic growth model
NASA Astrophysics Data System (ADS)
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Phase transition in tumor growth: I avascular development
NASA Astrophysics Data System (ADS)
Izquierdo-Kulich, E.; Rebelo, I.; Tejera, E.; Nieto-Villar, J. M.
2013-12-01
We propose a mechanism for avascular tumor growth based on a simple chemical network. This model presents a logistic behavior and shows a “second order” phase transition. We prove the fractal origin of the empirical logistics and Gompertz constant and its relation to mitosis and apoptosis rate. Finally, the thermodynamics framework developed demonstrates the entropy production rate as a Lyapunov function during avascular tumor growth.
Modeling the growth of Listeria monocytogenes on the surface of smear- or mold-ripened cheese
Schvartzman, M. Sol; Gonzalez-Barron, Ursula; Butler, Francis; Jordan, Kieran
2014-01-01
Surface-ripened cheeses are matured by means of manual or mechanical technologies posing a risk of cross-contamination, if any cheeses are contaminated with Listeria monocytogenes. In predictive microbiology, primary models are used to describe microbial responses, such as growth rate over time and secondary models explain how those responses change with environmental factors. In this way, primary models were used to assess the growth rate of L. monocytogenes during ripening of the cheeses and the secondary models to test how much the growth rate was affected by either the pH and/or the water activity (aw) of the cheeses. The two models combined can be used to predict outcomes. The purpose of these experiments was to test three primary (the modified Gompertz equation, the Baranyi and Roberts model, and the Logistic model) and three secondary (the Cardinal model, the Ratowski model, and the Presser model) mathematical models in order to define which combination of models would best predict the growth of L. monocytogenes on the surface of artificially contaminated surface-ripened cheeses. Growth on the surface of the cheese was assessed and modeled. The primary models were firstly fitted to the data and the effects of pH and aw on the growth rate (μmax) were incorporated and assessed one by one with the secondary models. The Logistic primary model by itself did not show a better fit of the data among the other primary models tested, but the inclusion of the Cardinal secondary model improved the final fit. The aw was not related to the growth of Listeria. This study suggests that surface-ripened cheese should be separately regulated within EU microbiological food legislation and results expressed as counts per surface area rather than per gram. PMID:25072033
Effect of combined function of temperature and water activity on the growth of Vibrio harveyi
Zhou, Kang; Gui, Meng; Li, Pinglan; Xing, Shaohua; Cui, Tingting; Peng, Zhaohui
2012-01-01
Vibrio harveyi is considered as a causative agent of the systemic disease, vibriosis, which occurs in many biological fields. The effects of temperatures (12.9–27.1 °C) and water activity (NaCl% 0.6%-3.4%) on V. harveyi were investigated. The behavior and growth characteristics of V. harveyi was studied and modeled. Growth curves were fitted by using Gompertz and Baranyi models, and the Baranyi model showed a better fittness. Then, the maximum growth rates (μmax) and lag phase durations (LPD, λ) obtained from both Gompertz and Baranyi model were modeled as a combination function of temperature and water activity using the response surface and Arrhenius-Davey models for secondary model. The value of r2, MSE, bias and accuracy factor suggest Baranyi model has better fitness than Gompertz model. Furthermore, validation of the developed models with independent data from ComBase also shown better interrelationship between observed and predicted growth parameter when using Baranyi model. PMID:24031965
Effect of combined function of temperature and water activity on the growth of Vibrio harveyi.
Zhou, Kang; Gui, Meng; Li, Pinglan; Xing, Shaohua; Cui, Tingting; Peng, Zhaohui
2012-10-01
Vibrio harveyi is considered as a causative agent of the systemic disease, vibriosis, which occurs in many biological fields. The effects of temperatures (12.9-27.1 °C) and water activity (NaCl% 0.6%-3.4%) on V. harveyi were investigated. The behavior and growth characteristics of V. harveyi was studied and modeled. Growth curves were fitted by using Gompertz and Baranyi models, and the Baranyi model showed a better fittness. Then, the maximum growth rates (μmax) and lag phase durations (LPD, λ) obtained from both Gompertz and Baranyi model were modeled as a combination function of temperature and water activity using the response surface and Arrhenius-Davey models for secondary model. The value of r(2), MSE, bias and accuracy factor suggest Baranyi model has better fitness than Gompertz model. Furthermore, validation of the developed models with independent data from ComBase also shown better interrelationship between observed and predicted growth parameter when using Baranyi model. PMID:24031965
On Selective Harvesting of an Inshore-Offshore Fishery: A Bioeconomic Model
ERIC Educational Resources Information Center
Purohit, D.; Chaudhuri, K. S.
2004-01-01
A bioeconomic model is developed for the selective harvesting of a single species, inshore-offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic…
Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis
Hadjiandreou, Marios M.; Rizki, Gizem; Achilleos, Achilleas; Strati, Katerina; Mitsis, Georgios D.
2015-01-01
Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results. PMID:26649886
Wendelberger, J.R.
1998-12-01
In reliability modeling, the term availability is used to represent the fraction of time that a process is operating successfully. Several different definitions have been proposed for different types of availability. One commonly used measure of availability is cumulative availability, which is defined as the ratio of the amount of time that a system is up and running to the total elapsed time. During the startup phase of a process, cumulative availability may be treated as a growth process. A procedure for modeling cumulative availability as a function of time is proposed. Estimates of other measures of availability are derived from the estimated cumulative availability function. The use of empirical Bayes techniques to improve the resulting estimates is also discussed.
[The issue of feasibility of a general theory of aging I. Generalized Gompertz-Makeham Law].
Golubev, A G
2009-01-01
Aging and longevity are interrelated so intimately that they should be treated with a unified theory. The longevity of every single cohort of living beings is determined by the rate of their dying-out. In most cases, mortality rates increase in accelerated fashions to reach values making the bulk of each finite cohort completely exhausted within a relatively narrow time interval shifted to the end of its resulting lifespan. Among simple functions with biologically interpretable parameters, the best fit to this pattern is demonstrated by the Gompertz-Makeham Law (GML): mu = C + lambda x e(gamma x t). A generalized form of GML mu = C(t) + lambda x e(-E(t)) is suggested and interpreted as a law of the dependency of mortality upon vitality rather than on age. It is reduced to the conventional GML when E depends linearly on t, that the age is an observable correlate of unobservable vitality. C(t) captures the inherently irresistible causes of death. The generalized GML can accommodate any mode of age-dependent functional decline, which should be placed into the exponent index to be translated into changes in mortality rate, and is compatible with any sort of cohort heterogeneity, which may be captured by substituting of GML parameters with relevant distributions or by combining of several generalized GML models. The generalized GML is suggested to result from the origin of life from the chemical world, which was associated with the transition of the role of the main variable in the Arrhenius equation k = A x exp[-Ea/(R x T)] for the dependency of chemical disintegration on temperature from T to Ea upon the transition from molecular to multimolecular prebiotic entities. Thus, the generalized GML is not a result of biological evolution but is a sort of chemical legacy of biology, which makes an important condition for life to evolve. PMID:19827677
Lattice models of biological growth
Young, D.A.; Corey, E.M. )
1990-06-15
We show that very simple iterative rules for the growth of cells on a two-dimensional lattice can simulate biological-growth phenomena realistically. We discuss random cellular automata models for the growth of fern gametophytes, branching fungi, and leaves, and for shape transformations useful in the study of biological variation and evolution. Although there are interesting analogies between biological and physical growth processes, we stress the uniqueness of biological automata behavior. The computer growth algorithms that successfully mimic observed growth behavior may be helpful in determining the underlying biochemical mechanisms of growth regulation.
Modeling Exponential Population Growth
ERIC Educational Resources Information Center
McCormick, Bonnie
2009-01-01
The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social…
Modeling microbial growth and dynamics.
Esser, Daniel S; Leveau, Johan H J; Meyer, Katrin M
2015-11-01
Modeling has become an important tool for widening our understanding of microbial growth in the context of applied microbiology and related to such processes as safe food production, wastewater treatment, bioremediation, or microbe-mediated mining. Various modeling techniques, such as primary, secondary and tertiary mathematical models, phenomenological models, mechanistic or kinetic models, reactive transport models, Bayesian network models, artificial neural networks, as well as agent-, individual-, and particle-based models have been applied to model microbial growth and activity in many applied fields. In this mini-review, we summarize the basic concepts of these models using examples and applications from food safety and wastewater treatment systems. We further review recent developments in other applied fields focusing on models that explicitly include spatial relationships. Using these examples, we point out the conceptual similarities across fields of application and encourage the combined use of different modeling techniques in hybrid models as well as their cross-disciplinary exchange. For instance, pattern-oriented modeling has its origin in ecology but may be employed to parameterize microbial growth models when experimental data are scarce. Models could also be used as virtual laboratories to optimize experimental design analogous to the virtual ecologist approach. Future microbial growth models will likely become more complex to benefit from the rich toolbox that is now available to microbial growth modelers. PMID:26298697
Weinberger, Christopher Robert
2013-08-01
Tin, lead, and lead-tin solders are the most commonly used solders due to their low melting temperatures. However, due to the toxicity problems, lead must now be removed from solder materials. This has lead to the re-emergence of the issue of tin whisker growth. Tin whiskers are a microelectronic packaging issue because they can lead to shorts if they grow to sufficient length. However, the cause of tin whisker growth is still not well understood and there is lack of robust methods to determine when and if whiskering will be a problem. This report summarizes some of the leading theories on whisker growth and attempts to provide some ideas towards establishing the role microstructure plays in whisker growth.
Modeling Population Growth and Extinction
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2009-01-01
The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…
Oh, S R; Kang, I; Oh, M H; Ha, S D
2014-01-01
The inhibitory effect of chlorine (50, 100, and 200 mg/kg) was investigated with and without UV radiation (300 mW·s/cm(2)) for the growth of Listeria monocytogenes in chicken breast meat. Using a polynomial model, predictive growth models were also developed as a function of chlorine concentration, UV exposure, and storage temperature (4, 10, and 15°C). A maximum L. monocytogenes reduction (0.8 log cfu, cfu/g) was obtained when combining chlorine at 200 mg/kg and UV at 300 mW·s/cm(2), and a maximum synergistic effect (0.4 log cfu/g) was observed when using chlorine at 100 mg/kg and UV at 300 mW·s/cm(2). Primary models developed for specific growth rate and lag time showed a good fitness (R(2) > 0.91), as determined by the reparameterized Gompertz equation. Secondary polynomial models were obtained using nonlinear regression analysis. The developed models were validated with mean square error, bias factor, and accuracy factor, which were 0.0003, 0.96, and 1.11, respectively, for specific growth rate and 7.69, 0.99, and 1.04, respectively, for lag time. The treatment of chlorine and UV did not change the color and texture of chicken breast after 7 d of storage at 4°C. As a result, the combination of chlorine at 100 mg/kg and UV at 300 mW·s/cm(2) appears to an effective method into inhibit L. monocytogenes growth in broiler carcasses with no negative effects on color and textural quality. Based on the validation results, the predictive models can be used to accurately predict L. monocytogenes growth in chicken breast. PMID:24570440
Stochastic Models of Human Growth.
ERIC Educational Resources Information Center
Goodrich, Robert L.
Stochastic difference equations of the Box-Jenkins form provide an adequate family of models on which to base the stochastic theory of human growth processes, but conventional time series identification methods do not apply to available data sets. A method to identify structure and parameters of stochastic difference equation models of human…
Czochralski crystal growth: Modeling study
NASA Technical Reports Server (NTRS)
Dudukovic, M. P.; Ramachandran, P. A.; Srivastava, R. K.; Dorsey, D.
1986-01-01
The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.
Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C.
2015-01-01
This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper. PMID:26230694
Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C
2015-01-01
This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper. PMID:26230694
Biophysical models of tumour growth
NASA Astrophysics Data System (ADS)
Tracqui, P.
2009-05-01
Tumour growth is a multifactorial process, which has stimulated in recent decades the development of numerous models trying to figure out the mechanisms controlling solid tumours morphogenesis. While the earliest models were focusing on cell proliferation kinetics, modulated by the availability of supplied nutrients, new modelling approaches emphasize the crucial role of several biophysical processes, including local matrix remodelling, active cell migration and traction, and reshaping of host tissue vasculature. After a brief presentation of this experimental background, this review will outline a number of representative models describing, at different scales, the growth of avascular and vascularized tumours. Special attention will be paid to the formulation of tumour-host tissue interactions that selectively drive changes in tumour size and morphology, and which are notably mediated by the mechanical status and elasticity of the tumour microenvironment. Emergence of invasive behaviour through growth instabilities at the tumour-host interface will be presented considering both reaction-diffusion and mechano-cellular models. In the latter part of the review, patient-oriented implications of tumour growth modelling are outlined in the context of brain tumours. Some conceptual views of the adaptive strategies and selective barriers that govern tumour evolution are presented in conclusion as potential guidelines for the development of future models.
Fingering in Stochastic Growth Models
Aristotelous, Andreas C.; Durrett, Richard
2015-01-01
Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) − θ)+ and die at rate δ(θ − u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and “fingering” at a threshold θc = 0.5, while in the second case fingering always occurs, i.e., θc = 0. PMID:26430353
Luo, Ke; Hong, Sung-Sam; Oh, Deog-Hwan
2015-09-01
The aim of this study was to model the growth kinetics of Listeria monocytogenes on ready-to-eat ham and sausage at different temperatures (4 to 35°C). The observed data fitted well with four primary models (Baranyi, modified Gompertz, logistic, and Huang) with high coefficients of determination (R(2) > 0.98) at all measured temperatures. After the mean square error (0.009 to 0.051), bias factors (0.99 to1.06), and accuracy factors (1.01 to 1.09) were obtained in all models, the square root and the natural logarithm model were employed to describe the relation between temperature and specific growth rate (SGR) and lag time (LT) derived from the primary models. These models were validated against the independent data observed from additional experiments using the acceptable prediction zone method and the proportion of the standard error of prediction. All secondary models based on each of the four primary models were acceptable to describe the growth of the pathogen in the two samples. The validation results indicate that the optimal primary model for estimating the SGR was the Baranyi model, and the optimal primary model for estimating LT was the logistic model in ready-to-eat (RTE) ham. The Baranyi model was also the optimal model to estimate the SGR and LT in RTE sausage. These results could be used to standardize predictive models, which are commonly used to identify critical control points in hazard analysis and critical control point systems or for the quantitative microbial risk assessment to improve the food safety of RTE meat products. PMID:26319721
NASA Astrophysics Data System (ADS)
Cabella, Brenno Caetano Troca; Ribeiro, Fabiano; Martinez, Alexandre Souto
2012-02-01
We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.
Modeling of intermediate phase growth
Umantsev, A.
2007-01-15
We introduced a continuum method for modeling of intermediate phase growth and numerically simulated three common experimental situations relevant to the physical metallurgy of soldering: growth of intermetallic compound layer from an unlimited amount of liquid and solid solders and growth of the compound from limited amounts of liquid solder. We found qualitative agreements with the experimental regimes of growth in all cases. For instance, the layer expands in both directions with respect to the base line when it grows from solid solder, and grows into the copper phase when the solder is molten. The quantitative agreement with the sharp-interface approximation was also achieved in these cases. In the cases of limited amounts of liquid solder we found the point of turnaround when the compound/solder boundary changed the direction of its motion. Although such behavior had been previously observed experimentally, the simulations revealed important information: the turnaround occurs approximately at the time of complete saturation of solder with copper. This result allows us to conclude that coarsening of the intermetallic compound structure starts only after the solder is practically saturated with copper.
Modeling delamination growth in composites
Reedy, E.D. Jr.; Mello, F.J.
1996-12-01
A method for modeling the initiation and growth of discrete delaminations in shell-like composite structures is presented. The laminate is divided into two or more sublaminates, with each sublaminate modeled with four-noded quadrilateral shell elements. A special, eight-noded hex constraint element connects opposing sublaminate shell elements. It supplies the nodal forces and moments needed to make the two opposing shell elements act as a single shell element until a prescribed failure criterion is satisfied. Once the failure criterion is attained, the connection is broken, creating or growing a discrete delamination. This approach has been implemented in a 3D finite element code. This code uses explicit time integration, and can analyze shell-like structures subjected to large deformations and complex contact conditions. The shell elements can use existing composite material models that include in-plane laminate failure modes. This analysis capability was developed to perform crashworthiness studies of composite structures, and is useful whenever there is a need to estimate peak loads, energy absorption, or the final shape of a highly deformed composite structure. This paper describes the eight-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. Particular attention is focused on the delamination growth criterion, and it is verified that calculated results do not depend on element size. In addition, results for double cantilever beam and end notched flexure specimens are presented and compared to measured data to assess the ability of the present approach to model a growing delamination.
A novel measurement method of microorganism growth by tunable diode laser-absorption spectroscopy
NASA Astrophysics Data System (ADS)
Xiang, Jindong; Shao, Jie; Ying, Chaofu; Wang, Liming; Guo, Jie
2015-05-01
The objective of this work was to attain essential parameters by using a Gompertz model that employed a new approach of wavelength modulation spectroscopy (WMS) to describe the microorganism growth. The measurement method of WMS introduces noninvasive technique instead of complicated invasive microorganism operation analysis and quickly obtains the accurate real-time measurement results. By using the WMS measurement, the specific growth curve of microorganism growth clearly displayed every three minute, which has characteristics of high sensitivity, high spectral resolution, fast time response and overcomes the randomness and error operation of traditional analysis methods. The measurement value of BF and AF in the range of 1.008 to 1.043 and the lower MSE showed that Gompertz model can fit the data well and be capable of describing bacteria growth rate and lag time. The results of experiment data suggested that the specific growth rate of microorganism depends on the temperature. With the increase of temperature ranging from 25 °C to 42 °C , the lag time of bacteria growth has been shortened. And the suitable temperature of bacteria growth is about 37 °C . Judging from the growth rate of microorganisms, we can identify the microbial species, not only to improve the precision and efficiency, but also to provides a rapidly sensitive way for microbial detection. The lag time of microorganism growth also provides a great application prospect for shelf life of the food safety.
Incidence of the Bertillon and Gompertz effects on the outcome of clinical trials
NASA Astrophysics Data System (ADS)
Roehner, Bertrand M.
2014-11-01
The accounts of medical trials provide very detailed information about the patients’ health conditions. On the contrary, almost no vital data such as marital status or age distribution are usually given. Yet, some of these factors can have a notable impact on the overall death rate, thereby changing the outcome and conclusions of the trial. This paper focuses on two of these variables. The first is marital status; its effect on life expectancy (which will be referred to as the Bertillon effect) may double death rates in all age intervals. The second variable is the age distribution of the oldest patients. Because of the exponential nature of Gompertz’s law changes in the distribution of ages in the oldest age group can have dramatic consequences on the overall number of deaths. One should recall that the death rate at the age of 82 is 40 times higher than at the age of 37. It will be seen that randomization alone can hardly take care of these problems. Appropriate remedies are easy to formulate however. First, the marital status of patients as well as the age distribution of those over 65 should be documented for both study groups. Then, thanks to these data and based on the Bertillon and Gompertz laws, it will become possible to perform appropriate corrections. Such corrections will notably improve the reliability and accuracy of the conclusions, especially in trials which include a large proportion of elderly subjects.
Finch, Caleb E; Beltrán-Sánchez, Hiram; Crimmins, Eileen M
2014-01-01
The past 200 years have enabled remarkable increases in human lifespans through improvements in the living environment that have nearly eliminated infections as a cause of death through improved hygiene, public health, medicine, and nutrition. We argue that the limit to lifespan may be approaching. Since 1997, no one has exceeded Jeanne Calment's record of 122.5 years, despite an exponential increase of centenarians. Moreover, the background mortality may be approaching a lower limit. We calculate from Gompertz coefficients that further increases in longevity to approach a life expectancy of 100 years in 21st century cohorts would require 50% slower mortality rate accelerations, which would be a fundamental change in the rate of human aging. Looking into the 21st century, we see further challenges to health and longevity from the continued burning of fossil fuels that contribute to air pollution as well as global warming. Besides increased heat waves to which elderly are vulnerable, global warming is anticipated to increase ozone levels and facilitate the spread of pathogens. We anticipate continuing socioeconomic disparities in life expectancy. PMID:24401556
Finch, Caleb E; Beltrán-Sánchez, Hiram; Crimmins, Eileen M
2014-01-01
The past 200 years have enabled remarkable increases in human lifespans thru improvements of the living environment that have nearly eliminated infections as a cause of death through improved hygiene- public health, medicine, and nutrition. We argue that the limit to lifespan may be approaching. Since 1997, no one has exceeded Jean Calment's record of 122.5 years, despite an exponential increase of centenarians. Moreover, the background mortality may be approaching a lower limit. We calculate from Gompertz coefficients that further increases in longevity to approach a life expectancy of 100 years in 21st C cohorts would require 50% slower mortality rate accelerations, which would be a fundamental change in the rate of human aging. Looking into the 21st C, we see further challenges to health and longevity from the continued burning of fossil fuels that contribute to air pollution, as well as global warming. Besides increased heat waves to which elderly are vulnerable, global warming is anticipated to increase ozone levels and to favor the spread of pathogens. We anticipate continuing socio-economic disparities of life expectancy. PMID:24401556
Capital Growth Paths of the Neoclassical Growth Model
Takahashi, Taro
2012-01-01
This paper derives the first-order approximated paths of both types of capital in the two-capital neoclassical growth model. The derived capital growth paths reveal that the short-run growth effect of capital injection differs considerably depending on which type of capital is enhanced. This result demonstrates the importance of well-targeted capital enhancement programs such as public sector projects and foreign aid. PMID:23185344
Clark, Jeremy S C; Kaczmarczyk, Mariusz; Mongiało, Zbigniew; Ignaczak, Paweł; Czajkowski, Andrzej A; Klęsk, Przemysław; Ciechanowicz, Andrzej
2013-08-01
Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies. PMID:23233550
Modelling the growth of feather crystals
Wood, H.J.; Hunt, J.D.; Evans, P.V.
1997-02-01
An existing numerical model of dendritic growth has been adapted to model the growth of twinned columnar dendrites (feather crystals) in a binary aluminium alloy, Examination of the effect of dendrite tip angle on growth has led to an hypothesis regarding the stability of a pointed tip morphology in these crystals.
Latent Growth Modeling for Logistic Response Functions
ERIC Educational Resources Information Center
Choi, Jaehwa; Harring, Jeffrey R.; Hancock, Gregory R.
2009-01-01
Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…
Modeling of Czochralski crystal growth
Ramachandran, P.A.; Dudukovic, M.P. . Chemical Reaction Engineering Lab.)
1991-05-01
The manufacture of high quality silicon crystals especially for power device applications requires the understanding and full quantification of the relationship between the process variables and the crystal properties. This cannot be achieved solely by experimental work and a systematic modeling study is needed. This document presents the results of such a study. A detailed finite element program was developed for the heat transfer in the crystal and the melt of the CZ process. A model was developed to predict the oxygen content of the CZ grown silicon as a function of the operating variables: crucible rotation rate, crystal rotation, crucible temperature and the heat flux to the melt. Preliminary work was also done to assess the effect of the magnetic field on the crystal oxygen content. A complete thermal stress a model was developed for the calculation of the resolved shear stresses in the crystal as a function of its growth history. Multivariable control theory was applied to CZ process and new control methods were suggested. 46 refs., 47 figs., 8 tabs.
A Growth Model for Multilevel Ordinal Data
ERIC Educational Resources Information Center
Segawa, Eisuke
2005-01-01
Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Theoretical model of ``fuzz'' growth
NASA Astrophysics Data System (ADS)
Krasheninnikov, Sergei; Smirnov, Roman
2012-10-01
Recent more detailed experiments on tungsten irradiation with low energy helium plasma, relevant to the near-wall plasma conditions in magnetic fusion reactor like ITER, demonstrated (e.g. see Ref. 1) a very dramatic change in both surface morphology and near surface material structure of the samples. In particular, it was shown that a long (mm-scale) and thin (nm-scale) fiber-like structures filled with nano-bubbles, so-called ``fuzz,'' start to grow. In this work theoretical model of ``fuzz'' growth [2] describing the main features observed in experiments is presented. This model, based on the assumption of enhancement of creep of tungsten containing significant fraction of helium atoms and clusters. The results of the MD simulations [3] support this idea and demonstrate a strong reduction of the yield strength for all temperature range. They also show that the ``flow'' of tungsten strongly facilitates coagulation of helium clusters and the formation of nano-bubbles.[4pt] [1] M. J. Baldwin, et al., J. Nucl. Mater. 390-391 (2009) 885;[0pt] [2] S. I. Krasheninnikov, Physica Scripta T145 (2011) 014040;[0pt] [3] R. D. Smirnov and S. I. Krasheninnikov, submitted to J. Nucl. Materials.
A universal model of ontogenetic growth
NASA Astrophysics Data System (ADS)
Martyushev, Leonid M.; Terentiev, Pavel S.
2015-06-01
The assumption that a single growth equation can be used to describe all biological objects on different organizational levels and a dimensional analysis are applied in order to substantiate universal model of ontogenetic growth. This model (the mass of a growing organism is a power function of time) is valid only in the initial period of growth. For the whole period of growth, a generalization of the model is advanced; it provides the same accuracy as previously known models of quantitative description of kinetic curves. Within the scope of the developed model, a number of interesting results related to allometry and biological time are obtained.
The Potential of Growth Mixture Modelling
ERIC Educational Resources Information Center
Muthen, Bengt
2006-01-01
The authors of the paper on growth mixture modelling (GMM) give a description of GMM and related techniques as applied to antisocial behaviour. They bring up the important issue of choice of model within the general framework of mixture modelling, especially the choice between latent class growth analysis (LCGA) techniques developed by Nagin and…
Testing mechanistic models of growth in insects.
Maino, James L; Kearney, Michael R
2015-11-22
Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. PMID:26609084
Transitions in a probabilistic interface growth model
NASA Astrophysics Data System (ADS)
Alves, S. G.; Moreira, J. G.
2011-04-01
We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding is strongest. We introduce a growth probability which is proportional to a power of the number ni of bindings of the site i: p_i\\propto n_i^\
Mansur, Ahmad Rois; Wang, Jun; Park, Myeong-Su; Oh, Deog-Hwan
2014-01-01
This study was conducted to investigate the disinfection efficacy of hurdle treatments (thermosonication plus slightly acidic electrolyzed water [SAcEW]) and to develop a model for describing the effect of storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) on the growth of Escherichia coli O157:H7 on fresh-cut kale treated with or without (control) thermosonication combined with SAcEW. The hurdle treatments of thermosonication plus SAcEW had strong bactericidal effects against E. coli O157:H7 on kale, with approximately 3.3-log reductions. A modified Gompertz model was used to describe growth parameters such as specific growth rate (SGR) and lag time (LT) as a function of storage temperature, with high coefficients of determination (R(2) > 0.98). SGR increased and LT declined with rising temperatures in all samples. A significant difference was found between the SGR values obtained from treated and untreated samples. Secondary models were established for SGR and LT to evaluate the effects of storage temperature on the growth kinetics of E. coli O157:H7 in treated and untreated kale. Statistical evaluation was carried out to validate the performance of the developed models, based on the additional experimental data not used for the model development. The validation step indicated that the overall predictions were inside the acceptable prediction zone and had lower standard errors, indicating that this new growth model can be used to assess the risk of E. coli O157:H7 contamination on kale. PMID:24405995
Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil
NASA Astrophysics Data System (ADS)
Moura, N. J.; Ribeiro, Marcelo B.
2013-05-01
This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz-Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (˜99%), with the Pareto power law, representing the tiny richest part (˜1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.
Modeling Tissue Growth Within Nonwoven Scaffolds Pores
Church, Jeffrey S.; Alexander, David L.J.; Russell, Stephen J.; Ingham, Eileen; Ramshaw, John A.M.; Werkmeister, Jerome A.
2011-01-01
In this study we present a novel approach for predicting tissue growth within the pores of fibrous tissue engineering scaffolds. Thin nonwoven polyethylene terephthalate scaffolds were prepared to characterize tissue growth within scaffold pores, by mouse NR6 fibroblast cells. On the basis of measurements of tissue lengths at fiber crossovers and along fiber segments, mathematical models were determined during the proliferative phase of cell growth. Tissue growth at fiber crossovers decreased with increasing interfiber angle, with exponential relationships determined on day 6 and 10 of culture. Analysis of tissue growth along fiber segments determined two growth profiles, one with enhanced growth as a result of increased tissue lengths near the fiber crossover, achieved in the latter stage of culture. Derived mathematical models were used in the development of a software program to visualize predicted tissue growth within a pore. This study identifies key pore parameters that contribute toward tissue growth, and suggests models for predicting this growth, based on fibroblast cells. Such models may be used in aiding scaffold design, for optimum pore infiltration during the tissue engineering process. PMID:20687775
Design issues for population growth models
López Fidalgo, J.; Ortiz Rodríguez, I.M.
2010-01-01
We briefly review and discuss design issues for population growth and decline models. We then use a flexible growth and decline model as an illustrative example and apply optimal design theory to find optimal sampling times for estimating model parameters, specific parameters and interesting functions of the model parameters for the model with two real applications. Robustness properties of the optimal designs are investigated when nominal values or the model is mis-specified, and also under a different optimality criterion. To facilitate use of optimal design ideas in practice, we also introduce a website for generating a variety of optimal designs for popular models from different disciplines. PMID:21647244
Some novel growth functions and their application with reference to growth in ostrich.
Faridi, A; López, S; Ammar, H; Salwa, K S; Golian, A; Thornley, J H M; France, J
2015-06-01
Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative β-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (Wf). The results from the first comparison showed that the functions generally gave acceptable values of R2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AICc). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into Wf gave the best fit, resulting in smaller AIC and AIC values compared with those in the other 2 approaches. On the basis of AICc, best fit was achieved with CBP, followed by gMM, Lomolino, and
A Practitioner's Guide to Growth Models
ERIC Educational Resources Information Center
Castellano, Katherine E.; Ho, Andrew D.
2013-01-01
This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…
Doona, Christopher J; Feeherry, Florence E; Ross, Edward W
2005-04-15
Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a(w), pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207-345 MPa (30,000-50,000 psi) and the temperature (T) range of 30-50 degrees C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial
Global Models of Growth and Competition
Gilpin, Michael E.; Ayala, Francisco J.
1973-01-01
Very precise data on the dynamics of a competitive system of two species of Drosophila have been obtained. By a curvilinear regression approach, analytical models of competition have been fitted. By statistical and biological criteria of simplicity, reality, generality, and accuracy, the best of these models has been chosen. This model represents an extension of the Lotka-Volterra model of competition; it adds a fourth parameter that controls the degree of nonlinearity in intraspecific growth regulation. It represents a similar extension of the logistic model of population growth. PMID:4519647
A Microkinetic Model of Calcite Step Growth.
Andersson, M P; Dobberschütz, S; Sand, K K; Tobler, D J; De Yoreo, J J; Stipp, S L S
2016-09-01
In spite of decades of research, mineral growth models based on ion attachment and detachment rates fail to predict behavior beyond a narrow range of conditions. Here we present a microkinetic model that accurately reproduces calcite growth over a very wide range of published experimental data for solution composition, saturation index, pH and impurities. We demonstrate that polynuclear complexes play a central role in mineral growth at high supersaturation and that a classical complexation model is sufficient to reproduce measured rates. Dehydration of the attaching species, not the mineral surface, is rate limiting. Density functional theory supports our conclusions. The model provides new insights into the molecular mechanisms of mineral growth that control biomineralization, mineral scaling and industrial material synthesis. PMID:27532505
Silk, Todd M; Roth, Tatiana M T; Donnelly, C W
2002-08-01
Detection of Listeria in food products is often limited by performance of enrichment media used to support growth of Listeria to detectable levels. In this study, growth curves were generated using healthy and heat-injured Listeria monocytogenes strain F5069 in three nonselective and five selective enrichment broths. Nonselective enrichment media included the current Food and Drug Administration Bacteriological Analytical Manual Listeria enrichment broth base (BAM), Listeria repair broth (LRB), and Trypticase soy broth. Selective enrichment media included BAM with selective agents and LRB with selective agents, BCM L. monocytogenes preenrichment broth, Fraser broth, and UVM-modified Listeria enrichment broth. The Gompertz equation was used to model the growth of L. monocytogenes. Gompertz parameters were used to calculate exponential growth rate, lag-phase duration (LPD), generation time, maximum population density (MPD), and time required for repair of injured cells. Statistical differences (P < 0.05) in broth performance were noted for LPD and MPD when healthy and injured cells were inoculated into the broths. With the exception of Fraser broth, there were no significant differences in the time required for the repair of injured cells. Results indicate that the distinction between selective and nonselective broths in their ability to grow healthy Listeria and to repair sublethally injured cells is not solely an elementary issue of presence or absence of selective agents. PMID:12182490
Cluster growth modeling of plateau erosion
NASA Technical Reports Server (NTRS)
Stark, Colin P.
1994-01-01
The pattern of erosion of a plateau along an escarpment may be modeled usng cluster growth techniques, recently popularized in models of drainage network evolution. If erosion on the scarp takes place in discrete events at rates subject to local substrate strength, the whole range of behavior is described by a combination of three cluster growth mechanisms: invasion percolation, Eden growth and diffusion-limited aggregation (DLA). These model the relative importance of preexisting substrate strength, background weathering, and seepage weathering and erosion respectively. The rate of seepage processes is determined by the efflux of groundwater at the plateau margin, which in turn is determined by the pressure field in the plateau aquifer. If this process acted alone, it would produce erosion patterns in the form of Laplacian fractals, with groundwater recharge from a distant source, or Poissionian fractals, with groundwater recharge uniform over the plateau. DLA is used to mimic the Laplacian or Poissonian potential field and the corresponding seepage growth process. The scaling structure of clusters grown by pure DLA, invasion percolation, or Eden growth is well known; this study presents a model which combines all three growth mechanisms for the first time. Mixed growth processes create clusters with different scaling properties and morphologies over distinct length scale ranges, and this is demonstrable in natural examples of plateau erosion.
Stochastic roots of growth phenomena
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
A nonparametric software-reliability growth model
NASA Technical Reports Server (NTRS)
Sofer, Ariela; Miller, Douglas R.
1991-01-01
The authors (1985) previously introduced a nonparametric model for software-reliability growth which is based on complete monotonicity of the failure rate. The authors extend the completely monotone software model by developing a method for providing long-range predictions of reliability growth, based on the model. They derive upper and lower bounds on extrapolation of the failure rate and the mean function. These are then used to obtain estimates for the future software failure rate and the mean future number of failures. Preliminary evaluation indicates that the method is competitive with parametric approaches, while being more robust.
Residual Structures in Latent Growth Curve Modeling
ERIC Educational Resources Information Center
Grimm, Kevin J.; Widaman, Keith F.
2010-01-01
Several alternatives are available for specifying the residual structure in latent growth curve modeling. Two specifications involve uncorrelated residuals and represent the most commonly used residual structures. The first, building on repeated measures analysis of variance and common specifications in multilevel models, forces residual variances…
CRITIQUE OF CARBON BASED TREE GROWTH MODELS
Simulation models of the processes that control carbohydrate balance in coniferous trees are reviewed, and their appropriateness for assessing pollution effects is considered. Currently such models are at the forefront of attempts to simulate the growth process of trees, but they...
Activist model of political party growth
NASA Astrophysics Data System (ADS)
Jeffs, Rebecca A.; Hayward, John; Roach, Paul A.; Wyburn, John
2016-01-01
The membership of British political parties has a direct influence on their political effectiveness. This paper applies the mathematics of epidemiology to the analysis of the growth and decline of such memberships. The party members are divided into activists and inactive members, where all activists influence the quality of party recruitment, but only a subset of activists recruit and thus govern numerical growth. The activists recruit for only a limited period, which acts as a restriction on further party growth. This Limited Activist model is applied to post-war and recent memberships of the Labour, Scottish National and Conservative parties. The model reproduces data trends, and relates realistically to historical narratives. It is concluded that the political parties analysed are not in danger of extinction but experience repeated periods of growth and decline in membership, albeit at lower numbers than in the past.
A stochastic model of eye lens growth.
Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven
2015-07-01
The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and radial lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. PMID:25816743
Thermal models pertaining to continental growth
NASA Technical Reports Server (NTRS)
Morgan, Paul; Ashwal, Lew
1988-01-01
Thermal models are important to understanding continental growth as the genesis, stabilization, and possible recycling of continental crust are closely related to the tectonic processes of the earth which are driven primarily by heat. The thermal energy budget of the earth was slowly decreasing since core formation, and thus the energy driving the terrestrial tectonic engine was decreasing. This fundamental observation was used to develop a logic tree defining the options for continental growth throughout earth history.
On a Competitive Model of Laplacian Growth
NASA Astrophysics Data System (ADS)
Loutsenko, Igor; Yermolayeva, Oksana; Zinsmeister, Michel
2011-11-01
We introduce a competitive model of Laplacian growth in both stochastic and deterministic versions. This defines two different aggregation laws with probabilities λ and 1- λ. The parameter λ varying from 0 to 1 is used to weight a ratio between the inner and outer harmonic measures that leads to a competition between the Eden-like process and the DLA solved with site-sticking conditions. We perform numerical and qualitative analysis of the competitive growth.
Statistical mechanics model of angiogenic tumor growth.
Ferreira, António Luis; Lipowska, Dorota; Lipowski, Adam
2012-01-01
We examine a lattice model of tumor growth where the survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the supply is correlated with the distribution of tumor cells, which as we suggest might mimic the angiogenic growth, the extinction shows different critical behavior. Such a correlation affects also the morphology of the growing tumors and drastically raises tumor-survival probability. PMID:22400505
Modeling Stromatolite Growth Under Oscillatory Flows
NASA Astrophysics Data System (ADS)
Patel, H. J.; Gong, J.; Tice, M. M.
2014-12-01
Stromatolite growth models based on diffusion limited aggregation (DLA) has been fairly successful at producing features commonly recognized in stromatolitic structures in the rock record. These models generally require slow mixing of solutes at time scales comparable to the growth of organisms and largely ignore fluid erosions. Recent research on microbial mats suggests that fluid flow might have a dominant control on the formation, deformation and erosion of surface microbial structures, raising the possibility that different styles of fluid flow may influence the morphology of stromatolites. Many stromatolites formed in relatively high energy, shallow water environments under oscillatory currents driven by wind-induced waves. In order to investigate the potential role of oscillatory flows in shaping stromatolites, we are constructing a numerical model of stromatolite growth parameterized by flume experiments with cyanobacterial biofilms. The model explicitly incorporates reaction-diffusion processes, surface deformation and erosion, biomass growth, sedimentation and mineral precipitation. A Lattice-Boltzmann numerical scheme was applied to the reaction-diffusion equations in order to boost computational efficiency. A basic finite element method was employed to compute surface deformation and erosion. Growth of biomass, sedimentation and carbonate precipitation was based on a modified discrete cellular automata scheme. This model will be used to test an alternative hypothesis for the formation of stromatolites in higher energy, shallow and oscillatory flow environments.
Reliability growth models for NASA applications
NASA Technical Reports Server (NTRS)
Taneja, Vidya S.
1991-01-01
The objective of any reliability growth study is prediction of reliability at some future instant. Another objective is statistical inference, estimation of reliability for reliability demonstration. A cause of concern for the development engineer and management is that reliability demands an excessive number of tests for reliability demonstration. For example, the Space Transportation Main Engine (STME) program requirements call for .99 reliability at 90 pct. confidence for demonstration. This requires running 230 tests with zero failure if a classical binomial model is used. It is therefore also an objective to explore the reliability growth models for reliability demonstration and tracking and their applicability to NASA programs. A reliability growth model is an analytical tool used to monitor the reliability progress during the development program and to establish a test plan to demonstrate an acceptable system reliability.
Assessment of MARMOT Grain Growth Model
Fromm, B.; Zhang, Y.; Schwen, D.; Brown, D.; Pokharel, R.
2015-12-01
This report assesses the MARMOT grain growth model by comparing modeling predictions with experimental results from thermal annealing. The purpose here is threefold: (1) to demonstrate the validation approach of using thermal annealing experiments with non-destructive characterization, (2) to test the reconstruction capability and computation efficiency in MOOSE, and (3) to validate the grain growth model and the associated parameters that are implemented in MARMOT for UO_{2}. To assure a rigorous comparison, the 2D and 3D initial experimental microstructures of UO_{2} samples were characterized using non-destructive Synchrotron x-ray. The same samples were then annealed at 2273K for grain growth, and their initial microstructures were used as initial conditions for simulated annealing at the same temperature using MARMOT. After annealing, the final experimental microstructures were characterized again to compare with the results from simulations. So far, comparison between modeling and experiments has been done for 2D microstructures, and 3D comparison is underway. The preliminary results demonstrated the usefulness of the non-destructive characterization method for MARMOT grain growth model validation. A detailed analysis of the 3D microstructures is in progress to fully validate the current model in MARMOT.
Modelling microstructurally sensitive fatigue short crack growth
NASA Astrophysics Data System (ADS)
de Los Rios, E. R.; Xin, X. J.; Navarro, A.
1994-10-01
Microstructurally sensitive fatigue short crack growth can occur in many engineering components devoid of large defects. Continuum mechanics principles, including linear elastic fracture mechanics, used in damage tolerance design and life prediction methods are not applicable in these situations and therefore new concepts need to be developed to characterize this type of growth. A microstructurally sensitive model of fatigue crack growth is presented in which the effect of microstructure is dominant in the early stage of growth but plays a negligible role after the crack has gone through the transition from structure-sensitive to structure-insensitive growth. The effect of both microstructure and structure sensitive variables on the transition from short cracks to continuum mechanics and the conditions for crack instability leading to final failure are examined. The microstructural variables incorporated in the equations that describe the model are those controlling the extent and intensity of crack tip plasticity such as grain size, precipitation and dispersion hardening, strain hardening and mis-orientation between grains. It is expected that the concepts developed within the model will form the basis for the design of new crack-resistant materials.
New theories of root growth modelling
NASA Astrophysics Data System (ADS)
Landl, Magdalena; Schnepf, Andrea; Vanderborght, Jan; Huber, Katrin; Javaux, Mathieu; Bengough, A. Glyn; Vereecken, Harry
2016-04-01
In dynamic root architecture models, root growth is represented by moving root tips whose line trajectory results in the creation of new root segments. Typically, the direction of root growth is calculated as the vector sum of various direction-affecting components. However, in our simulations this did not reproduce experimental observations of root growth in structured soil. We therefore developed a new approach to predict the root growth direction. In this approach we distinguish between, firstly, driving forces for root growth, i.e. the force exerted by the root which points in the direction of the previous root segment and gravitropism, and, secondly, the soil mechanical resistance to root growth or penetration resistance. The latter can be anisotropic, i.e. depending on the direction of growth, which leads to a difference between the direction of the driving force and the direction of the root tip movement. Anisotropy of penetration resistance can be caused either by microscale differences in soil structure or by macroscale features, including macropores. Anisotropy at the microscale is neglected in our model. To allow for this, we include a normally distributed random deflection angle α to the force which points in the direction of the previous root segment with zero mean and a standard deviation σ. The standard deviation σ is scaled, so that the deflection from the original root tip location does not depend on the spatial resolution of the root system model. Similarly to the water flow equation, the direction of the root tip movement corresponds to the water flux vector while the driving forces are related to the water potential gradient. The analogue of the hydraulic conductivity tensor is the root penetrability tensor. It is determined by the inverse of soil penetration resistance and describes the ease with which a root can penetrate the soil. By adapting the three dimensional soil and root water uptake model R-SWMS (Javaux et al., 2008) in this way
NASA Technical Reports Server (NTRS)
Thorndike, Alan S.
1992-01-01
My purpose here is to present a simplified treatment of the growth of sea ice. By ignoring many details, it is possible to obtain several results that help to clarify the ways in which the sea ice cover will respond to climate change. Three models are discussed. The first deals with the growth of sea ice during the cold season. The second describes the cycle of growth and melting for perennial ice. The third model extends the second to account for the possibility that the ice melts away entirely in the summer. In each case, the objective is to understand what physical processes are most important, what ice properties determine the ice behavior, and to which climate variables the system is most sensitive.
Modeling duckweed growth in wastewater treatment systems
Landesman, L.; Parker, N.C.; Fedler, C.B.; Konikoff, M.
2005-01-01
Species of the genera Lemnaceae, or duckweeds, are floating aquatic plants that show great promise for both wastewater treatment and livestock feed production. Research conducted in the Southern High Plains of Texas has shown that Lemna obscura grew well in cattle feedlot runoff water and produced leaf tissue with a high protein content. A model or mathematical expression derived from duckweed growth data was used to fit data from experiments conducted in a greenhouse in Lubbock, Texas. The relationship between duckweed growth and the total nitrogen concentration in the mediium follows the Mitscherlich Function and is similar to that of other plants. Empirically derived model equations have successfully predicted the growth response of Lemna obscura.
A tumor growth model with deformable ECM
NASA Astrophysics Data System (ADS)
Sciumè, G.; Santagiuliana, R.; Ferrari, M.; Decuzzi, P.; Schrefler, B. A.
2014-12-01
Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.
A tumor growth model with deformable ECM
Sciumè, G; Santagiuliana, R; Ferrari, M; Decuzzi, P; Schrefler, B A
2015-01-01
Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution. PMID:25427284
Modeling Fish Growth in Low Dissolved Oxygen
ERIC Educational Resources Information Center
Neilan, Rachael Miller
2013-01-01
This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…
Interaction Effects in Growth Modeling: A Full Model.
ERIC Educational Resources Information Center
Wen, Zhonglin; Marsh, Herbert W.; Hau, Kit-Tai
2002-01-01
Points out two concerns with recent research by F. Li and others (2000) and T. Duncan and others (1999) that extended the structural equation model of latent interactions developed by K. Joreskog and F. Yang (1996) to latent growth modeling. Used mathematical derivation and a comparison of alternative models fitted to simulated data to develop a…
Unrestricted Mixture Models for Class Identification in Growth Mixture Modeling
ERIC Educational Resources Information Center
Liu, Min; Hancock, Gregory R.
2014-01-01
Growth mixture modeling has gained much attention in applied and methodological social science research recently, but the selection of the number of latent classes for such models remains a challenging issue, especially when the assumption of proper model specification is violated. The current simulation study compared the performance of a linear…
Evolutionary model of an anonymous consumer durable market
NASA Astrophysics Data System (ADS)
Kaldasch, Joachim
2011-07-01
An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation. The theory suggests that products play the role of species in biological evolutionary models. It implies that the evolution of man-made products can be arranged into an evolutionary tree. The model suggests that each product can be characterized by its product fitness. The fitness space contains elements of both sites of the market, supply and demand. The unit sales of products with a higher product fitness compared to the mean fitness increase. Durables with a constant fitness advantage replace other goods according to a logistic law. The model predicts in particular that the mean price exhibits an exponential decrease over a long time period for durable goods. The evolutionary diffusion process is directly related to this price decline and is governed by Gompertz equation. Therefore it is denoted as Gompertz diffusion. Describing the aggregate sales as the sum of first, multiple and replacement purchase the product life cycle can be derived. Replacement purchase causes periodic variations of the sales determined by the finite lifetime of the good (Juglar cycles). The model suggests that both, Bass- and Gompertz diffusion may contribute to the product life cycle of a consumer durable. The theory contains the standard equilibrium view of a market as a special case. It depends on the time scale, whether an equilibrium or evolutionary description is more appropriate. The evolutionary framework is used to derive also the size, growth rate and price distribution of manufacturing business units. It predicts that the size distribution of the business units (products) is lognormal
Modeling error distributions of growth curve models through Bayesian methods.
Zhang, Zhiyong
2016-06-01
Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided. PMID:26019004
Modeling Growth of Nanostructures in Plasmas
NASA Technical Reports Server (NTRS)
Hwang, Helen H.; Bose, Deepak; Govindan, T. R.; Meyyappan, M.
2004-01-01
As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.
Koopman, Jacob J.E.; van Heemst, Diana; van Bodegom, David; Bonkowski, Michael S.; Sun, Liou Y.; Bartke, Andrzej
2016-01-01
Caloric restriction and genetic disruption of growth hormone signaling have been shown to counteract aging in mice. The effects of these interventions on aging are examined through age-dependent survival or through the increase in age-dependent mortality rates on a logarithmic scale fitted to the Gompertz model. However, these methods have limitations that impede a fully comprehensive disclosure of these effects. Here we examine the effects of these interventions on murine aging through the increase in age-dependent mortality rates on a linear scale without fitting them to a model like the Gompertz model. Whereas these interventions negligibly and non-consistently affected the aging rates when examined through the age-dependent mortality rates on a logarithmic scale, they caused the aging rates to increase at higher ages and to higher levels when examined through the age-dependent mortality rates on a linear scale. These results add to the debate whether these interventions postpone or slow aging and to the understanding of the mechanisms by which they affect aging. Since different methods yield different results, it is worthwhile to compare their results in future research to obtain further insights into the effects of dietary, genetic, and other interventions on the aging of mice and other species. PMID:26959761
A nonparametric software reliability growth model
NASA Technical Reports Server (NTRS)
Miller, Douglas R.; Sofer, Ariela
1988-01-01
Miller and Sofer have presented a nonparametric method for estimating the failure rate of a software program. The method is based on the complete monotonicity property of the failure rate function, and uses a regression approach to obtain estimates of the current software failure rate. This completely monotone software model is extended. It is shown how it can also provide long-range predictions of future reliability growth. Preliminary testing indicates that the method is competitive with parametric approaches, while being more robust.
Macrophyte growth in shallow streams: biomass model
Wright, R.M.; Mc Donnell, A.J.
1986-10-01
An assessment was made of the water quality and the magnitude of growth of rooted aquatic macrophytes in a nutrient-enriched, shallow stream system in order to provide a basis for evaluating the recovery of the ecosystem following the implementation of a program of phosphorus removal. Field investigations defined the temporal and spatial changes of plant biomass in selected study sections. A model to predict changes in macrophyte biomass as a function of varying environmental factors including nutrient flux was developed, calibrated and validated. The potential of the biomass model as a management tool to assess the impact of nutrient reductions on stream oxygen budgets was demonstrated.
[Postnatal growth patterns in eight species of herons and egrets (Ciconiiformes: Ardeidae)].
Avila, Dennis Denis
2011-06-01
Avian postnatal growth has received considerable attention and its ecological implications have been deeply analyzed. In this current paper, I describe the patterns of culmen and tarsus growth, as well as of weight gain patterns in eight species of herons and egrets (Aves: Ardeidae) found in the Birama Swamp in Eastern Cuba. Between 1998 and 2006,714 nestlings of the following species were measured every two days: Butorides virescens, Bubulcus ibis, Egretta thula, E. tricolor, E. caerulea, E. rufescens, Ardea alba and Nycticorax nycticorax. Logistic and Gompertz equations were adjusted to data using non-lineal regression models with adult values as the asymptote. For each species, the following were determined and recorded: growth rate, age at inflexion, instantaneous growth rates at each age interval, and time taken to reach 90% of adult size. Reported hatchling sizes were similar in other localities, with a variation coefficient ranging between 10-19%. At hatch, each species exhibited differing sizes relative to adult values. In all cases, Gompertz equations were best fitted to explain more variance and lesser residuals. Rates of weight change and tarsus growth were alometrically related to the log of adult weight. Two main growth processes were identified: a physical extension in dimensions of each measurement reflecting inter-specific morphometric differences, and a lineal increase of the growth period from Green Heron to Great Egret. The Black-crowned Night Heron, Cattle Egret and Reddish Egret exhibited some unique measurement characteristics in comparison to the remaining members of the family. All results support the hypothesis that hypermorphosis, as the main evolutionary process in the microevolution of Ardeidae, is caused by a delayed final moment of growth. PMID:21721238
Growth/reflectance model interface for wheat and corresponding model
NASA Technical Reports Server (NTRS)
Suits, G. H.; Sieron, R.; Odenweller, J.
1984-01-01
The use of modeling to explore the possibility of discovering new and useful crop condition indicators which might be available from the Thematic Mapper and to connect these symptoms to the biological causes in the crop is discussed. A crop growth model was used to predict the day to day growth features of the crop as it responds biologically to the various environmental factors. A reflectance model was used to predict the character of the interaction of daylight with the predicted growth features. An atmospheric path radiance was added to the reflected daylight to simulate the radiance appearing at the sensor. Finally, the digitized data sent to a ground station were calculated. The crop under investigation is wheat.
Universal Accretion Growth Using Sandpile Models
NASA Astrophysics Data System (ADS)
Datta, Srabani; McKie, Shane; Spencer, Ralph
2015-08-01
The Bak-Tang- Wiesenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around thesystem till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power-law distribution in cascade sizes having slope -5/3. This self-similarity of structureis synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions influid turbulence. We apply the BTW sandpile model to study growth on a 2 dimensional rotating lattice in a magnetic field. In this paper, we show that this is a naturally occuring universal process giving rise to scale-freestructures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a widerange of objects including molecular clouds, accretion disks and perhaps galaxies.
SOA multiday growth: Model artifact or reality?
NASA Astrophysics Data System (ADS)
Lee-Taylor, J. M.; Madronich, S.; Aumont, B.; Hodzic, A.; Camredon, M.; Valorso, R.
2013-12-01
Simulations of SOA gas-particle partitioning with the explicit gas-phase chemical mechanism generator GECKO-A show significant SOA mass growth continuing for several days, even as the initial air parcel is diluted into the regional atmosphere. This result is a robust feature of our model and occurs with both anthropogenic and biogenic precursors. The growth originates from continuing oxidation of gas-phase precursors which persist in equilibrium with the particle phase. This result implies that sources of aerosol precursors could influence the chemical and radiative characteristics of the atmosphere over a wider region than previously imagined, and that SOA measurements near precursor sources may routinely underestimate this influence. It highlights the need to better understand the sink terms in the SOA budget.
Trans-theta logistics: a new family of population growth sigmoid functions.
Kozusko, F; Bourdeau, M
2011-12-01
Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves. PMID:21528359
Technological growth curves. A competition of forecasting models
Young, P.
1993-12-01
In order to determine procedures for appropriate model selection of technological growth curves, numerous time series that were representative of growth behavior were collected and categorized according to data characteristics. Nine different growth curve models were each fitted onto the various data sets in an attempt to determine which growth curve models achieved the best forecasts for differing types of growth data. The analysis of the results gives rise to a new approach for selecting appropriate growth curve models for a given set of data, prior to fitting the models, based on the characteristics of the data sets. 58 refs., 9 tabs.
Stochastic model for tumor growth with immunization
NASA Astrophysics Data System (ADS)
Bose, Thomas; Trimper, Steffen
2009-05-01
We analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending on the finite correlation time, the immunization rate, and the strength of the cross correlation. Ps offers a maximum which becomes more pronounced for increasing immunization rate. The mean-first-passage time is also calculated in order to find out under which conditions the tumor can suffer extinction. Its characteristics are again controlled by the degree of immunization and the strength of the cross correlation. The behavior observed can be interpreted in terms of a biological model of tumor evolution.
A competition model for wormhole growth
NASA Astrophysics Data System (ADS)
Cabeza Diaz de Cerio, Yoar; Carrera, Jesus; Hidalgo, Juan J.
2016-04-01
Flow preferential pathways generated by dissolution are commonly known as wormholes. Wormhole generation and evolution are topics of interest not only for karst aquifer studies but also for fields as CO2 storage and oil industry among others. The objective of this work is to show that given an initial perturbation, the development of the dissolution pattern can be considered deterministic. This means that the evolution of the effective hydraulic conductivity can be predicted. To this end we use a wormhole growth model in which wormholes compete for the available water. In the competition model the wormholes grow proportionally to the flow rate through them. The wormhole flow rate is a function of the wormholes lengths and distances between them. We derive empirical expressions for the flow rates from steady state flow synthetic models with different geometries. Finally, we perform series of simulations using this competition model, applying random initial perturbations and different number of wormholes for each set of simulations and we study the evolution of the dissolution pattern. We find that the resulting wormhole patterns are in good agreement with others generated with much more complex models.
Genetic parameter estimates of growth curve and reproduction traits in Japanese quail.
Narinc, Dogan; Karaman, Emre; Aksoy, Tulin; Firat, Mehmet Ziya
2014-01-01
The goal of selection studies in broilers is to obtain genetically superior chicks in terms of major economic traits, which are mainly growth rate, meat yield, and feed conversion ratio. Multiple selection schedules for growth and reproduction are used in selection programs within commercial broiler dam lines. Modern genetic improvement methods have not been applied in experimental quail lines. The current research was conducted to estimate heritabilities and genetic correlations for growth and reproduction traits in a Japanese quail flock. The Gompertz equation was used to determine growth curve parameters. The Gibbs sampling under a multi-trait animal model was applied to estimate the heritabilities and genetic correlations for these traits. A total of 948 quail were used with complete pedigree information to estimate the genetic parameters. Heritability estimates of BW, absolute and relative growth rates at 5 wk of age (AGR and RGR), β0 and β2 parameters, and age at point of inflection (IPT) of Gompertz growth curve, total egg number (EN) from the day of first lay to 24 wk of age were moderate to high, with values ranging from 0.25 to 0.40. A low heritability (0.07) for fertility (FR) and a strong genetic correlation (0.83) between FR and EN were estimated in our study. Body weight exhibited negative genetic correlation with EN, FR, RGR, and IPT. This genetic antagonism among the mentioned traits may be overcome using modern poultry breeding methods such as selection using multi-trait best linear unbiased prediction and crossbreeding. PMID:24570419
Regime Switching in the Latent Growth Curve Mixture Model
ERIC Educational Resources Information Center
Dolan, Conor V.; Schmittmann, Verena D.; Lubke, Gitta H.; Neale, Michael C.
2005-01-01
A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing…
Flower Power: Sunflowers as a Model for Logistic Growth
ERIC Educational Resources Information Center
Fernandez, Eileen; Geist, Kristi A.
2011-01-01
Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…
Silvani, Vanesa Analía; Bidondo, Laura Fernández; Bompadre, María Josefina; Colombo, Roxana Paula; Pérgola, Mariana; Bompadre, Agustín; Fracchia, Sebastián; Godeas, Alicia
2014-01-01
The growth dynamics of extraradical mycelium and spore formation of 14 "Rhizophagus" isolates from different sites in Argentina were evaluated under monoxenic conditions. A modified Gompertz model was used to characterize the development of mycelium and spores for each isolate under the same conditions. The lag time, maximal growth rate and total quantity of both extraradical hyphae and spores were determined. Wide variability among isolates was detected, and all growth parameters were significantly altered by fungal isolate. Discriminant analysis differentiated isolates primarily based on the extent of extraradical hyphae produced, yet such differences did not conclusively correspond to phylogenetic relationships among closely related isolates based on partial SSU sequences. Given that the "Rhizophagus" isolates were grown under controlled conditions for many generations, the expression of phenotypic variability could be attributed to genetic differences that are not completely resolved by phylogenetic analysis employing the small ribosomal gene. PMID:24891409
Modeling Hematite Bioreduction under Growth Conditions
NASA Astrophysics Data System (ADS)
Yu, J.; Chen, C.; Yeh, G.; Burgos, W. D.; Mynyard, M. L.
2004-12-01
The focus of this work is on simulating and analyzing bioreduction kinetics of natural hematite-coated sand by dissimilatory metal-reducing bacterium (DMRB), Shewanella putrefaciens CN32, under growth conditions with lactate as the electron donor. A reaction-based biogeochemical model was used. A series of batch experiments with different initial conditions were performed to determine the rate formulations/parameters for hematite bioreduction and related reactions. Three different kinetic reaction rate formations were used to model hematite bioreduction. The consistency of mass conservation equations was assessed. Assumptions regarding equilibrium reactions were also assessed. Column experiments focused on transient reactive transport were conducted under otherwise identical conditions, except that the flow rate was systematically varied. The determined rate formulations/parameters were systematically tested with these column experiments using a reactive biogeochemical transport model that coupled hydrologic transport and reactive biogeochemistry. The model simulated the hematite bioreduction of hematite-coated sand in column experiments reasonably well using rate formulation/parameters determined from batch experiments. This study supports the hypothesis that mechanistic-based reaction rates of batch experiments can be scaled up and ported to column experiments.
Latent Growth Modeling of Longitudinal Data: A Finite Growth Mixture Modeling Approach.
ERIC Educational Resources Information Center
Li, Fuzhong; Duncan, Terry E.; Duncan, Susan C.; Acock, Alan
2001-01-01
Presents a new approach that extends conventional random coefficient growth models to incorporate a categorical latent trajectory variable representing latent classes or mixtures. Provides a didactic example of this new methodology using adolescent alcohol use data and discusses the method as a tool for mapping hypotheses of development onto…
ERIC Educational Resources Information Center
Grady, Matthew W.; Beretvas, S. Natasha
2010-01-01
Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve…
Modeling Solid Rayleigh-Taylor Growth
Kaul, Ann M
2010-09-20
Intense impulses applied to solid materials result in high strain rates, strong plastic strains and significant temperature increments. Data in such regimes would allow confidence in extending material strength models to strain rates of 10{sup 6}-10{sup 7} s{sup -1}. High explosives can be used to accelerate a plate with a perturbation on the side facing the HE, resulting in a Rayleigh-Taylor-like perturbation growth that depends on amplitude and wavelength of the initial surface perturbation, strength of the material, time dependence of the driving pressure force, and temperature of the material. Such experiments have been conducted on perturbed copper plates at LANL, using the LANSCE proton radiography beam to obtain multiple frames of data for each experiment. The results of numerical simulations of these experiments using a 2-D ALE code are presented.
Evaluating Latent Growth Curve Models Using Individual Fit Statistics
ERIC Educational Resources Information Center
Coffman, Donna L.; Millsap, Roger E.
2006-01-01
The usefulness of assessing individual fit in latent growth curve models was examined. The study used simulated data based on an unconditional and a conditional latent growth curve model with a linear component and a small quadratic component and a linear model was fit to the data. Then the overall fit of linear and quadratic models to these data…
The research on Virtual Plants Growth Based on DLA Model
NASA Astrophysics Data System (ADS)
Zou, YunLan; Chai, Bencheng
This article summarizes the separated Evolutionary Algorithm in fractal algorithm of Diffusion Limited Aggregation model (i.e. DLA model) and put forward the virtual plant growth realization in computer based on DLA model. The method is carried out in the VB6.0 environment to achieve and verify the plant growth based on DLA model.
Reactive burn models and ignition & growth concept
Menikoff, Ralph S; Shaw, Milton S
2010-01-01
Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition and Growth concept, introduced by Lee and Tarver in 1980, as the basis for reactive burn models. A homogeneized burn rate needs to account for three mesoscale physical effects (i) the density of burnt hot spots, which depends on the lead shock strength; (ii) the growth of the burn fronts triggered by hot spots, which depends on the local deflagration speed; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent hot spots. These effects can be combined and the burn model defined by specifying the reaction progress variable {lambda}(t) as a function of a dimensionless reaction length {tau}{sub hs}(t)/{ell}{sub hs}, rather than by xpecifying an explicit burn rate. The length scale {ell}{sub hs} is the average distance between hot spots, which is proportional to [N{sub hs}(P{sub s})]{sup -1/3}, where N{sub hs} is the number density of hot spots activated by the lead shock. The reaction length {tau}{sub hs}(t) = {line_integral}{sub 0}{sup t} D(P(t'))dt' is the distance the burn front propagates from a single hot spot, where D is the deflagration speed and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. They have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments.
Microscopic kinetic model for polymer crystal growth
NASA Astrophysics Data System (ADS)
Hu, Wenbing
2011-03-01
Linear crystal growth rates characterize the net result of competition between growth and melting at the liquid-solid interfaces. The rate equation for polymer crystal growth can be derived with a barrier term for crystal growth and with a driving force term of excess lamellar thickness, provided that growth and melting share the same rate-determining steps at the growth front. Such an ansatz can be verified by the kinetic symmetry between growth and melting around the melting point of lamellar crystals, as made in our recent dynamic Monte Carlo simulations. The profile of the growth/melting front appears as wedge-shaped, with the free energy barrier for intramolecular secondary crystal nucleation at its top, and with the driving force gained via instant thickening at its bottom. Such a scenario explains unique phenomena on polymer crystal growth, such as chain folding, regime transitions, molecular segregation of polydisperse polymers, self-poisoning with integer-number chain-folding of short chains, and colligative growth rates of binary mixtures of two chain lengths. Financial support from NNSFC No. 20825415 and NBRPC No. 2011CB606100 is acknowledged.
Variation in growth form and precocity at birth in eutherian mammals.
Gaillard, J M; Pontier, D; Allaine, D; Loison, A; Herve, J C; Heizmann, A
1997-01-01
Using the flexible Chapman-Richards model for describing the growth curves from birth to adulthood of 69 species of eutherian mammals, we demonstrate that growth form differs among eutherian mammals. Thereby the commonly used Gompertz model can no longer be considered as the general model for describing mammalian growth. Precocial mammals have their peak growth rate earlier in the growth process than altricial mammals. However, the position on the altricial-precocial continuum accounts for most growth-form differences only between mammalian lineages. Within mammalian genera differences in growth form are not related to precocity at birth. This indicates that growth form may have been associated with precocity at birth early in mammalian evolution, when broad patterns of body development radiated. We discuss four non-exclusive interpretations to account for the role of precocity at birth on the observed variation in growth form among mammals. Precocial and altricial mammals could differ according to (i) the distribution of energy output by the mother, (ii) the ability of the young to assimilate the milk yield, (iii) the allocation of energy by the young between competing functions and (iv) the position of birth between conception and attainment of physical maturity. PMID:9225478
Local Solutions in the Estimation of Growth Mixture Models
ERIC Educational Resources Information Center
Hipp, John R.; Bauer, Daniel J.
2006-01-01
Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…
Parameter Estimates in Differential Equation Models for Population Growth
ERIC Educational Resources Information Center
Winkel, Brian J.
2011-01-01
We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…
Modelling short crack growth behaviour in nickel-base superalloys
NASA Astrophysics Data System (ADS)
Grabowski, L.; King, J. E.
1992-06-01
This paper provides a description of the features and mechanisms of facetted short crack growth in Ni-base superalloys and briefly reviews existing short crack growth models in terms of their application to Ni-base alloys. The concept of soft barriers is introduced to produce a new two-phase model for local microstructural effects on short crack growth in Waspaloy. This is derived from detailed observations of crack growth through individual grains. The model differs from all previous approaches in highlighting the importance of crack path perturbations within grains. Potential applications of the model in alloy development are discussed.
The Crop Growth Model in the Wind Erosion Prediction System
Technology Transfer Automated Retrieval System (TEKTRAN)
The primary purpose of the crop growth submodel (CROP) in the Wind Erosion Prediction System (WEPS) is to obtain realistic estimates of plant growth so that the influence of vegetative cover on wind erosion can be properly evaluated. Most crop growth models focus on estimating final crop yield. CROP...
Spiral Growth in Plants: Models and Simulations
ERIC Educational Resources Information Center
Allen, Bradford D.
2004-01-01
The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…
Detecting Growth Shape Misspecifications in Latent Growth Models: An Evaluation of Fit Indexes
ERIC Educational Resources Information Center
Leite, Walter L.; Stapleton, Laura M.
2011-01-01
In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…
Brain tumor modeling: glioma growth and interaction with chemotherapy
NASA Astrophysics Data System (ADS)
Banaem, Hossein Y.; Ahmadian, Alireza; Saberi, Hooshangh; Daneshmehr, Alireza; Khodadad, Davood
2011-10-01
In last decade increasingly mathematical models of tumor growths have been studied, particularly on solid tumors which growth mainly caused by cellular proliferation. In this paper we propose a modified model to simulate the growth of gliomas in different stages. Glioma growth is modeled by a reaction-advection-diffusion. We begin with a model of untreated gliomas and continue with models of polyclonal glioma following chemotherapy. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter. Tumor growth is characterized by a dangerous change in the control mechanisms, which normally maintain a balance between the rate of proliferation and the rate of apoptosis (controlled cell death). Result shows that this model closes to clinical finding and can simulate brain tumor behavior properly.
A new computational growth model for sea urchin skeletons.
Zachos, Louis G
2009-08-01
A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era. PMID:19376133
Extended Eden model reproduces growth of an acellular slime mold
NASA Astrophysics Data System (ADS)
Wagner, Geri; Halvorsrud, Ragnhild; Meakin, Paul
1999-11-01
A stochastic growth model was used to simulate the growth of the acellular slime mold Physarum polycephalum on substrates where the nutrients were confined in separate drops. Growth of Physarum on such substrates was previously studied experimentally and found to produce a range of different growth patterns [Phys. Rev. E 57, 941 (1998)]. The model represented the aging of cluster sites and differed from the original Eden model in that the occupation probability of perimeter sites depended on the time of occupation of adjacent cluster sites. This feature led to a bias in the selection of growth directions. A moderate degree of persistence was found to be crucial to reproduce the biological growth patterns under various conditions. Persistence in growth combined quick propagation in heterogeneous environments with a high probability of locating sources of nutrients.
Modeling growth of Clostridium perfringens in pea soup during cooling.
de Jong, Aarieke E I; Beumer, Rijkel R; Zwietering, Marcel H
2005-02-01
Clostridium perfringens is a pathogen that mainly causes food poisoning outbreaks when large quantities of food are prepared. Therefore, a model was developed to predict the effect of different cooling procedures on the growth of this pathogen during cooling of food: Dutch pea soup. First, a growth rate model based on interpretable parameters was used to predict growth during linear cooling of pea soup. Second, a temperature model for cooling pea soup was constructed by fitting the model to experimental data published earlier. This cooling model was used to estimate the effect of various cooling environments on average cooling times, taking into account the effect of stirring and product volume. The growth model systematically overestimated growth of C. perfringens during cooling in air, but this effect was limited to less than 0.5 log N/ml and this was considered to be acceptable for practical purposes. It was demonstrated that the growth model for C. perfringens combined with the cooling model for pea soup could be used to sufficiently predict growth of C. perfringens in different volume sizes of pea soup during cooling in air as well as the effect of stirring, different cooling temperatures, and various cooling environments on the growth of C. perfringens in pea soup. Although fine-tuning may be needed to eliminate inaccuracies, it was concluded that the combined model could be a useful tool for designing good manufacturing practices (GMP) procedures. PMID:15787757
Computational modeling of hypertensive growth in the human carotid artery
NASA Astrophysics Data System (ADS)
Sáez, Pablo; Peña, Estefania; Martínez, Miguel Angel; Kuhl, Ellen
2014-06-01
Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.
A Mathematical Model Coupling Tumor Growth and Angiogenesis
Gomez, Hector
2016-01-01
We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments. PMID:26891163
Modeling the effects of ozone on soybean growth and yield.
Kobayashi, K; Miller, J E; Flagler, R B; Heck, W W
1990-01-01
A simple mechanistic model was developed based on an existing growth model in order to address the mechanisms of the effects of ozone on growth and yield of soybean [Glycine max. (L.) Merr. 'Davis'] and interacting effects of other environmental stresses. The model simulates daily growth of soybean plants using environmental data including shortwave radiation, temperature, precipitation, irrigation and ozone concentration. Leaf growth, dry matter accumulation, water budget, nitrogen input and seed growth linked to senescence and abscission of leaves are described in the model. The effects of ozone are modeled as reduced photosynthate production and accelerated senescence. The model was applied to the open-top chamber experiments in which soybean plants were exposed to ozone under two levels of soil moisture regimes. After calibrating the model to the growth data and seed yield, goodness-of-fit of the model was tested. The model fitted well for top dry weight in the vegetative growth phase and also at maturity. The effect of ozone on seen yield was also described satisfactorily by the model. The simulation showed apparent interaction between the effect of ozone and soil moisture stress on the seed yield. The model revealed that further work is needed concerning the effect of ozone on the senescence process and the consequences of alteration of canopy microclimate by the open-top chambers. PMID:15092277
Integrating Polarities: A Model for Growth.
ERIC Educational Resources Information Center
Long, Vonda Olson
1984-01-01
Suggests that the learning of sex roles is based on a bipolar dichotomy of gender-appropriate behaviors. Response alternatives are discussed including the single polarity, bipolar acceptance, and integration of polarities. Contends that integration is essential for growth. (JAC)
Stochastic growth logistic model with aftereffect for batch fermentation process
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Stochastic growth logistic model with aftereffect for batch fermentation process
NASA Astrophysics Data System (ADS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-06-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Agent-Based Modeling of Growth Processes
ERIC Educational Resources Information Center
Abraham, Ralph
2014-01-01
Growth processes abound in nature, and are frequently the target of modeling exercises in the sciences. In this article we illustrate an agent-based approach to modeling, in the case of a single example from the social sciences: bullying.
Nonlinear Growth Models in M"plus" and SAS
ERIC Educational Resources Information Center
Grimm, Kevin J.; Ram, Nilam
2009-01-01
Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear mixed-effects…
A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits
Blasco, Agustín; Piles, Miriam; Varona, Luis
2003-01-01
Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear. PMID:12605849
Comparison of Two Pasture Growth Models of Differing Complexity
Technology Transfer Automated Retrieval System (TEKTRAN)
Two pasture growth models that share many common features but differ in model complexity have been developed for incorporation into the Integrated Farm System Model (IFSM). Major differences between models include the explicit representation of roots in the more complex model, and their effects on c...
When growth models are not universal: evidence from marine invertebrates
Hirst, Andrew G.; Forster, Jack
2013-01-01
The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691
A von Bertalanffy growth model with a seasonally varying coefficient
Cloern, James E.; Nichols, Frederic H.
1978-01-01
The von Bertalanffy model of body growth is inappropriate for organisms whose growth is restricted to a seasonal period because it assumes that growth rate is invariant with time. Incorporation of a time-varying coefficient significantly improves the capability of the von Bertalanffy equation to describe changing body size of both the bivalve mollusc Macoma balthicain San Francisco Bay and the flathead sole, Hippoglossoides elassodon, in Washington state. This simple modification of the von Bertalanffy model should offer improved predictions of body growth for a variety of other aquatic animals.
Woehl, Taylor J.; Park, Chiwoo; Evans, James E.; Arslan, Ilke; Ristenpart, William D.; Browning, Nigel D.
2014-01-08
Direct observations of solution-phase nanoparticle growth using in situ liquid transmission electron microscopy (TEM) have demonstrated the importance of “non-classical” growth mechanisms, such as aggregation and coalescence, on the growth and final morphology of nanocrystals at the atomic and single nanoparticle scales. To date, groups have quantitatively interpreted the mean growth rate of nanoparticles in terms of the Lifshitz-Slyozov-Wagner (LSW) model for Ostwald ripening, but less attention has been paid to modeling the corresponding particle size distribution. Here we use in situ fluid stage scanning TEM to demonstrate that silver nanoparticles grow by a length-scale dependent mechanism, where individual nanoparticles grow by monomer attachment but ensemble-scale growth is dominated by aggregation. Although our observed mean nanoparticle growth rate is consistent with the LSW model, we show that the corresponding particle size distribution is broader and more symmetric than predicted by LSW. Following direct observations of aggregation, we interpret the ensemble-scale growth using Smoluchowski kinetics and demonstrate that the Smoluchowski model quantitatively captures the mean growth rate and particle size distribution.
Gao, C Q; Yang, J X; Chen, M X; Yan, H C; Wang, X Q
2016-04-01
Two experiments were conducted to fit growth curves, and determine age-related changes in carcass characteristics, organs, serum biochemical parameters, and gene expression of intestinal nutrient transporters in domestic pigeon (Columba livia). In experiment 1, body weight (BW) of 30 pigeons was respectively determined at 1, 3, 7, 14, 21, 28, and 35 days old to fit growth curves and to describe the growth of pigeons. In experiment 2, eighty-four 1-day-old squabs were grouped by weight into 7 groups. On d 1, 3, 7, 14, 21, 28, and 35, twelve birds from each group were randomly selected for slaughter and post-slaughter analysis. The results showed that BW of pigeons increased rapidly from d 1 to d 28 (a 25.7-fold increase), and then had little change until d 35. The Logistic, Gompertz, and Von Bertalanffy functions can all be well fitted with the growth curve of domestic pigeons (R2>0.90) and the Gompertz model showed the highest R2value among the models (R2=0.9997). The equation of Gompertz model was Y=507.72×e-(3.76exp(-0.17t))(Y=BW of pigeon (g); t=time (day)). In addition, breast meat yield (%) increased with age throughout the experiment, whereas the leg meat yield (%) reached to the peak on d 14. Serum total protein, albumin, globulin, and glucose concentration were increased with age, whereas serum uric acid concentration was decreased (P<0.05). Furthermore, the gene expressions of nutrient transporters (y+LAT2, LAT1, B0AT1, PepT1, and NHE2) in jejunum of pigeon were increased with age. The results of correlation analysis showed the gene expressions of B0AT1, PepT1, and NHE2 had positive correlations with BW (0.73
Modeling growth curves to track growing obesity
Technology Transfer Automated Retrieval System (TEKTRAN)
Our purpose was to examine the relationship between total physical activity (PA) and PA at various intensity levels with insulin resistance at increasing waist circumference and skinfold thickness levels. Being able to describe growth appropriately and succinctly is important in many nutrition and p...
Charter School Innovations: A Teacher Growth Model
ERIC Educational Resources Information Center
Radoslovich, Julie; Roberts, Shelley; Plaza, Andres
2014-01-01
Committed to being a charter school with a professional learning community that empowers teachers, New Mexico's South Valley Academy (SVA) staff transformed its state evaluation process into a practitioner action research process (Anderson, Herr, & Nihlen, 2007). While teachers self-diagnose growth needs and play active roles in improving…
Numerical solution of the Penna model of biological aging with age-modified mutation rate.
Magdoń-Maksymowicz, M S; Maksymowicz, A Z
2009-06-01
In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a), where a is the parent's age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a. As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a), a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1). The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe et al. [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe et al. PMID:19658536
Calcite growth kinetics: Modeling the effect of solution stoichiometry
NASA Astrophysics Data System (ADS)
Wolthers, Mariëtte; Nehrke, Gernot; Gustafsson, Jon Petter; Van Cappellen, Philippe
2012-01-01
Until recently the influence of solution stoichiometry on calcite crystal growth kinetics has attracted little attention, despite the fact that in most aqueous environments calcite precipitates from non-stoichiometric solution. In order to account for the dependence of the calcite crystal growth rate on the cation to anion ratio in solution, we extend the growth model for binary symmetrical electrolyte crystals of Zhang and Nancollas (1998) by combining it with the surface complexation model for the chemical structure of the calcite-aqueous solution interface of Wolthers et al. (2008). To maintain crystal stoichiometry, the rate of attachment of calcium ions to step edges is assumed to equal the rate of attachment of carbonate plus bicarbonate ions. The model parameters are optimized by fitting the model to the step velocities obtained previously by atomic force microscopy (AFM, Teng et al., 2000; Stack and Grantham, 2010). A variable surface roughness factor is introduced in order to reconcile the new process-based growth model with bulk precipitation rates measured in seeded calcite growth experiments. For practical applications, we further present empirical parabolic rate equations fitted to bulk growth rates of calcite in common background electrolytes and in artificial seawater-type solutions. Both the process-based and empirical growth rate equations agree with measured calcite growth rates over broad ranges of ionic strength, pH, solution stoichiometry and degree of supersaturation.
Phase transitions in tumor growth: II prostate cancer cell lines
NASA Astrophysics Data System (ADS)
Llanos-Pérez, J. A.; Betancourt-Mar, A.; De Miguel, M. P.; Izquierdo-Kulich, E.; Royuela-García, M.; Tejera, E.; Nieto-Villar, J. M.
2015-05-01
We propose a mechanism for prostate cancer cell lines growth, LNCaP and PC3 based on a Gompertz dynamics. This growth exhibits a multifractal behavior and a "second order" phase transition. Finally, it was found that the cellular line PC3 exhibits a higher value of entropy production rate compared to LNCaP, which is indicative of the robustness of PC3, over to LNCaP and may be a quantitative index of metastatic potential tumors.
Modeling insights on the melt growth of cadmium zinc telluride
NASA Astrophysics Data System (ADS)
Derby, Jeffrey J.; Zhang, Nan; Yeckel, Andrew
2013-09-01
Computational modeling has provided the understanding needed to unravel many of the unusual characteristics of the melt growth of cadmium zinc telluride. Results are presented that clarify the origin and benefit of horizontal Bridgman shelf growth employed for infrared substrate material. Another example provides insight on how a non-classical approach may provide improved outcomes using multiple-zone, gradient-freeze furnaces for the vertical Bridgman growth of bulk material for gamma radiation detectors.
Simulating unstressed crop development and growth using the Unified Plant Growth Model (UPGM)
Technology Transfer Automated Retrieval System (TEKTRAN)
Since development of the EPIC model in 1989, many versions of the plant growth component have been incorporated into other erosion and crop management models and subsequently modified to meet model objectives (e.g., WEPS, WEPP, SWAT, ALMANAC, GPFARM). This has resulted in different versions of the ...
Software reliability growth models dominated by randomness
NASA Technical Reports Server (NTRS)
Shen, Wenhui; Wilson, Larry
1989-01-01
The Jelinski-Moranda and Geometric models for software reliability failed the consistency test which was proposed. These models were challenged to take data which comes from a process which they have correctly modeled and to make predictions about the reliability of that process. It was found that either model, given data precisely from a process it correctly models, will usually fail to make good predictions. These problems are attributed to randomness in the data used as input to the models and a remedy is indicated for this lack of robustness, namely replication of data.
Modelling the Growth of Swine Flu
ERIC Educational Resources Information Center
Thomson, Ian
2010-01-01
The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…
Dissipative-particle-dynamics model of biofilm growth
Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.; Scheibe, Timothy D.
2011-06-13
A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.
A Nonlinear Viscous Model for Sn-Whisker Growth
NASA Astrophysics Data System (ADS)
Yang, Fuqian
2016-04-01
Based on the mechanism of the grain boundary fluid flow, a nonlinear viscous model for the growth of Sn-whiskers is proposed. This model consists of two units, one with a stress exponent of one and one with a stress exponent of n -1. By letting one of the constants be zero in the model, the constitutive relationship reduces to a linear flow relation or a power-law relation, representing the flow behavior of various metals. Closed-form solutions for the growth behavior of a whisker are derived, which can be used to predict the whisker growth and the stress evolution.
Plant Growth Models Using Artificial Neural Networks
NASA Technical Reports Server (NTRS)
Bubenheim, David
1997-01-01
In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.
Modeling and design of PVT growth of silicon carbide crystals
NASA Astrophysics Data System (ADS)
Ma, Ronghui
2003-10-01
Physical vapor transport method (PVT) is an important technique for growing SiC bulk crystals, which is a promising semiconductor material for electrical and optoelectronic applications in the areas of high power, high temperature, high frequency and strong radiation. The ever-increasing demand for SiC substrates of high quality and large diameter has motivated extensive research effort on the growth of SiC boule using PVT method. The PVT growth process involves highly complex physics and elaborate system that significantly affect the rate of growth, growth area and defect density. This dissertation is aimed at developing a fundamental understanding of the growth process and identifying the foremost process conditions and parameters that affect crystal productivity and quality. To achieve this goal, we have developed a comprehensive model that involves major physical mechanisms of PVT growth, i.e. , transport of energy and vapor species, chemical reaction, growth kinetics, and anisotropic thermal stresses. Moreover, the multiplication of dislocation is integrated into this model to correlate thermal stresses to dislocation distribution. Through this work a relationship is established between the transport phenomena at the macroscale and defect development at the microscale. Finite volume method with adaptive non-orthogonal grid has been used for the thermal and mechanical calculations in the complex geometry. Using this integrated model, we have carried out numerical simulation of SiC growth process to predict the global temperature distribution in the furnace, the rate of growth and the shape of the as-grown crystals. In addition, the thermal stresses in the growing crystal and the dislocation distribution are also calculated. It is found that the temperature distribution in the induction-heated growth chamber is quite non-uniform. Under the growth temperatures, thermal radiation is the dominant heat transfer mode and accurate modeling is essential. The rate of
Personalized approach to growth hormone treatment: clinical use of growth prediction models.
Wit, J M; Ranke, M B; Albertsson-Wikland, K; Carrascosa, A; Rosenfeld, R G; Van Buuren, S; Kristrom, B; Schoenau, E; Audi, L; Hokken-Koelega, A C S; Bang, P; Jung, H; Blum, W F; Silverman, L A; Cohen, P; Cianfarani, S; Deal, C; Clayton, P E; de Graaff, L; Dahlgren, J; Kleintjens, J; Roelants, M
2013-01-01
The goal of growth hormone (GH) treatment in a short child is to attain a fast catch-up growth toward the target height (TH) standard deviation score (SDS), followed by a maintenance phase, a proper pubertal height gain, and an adult height close to TH. The short-term response variable of GH treatment, first-year height velocity (HV) (cm/year or change in height SDS), can either be compared with GH response charts for diagnosis, age and gender, or with predicted HV based on prediction models. Three types of prediction models have been described: the Kabi International Growth Hormone Study models, the Gothenburg models and the Cologne model. With these models, 50-80% of the variance could be explained. When used prospectively, individualized dosing reduces the variation in growth response in comparison with a fixed dose per body weight. Insulin-like growth factor-I-based dose titration also led to a decrease in the variation. It is uncertain whether adding biochemical, genetic or proteomic markers may improve the accuracy of the prediction. Prediction models may lead to a more evidence-based approach to determine the GH dose regimen and may reduce the drug costs for GH treatment. There is a need for user-friendly software programs to make prediction models easily available in the clinic. PMID:23735882
The Aponeurotic Tension Model of Craniofacial Growth in Man
Standerwick, Richard G; Roberts, W. Eugene
2009-01-01
Craniofacial growth is a scientific crossroad for the fundamental mechanisms of musculoskeletal physiology. Better understanding of growth and development will provide new insights into repair, regeneration and adaptation to applied loads. Traditional craniofacial growth concepts are insufficient to explain the dynamics of airway/vocal tract development, cranial rotation, basicranial flexion and the role of the cranial base in expression of facial proportions. A testable hypothesis is needed to explore the physiological pressure propelling midface growth and the role of neural factors in expression of musculoskeletal adaptation after the cessation of anterior cranial base growth. A novel model for craniofacial growth is proposed for: 1. brain growth and craniofacial adaptation up to the age of 20; 2. explaining growth force vectors; 3. defining the role of muscle plasticity as a conduit for craniofacial growth forces; and 4. describing the effect of cranial rotation in the expression of facial form. Growth of the viscerocranium is believed to be influenced by the superficial musculoaponeurotic systems (SMAS) of the head through residual tension in the occipitofrontalis muscle as a result of cephalad brain growth and cranial rotation. The coordinated effects of the regional SMAS develop a craniofacial musculoaponeurotic system (CFMAS), which is believed to affect maxillary and mandibular development. PMID:19572022
Crop growth dynamics modeling using time-series satellite imagery
NASA Astrophysics Data System (ADS)
Zhao, Yu
2014-11-01
In modern agriculture, remote sensing technology plays an essential role in monitoring crop growth and crop yield prediction. To monitor crop growth and predict crop yield, accurate and timely crop growth information is significant, in particularly for large scale farming. As the high cost and low data availability of high-resolution satellite images such as RapidEye, we focus on the time-series low resolution satellite imagery. In this research, NDVI curve, which was retrieved from satellite images of MODIS 8-days 250m surface reflectance, was applied to monitor soybean's yield. Conventional model and vegetation index for yield prediction has problems on describing the growth basic processes affecting yield component formation. In our research, a novel method is developed to well model the Crop Growth Dynamics (CGD) and generate CGD index to describe the soybean's yield component formation. We analyze the standard growth stage of soybean and to model the growth process, we have two key calculate process. The first is normalization of the NDVI-curve coordinate and division of the crop growth based on the standard development stages using EAT (Effective accumulated temperature).The second is modeling the biological growth on each development stage through analyzing the factors of yield component formation. The evaluation was performed through the soybean yield prediction using the CGD Index in the growth stage when the whole dataset for modeling is available and we got precision of 88.5% which is about 10% higher than the conventional method. The validation results showed that prediction accuracy using our CGD modeling is satisfied and can be applied in practice of large scale soybean yield monitoring.
Models and Determinants of Vocabulary Growth from Kindergarten to Adulthood
ERIC Educational Resources Information Center
Beitchman, Joseph H.; Jiang, Hedy; Koyama, Emiko; Johnson, Carla J.; Escobar, Michael; Atkinson, Leslie; Brownlie, E. B.; Vida, Ron
2008-01-01
Background: Increasing evidence suggests that childhood language problems persist into early adulthood. Nevertheless, little is known about how individual and environmental characteristics influence the language growth of individuals identified with speech/language problems. Method: Individual growth curve models were utilised to examine how…
Crop Growth Modeling in the Wind Erosion Prediction System
Technology Transfer Automated Retrieval System (TEKTRAN)
On land used for the production of food and fiber, the amount of growing crop and crop residue remaining on the field during no growth periods often determine whether the field is susceptible to the erosion of the soil by wind. The crop growth sub-model component of the Wind Erosion Prediction Syste...
CELL-BASE URBAN GROWTH MODEL TO 2020
SLEUTH (formerly known as the Urban Growth Model) uses a cellular automata simulation approach to illustrate future urbanization based on historic patterns of land transition. Its scale is dependent on cell size, and it applies growth rules to geographic data on a cell-by-cell b...
A Practitioner's Guide to Growth Models
ERIC Educational Resources Information Center
Castellano, Katherine E.; Ho, Andrew D.
2013-01-01
This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…
Evaluating the Predictive Value of Growth Prediction Models
ERIC Educational Resources Information Center
Murphy, Daniel L.; Gaertner, Matthew N.
2014-01-01
This study evaluates four growth prediction models--projection, student growth percentile, trajectory, and transition table--commonly used to forecast (and give schools credit for) middle school students' future proficiency. Analyses focused on vertically scaled summative mathematics assessments, and two performance standards conditions (high…
Phase-field model of island growth in epitaxy
NASA Astrophysics Data System (ADS)
Yu, Yan-Mei; Liu, Bang-Gui
2004-02-01
Nucleation and growth of islands in epitaxy is simulated using a continuum phase-field model. In addition to local density of adatoms, a local phase-field variable, varying in the real space, is introduced to describe the epitaxial islands. Evolution of this phase field is determined by a time-dependent Ginzburg-Landau-like equation coupled to a diffusive transport equation of adatoms. When applied to nucleation and growth of islands in the submonolayer regime, this model reproduces both the scaling laws of island density and experimental size and spatial distributions of islands. For island growth in the multilayer regime, this phase-field model reproduces mound structures consistent with experimental images concerned. Accurate coarsening and roughening exponents of the mounds are obtained in this model. Compared with atomic models and mean-field models, this model can provide a fine visualized morphology of islands at large space and time scales of practical engineering interests.
Phase-field model of island growth in epitaxy.
Yu, Yan-Mei; Liu, Bang-Gui
2004-02-01
Nucleation and growth of islands in epitaxy is simulated using a continuum phase-field model. In addition to local density of adatoms, a local phase-field variable, varying in the real space, is introduced to describe the epitaxial islands. Evolution of this phase field is determined by a time-dependent Ginzburg-Landau-like equation coupled to a diffusive transport equation of adatoms. When applied to nucleation and growth of islands in the submonolayer regime, this model reproduces both the scaling laws of island density and experimental size and spatial distributions of islands. For island growth in the multilayer regime, this phase-field model reproduces mound structures consistent with experimental images concerned. Accurate coarsening and roughening exponents of the mounds are obtained in this model. Compared with atomic models and mean-field models, this model can provide a fine visualized morphology of islands at large space and time scales of practical engineering interests. PMID:14995452
A Gompertzian model with random effects to cervical cancer growth
NASA Astrophysics Data System (ADS)
Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati
2015-05-01
In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.
Gompertzian stochastic model with delay effect to cervical cancer growth
NASA Astrophysics Data System (ADS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Gompertzian stochastic model with delay effect to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
A Gompertzian model with random effects to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati
2015-05-15
In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.
3D modeling of metallic grain growth
George, D.; Carlson, N.; Gammel, J.T.; Kuprat, A.
1999-06-01
This paper will describe simulating metallic grain growth using the Gradient Weighted Moving Finite Elements code, GRAIN3D. The authors also describe the set of mesh topology change operations developed to respond to changes in the physical topology such as the collapse of grains and to maintain uniform calculational mesh quality. Validation of the method is demonstrated by comparison to analytic calculations. The authors present results of multigrain simulations where grain boundaries evolve by mean curvature motion and include results which incorporate grain boundary orientation dependence.
Modeling the Growth Rates of Tetragonal Lysozyme Crystal Faces
NASA Technical Reports Server (NTRS)
Li, Meirong; Nadarajah, Arunan; Pusey, Marc L.
1998-01-01
with respect to its concentration at saturation in order to apply growth rate models to this process. The measured growth rates were then compared with the predicted ones from several dislocation and 2D nucleation growth models, employing tetramer and octamer growth units in polydisperse solutions and monomer units in monodisperse solutions. For the (110) face, the calculations consistently showed that the measured growth rates followed the expected model relations with octamer growth units. For the (101) face, it is not possible to obtain a clear agreement between the predicted and measured growth rates for a single growth unit as done for the (110) face. However, the calculations do indicate that the average size of the growth unit is between a tetramer and an octamer. This suggests that tetramers, octamers and other intermediate size growth units all participate in the growth process for this face. These calculations show that it is possible to model the macroscopic protein crystal growth rates if the molecular level processes can be account for, particularly protein aggregation processes in the bulk solution. Our recent investigations of tetragonal lysozyme crystals employing high resolution atomic force microscopy scans have further confirmed the growth of these crystals by aggregate growth units corresponding to 4(sub 3) helices.
Alexandrium minutum growth controlled by phosphorus . An applied model
NASA Astrophysics Data System (ADS)
Chapelle, A.; Labry, C.; Sourisseau, M.; Lebreton, C.; Youenou, A.; Crassous, M. P.
2010-11-01
Toxic algae are a worldwide problem threatening aquaculture, public health and tourism. Alexandrium, a toxic dinoflagellate proliferates in Northwest France estuaries (i.e. the Penzé estuary) causing Paralytic Shellfish Poisoning events. Vegetative growth, and in particular the role of nutrient uptake and growth rate, are crucial parameters to understand toxic blooms. With the goal of modelling in situ Alexandrium blooms related to environmental parameters, we first try to calibrate a zero-dimensional box model of Alexandrium growth. This work focuses on phosphorus nutrition. Our objective is to calibrate Alexandrium minutum as well as Heterocapsa triquetra (a non-toxic dinoflagellate) growth under different rates of phosphorus supply, other factors being optimal and constant. Laboratory experiments are used to calibrate two growth models and three uptake models for each species. Models are then used to simulate monospecific batch and semi-continuous experiments as well as competition between the two algae (mixed cultures). Results show that the Droop growth model together with linear uptake versus quota can represent most of our observations, although a power law uptake function can more accurately simulate our phosphorus uptake data. We note that such models have limitations in non steady-state situations and cell quotas can depend on a variety of factors, so care must be taken in extrapolating these results beyond the specific conditions studied.
Marvig, C L; Kristiansen, R M; Nielsen, D S
2015-01-01
The most notorious spoilage organism of sweet intermediate moisture foods (IMFs) is Zygosaccharomyces rouxii, which can grow at low water activity, low pH and in the presence of organic acids. Together with an increased consumer demand for preservative free and healthier food products with less sugar and fat and a traditionally long self-life of sweet IMFs, the presence of Z. rouxii in the raw materials for IMFs has made assessment of the microbiological stability a significant hurdle in product development. Therefore, knowledge on growth/no growth boundaries of Z. rouxii in sweet IMFs is important to ensure microbiological stability and aid product development. Several models have been developed for fat based, sweet IMFs. However, fruit/sugar based IMFs, such as fruit based chocolate fillings and jams, have lower pH and aw than what is accounted for in previously developed models. In the present study growth/no growth models for acidified sweet IMFs were developed with the variables aw (0.65-0.80), pH (2.5-4.0), ethanol (0-14.5% (w/w) in water phase) and time (0-90 days). Two different strains of Z. rouxii previously found to show pronounced resistance to the investigated variables were included in model development, to account for strain differences. For both strains data sets with and without the presence of sorbic acid (250 ppm on product basis) were built. Incorporation of time as an exploratory variable in the models gave the possibility to predict the growth/no growth boundaries at each time between 0 and 90 days without decreasing the predictive power of the models. The influence of ethanol and aw on the growth/no growth boundary of Z. rouxii was most pronounced in the first 30 days and 60 days of incubation, respectively. The effect of pH was almost negligible in the range of 2.5-4.0. The presence of low levels of sorbic acid (250 ppm) eliminated growth of both strains at all conditions tested. The two strains tested have previously been shown to have
Mothers' explanatory models of lack of child growth.
Reifsnider, E; Allan, J; Percy, M
2000-01-01
This qualitative study elicited the explanatory models (EMs) of child growth held by mothers of growth-deficient children. EMs are culturally constructed explanations for a specific illness and its treatment (Kleinman, 1980). The EM concept was adapted for this study to focus on a child health condition instead of an illness. The sample comprised 22 mothers of growth deficient children who were interviewed 2 years after the conclusion of an intervention study to promote child growth. Growth deficiency was defined as below the 10th percentile for weight, height, or weight for height on the National Center for Health Statistics (NCHS) growth grids (Hamill, Drzid, Johnson, Reed, & Roche, 1976). Three major domains were identified in the EMs of growth held by mothers: (1) illness or heredity (etiology); (2) keeping track of growth (course); and (3) helping my child grow (treatment). The mothers in this study were concerned about their children's size and growth patterns and they monitored their children's growth with the methods available to them. They identified illnesses and allergies as environmental factors that negatively impact their children's growth. All mothers viewed size as a function of heredity. The findings from this study suggest that an emphasis on size will not encourage mothers to focus on their children's growth. The EMs for growth and size were different. Health care providers may be more effective in enhancing children's growth by teaching parents how to deal with the day-to-day problems of children who are picky eaters, stretching limited food money, creating mealtime schedules, and dealing with illnesses before they become severe. PMID:11115141
Wang, Yuan; Chung, Moo K; Vorperian, Houri K
2013-11-13
The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types. PMID:24226094
Wang, Yuan; Chung, Moo K.; Vorperian, Houri K.
2014-01-01
The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types. PMID:24226094
Sheet nacre growth mechanism: a Voronoi model.
Rousseau, Marthe; Lopez, Evelyne; Couté, Alain; Mascarel, Gérard; Smith, David C; Naslain, Roger; Bourrat, Xavier
2005-02-01
Shell nacre (mother of pearl) of Pinctada margaritifera was analyzed by scanning electron microscopy. The originality of this work concerns the sampling performed to observe incipient nacre on the mantle side. The whole animal is embedded in methyl methacrylate followed by separation of the shell from the hardened mantle. It is revealed this way how each future nacre layer pre-exists as a film or compartment. Experimental observations also show for the first time, the progressive lateral crystallization inside this film, finishing under the form of a non-periodic pattern of polygonal tablets of bio-aragonite. It is evidenced that nuclei appear in the film in the vicinity of the zone where aragonite tablets of the underlying layer get in contact to each other. A possible explanation is given to show how nucleation is probably launched in time and space by a signal coming from the underlying layer. Finally, it is evidenced that tablets form a Voronoi tiling of the space: this suggests that their growth is controlled by an "aggregation-like" process of "crystallites" and not directly by the aragonite lattice growth. PMID:15681231
Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method
NASA Astrophysics Data System (ADS)
Chang, Albert Ling Sheng; Maisin, Navies
Cocoa pod growth modelling are useful in crop management, pest and disease management and yield forecasting. Recently, the Beta Growth Function has been used to determine the pod growth model due to its unique for the plant organ growth which is zero growth rate at both the start and end of a precisely defined growth period. Specific pod size (7cm to 10cm in length) is useful in cocoa pod borer (CPB) management for pod sleeving or pesticide spraying. The Beta Growth Function is well-fitted to the pods growth data of four different cocoa clones under non-linear function with time (t) as its independent variable which measured pod length and diameter weekly started at 8 weeks after fertilization occur until pods ripen. However, the same pod length among the clones did not indicate the same pod age since the morphological characteristics for cocoa pods vary among the clones. Depending on pod size for all the clones as guideline in CPB management did not give information on pod age, therefore it is important to study the pod age at specific pod sizes on different clones. Hence, Newton Raphson method is used to solve the non-linear equation of the Beta Growth Function of four different group of cocoa pod at specific pod size.
Mediation Analysis in a Latent Growth Curve Modeling Framework
ERIC Educational Resources Information Center
von Soest, Tilmann; Hagtvet, Knut A.
2011-01-01
This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and…
Latent Growth Curves within Developmental Structural Equation Models.
ERIC Educational Resources Information Center
McArdle, J. J.; Epstein, David
1987-01-01
Uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. The model describes a latent growth curve model that permits the estimation of parameters representing individual and group dynamics. (Author/RH)
Evaluating Teachers and Schools Using Student Growth Models
ERIC Educational Resources Information Center
Schafer, William D.; Lissitz, Robert W.; Zhu, Xiaoshu; Zhang, Yuan; Hou, Xiaodong; Li, Ying
2012-01-01
Interest in Student Growth Modeling (SGM) and Value Added Modeling (VAM) arises from educators concerned with measuring the effectiveness of teaching and other school activities through changes in student performance as a companion and perhaps even an alternative to status. Several formal statistical models have been proposed for year-to-year…
Model of selective growth of III-V nanowires
NASA Astrophysics Data System (ADS)
Dubrovskii, V. G.
2015-12-01
A kinetic model of growth of nanowires of III-V semiconductor compounds (including nitride ones) in the absence of metal catalyst is proposed; these conditions correspond to the methods of selective epitaxy or self-induced growth. A stationary solution for the nanowire growth rate is obtained, which indicates that the growth can be limited by not only the kinetics of III-group element with allowance for the surface diffusion (as was suggested earlier), but also the flow of the V-group element. Different modes are characterized by radically different dependences of the growth rate on the nanowire radius. Under arsenicenriched conditions, a typical dependence with a maximum and decay at large radii (limited by the gallium adatom diffusion) is observed. Under gallium-enriched conditions, there is a transition to the growth rate that is practically independent of the radius and linearly increases with an increase in the arsenic flow.
Escherichia coli growth under modeled reduced gravity
NASA Technical Reports Server (NTRS)
Baker, Paul W.; Meyer, Michelle L.; Leff, Laura G.
2004-01-01
Bacteria exhibit varying responses to modeled reduced gravity that can be simulated by clino-rotation. When Escherichia coli was subjected to different rotation speeds during clino-rotation, significant differences between modeled reduced gravity and normal gravity controls were observed only at higher speeds (30-50 rpm). There was no apparent affect of removing samples on the results obtained. When E. coli was grown in minimal medium (at 40 rpm), cell size was not affected by modeled reduced gravity and there were few differences in cell numbers. However, in higher nutrient conditions (i.e., dilute nutrient broth), total cell numbers were higher and cells were smaller under reduced gravity compared to normal gravity controls. Overall, the responses to modeled reduced gravity varied with nutrient conditions; larger surface to volume ratios may help compensate for the zone of nutrient depletion around the cells under modeled reduced gravity.
An Integrated Model of Posttraumatic Stress and Growth.
Lancaster, Steven L; Klein, Keith R; Nadia, Cyrus; Szabo, Lisa; Mogerman, Ben
2015-01-01
A number of recent models have examined cognitive predictors of posttraumatic stress and posttraumatic growth (S. Barton, A. Boals, & L. Knowles, 2013; J. Groleau, L. Calhoun, A. Cann, & G. Tedeschi, 2013; K. N. Triplett, R. G. Tedeschi, A. Cann, L. G. Calhoun, & C. L. Reeve, 2012). The current study examined an integrated model of predictors of distress and perceived growth in 194 college undergraduates. Domains covered included the roles of core belief challenge, event centrality, posttrauma cognitions, and event-related rumination. Negative cognitions about the self and the centrality of the event directly predicted both growth and distress, although intrusive rumination predicted only posttraumatic stress disorder symptoms, and deliberate rumination predicted only posttraumatic growth. Future research should continue to examine the shared and unique predictors of postevent growth and distress. PMID:26011515
Modeling the effects of health on economic growth.
Bhargava, A; Jamison, D T; Lau, L J; Murray, C J
2001-05-01
This paper investigates the effects of health indicators such as adult survival rates (ASR) on GDP growth rates at 5-year intervals in several countries. Panel data were analyzed on GDP series based on purchasing power adjustments and on exchange rates. First, we developed a framework for modeling the inter-relationships between GDP growth rates and explanatory variables by re-examining the life expectancy-income relationship. Second, models for growth rates were estimated taking into account the interaction between ASR and lagged GDP level; issues of endogeneity and reverse causality were addressed. Lastly, we computed confidence intervals for the effect of ASR on growth rate and applied a test for parameter stability. The results showed positive effects of ASR on GDP growth rates in low-income countries. PMID:11373839
Growth model of binary alloy nanopowders for thermal plasma synthesis
Shigeta, Masaya; Watanabe, Takayuki
2010-08-15
A new model is developed for numerical analysis of the entire growth process of binary alloy nanopowders in thermal plasma synthesis. The model can express any nanopowder profile in the particle size-composition distribution (PSCD). Moreover, its numerical solution algorithm is arithmetic and straightforward so that the model is easy to use. By virtue of these features, the model effectively simulates the collective and simultaneous combined process of binary homogeneous nucleation, binary heterogeneous cocondensation, and coagulation among nanoparticles. The effect of the freezing point depression due to nanoscale particle diameters is also considered in the model. In this study, the metal-silicon systems are particularly chosen as representative binary systems involving cocondensation processes. In consequence, the numerical calculation with the present model reveals the growth mechanisms of the Mo-Si and Ti-Si nanopowders by exhibiting their PSCD evolutions. The difference of the materials' saturation pressures strongly affects the growth behaviors and mature states of the binary alloy nanopowder.
A Phase-Field Model for Grain Growth
Chen, L.Q.; Fan, D.N.; Tikare, V.
1998-12-23
A phase-field model for grain growth is briefly described. In this model, a poly-crystalline microstructure is represented by multiple structural order parameter fields whose temporal and spatial evolutions follow the time-dependent Ginzburg-Landau (TDGL) equations. Results from phase-field simulations of two-dimensional (2D) grain growth will be summarized and preliminary results on three-dimensional (3D) grain growth will be presented. The physical interpretation of the structural order parameter fields and the efficient and accurate semi-implicit Fourier spectral method for solving the TDGL equations will be briefly discussed.
A monomer-trimer model supports intermittent glucagon fibril growth
NASA Astrophysics Data System (ADS)
Košmrlj, Andrej; Cordsen, Pia; Kyrsting, Anders; Otzen, Daniel E.; Oddershede, Lene B.; Jensen, Mogens H.
2015-03-01
We investigate in vitro fibrillation kinetics of the hormone peptide glucagon at various concentrations using confocal microscopy and determine the glucagon fibril persistence length 60μm. At all concentrations we observe that periods of individual fibril growth are interrupted by periods of stasis. The growth probability is large at high and low concentrations and is reduced for intermediate glucagon concentrations. To explain this behavior we propose a simple model, where fibrils come in two forms, one built entirely from glucagon monomers and one entirely from glucagon trimers. The opposite building blocks act as fibril growth blockers, and this generic model reproduces experimental behavior well.
A cellular automaton model for tumor growth in heterogeneous environment
NASA Astrophysics Data System (ADS)
Jiao, Yang; Torquato, Sal
2011-03-01
Cancer is not a single disease: it exhibits heterogeneity on different spatial and temporal scales and strongly interacts with its host environment. Most mathematical modeling of malignant tumor growth has assumed a homogeneous host environment. We have developed a cellular automaton model for tumor growth that explicitly incorporates the structural heterogeneity of the host environment such as tumor stroma. We show that these structural heterogeneities have non-trivial effects on the tumor growth dynamics and prognosis. Y. J. is supported by PSOC, NCI.
Eye growth and myopia development: Unifying theory and Matlab model.
Hung, George K; Mahadas, Kausalendra; Mohammad, Faisal
2016-03-01
The aim of this article is to present an updated unifying theory of the mechanisms underlying eye growth and myopia development. A series of model simulation programs were developed to illustrate the mechanism of eye growth regulation and myopia development. Two fundamental processes are presumed to govern the relationship between physiological optics and eye growth: genetically pre-programmed signaling and blur feedback. Cornea/lens is considered to have only a genetically pre-programmed component, whereas eye growth is considered to have both a genetically pre-programmed and a blur feedback component. Moreover, based on the Incremental Retinal-Defocus Theory (IRDT), the rate of change of blur size provides the direction for blur-driven regulation. The various factors affecting eye growth are shown in 5 simulations: (1 - unregulated eye growth): blur feedback is rendered ineffective, as in the case of form deprivation, so there is only genetically pre-programmed eye growth, generally resulting in myopia; (2 - regulated eye growth): blur feedback regulation demonstrates the emmetropization process, with abnormally excessive or reduced eye growth leading to myopia and hyperopia, respectively; (3 - repeated near-far viewing): simulation of large-to-small change in blur size as seen in the accommodative stimulus/response function, and via IRDT as well as nearwork-induced transient myopia (NITM), leading to the development of myopia; (4 - neurochemical bulk flow and diffusion): release of dopamine from the inner plexiform layer of the retina, and the subsequent diffusion and relay of neurochemical cascade show that a decrease in dopamine results in a reduction of proteoglycan synthesis rate, which leads to myopia; (5 - Simulink model): model of genetically pre-programmed signaling and blur feedback components that allows for different input functions to simulate experimental manipulations that result in hyperopia, emmetropia, and myopia. These model simulation programs
Another brick in the cell wall: biosynthesis dependent growth model.
Barbacci, Adelin; Lahaye, Marc; Magnenet, Vincent
2013-01-01
Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper. PMID:24066142
Another Brick in the Cell Wall: Biosynthesis Dependent Growth Model
Barbacci, Adelin; Lahaye, Marc; Magnenet, Vincent
2013-01-01
Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper. PMID:24066142
Modelling Childhood Growth Using Fractional Polynomials and Linear Splines
Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.
2014-01-01
Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651
Lee, J. H.; Oh, S.-H.; Lee, Y. M.; Kim, Y. S.; Son, H. J.; Jeong, D. J.; Whitley, N. C.; Kim, J. J.
2014-01-01
The objective of this study was to estimate the parameters of Gompertz growth curves with the measurements of body conformation, real-time ultrasound longissimus dorsi muscle area (LMA) and backfat thickness (BFT) in Hanwoo cows. The Hanwoo cows (n = 3,373) were born in 97 Hanwoo commercial farms in the 17 cities or counties of Gyeongbuk province, Korea, between 2000 and 2007. A total of 5,504 ultrasound measurements were collected for the cows at the age of 13 to 165 months in 2007 and 2008. Wither height (HW), rump height (HR), the horizontal distance between the top of the hips (WH), and girth of chest (GC) were also measured. Analysis of variance was conducted to investigate variables affecting LMA and BFT. The effect of farm nested in location was included in the statistical model, as well as the effects of HW, HR, WH, and GC as covariates. All of the effects were significant in the analysis of variance for LMA and BFT (p<0.01), except for the HR effect for LMA. The two ultrasound measures and the four body conformation traits were fitted to a Gompertz growth curve function to estimate parameters. Upper asymptotic weights were estimated as 54.0 cm2, 7.67 mm, 125.6 cm, 126.4 cm, 29.3 cm, and 184.1 cm, for LMA, BFT, HW, HR, WH, and GC, respectively. Results of ultrasound measurements showed that Hanwoo cows had smaller LMA and greater BFT than other western cattle breeds, suggesting that care must be taken to select for thick BFT rather than an increase of only beef yield. More ultrasound records per cow are needed to get accurate estimates of growth curve, which, thus, helps producers select animals with high accuracy. PMID:25178367
Development, Selection, and Validation of Tumor Growth Models
NASA Astrophysics Data System (ADS)
Shahmoradi, Amir; Lima, Ernesto; Oden, J. Tinsley
In recent years, a multitude of different mathematical approaches have been taken to develop multiscale models of solid tumor growth. Prime successful examples include the lattice-based, agent-based (off-lattice), and phase-field approaches, or a hybrid of these models applied to multiple scales of tumor, from subcellular to tissue level. Of overriding importance is the predictive power of these models, particularly in the presence of uncertainties. This presentation describes our attempt at developing lattice-based, agent-based and phase-field models of tumor growth and assessing their predictive power through new adaptive algorithms for model selection and model validation embodied in the Occam Plausibility Algorithm (OPAL), that brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Institute for Computational Engineering and Sciences.
The deviation of growth model for transparent conductive graphene
2014-01-01
An approximate growth model was employed to predict the time required to grow a graphene film by chemical vapor deposition (CVD). Monolayer graphene films were synthesized on Cu foil at various hydrogen flow rates from 10 to 50 sccm. The sheet resistance of the graphene film was 310Ω/□ and the optical transmittance was 97.7%. The Raman intensity ratio of the G-peak to the 2D peak of the graphene film was as high as ~4 when the hydrogen flow rate was 30 sccm. The fitting curve obtained by the deviation equation of growth model closely matches the data. We believe that under the same conditions and with the same setup, the presented growth model can help manufacturers and academics to predict graphene growth time more accurately. PMID:25364316
Modelling the effect of fluctuating herbicide concentrations on algae growth.
Copin, Pierre-Jean; Coutu, Sylvain; Chèvre, Nathalie
2015-03-01
Herbicide concentrations fluctuate widely in watercourses after crop applications and rain events. The level of concentrations in pulses can exceed the water chronic quality criteria. In the present study, we proposed modelling the effects of successive pulse exposure on algae. The deterministic model proposed is based on two parameters: (i) the typical growth rate of the algae, obtained by monitoring growth rates of several successive batch cultures in growth media, characterizing both the growth of the control and during the recovery periods; (ii) the growth rate of the algae exposed to pulses, determined from a dose-response curve obtained with a standard toxicity test. We focused on the herbicide isoproturon and on the freshwater alga Scenedesmus vacuolatus, and we validated the model prediction based on effect measured during five sequential pulse exposures in laboratory. The comparison between the laboratory and the modelled effects illustrated that the results yielded were consistent, making the model suitable for effect prediction of the herbicide photosystem II inhibitor isoproturon on the alga S. vacuolatus. More generally, modelling showed that both pulse duration and level of concentration play a crucial role. The application of the model to a real case demonstrated that both the highest peaks and the low peaks with a long duration affect principally the cell density inhibition of the alga S. vacuolatus. It is therefore essential to detect these characteristic pulses when monitoring of herbicide concentrations are conducted in rivers. PMID:25499055
A mathematical model of the growth of uterine myomas.
Chen, C Y; Ward, J P
2014-12-01
Uterine myomas or fibroids are common, benign smooth muscle tumours that can grow to 10 cm or more in diameter and are routinely removed surgically. They are typically slow- growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material, based on a linear stress-strain relationship, and Darcy's law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of nonlinear partial differential equations with two moving boundaries. Numerical solutions of the model successfully reproduce qualitatively the clinically observed three-phase "fast-slow-fast" growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch-like cell growth response to stress. Analysis of large-time solutions reveal that while there is a functioning vasculature throughout the myoma, exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is also presented, and in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model. PMID:25466579
Modeling Dynamic Height and Crown Growth in Trees
NASA Astrophysics Data System (ADS)
Franklin, O.; Fransson, P.; Brännström, Å.
2015-12-01
Previously we have shown how principles based on productivity maximization (e.g. maximization of net primary production, net growth maximization, or functional balance) can explain allocation responses to resources, such as nutrients and light (Franklin et al., 2012). However, the success of these approaches depend on how well they align with the ultimate driver of plant behavior, fitness, or life time reproductive success. Consequently, they may not fully explain how allocation changes during the life cycle of trees where not only growth but also survival and reproduction are important. In addition, maximizing instantaneous productivity does not account for path dependence of tree growth. For example, maximizing productivity during early growth in shade may delay emergence in the forest canopy and reduce lifetime fitness compared to a more height oriented strategy. Here we present an approach to model how growth of stem diameter and leaf area in relation to stem height dynamically responds to light conditions in a way that maximizes life-time fitness (rather than instantaneous growth). The model is able to predict growth of trees growing in different types of forests, including trees emerging under a closed canopy and seedlings planted in a clear-cut area. It can also predict the response to sudden changes in the light environment, due to disturbances or harvesting. We envisage two main applications of the model, (i) Modeling effects of forest management, including thinning and planting (ii) Elucidating height growth strategies in trees and how they can be represented in vegetation models. ReferenceFranklin O, Johansson J, Dewar RC, Dieckmann U, McMurtrie RE, Brännström Å, Dybzinski R. 2012. Modeling carbon allocation in trees: a search for principles. Tree Physiology 32(6): 648-666.
Irreversible growth model for virus capsid assembly
NASA Astrophysics Data System (ADS)
Hicks, Stephen D.; Henley, C. L.
2006-09-01
We model the spontaneous assembly of a capsid (a virus’ closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an elastic Hamiltonian with stretching and bending stiffness and a spontaneous curvature, and (ii) a set of rate constants for the addition of new units or bonds. An ensemble of highly irregular capsids is generated, unlike the well-known icosahedrally symmetric viruses, but (we argue) plausible as a way to model the irregular capsids of retroviruses such as HIV. We found that (i) the probability of successful capsid completion decays exponentially with capsid size; (ii) capsid size depends strongly on spontaneous curvature and weakly on the ratio of the bending and stretching elastic stiffnesses of the shell; (iii) the degree of localization of Gaussian curvature (a measure of facetedness) depends heavily on the ratio of elastic stiffnesses.
Small Business Training Models for Community Growth.
ERIC Educational Resources Information Center
Jellison, Holly M., Ed.
Nine successful community college programs for small business management training are described in this report in terms of their college and economic context, purpose, offerings, delivery modes, operating and marketing strategies, community outreach, support services, faculty and staff, evaluation, and future directions. The model programs are…
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1985-01-01
Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Populational Growth Models Proportional to Beta Densities with Allee Effect
NASA Astrophysics Data System (ADS)
Aleixo, Sandra M.; Rocha, J. Leonel; Pestana, Dinis D.
2009-05-01
We consider populations growth models with Allee effect, proportional to beta densities with shape parameters p and 2, where the dynamical complexity is related with the Malthusian parameter r. For p>2, these models exhibit a population dynamics with natural Allee effect. However, in the case of 1
models do not include this effect. In order to inforce it, we present some alternative models and investigate their dynamics, presenting some important results.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
NASA Astrophysics Data System (ADS)
Chen, Cheng; Chen, Zheng; Zhang, Jing; Yang, Tao; Du, Xiu-Juan
2012-11-01
We modify the anisotropic phase-field crystal model (APFC), and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.
Model-Based Design of Growth-Attenuated Viruses
Lim, Kwang-il; Lang, Tobias; Lam, Vy; Yin, John
2006-01-01
Live-virus vaccines activate both humoral and cell-mediated immunity, require only a single boosting, and generally provide longer immune protection than killed or subunit vaccines. However, growth of live-virus vaccines must be attenuated to minimize their potential pathogenic effects, and mechanisms of attenuation by conventional serial-transfer viral adaptation are not well-understood. New methods of attenuation based on rational engineering of viral genomes may offer a potentially greater control if one can link defined genetic modifications to changes in virus growth. To begin to establish such links between genotype and growth phenotype, we developed a computer model for the intracellular growth of vesicular stomatitis virus (VSV), a well-studied, nonsegmented, negative-stranded RNA virus. Our model incorporated established regulatory mechanisms of VSV while integrating key wild-type infection steps: hijacking of host resources, transcription, translation, and replication, followed by assembly and release of progeny VSV particles. Generalization of the wild-type model to allow for genome rearrangements matched the experimentally observed attenuation ranking for recombinant VSV strains that altered the genome position of their nucleocapsid gene. Finally, our simulations captured previously reported experimental results showing how altering the positions of other VSV genes has the potential to attenuate the VSV growth while overexpressing the immunogenic VSV surface glycoprotein. Such models will facilitate the engineering of new live-virus vaccines by linking genomic manipulations to controlled changes in virus gene-expression and growth. PMID:16948530
Computational modeling of hypertensive growth in the human carotid artery
Sáez, Pablo; Peña, Estefania; Martínez, Miguel Angel; Kuhl, Ellen
2014-01-01
Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively. PMID:25342868
Mathematical Modeling of Tumor Cell Growth and Immune System Interactions
NASA Astrophysics Data System (ADS)
Rihan, Fathalla A.; Safan, Muntaser; Abdeen, Mohamed A.; Abdel-Rahman, Duaa H.
In this paper, we provide a family of ordinary and delay differential equations to describe the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells, and the rate of influx of IL2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor-dormancy.
Modeling Gas Exchange in a Closed Plant Growth Chamber
NASA Technical Reports Server (NTRS)
Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.
1994-01-01
Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant a growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.
Modeling gas exchange in a closed plant growth chamber
NASA Technical Reports Server (NTRS)
Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.
1994-01-01
Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.
Nonlinear and Quasi-Simplex Patterns in Latent Growth Models
ERIC Educational Resources Information Center
Bianconcini, Silvia
2012-01-01
In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the…
The Multigroup Multilevel Categorical Latent Growth Curve Models
ERIC Educational Resources Information Center
Hung, Lai-Fa
2010-01-01
Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…
Sensitivity of Fit Indices to Misspecification in Growth Curve Models
ERIC Educational Resources Information Center
Wu, Wei; West, Stephen G.
2010-01-01
This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…
Study of Academic Growth Using Simplex Models. Final Report.
ERIC Educational Resources Information Center
Werts, Charles E.; Linn, Robert L.
Forming a sequence covering the various aspects of the simplex model, four articles are presented here under the following titles: "A Simplex Model for Analyzing Academic Growth", "Analyzing Ratings With Correlated Intrajudge Measurement Errors", "The Correlation of States With Gain", and "The Reliability of College Grades from Longitudinal Data".…
A Cautionary Note on Modeling Growth Trends in Longitudinal Data
ERIC Educational Resources Information Center
Kuljanin, Goran; Braun, Michael T.; DeShon, Richard P.
2011-01-01
Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a…
Practical Formulations of the Latent Growth Item Response Model
ERIC Educational Resources Information Center
McGuire, Leah Walker
2010-01-01
Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with…
Energy model of radial growth of a nanotubular crystal
NASA Astrophysics Data System (ADS)
Krasilin, A. A.; Gusarov, V. V.
2016-01-01
An energy model of the formation of multiwall nanoscrolls from thin layers is proposed. It is established that the radial growth of a nanoscroll can be accompanied by variation of the ratio of its internal and external diameters. The influence of the main physical parameters of the model on this ratio is considered.
Phase field modeling of grain growth in porous polycrystalline solids
NASA Astrophysics Data System (ADS)
Ahmed, Karim E.
The concurrent evolution of grain size and porosity in porous polycrystalline solids is a technically important problem. All the physical properties of such materials depend strongly on pore fraction and pore and grain sizes and distributions. Theoretical models for the pore-grain boundary interactions during grain growth usually employ restrictive, unrealistic assumptions on the pore and grain shapes and motions to render the problem tractable. However, these assumptions limit the models to be only of qualitative nature and hence cannot be used for predictions. This has motivated us to develop a novel phase field model to investigate the process of grain growth in porous polycrystalline solids. Based on a dynamical system of coupled Cahn-Hilliard and All en-Cahn equations, the model couples the curvature-driven grain boundary motion and the migration of pores via surface diffusion. As such, the model accounts for all possible interactions between the pore and grain boundary, which highly influence the grain growth kinetics. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. The model was used to investigate the effect of porosity on the kinetics of grain growth in UO2 and CeO2 in 2D and 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four- grain junctions were found to transform to edge pores (pores on two-grain junction) before complete separation. The simulations demonstrated that inhomogeneous distribution of pores and pore breakaway lead to abnormal grain growth. The simulations also showed that grain growth kinetics in these materials changes from boundary-controlled to pore-controlled as the amount of porosity increases. The kinetic growth
Modeling the growth of CZT by the EDG process
NASA Astrophysics Data System (ADS)
Derby, Jeffrey J.; Gasperino, David; Lun, Lisa; Yeckel, Andrew
2008-08-01
The overall goal of this research is to develop and apply computational modeling to better understand the processes used to grow bulk crystals employed in radiation detectors. Specifically, the work discussed here aims at understanding the growth of cadmium zinc telluride (CZT), a material of long interest to the detector community. We consider the growth of CZT via gradient freeze processes in electrodynamic multizone furnaces and show how crucible mounting and design are predicted to affect conditions for crystal growth. Analysis of these systems will be essential for for significant materials improvement, i.e., growing larger crystals with superior quality and at a lower cost.
A thermodynamic model for growth mechanisms of multiwall carbon nanotubes.
Kaatz, Forrest H.; Overmyer, Donald L.; Siegal, Michael P.
2006-02-01
Multiwall carbon nanotubes are grown via thermal chemical vapor deposition between temperatures of 630 and 830 C using acetylene in nitrogen as the carbon source. This process is modeled using classical thermodynamics to explain the total carbon deposition as a function of time and temperature. An activation energy of 1.60 eV is inferred for nanotube growth after considering the carbon solubility term. Scanning electron microscopy shows growth with diameters increasing linearly with time. Transmission electron microscopy and Raman spectroscopy show multiwall nanotubes surrounded by a glassy-carbon sheath, which grows with increasing wall thickness as growth temperatures and times rise.
Quantitative model of the growth of floodplains by vertical accretion
Moody, J.A.; Troutman, B.M.
2000-01-01
A simple one-dimensional model is developed to quantitatively predict the change in elevation, over a period of decades, for vertically accreting floodplains. This unsteady model approximates the monotonic growth of a floodplain as an incremental but constant increase of net sediment deposition per flood for those floods of a partial duration series that exceed a threshold discharge corresponding to the elevation of the floodplain. Sediment deposition from each flood increases the elevation of the floodplain and consequently the magnitude of the threshold discharge resulting in a decrease in the number of floods and growth rate of the floodplain. Floodplain growth curves predicted by this model are compared to empirical growth curves based on dendrochronology and to direct field measurements at five floodplain sites. The model was used to predict the value of net sediment deposition per flood which best fits (in a least squares sense) the empirical and field measurements; these values fall within the range of independent estimates of the net sediment deposition per flood based on empirical equations. These empirical equations permit the application of the model to estimate of floodplain growth for other floodplains throughout the world which do not have detailed data of sediment deposition during individual floods. Copyright (C) 2000 John Wiley and Sons, Ltd.
Modelling grain growth in the framework of Rational Extended Thermodynamics
NASA Astrophysics Data System (ADS)
Kertsch, Lukas; Helm, Dirk
2016-05-01
Grain growth is a significant phenomenon for the thermomechanical processing of metals. Since the mobility of the grain boundaries is thermally activated and energy stored in the grain boundaries is released during their motion, a mutual interaction with the process conditions occurs. To model such phenomena, a thermodynamic framework for the representation of thermomechanical coupling phenomena in metals including a microstructure description is required. For this purpose, Rational Extended Thermodynamics appears to be a useful tool. We apply an entropy principle to derive a thermodynamically consistent model for grain coarsening due to the growth and shrinkage of individual grains. Despite the rather different approaches applied, we obtain a grain growth model which is similar to existing ones and can be regarded as a thermodynamic extension of that by Hillert (1965) to more general systems. To demonstrate the applicability of the model, we compare our simulation results to grain growth experiments in pure copper by different authors, which we are able to reproduce very accurately. Finally, we study the implications of the energy release due to grain growth on the energy balance. The present unified approach combining a microstructure description and continuum mechanics is ready to be further used to develop more elaborate material models for complex thermo-chemo-mechanical coupling phenomena.
A CARTILAGE GROWTH MIXTURE MODEL WITH COLLAGEN REMODELING: VALIDATION PROTOCOLS
Klisch, Stephen M.; Asanbaeva, Anna; Oungoulian, Sevan R.; Masuda, Koichi; Thonar, Eugene J-MA; Davol, Andrew; Sah, Robert L.
2009-01-01
A cartilage growth mixture (CGM) model is proposed to address limitations of a model used in a previous study. New stress constitutive equations for the solid matrix are derived and collagen (COL) remodeling is incorporated into the CGM model by allowing the intrinsic COL material constants to evolve during growth. An analytical validation protocol based on experimental data from a recent in vitro growth study is developed. Available data included measurements of tissue volume, biochemical composition, and tensile modulus for bovine calf articular cartilage (AC) explants harvested at three depths and incubated for 13 days in 20% FBS and 20% FBS+β-aminopropionitrile. The proposed CGM model can match tissue biochemical content and volume exactly while predicting theoretical values of tensile moduli that do not significantly differ from experimental values. Also, theoretical values of a scalar COL remodeling factor are positively correlated with COL crosslink content, and mass growth functions are positively correlated with cell density. The results suggest that the CGM model may help to guide in vitro growth protocols for AC tissue via the a priori prediction of geometric and biomechanical properties. PMID:18532855
Chen, Qi; Hughes, Jan N.; Kwok, Oi-Man
2013-01-01
The authors investigated the differential effect of retention on the development of academic achievement from grade one to five on children retained in first grade over six years. Growth Mixture Model (GMM) analyses supported the existence of two distinct trajectory groups of retained children for both reading and math among 125 ethnically and linguistically diverse retained children. For each achievement domain, a low intercept/higher growth group (Class 1) and a high intercept/slower growth group (Class 2) were identified. Furthermore, Class 1 children were found to score lower on several measures of learning related skills (LRS) variables and were characterized by having poorer self-regulation and less prosocial behaviors, compared to the other group. Findings suggest that some children appear to benefit more from retention, in terms of higher reading and math growth, than others. Study findings have implications for selecting children into retention intervention and early intervention. PMID:24771882
Griebeler, Eva Maria; Klein, Nicole; Sander, P. Martin
2013-01-01
Information on aging, maturation, and growth is important for understanding life histories of organisms. In extinct dinosaurs, such information can be derived from the histological growth record preserved in the mid-shaft cortex of long bones. Here, we construct growth models to estimate ages at death, ages at sexual maturity, ages at which individuals were fully-grown, and maximum growth rates from the growth record preserved in long bones of six sauropod dinosaur individuals (one indeterminate mamenchisaurid, two Apatosaurus sp., two indeterminate diplodocids, and one Camarasaurus sp.) and one basal sauropodomorph dinosaur individual (Plateosaurus engelhardti). Using these estimates, we establish allometries between body mass and each of these traits and compare these to extant taxa. Growth models considered for each dinosaur individual were the von Bertalanffy model, the Gompertz model, and the logistic model (LGM), all of which have inherently fixed inflection points, and the Chapman-Richards model in which the point is not fixed. We use the arithmetic mean of the age at the inflection point and of the age at which 90% of asymptotic mass is reached to assess respectively the age at sexual maturity or the age at onset of reproduction, because unambiguous indicators of maturity in Sauropodomorpha are lacking. According to an AIC-based model selection process, the LGM was the best model for our sauropodomorph sample. Allometries established are consistent with literature data on other Sauropodomorpha. All Sauropodomorpha reached full size within a time span similar to scaled-up modern mammalian megaherbivores and had similar maximum growth rates to scaled-up modern megaherbivores and ratites, but growth rates of Sauropodomorpha were lower than of an average mammal. Sauropodomorph ages at death probably were lower than that of average scaled-up ratites and megaherbivores. Sauropodomorpha were older at maturation than scaled-up ratites and average mammals, but
Using the Expolinear Growth Equation for Modelling Crop Growth in Year‐round Cut Chrysanthemum
LEE, JEONG HYUN; GOUDRIAAN, JAN; CHALLA, HUGO
2003-01-01
The aim of this study was to predict crop growth of year‐round cut chrysanthemum (Chrysanthemum morifolium Ramat.) based on an empirical model of potential crop growth rate as a function of daily incident photosynthetically active radiation (PAR, MJ m–2 d–1), using generalized estimated parameters of the expolinear growth equation. For development of the model, chrysanthemum crops were grown in four experiments at different plant densities (32, 48, 64 and 80 plants m–2), during different seasons (planting in January, May–June and September) and under different light regimes [natural light, shading to 66 and 43 % of natural light, and supplementary assimilation light (ASS, 40–48 µmol m–2 s–1)]. The expolinear growth equation as a function of time (EXPOT) or as a function of incident PAR integral (EXPOPAR) effectively described periodically measured total dry mass of shoot (R2 > 0·98). However, growth parameter estimates for the fitted EXPOPAR were more suitable as they were not correlated to each other. Coefficients of EXPOPAR characterized the relative growth rate per incident PAR integral [rm,i (MJ m–2)–1] and light use efficiency (LUE, g MJ–1) at closed canopy. In all four experiments, no interaction effects between treatments on crop growth parameters were found. rm,i and LUE were not different between ASS and natural light treatments, but were increased significantly when light levels were reduced by shading in the summer experiments. There was no consistent effect of plant density on growth parameters. rm,i and LUE showed hyperbolic relationships to average daily incident PAR averaged over 10‐d periods after planting (rm,i) or before final harvest (LUE). Based on those relationships, maximum relative growth rate (rm, g g–1 d–1) and maximum crop growth rate (cm, g m–2 d–1) were described successfully by rectangular hyperbolic relationships to daily incident PAR. In model validation, total dry mass of shoot (Wshoot, g m
Effects of the environment on fish juvenile growth in West African stressful estuaries
NASA Astrophysics Data System (ADS)
Diouf, K.; Guilhaumon, F.; Aliaume, C.; Ndiaye, P.; Chi, T. Do; Panfili, J.
2009-06-01
The knowledge of juvenile fish growth in extreme environmental conditions is a key to the understanding of adaptive responses and to the relevant management of natural populations. The juvenile growth of an extreme euryhaline tilapia species, Sarotherodon melanotheron (Cichlidae), was examined across a salinity gradient (20-118) in several West African estuarine ecosystems. Juveniles were collected during the reproduction period of two consecutive years (2003 and 2004) in six locations in the Saloum (Senegal) and Gambia estuaries. Age and growth were estimated using daily otolith microincrements. For each individual, otolith growth rates showed three different stages (slow, fast, decreasing): around 4 ± 0.5 μm d -1 during the first five days, 9 ± 0.5 μm d -1 during the next 15 days and 4 ± 0.50 μm d -1 at 60 days. Growth modelling and model comparisons were objectively made within an information theory framework using the multi-model inference from five growth models (linear, power, Gompertz, von Bertalanffy, and logistic). The combination of both the model adjustment inspection and the information theory model selection procedure allowed identification of the final set of models, including the less parameterised ones. The estimated growth rates were variable across spatial scales but not across temporal scales (except for one location), following exactly the salinity gradient with growth decrease towards the hypersaline conditions. The salinity gradient was closely related to all measured variables (condition factor, mean age, multi-model absolute growth rate) demonstrating the strong effect of hypersaline environmental conditions—induced by climate changes—on fish populations at an early stage.
Modeling the atomistic growth behavior of gold nanoparticles in solution
NASA Astrophysics Data System (ADS)
Turner, C. Heath; Lei, Yu; Bao, Yuping
2016-04-01
The properties of gold nanoparticles strongly depend on their three-dimensional atomic structure, leading to an increased emphasis on controlling and predicting nanoparticle structural evolution during the synthesis process. In order to provide this atomistic-level insight and establish a link to the experimentally-observed growth behavior, a kinetic Monte Carlo simulation (KMC) approach is developed for capturing Au nanoparticle growth characteristics. The advantage of this approach is that, compared to traditional molecular dynamics simulations, the atomistic nanoparticle structural evolution can be tracked on time scales that approach the actual experiments. This has enabled several different comparisons against experimental benchmarks, and it has helped transition the KMC simulations from a hypothetical toy model into a more experimentally-relevant test-bed. The model is initially parameterized by performing a series of automated comparisons of Au nanoparticle growth curves versus the experimental observations, and then the refined model allows for detailed structural analysis of the nanoparticle growth behavior. Although the Au nanoparticles are roughly spherical, the maximum/minimum dimensions deviate from the average by approximately 12.5%, which is consistent with the corresponding experiments. Also, a surface texture analysis highlights the changes in the surface structure as a function of time. While the nanoparticles show similar surface structures throughout the growth process, there can be some significant differences during the initial growth at different synthesis conditions.
Modeling the atomistic growth behavior of gold nanoparticles in solution.
Turner, C Heath; Lei, Yu; Bao, Yuping
2016-04-28
The properties of gold nanoparticles strongly depend on their three-dimensional atomic structure, leading to an increased emphasis on controlling and predicting nanoparticle structural evolution during the synthesis process. In order to provide this atomistic-level insight and establish a link to the experimentally-observed growth behavior, a kinetic Monte Carlo simulation (KMC) approach is developed for capturing Au nanoparticle growth characteristics. The advantage of this approach is that, compared to traditional molecular dynamics simulations, the atomistic nanoparticle structural evolution can be tracked on time scales that approach the actual experiments. This has enabled several different comparisons against experimental benchmarks, and it has helped transition the KMC simulations from a hypothetical toy model into a more experimentally-relevant test-bed. The model is initially parameterized by performing a series of automated comparisons of Au nanoparticle growth curves versus the experimental observations, and then the refined model allows for detailed structural analysis of the nanoparticle growth behavior. Although the Au nanoparticles are roughly spherical, the maximum/minimum dimensions deviate from the average by approximately 12.5%, which is consistent with the corresponding experiments. Also, a surface texture analysis highlights the changes in the surface structure as a function of time. While the nanoparticles show similar surface structures throughout the growth process, there can be some significant differences during the initial growth at different synthesis conditions. PMID:27091290
A Model for Tetragonal Lysozyme Crystal Nucleation and Growth
NASA Technical Reports Server (NTRS)
Pusey, Marc L.; Curreri, Peter A. (Technical Monitor)
2002-01-01
Macromolecular crystallization is a complex process, involving a system that typically has 5 or more components (macromolecule, water, buffer + counter ion, and precipitant). Whereas small molecules have only a few contacts in the crystal lattice, macromolecules generally have 10's or even 100's of contacts between molecules. These can range from hydrogen bonds (direct or water-mediated), through van der Waals, hydrophobic, salt bridges, and ion-mediated contacts. The latter interactions are stronger and require some specificity in the molecular alignment, while the others are weaker, more prevalent, and more promiscuous, i.e., can be readily broken and reformed between other sites. Formation of a consistent, ordered, 3D structure may be difficult or impossible in the absence of any or presence of too many strong interactions. Further complicating the process is the inherent structural asymmetry of monomeric (single chain) macromolecules. The process of crystal nucleation and growth involves the ordered assembly of growth units into a defined 3D lattice. We suggest that for many macromolecules, particularly those that are monomeric, this involves a preliminary solution-phase assembly process into a growth unit having some symmetry prior to addition to the lattice, recapitulating the initial stages of the nucleation process. If this model is correct then fluids and crystal growth models assuming a strictly monodisperse nutrient solution need to be revised. This model has been developed from experimental evidence based upon face growth rate, AFM, and fluorescence energy transfer data for the nucleation and growth of tetragonal lysozyme crystals.
Hajmeer, M; Basheer, I
2002-10-01
In this paper, we propose to use probabilistic neural networks (PNNs) for classification of bacterial growth/no-growth data and modeling the probability of growth. The PNN approach combines both Bayes theorem of conditional probability and Parzen's method for estimating the probability density functions of the random variables. Unlike other neural network training paradigms, PNNs are characterized by high training speed and their ability to produce confidence levels for their classification decision. As a practical application of the proposed approach, PNNs were investigated for their ability in classification of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most frequently used traditional statistical method based on logistic regression and multilayer feedforward artificial neural network (MFANN) trained by error backpropagation was also carried out. The PNN-based models were found to outperform linear and nonlinear logistic regression and MFANN in both the classification accuracy and ease by which PNN-based models are developed. PMID:12133614
Rock Physics Models of Biofilm Growth in Porous Media
NASA Astrophysics Data System (ADS)
Jaiswal, P.; alhadhrami, F. M.; Atekwana, E. A.
2013-12-01
Recent studies suggest the potential to use acoustic techniques to image biofilm growth in porous media. Nonetheless the interpretation of the seismic response to biofilm growth and development remains speculative because of the lack of quantitative petrophysical models that can relate changes in biofilm saturation to changes in seismic attributes. Here, we report our efforts in developing quantitative rock physics models to biofilm saturation with increasing and decreasing P-wave velocity (VP) and amplitudes recorded in the Davis et al. [2010] physical scale experiment. We adapted rock physics models developed for modeling gas hydrates in unconsolidated sediments. Two distinct growth models, which appear to be a function of pore throat size, are needed to explain the experimental data. First, introduction of biofilm as an additional mineral grain in the sediment matrix (load-bearing mode) is needed to explain the increasing time-lapse VP. Second, introduction of biofilm as part of the pore fluid (pore-filling mode) is required to explain the decreasing time-lapse VP. To explain the time-lapse VP, up to 15% of the pore volume was required to be saturated with biofilm. The recorded seismic amplitudes, which can be expressed as a function of porosity, permeability and grain size, showed a monotonic time-lapse decay except on Day 3 at a few selected locations, where it increased. Since porosity changes are constrained by VP, amplitude increase could be modeled by increasing hydraulic conductivity. Time lapse VP at locations with increasing amplitudes suggest that these locations have a load-bearing growth style. We conclude that permeability can increase by up to 10% at low (~2%) biofilm saturation in load-bearing growth style due to the development of channels within the biofilm structure. Developing a rock physics model for the biofilm growth in general may help create a field guide for interpreting porosity and permeability changes in bioremediation, MEOR and
Plant growth and architectural modelling and its applications
Guo, Yan; Fourcaud, Thierry; Jaeger, Marc; Zhang, Xiaopeng; Li, Baoguo
2011-01-01
Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels. PMID:21638797
Quantitative Models of CAI Rim Layer Growth
NASA Astrophysics Data System (ADS)
Ruzicka, A.; Boynton, W. V.
1995-09-01
. None of these variations in rim layers are correlated with the modal compositions of the CAIs. In our models, we investigated the reaction of CAI interiors (containing M + S + F) with various proportions of vapor (V), O, and D in the 5-component system MgO-AlO(sub)3/2- CaO-SiO2-TiO2. Representative compositions were assumed for the solids. Most likely, a vapor reacting with CAIs would have small (e.g., solar) or trivial abundances of Al, Ca, and Ti compared to Si and Mg, and such Al-, Ca-, and Ti-poor compositions were assumed for the vapor. The model zone sequence MSF|S|A|D|V can form when Mg/[Mg+Si] 0.28-0.47 in the vapor, and is consistent with rims that contain an A layer but that lack an O layer. The zone sequence MSF|S|D|VO, which can form when Mg/[Mg+Si] 0-0.47 in the vapor, may explain rims that lack an A (and M) layer and that have an porous (or poorly compacted) O layer. Finally, the model zone sequence MSF|S|A|D|O +/- D is consistent with rims that contain both an A layer and an compact O layer, but this sequence can form only if the system experienced open-system loss of Ca at the D-O contact, with Ca-poor vapor being a possible open-system sink for Ca. The occasional presence of M in a mono- or bi-mineralic layer within rims apparently cannot be explained by the models, possibly indicating that the rims did not fully attain a steady-state condition. References: [1] Boynton W. V. and Wark D. A. (1985) Meteoritics, 20, 117-118. [2] Murrell M. T. and Burnett D. S. (1987) GCA, 51, 985-999. [3] Ruzicka A. and Boynton W. V. (1994) Meteoritics, 29, 529. [4] MacPherson G. J. et al. (1981) Proc. LPS 12B, 1079-1091. [5] Wark D. A. et al. (1988) LPS XIX, 1230-1231.