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
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
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.
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.
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.
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.
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
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
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
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.
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...
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…
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
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.
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.
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
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.
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
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
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.
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…
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…
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…
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.
[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
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.
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.
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
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.
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,…
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,…
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.
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.
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
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
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.
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.
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.
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
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.
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
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.
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.
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.…
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.
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.
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...
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…
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...
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
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.
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.
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
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
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
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…
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…
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)
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 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 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 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…
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.
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.
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.
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
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
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.
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…
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".…
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.
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
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
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.
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
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.
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
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.
NASA Technical Reports Server (NTRS)
Miller, Adam M.; Edeen, Marybeth; Sirko, Robert J.
1992-01-01
This paper describes the approach and results of an effort to characterize plant growth under various environmental conditions at the Johnson Space Center variable pressure growth chamber. Using a field of applied mathematics and statistics known as design of experiments (DOE), we developed a test plan for varying environmental parameters during a lettuce growth experiment. The test plan was developed using a Box-Behnken approach to DOE. As a result of the experimental runs, we have developed empirical models of both the transpiration process and carbon dioxide assimilation for Waldman's Green lettuce over specified ranges of environmental parameters including carbon dioxide concentration, light intensity, dew-point temperature, and air velocity. This model also predicts transpiration and carbon dioxide assimilation for different ages of the plant canopy.
Modeling of Tumor Growth Based on Adomian Decomposition Method
NASA Astrophysics Data System (ADS)
Mahiddin, Norhasimah; Ali, Siti Aishah Hashim
2008-01-01
Modeling of a growing tumor over time is extremely difficult. This is due to the complex biological phenomena underlying cancer growth. Existing models mostly based on numerical methods and could describe spherically-shaped avascular tumors but they cannot match the highly heterogeneous and complex shaped tumors seen in cancer patients. We propose a new technique based on decomposition method to solve analytically cancer model.
Modeling of thin film GaAs growth
NASA Technical Reports Server (NTRS)
Heinbockel, J. H.
1982-01-01
A potential scaling Monte Carlo model of crystal growth is developed. The model is a modification of the solid-on-solid method for studying crystal growth in that potentials at surface sites are continuously updated on a time scale reflecting the surface events of migration, incorporation and evaporation. The model allows for B on A type of crystal growth and lattice disregistry by the assignment of potential values at various surface sites. The surface adatoms are periodically assigned a random energy from a Boltzmann distribution and this energy determines whether the adatoms evaporate, migrate or remain stationary during the sampling interval. For each addition or migration of an adatom, the surface potentials are adjusted to reflect the adsorption, migration or desorption potential changes.
Thermal spike model of ion-induced grain growth
Alexander, D.E. ); Was, G.S. . Dept. of Nuclear Engineering)
1990-11-01
A thermal spike model has been developed to describe the phenomenon of ion irradiation-induced grain growth in metal alloy thin films. In single phase films where the driving force for grain growth is the reduction of grain boundary curvature, the model shows that ion-induced grain boundary mobility, M{sub ion}, is proportional to the quantity F{sub D}{sup 2}/{Delta}H{sub coh}{sup 3}, where F{sub D} is the deposited ion damage energy and {Delta}H{sub coh} is the cohesive energy of the element or alloy. Experimental strain growth results from ion irradiated coevaporated binary alloy films compare favorably with model predictions. 11 refs., 1 fig., 1 tab.
Model for calcium dependent oscillatory growth in pollen tubes.
Kroeger, Jens H; Geitmann, Anja; Grant, Martin
2008-07-21
Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels. PMID:18471831
Ba, A; Diouf, K; Guilhaumon, F; Panfili, J
2015-10-01
Age and growth of Rhizoprionodon acutus were estimated from vertebrae age bands. From December 2009 to November 2010, 423 R. acutus between 37 and 112 cm total length (LT ) were sampled along the Senegalese coast. Marginal increment ratio was used to check annual band deposition. Three growth models were adjusted to the length at age and compared using Akaike's information criterion. The Gompertz growth model with estimated size at birth appeared to be the best and resulted in growth parameters of L∞ = 139.55 (LT ) and K = 0.17 year(-1) for females and L∞ = 126.52 (LT ) and K = 0.18 year(-1) for males. The largest female and male examined were 8 and 9 years old, but the majority was between 1 and 3 years old. Ages at maturity estimated were 5.8 and 4.8 years for females and males, respectively. These results suggest that R. acutus is a slow-growing species, which render the species particularly vulnerable to heavy fishery exploitation. The growth parameters estimated in this study are crucial for stock assessments and for demographic analyses to evaluate the sustainability of commercial harvests. PMID:26436372
Modeling sugarcane growth in response to age, insolation, and temperature
How, K.T.S.
1986-01-01
Modeling sugarcane growth in response to age of cane, insolation and air temperature using first-order multiple regression analysis and a nonlinear approach is investigated. Data are restricted to one variety from irrigated fields to eliminate the impact of varietal response and rainfall. Ten first-order models are investigated. The predictant is cane yield from 600 field tests. The predictors are cumulative values of insolation, maximum temperature, and minimum temperature for 3, 6, 12, and 18 months, or for each crop period derived from weather observations near the test plots. The low R-square values indicate that the selected predictor variables could not account for a substantial proportion of the variations of cane yield and the models have limited predictive values. The nonlinear model is based on known functional relationships between growth and age, growth and insolation, and growth and maximum temperature. A mathematical expression that integrates the effect of age, insolation and maximum temperature is developed. The constant terms and coefficients of the equation are determined from the requirement that the model must produce results that are reasonable when compared with observed monthly elongation data. The nonlinear model is validated and tested using another set of data.
Modeling Intrinsic Heterogeneity and Growth of Cancer Cells
Greene, James M.; Levy, Doron; Fung, King L.; Silva de Souza, Paloma; Gottesman, Michael M.; Lavi, Orit
2014-01-01
Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multi-drug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level. PMID:25457229
ERIC Educational Resources Information Center
Chen, Qi; Hughes, Jan N.; Kwok, Oi-Man
2014-01-01
The authors investigated the differential effect of retention on the development of academic achievement from grades 1 to 5 on children retained in grade 1 over 6 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…
Deterministic versus stochastic aspects of superexponential population growth models
NASA Astrophysics Data System (ADS)
Grosjean, Nicolas; Huillet, Thierry
2016-08-01
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.
Von Neumann's growth model: Statistical mechanics and biological applications
NASA Astrophysics Data System (ADS)
De Martino, A.; Marinari, E.; Romualdi, A.
2012-09-01
We review recent work on the statistical mechanics of Von Neumann's growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann's model can be helpful in uncovering functional organization principles of cell energetics.
Modelling the initial stage of porous alumina growth during anodization
NASA Astrophysics Data System (ADS)
Aryslanova, E. M.; Alfimov, A. V.; Chivilikhin, S. A.
2013-05-01
Artificially on the surface of aluminum there may be build a thick layer of Al2O3, which has a porous structure. In this paper we present a model of growth of porous alumina in the initial stage of anodizing, identifying dependencies anodizing parameters on the rate of growth of the film and the distance between the pores and as a result of the created model equations were found for changes in the disturbance of alumina for the initial stage of anodizing aluminum oxide porous border aluminum-alumina and alumina-electrolyte, with the influence of surface diffusion of aluminum oxide.
Fatigue crack growth with single overload - Measurement and modeling
NASA Technical Reports Server (NTRS)
Davidson, D. L.; Hudak, S. J., Jr.; Dexter, R. J.
1987-01-01
This paper compares experiments with an analytical model of fatigue crack growth under variable amplitude. The stereoimaging technique was used to measure displacements near the tips of fatigue cracks undergoing simple variations in load amplitude-single overloads and overload/underload combinations. Measured displacements were used to compute strains, and stresses were determined from the strains. Local values of crack driving force (Delta-K effective) were determined using both locally measured opening loads and crack tip opening displacements. Experimental results were compared with simulations made for the same load variation conditions using Newman's FAST-2 model. Residual stresses caused by overloads, crack opening loads, and growth retardation periods were compared.
Kinetic model of particle-inhibited grain growth
NASA Astrophysics Data System (ADS)
Thompson, Gary Scott
The effects of second phase particles on matrix grain growth kinetics were investigated using Al2O3-SiC as a model system. In particular, the validity of the conclusion drawn from a previous kinetic analysis that the kinetics of particle-inhibited grain growth in Al2 O3-SiC samples with an intermediate volume fraction of second phase could be well quantified by a modified-Zener model was investigated. A critical analysis of assumptions made during the previous kinetic analysis revealed oversimplifications which affect the validity of the conclusion. Specifically, the degree of interaction between particles and grain boundaries was assumed to be independent of the mean second phase particle size and size distribution. In contrast, current measurements indicate that the degree of interaction in Al2O3-SiC is dependent on these parameters. An improved kinetic model for particle-inhibited grain growth in Al 2O3-SiC was developed using a modified-Zener approach. The comparison of model predictions with experimental grain growth data indicated that significant discrepancies (as much as 4--5 orders of magnitude) existed. Based on this, it was concluded that particles had a much more significant effect on grain growth kinetics than that caused by a simple reduction of the boundary driving force due to the removal of boundary area. Consequently, it was also concluded that the conclusion drawn from the earlier kinetic analysis regarding the validity of a modified-Zener model was incorrect. Discrepancies between model and experiment were found to be the result of a significant decrease in experimental growth rate constant not predicted by the model. Possible physical mechanisms for such a decrease were investigated. The investigation of a small amount of SiO2 on grain growth in Al2O3 indicated that the decrease was not the result of a decrease in grain boundary mobility due to impurity contamination by particles. By process of elimination and based on previous observations
MODELING GROWTH OF AU-CU NANOCRYSTALLIINE COATINGS
Jankowski, A F
2005-09-22
The electrodeposition process parameters of current density, pulse duration, and cell potential affect both the structure and composition of the foils. The mechanism for nucleation and growth as determined from current transients yield relationships for nucleus density and nucleation rate. To develop an understanding of the role of the process parameters on grain size--as a design structural parameter to control strength, for example, a formulation is presented to model the affects of the deposition energetics on grain size and morphology. An activation energy for the deposition process is modeled that reveals different growth mechanisms, wherein nucleation and diffusion effects are each dominant as dependent upon pulse duration. A diffusion coefficient common for each of the pulsed growth modes demarcates an observed transition in growth from smooth to rough surfaces. Empirical relationships are developed that relate the parameters of the deposition process to the morphology and grain size at the nanoscale. Regimes for nanocrystalline growth include a short and long pulse mode, each with distinct activation energies. The long pulse has the additional contribution of bulk-like diffusion whereas the short pulse is limited to surface diffusion and nucleation. For either pulse condition, a transition from a rough (or nodular) growth to a smooth surface results with an increase in the kinetics of diffusion.
Photorealistic Modeling of the Growth of Filamentous Specimens
NASA Astrophysics Data System (ADS)
Sedlář, Jiří; Flusser, Jan; Sedlářová, Michaela
2007-12-01
We present a new method for modeling the development of settled specimens with filamentous growth patterns, such as fungi and oomycetes. In phytopathology, the growth parameters of such microorganisms are frequently examined. Their development is documented repeatedly, in a defined time sequence, leaving the growth pattern incomplete. This restriction can be overcome by reconstructing the missing images from the images acquired at consecutive observation sessions. Image warping is a convenient tool for such purposes. In the proposed method, the parameters of the geometric transformation are estimated by means of the growth tracking based on the morphological skeleton. The result is a sequence of photorealistic artificial images that show the development of the specimen within the interval between observations.
Clark, Ryan P; Schuenke, Mark; Keeton, Stephanie M; Staron, Robert S; Kopchick, John J
2006-01-01
The precise effects of growth hormone (GH) and insulin-like growth factor I (IGF-I) on muscle development and physiology are relatively unknown. Furthermore, there have been conflicting reports on the effects of GH/IGF-I on muscle. Distinguishing the direct effects of GH versus those of IGF-I is problematic, but animal models with altered GH/IGF-I action could help to alleviate some of the conflicting results and help to determine the independent actions of GH and IGF-I. The phenotypes of several mouse models, namely the GH receptor-gene-disrupted (GHR -/-) mouse and a variety of IGF-I -/- mice, are summarized, which ultimately will aid our understanding of this complex area. PMID:17259718
Modelling of strongly coupled particle growth and aggregation
NASA Astrophysics Data System (ADS)
Gruy, F.; Touboul, E.
2013-02-01
The mathematical modelling of the dynamics of particle suspension is based on the population balance equation (PBE). PBE is an integro-differential equation for the population density that is a function of time t, space coordinates and internal parameters. Usually, the particle is characterized by a unique parameter, e.g. the matter volume v. PBE consists of several terms: for instance, the growth rate and the aggregation rate. So, the growth rate is a function of v and t. In classical modelling, the growth and the aggregation are independently considered, i.e. they are not coupled. However, current applications occur where the growth and the aggregation are coupled, i.e. the change of the particle volume with time is depending on its initial value v0, that in turn is related to an aggregation event. As a consequence, the dynamics of the suspension does not obey the classical Von Smoluchowski equation. This paper revisits this problem by proposing a new modelling by using a bivariate PBE (with two internal variables: v and v0) and by solving the PBE by means of a numerical method and Monte Carlo simulations. This is applied to a physicochemical system with a simple growth law and a constant aggregation kernel.
Drew, M; White, W T; Dharmadi; Harry, A V; Huveneers, C
2015-01-01
Indonesia has the greatest reported chondrichthyan catches worldwide, with c.110,000 t caught annually. The pelagic thresher (Alopias pelagicus) and scalloped hammerhead (Sphryna lewini) together comprise about 25% of the total catches of sharks landed in Indonesia. Age and growth parameters were estimated for A. pelagicus and S. lewini from growth-band counts of thin-cut vertebral sections. Alopias pelagicus (n = 158) and S. lewini (n = 157) vertebrae were collected from three Indonesian fish markets over a 5 year period. A multi-model analysis was used to estimate growth parameters for both species. The models of best fit for males and females for A. pelagicus was the three-parameter logistic (L∞ = 3169 mm LT , k = 0·2) and the two-parameter von Bertalanffy models (L∞ = 3281 mm LT , k = 0·12). Age at maturity was calculated to be 10·4 and 13·2 years for males and females, respectively, and these are the oldest estimated for this species. The samples of S. lewini were heavily biased towards females, and the model of best fit for males and females was the three-parameter Gompertz (L∞ = 2598 mm LT , k = 0·15) and the two-parameter Gompertz (L∞ = 2896 mm LT , k= 0·16). Age at maturity was calculated to be 8·9 and 13·2 years for males and females, respectively. Although numerous age and growth studies have previously been undertaken on S. lewini, few studies have been able to obtain adequate samples from all components of the population because adult females, adult males and juveniles often reside in different areas. For the first time, sex bias in this study was towards sexually mature females, which are commonly lacking in previous biological studies on S. lewini. Additionally, some of the oldest aged specimens and highest age at maturity for both species were observed in this study. Both species exhibit slow rates of growth and late age at maturity, highlighting the need for a re-assessment of the relative resilience of these two
Continuous percolation transition in suppressed random cluster growth model
NASA Astrophysics Data System (ADS)
Roy, Bappaditya; Santra, S. B.
2016-05-01
A new suppressed cluster growth model on 2D square lattice combining Hoshen-Kopelman and Leath approaches is studied here. The lattice sites are initially occupied randomly with probability (ρ). The empty perimeter sites of the clusters of occupied sites are grown with a cluster size dependent probability. The growth probability is then lowest for the largest cluster and highest for the smallest cluster. At the end of growth process all the cluster related quantities are estimated and they are found to display power law scaling as in percolation transition. However, the values of the critical exponents vary continuously with ρ, the initial seed concentration. At higher values of ρ, the model belongs the percolation universality class.
Cinder cone growth modeled after Northeast crater, Mount Etna, Sicily
NASA Technical Reports Server (NTRS)
Mcgetchin, T. R.; Settle, M.; Chouet, B. A.
1974-01-01
The structure, physical properties of ejecta, ballistics, and growth of Northeast crater, a young pyroclastic cone that originated in 1911 near the summit of Mount Etna, Sicily, were studied in order to form a model of volcano cinder cone growth. Four stages of growth were discerned: (1) a simple cone; (2) a cone with an outward-dipping talus slope; (3) destruction of rounded rim by the inward migration of the upper edge of the talus pile; and (4) extension of limits of talus pile beyond the ballistic limit of ejecta trajectories. The model is used to predict the features of lunar and Martian cones, assuming that they erupted under conditions qualitatively similar to Etna's Northeast crater.
Modelling mussel growth in ecosystems with low suspended matter loads
NASA Astrophysics Data System (ADS)
Duarte, P.; Fernández-Reiriz, M. J.; Filgueira, R.; Labarta, U.
2010-10-01
Over the last decades a large number of bivalve growth models were described in the literature with most emphasis on cultivated species with important economic value. These models describe the rates of energy absorption and utilization as a function of environmental conditions. Some of the most important issues in bivalve modelling are water pumping, filtration, pre-ingestive rejection/pseudofaeces production and ingestion of living and non-living organic and inorganic matter. According to some authors, bivalve suspension-feeders may selectively ingest and/or digest different food items whilst making adjustments to maximize the utilization of chlorophyll rich particles. In clear water ecosystems such as the Galician Rias (total particulate matter ( TPM) < 3 mg l - 1 ), where most of the available seston is phytoplankton, selective processes may be less important than in turbid waters with high TPM loads. The main objectives of this work were to develop, implement and calibrate an Individual Based Model of mussel growth, configured and parameterized for the environmental conditions of ecosystems with low suspended matter loads such as the Galician Rias. Model runs were made for a large number of individual mussels, each with a random parameter set, selected among possible parameter ranges reported in the literature, allowing a quick model calibration and an evaluation of those parameters explaining most of the variance in predicted mussel growth. Obtained results provide a useful feedback for upcoming experimental work where efforts should be concentrated on accurate estimates of these more influential parameters to improve model results.
A phase-field model of island growth in epitaxy
NASA Astrophysics Data System (ADS)
Liu, Bang-Gui
2004-03-01
A phase-field model was proposed to simulate nucleation and growth of islands in epitaxy. 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. Reference: Yan-Mei Yu and Bang-Gui Liu, Phys Rev E (accepted Dec 2003).
Isotropic model for cluster growth on a regular lattice
NASA Astrophysics Data System (ADS)
Yates, Christian A.; Baker, Ruth E.
2013-08-01
There exists a plethora of mathematical models for cluster growth and/or aggregation on regular lattices. Almost all suffer from inherent anisotropy caused by the regular lattice upon which they are grown. We analyze the little-known model for stochastic cluster growth on a regular lattice first introduced by Ferreira Jr. and Alves [J. Stat. Mech. Theo. & Exp.1742-546810.1088/1742-5468/2006/11/P11007 (2006) P11007], which produces circular clusters with no discernible anisotropy. We demonstrate that even in the noise-reduced limit the clusters remain circular. We adapt the model by introducing a specific rearrangement algorithm so that, rather than adding elements to the cluster from the outside (corresponding to apical growth), our model uses mitosis-like cell splitting events to increase the cluster size. We analyze the surface scaling properties of our model and compare it to the behavior of more traditional models. In “1+1” dimensions we discover and explore a new, nonmonotonic surface thickness scaling relationship which differs significantly from the Family-Vicsek scaling relationship. This suggests that, for models whose clusters do not grow through particle additions which are solely dependent on surface considerations, the traditional classification into “universality classes” may not be appropriate.
Cumulative growth of minor hysteresis loops in the Kolmogorov model
Meilikhov, E. Z. Farzetdinova, R. M.
2013-01-15
The phenomenon of nonrepeatability of successive remagnetization cycles in Co/M (M = Pt, Pd, Au) multilayer film structures is explained in the framework of the Kolmogorov crystallization model. It is shown that this model of phase transitions can be adapted so as to adequately describe the process of magnetic relaxation in the indicated systems with 'memory.' For this purpose, it is necessary to introduce some additional elements into the model, in particular, (i) to take into account the fact that every cycle starts from a state 'inherited' from the preceding cycle and (ii) to assume that the rate of growth of a new magnetic phase depends on the cycle number. This modified model provides a quite satisfactory qualitative and quantitative description of all features of successive magnetic relaxation cycles in the system under consideration, including the surprising phenomenon of cumulative growth of minor hysteresis loops.
Simulation of optical diagnostics for crystal growth: models and results
NASA Astrophysics Data System (ADS)
Banish, Michele R.; Clark, Rodney L.; Kathman, Alan D.; Lawson, Shelah M.
1991-12-01
A computer simulation of a two-color holographic interferometric (TCHI) optical system was performed using a physical (wave) optics model. This model accurately simulates propagation through time-varying, 2-D or 3-D concentration and temperature fields as a wave phenomenon. The model calculates wavefront deformations that can be used to generate fringe patterns. This simulation modeled a proposed TriGlycine sulphate TGS flight experiment by propagating through the simplified onion-like refractive index distribution of the growing crystal and calculating the recorded wavefront deformation. The phase of this wavefront was used to generate sample interferograms that map index of refraction variation. Two such fringe patterns, generated at different wavelengths, were used to extract the original temperature and concentration field characteristics within the growth chamber. This proves feasibility for this TCHI crystal growth diagnostic technique. This simulation provides feedback to the experimental design process.
Fan, Senqing; Chen, Shiping; Tang, Xiaoyu; Xiao, Zeyi; Deng, Qing; Yao, Peina; Sun, Zhaopeng; Zhang, Yan; Chen, Chunyan
2015-02-01
Unstructured kinetic models were proposed to describe the principal kinetics involved in ethanol fermentation in a continuous and closed-circulating fermentation (CCCF) process with a pervaporation membrane bioreactor. After ethanol was removed in situ from the broth by the membrane pervaporation, the secondary metabolites accumulated in the broth became the inhibitors to cell growth. The cell death rate related to the deterioration of the culture environment was described as a function of the cell concentration and fermentation time. In CCCF process, 609.8 g L(-1) and 750.1 g L(-1) of ethanol production were obtained in the first run and second run, respectively. The modified Gompertz model, correlating the ethanol production with the fermentation period, could be used to describe the ethanol production during CCCF process. The fitting results by the models showed good agreement with the experimental data. These models could be employed for the CCCF process technology development for ethanol fermentation. PMID:25490098
NASA Astrophysics Data System (ADS)
Yeckel, Andrew
2016-09-01
A thermocapillary model of edge-defined film-fed growth (EFG) is developed to analyze an experimental system for high speed growth of cesium iodide as a model system for halide scintillator production. The model simulates heat transfer and fluid dynamics in the die, melt, and crystal under conditions of steady growth. Appropriate mass, force, and energy balances are used to compute self-consistent shapes of the growth interface and melt-vapor meniscus. The model is applied to study the effects of growth rate, die geometry, and furnace heat transfer on the limits of system operability. An inverse problem formulation is used to seek operable states at high growth rates by adjusting the overall temperature level and thermal gradient in the furnace. The model predicts that steady growth is feasible at rates greater than 20 mm/h for crystals up to 18 mm in diameter under reasonable furnace gradients.
A Role for M-Matrices in Modelling Population Growth
ERIC Educational Resources Information Center
James, Glyn; Rumchev, Ventsi
2006-01-01
Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results,…
Modeling of the growth of filamentous fungi in artificial microstructures
NASA Astrophysics Data System (ADS)
Nicolau, Dan V., Jr.; Hanson, Kristi; Nicolau, Dan V.
2006-01-01
We present a stochastic and spatial Monte Carlo model for the growth of a fungal colony in microstructures. This model is based on an "L-system-like" representation of filaments as individual objects. Each of these can both grow in space (and be diverted by obstacles) and can send new branches. All parameters in the model such as filament dimensions, the growth speed, behavior at and around obstacles, branching angle and frequency and others are obtained from experimental studies of growth in artificial microstructures. We investigate four different possible "strategies" the colony might use to achieve the tasks of (a) filling the available space and (2) finding its way out of the structures. The simulation results indicate that a combination of directional memory and a stop-and-branch behavior at corners gives the best results and observe that in fact this is similar to the experimentally observed behavior of the fungi. The model is expected to be of use in studying the colonization of microstructures by fungi and in the design of devices either using fungal growth or aiming to inhibit it.
Multiscale Models in the Biomechanics of Plant Growth
Fozard, John A.
2015-01-01
Plant growth occurs through the coordinated expansion of tightly adherent cells, driven by regulated softening of cell walls. It is an intrinsically multiscale process, with the integrated properties of multiple cell walls shaping the whole tissue. Multiscale models encode physical relationships to bring new understanding to plant physiology and development. PMID:25729061
Building Context with Tumor Growth Modeling Projects in Differential Equations
ERIC Educational Resources Information Center
Beier, Julie C.; Gevertz, Jana L.; Howard, Keith E.
2015-01-01
The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss…
Twelve Frequently Asked Questions about Growth Curve Modeling
ERIC Educational Resources Information Center
Curran, Patrick J.; Obeidat, Khawla; Losardo, Diane
2010-01-01
Longitudinal data analysis has long played a significant role in empirical research within the developmental sciences. The past decade has given rise to a host of new and exciting analytic methods for studying between-person differences in within-person change. These methods are broadly organized under the term "growth curve models." The…
Developmental Trajectories of Adolescent Popularity: A Growth Curve Modelling Analysis
ERIC Educational Resources Information Center
Cillessen, Antonius H. N.; Borch, Casey
2006-01-01
Growth curve modelling was used to examine developmental trajectories of sociometric and perceived popularity across eight years in adolescence, and the effects of gender, overt aggression, and relational aggression on these trajectories. Participants were 303 initially popular students (167 girls, 136 boys) for whom sociometric data were…
Growth Model Comparison Study: A Summary of Results
ERIC Educational Resources Information Center
Auty, Bill; Brockmann, Frank
2012-01-01
School accountability is subject to considerable scrutiny. It generates sharp political debate, policy challenges, and continuous discussion. Growth models are now a part of that discussion. To many practitioners the sheer volume of "important to know" information is daunting. The members of the Technical Issues in Large Scale Assessment (TILSA)…
Optimization of a new mathematical model for bacterial growth
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...
Diagnostics of Robust Growth Curve Modeling Using Student's "t" Distribution
ERIC Educational Resources Information Center
Tong, Xin; Zhang, Zhiyong
2012-01-01
Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors…
A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces
Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H.
2014-02-02
In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.
Modeling Pacing Behavior and Test Speededness Using Latent Growth Curve Models
ERIC Educational Resources Information Center
Kahraman, Nilufer; Cuddy, Monica M.; Clauser, Brian E.
2013-01-01
This research explores the usefulness of latent growth curve modeling in the study of pacing behavior and test speededness. Examinee response times from a high-stakes, computerized examination, collected before and after the examination was subjected to a timing change, were analyzed using a series of latent growth curve models to detect…
Growth protocols for model plants in developmental biology.
Hennig, Lars
2010-01-01
Arabidopsis is the dominating model species for plant developmental biology, but other species serve as models for processes that cannot be studied in Arabidopsis, such as compound leaf or wood formation, or to test the universality of developmental mechanisms initially identified in Arabidopsis. Research in plant developmental biology depends critically on robust growth protocols that will support reproducible development. Here, protocols are given to grow Antirrhinum, Arabidopsis, Brachypodium, maize, Medicago, Petunia, rice, and tomato in the laboratory. PMID:20734250
Hybrid models of cell and tissue dynamics in tumor growth.
Kim, Yangjin; Othmer, Hans G
2015-12-01
Hybrid models of tumor growth, in which some regions are described at the cell level and others at the continuum level, provide a flexible description that allows alterations of cell-level properties and detailed descriptions of the interaction with the tumor environment, yet retain the computational advantages of continuum models where appropriate. We review aspects of the general approach and discuss applications to breast cancer and glioblastoma. PMID:26775860
Network effects in a human capital based economic growth model
NASA Astrophysics Data System (ADS)
Vaz Martins, Teresa; Araújo, Tanya; Augusta Santos, Maria; St Aubyn, Miguel
2009-06-01
We revisit a recently introduced agent model [ACS, 11, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents’ social network, both on an agent’s decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.
[Growth modeling of Albizia niopoides (Mimosaceae) using dendrochronological methods].
Giraldo, Víctor David; del Valle, Jorge Ignacio
2012-09-01
The annual growth rings in tropical trees are fairly common, but their study is relatively recent. Growth rings were found in trees of Albizia niopoides from the Porce River Canyon, Central Cordillera of the Colombian Andes. A total of 33 cross-sections were collected from trees distributed throughout the study area from 664-870masl. Cross-dating, spaguetti plot and 14C analyses were used to demonstrate ring annuality, assuming as hypothesis that these are real annual growth rings. A combination of descriptive analysis of time series (smoothing and pre-whitening) to filter climate noise and nonlinear regression with weighted residuals was used to fit the diameter to Korfs growth model, in which the coefficient of determination reaches values close to 100%. The positive residual autocorrelation of order 1, although not significant, is explained by the existence of energy reserves in the stem and by the accumulation of diameter increments required for the construction of the diameter growth model. The current and mean annual maximum increment rates are 1.03 and 0.94cm/year at ages 18 and 46 years old, respectively. These trees are classified within the group of fast growing species which can reach a cut diameter of over 50cm in approximately 52 years. PMID:23025084
Coupled Growth and Division of Model Protocell Membranes
2009-01-01
The generation of synthetic forms of cellular life requires solutions to the problem of how biological processes such as cyclic growth and division could emerge from purely physical and chemical systems. Small unilamellar fatty acid vesicles grow when fed with fatty acid micelles and can be forced to divide by extrusion, but this artificial division process results in significant loss of protocell contents during each division cycle. Here we describe a simple and efficient pathway for model protocell membrane growth and division. The growth of large multilamellar fatty acid vesicles fed with fatty acid micelles, in a solution where solute permeation across the membranes is slow, results in the transformation of initially spherical vesicles into long thread-like vesicles, a process driven by the transient imbalance between surface area and volume growth. Modest shear forces are then sufficient to cause the thread-like vesicles to divide into multiple daughter vesicles without loss of internal contents. In an environment of gentle shear, protocell growth and division are thus coupled processes. We show that model protocells can proceed through multiple cycles of reproduction. Encapsulated RNA molecules, representing a primitive genome, are distributed to the daughter vesicles. Our observations bring us closer to the laboratory synthesis of a complete protocell consisting of a self-replicating genome and a self-replicating membrane compartment. In addition, the robustness and simplicity of this pathway suggests that similar processes might have occurred under the prebiotic conditions of the early Earth. PMID:19323552
A Predictive Model of High Shear Thrombus Growth.
Mehrabadi, Marmar; Casa, Lauren D C; Aidun, Cyrus K; Ku, David N
2016-08-01
The ability to predict the timescale of thrombotic occlusion in stenotic vessels may improve patient risk assessment for thrombotic events. In blood contacting devices, thrombosis predictions can lead to improved designs to minimize thrombotic risks. We have developed and validated a model of high shear thrombosis based on empirical correlations between thrombus growth and shear rate. A mathematical model was developed to predict the growth of thrombus based on the hemodynamic shear rate. The model predicts thrombus deposition based on initial geometric and fluid mechanic conditions, which are updated throughout the simulation to reflect the changing lumen dimensions. The model was validated by comparing predictions against actual thrombus growth in six separate in vitro experiments: stenotic glass capillary tubes (diameter = 345 µm) at three shear rates, the PFA-100(®) system, two microfluidic channel dimensions (heights = 300 and 82 µm), and a stenotic aortic graft (diameter = 5.5 mm). Comparison of the predicted occlusion times to experimental results shows excellent agreement. The model is also applied to a clinical angiography image to illustrate the time course of thrombosis in a stenotic carotid artery after plaque cap rupture. Our model can accurately predict thrombotic occlusion time over a wide range of hemodynamic conditions. PMID:26795978
Mathematical Modeling of Branching Morphogenesis and Vascular Tumor Growth
NASA Astrophysics Data System (ADS)
Yan, Huaming
Feedback regulation of cell lineages is known to play an important role in tissue size control, but the effect in tissue morphogenesis has yet to be explored. We first use a non-spatial model to show that a combination of positive and negative feedback on stem and/or progenitor cell self-renewal leads to bistable or bi-modal growth behaviors and ultrasensitivity to external growth cues. Next, a spatiotemporal model is used to demonstrate spatial patterns such as local budding and branching arise in this setting, and are not consequences of Turing-type instabilities. We next extend the model to a three-dimensional hybrid discrete-continuum model of tumor growth to study the effects of angiogenesis, tumor progression and cancer therapies. We account for the crosstalk between the vasculature and cancer stem cells (CSCs), and CSC transdifferentiation into vascular endothelial cells (gECs), as observed experimentally. The vasculature stabilizes tumor invasiveness but considerably enhances growth. A gEC network structure forms spontaneously within the hypoxic core, consistent with experimental findings. The model is then used to study cancer therapeutics. We demonstrate that traditional anti-angiogenic therapies decelerate tumor growth, but make the tumor highly invasive. Chemotherapies help to reduce tumor sizes, but cannot control the invasion. Anti-CSC therapies that promote differentiation or disturb the stem cell niche effectively reduce tumor invasiveness. However, gECs inherit mutations present in CSCs and are resistant to traditional therapies. We show that anti-gEC treatments block the support on CSCs by gECs, and reduce both tumor size and invasiveness. Our study suggests that therapies targeting the vasculature, CSCs and gECs, when combined, are highly synergistic and are capable of controlling both tumor size and shape.
Progress in Representing Microphysical Processes in a Snow Growth Model
NASA Astrophysics Data System (ADS)
Erfani, Ehsan; Mitchell, David
2015-04-01
A steady-state snow growth model (SGM) has been developed based on the microphysical growth processes of vapor deposition, aggregation and riming. Climate models use mass-dimension (m-D) and area-dimension (A-D) power laws (e.g. m = αDβ) to formulate ice particle growth rates, however it is well known that the m-D and A-D power laws for the smallest ice particles differ considerably from the power laws for the largest particles. To overcome this problem, β and α are predicted as a function of diameter where the m-D expression is a 2nd-order polynomial in log-log space. By tailoring these m-D and A-D relationships to the SGM, ice particle growth rates and fall speeds are represented more accurately and realistically. The predicted size spectra by SGM are in good agreement with observed spectra from Colorado Airborne Mixed-Phase Cloud Study (CAMPS). Although ice particle riming often has little impact on ice particle size, its impact on ice particle mass and projected area can be considerable. A method is introduced to calculate rimed mass and area from unrimed mass and area, and from maximum mass and area that can be achieved by riming. The treatment for riming is explicit, accounting for the dependence of collision efficiency on droplet and ice particle size using both hydrodynamic theory and experimental measurements. It appears that the riming process is essential in characterizing the snowfall rates. Moreover, increase in cloud condensation nuclei (CCN), due to aerosols, can modify cloud droplet SD (size distribution) and therefore decrease the snowfall rate. So, snowfall rate is sensitive to the shape of cloud droplet SD. It is speculated that by implementing the new m-D and A-D treatment, and riming growth in any climate model, the ice particle growth rates will become more accurate.
Advanced Finite Element Modeling of Low Cycle Fatigue Crack Growth
NASA Technical Reports Server (NTRS)
Gregg, Wayne; McGill, Preston; Swanson, Greg; Wells, Doug; Throckmorton, D. A. (Technical Monitor)
2001-01-01
This document (a viewgraph presentation) assumes a crack-like defect of a size which may be missed in inspection will exist in most critical location of any critical structure or component. Flaw existence assumption is usually, but not always, conservative based on past experiences in NASA and knowledge of manufacturing processes. Cyclic, environmental, and sustained loads used to generate stresses on models. Fracture Mechanics analysis used to predict crack growth and residual strength. Must show that defective structure will still provide four times required mission lifetime. Special exemptions cover redundant structures, low risk parts, etc. Assessments require specialized software tools, experienced analysts, and reliable material crack growth rate test database.
Emergent properties of a computational model of tumour growth
2016-01-01
While there have been enormous advances in our understanding of the genetic drivers and molecular pathways involved in cancer in recent decades, there also remain key areas of dispute with respect to fundamental theories of cancer. The accumulation of vast new datasets from genomics and other fields, in addition to detailed descriptions of molecular pathways, cloud the issues and lead to ever greater complexity. One strategy in dealing with such complexity is to develop models to replicate salient features of the system and therefore to generate hypotheses which reflect on the real system. A simple tumour growth model is outlined which displays emergent behaviours that correspond to a number of clinically relevant phenomena including tumour growth, intra-tumour heterogeneity, growth arrest and accelerated repopulation following cytotoxic insult. Analysis of model data suggests that the processes of cell competition and apoptosis are key drivers of these emergent behaviours. Questions are raised as to the role of cell competition and cell death in physical cancer growth and the relevance that these have to cancer research in general is discussed. PMID:27413638
A Big Bang model of human colorectal tumor growth.
Sottoriva, Andrea; Kang, Haeyoun; Ma, Zhicheng; Graham, Trevor A; Salomon, Matthew P; Zhao, Junsong; Marjoram, Paul; Siegmund, Kimberly; Press, Michael F; Shibata, Darryl; Curtis, Christina
2015-03-01
What happens in early, still undetectable human malignancies is unknown because direct observations are impractical. Here we present and validate a 'Big Bang' model, whereby tumors grow predominantly as a single expansion producing numerous intermixed subclones that are not subject to stringent selection and where both public (clonal) and most detectable private (subclonal) alterations arise early during growth. Genomic profiling of 349 individual glands from 15 colorectal tumors showed an absence of selective sweeps, uniformly high intratumoral heterogeneity (ITH) and subclone mixing in distant regions, as postulated by our model. We also verified the prediction that most detectable ITH originates from early private alterations and not from later clonal expansions, thus exposing the profile of the primordial tumor. Moreover, some tumors appear 'born to be bad', with subclone mixing indicative of early malignant potential. This new model provides a quantitative framework to interpret tumor growth dynamics and the origins of ITH, with important clinical implications. PMID:25665006
Microphysical fundamentals governing cirrus cloud growth: Modeling studies
NASA Technical Reports Server (NTRS)
Sassen, Kenneth; Dodd, Gregory C.; Starr, David
1990-01-01
For application to Global Climate Models, large scale numerical models of cirrus cloud formation and maintenance need to be refined to more reliably simulate the effects and feedbacks of high level clouds. A key aspect is how ice crystal growth is initiated in cirrus, which has started a cloud microphysical controversy between camps either believing that heterogeneous or homogeneous drop freezing is predominantly responsible for cold cirrus ice crystal nucleation. In view of convincing evidence for the existence of highly supercooled cloud droplets in the middle and upper troposphere, however, it is concluded that active ice nuclei are rather scarce at cirrus cloud altitudes, and so a new understanding of cirrus cloud formation is needed. This understanding is sought through an examination of cirrus cloud growth models.
An autoregressive growth model for longitudinal item analysis.
Jeon, Minjeong; Rabe-Hesketh, Sophia
2016-09-01
A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students' self-esteem. PMID:26645083
Predictive Models for Nanostructure Evolution during Epitaxial Thin Film Growth
NASA Astrophysics Data System (ADS)
Evans, Jim
2004-03-01
We describe the development of a realistic atomistic lattice-gas (LG) model for multilayer homoepitaxial growth of metal(100) films at higher deposition temperatures (T). The model is tailored to incorporate the essential physical processes underlying growth, and is thus efficiently simulated using KMC [1]. It is shown to reliably predict film morphologies up to 1000's layers for a broad range of deposition conditions (T, flux), in fact revealing quite unexpected behavior. Specifically, we consider the Ag/Ag(100) system - the perceived prototype for smooth quasi-layer-by-layer growth at higher T. We predict the formation of mounds (multilayer stacks of islands) above 150K due to a small non-uniform step edge barrier. Initial growth at 300K is indeed smooth, but subsequent growth is actually extremely rough, corresponding to prolonged mound steepening. Thin films grow rougher at lower T down to 200K, but thick films grow smoother. Experiments confirm these surprising predictions [1,2]. We also find that long-time mound dynamics is quite distinct from predictions of standard continuum theories. For Ag/Ag(100) growth below 150K in the absence of terrace diffusion, one finds self-affine growth of films containing bulk vacancies [3], the latter feature being confirmed by X-ray scattering studies [4]. This regime can be modeled by accelerated MD [5], generic self-teaching KMC [6], or tailored LG models (distinct from the above model for higher T) [3,7]. Using the latter, we identify the key processes controlling morphology from 0-150K as capture of deposited atoms on the sides of nanoprotrusions, and the activation of low-barrier interlayer thermal diffusion processes. [1] Caspersen et al. PRB 65 (2002) 193407. [2] Elliott et al. PRB 54 (1996) 17938. [3] Stoldt et al. PRL 85 (2000) 800. [4] Botez et al. PRB 66 (2002) 075418. [5] Montalenti et al. PRL 87 (2001) 126101. [6] Henkelman et al. PRL 90 (2003) 116101. [7] Caspersen et al. PRB 64 (2001) 075401.
NASA Astrophysics Data System (ADS)
Li, Gang; Chen, Xinjun; Feng, Bo
2008-11-01
Although chub mackerel ( Scomber japonicus) is a primary pelagic fish species, we have only limited knowledge on its key life history processes. The present work studied the age and growth of chub mackerel in the East China and Yellow Seas. Age was determined by interpreting and counting growth rings on the sagitta otoliths of 252 adult fish caught by the Chinese commercial purse seine fleet during the period from November 2006 to January 2007 and 150 juveniles from bottom trawl surveys on the spawning ground in May 2006. The difference between the assumed birth date of 1st April and date of capture was used to adjust the age determined from counting the number of complete translucent rings. The parameters of three commonly used growth models, the von Bertalanffy, Logistic and Gompertz models, were estimated using the maximum likelihood method. Based on the Akaike Information Criterion ( AIC), the von Bertalanffy growth model was found to be the most appropriate model. The size-at-age and size-at-maturity values were also found to decrease greatly compared with the results achieved in the 1950s, which was caused by heavy exploitation over the last few decades.
Modelling the interaction between flooding events and economic growth
NASA Astrophysics Data System (ADS)
Grames, J.; Prskawetz, A.; Grass, D.; Blöschl, G.
2015-06-01
Socio-hydrology describes the interaction between the socio-economy and water. Recent models analyze the interplay of community risk-coping culture, flooding damage and economic growth (Di Baldassarre et al., 2013; Viglione et al., 2014). These models descriptively explain the feedbacks between socio-economic development and natural disasters like floods. Contrary to these descriptive models, our approach develops an optimization model, where the intertemporal decision of an economic agent interacts with the hydrological system. In order to build this first economic growth model describing the interaction between the consumption and investment decisions of an economic agent and the occurrence of flooding events, we transform an existing descriptive stochastic model into an optimal deterministic model. The intermediate step is to formulate and simulate a descriptive deterministic model. We develop a periodic water function to approximate the former discrete stochastic time series of rainfall events. Due to the non-autonomous exogenous periodic rainfall function the long-term path of consumption and investment will be periodic.
Directional entropy based model for diffusivity-driven tumor growth.
de Oliveira, Marcelo E; Neto, Luiz M G
2016-04-01
In this work, we present and investigate a multiscale model to simulate 3D growth of glioblastomas (GBMs) that incorporates features of the tumor microenvironment and derives macroscopic growth laws from microscopic tissue structure information. We propose a normalized version of the Shannon entropy as an alternative measure of the directional anisotropy for an estimation of the diffusivity tensor in cases where the latter is unknown. In our formulation, the tumor aggressiveness and morphological behavior is tissue-type dependent, i.e. alterations in white and gray matter regions (which can e.g. be induced by normal aging in healthy individuals or neurodegenerative diseases) affect both tumor growth rates and their morphology. The feasibility of this new conceptual approach is supported by previous observations that the fractal dimension, which correlates with the Shannon entropy we calculate, is a quantitative parameter that characterizes the variability of brain tissue, thus, justifying the further evaluation of this new conceptual approach. PMID:27105991
Quantifying strain variability in modeling growth of Listeria monocytogenes.
Aryani, D C; den Besten, H M W; Hazeleger, W C; Zwietering, M H
2015-09-01
Prediction of microbial growth kinetics can differ from the actual behavior of the target microorganisms. In the present study, the impact of strain variability on maximum specific growth rate (μmax) (h(-1)) was quantified using twenty Listeria monocytogenes strains. The μmax was determined as function of four different variables, namely pH, water activity (aw)/NaCl concentration [NaCl], undissociated lactic acid concentration ([HA]), and temperature (T). The strain variability was compared to biological and experimental variabilities to determine their importance. The experiment was done in duplicate at the same time to quantify experimental variability and reproduced at least twice on different experimental days to quantify biological (reproduction) variability. For all variables, experimental variability was clearly lower than biological variability and strain variability; and remarkably, biological variability was similar to strain variability. Strain variability in cardinal growth parameters, namely pHmin, [NaCl]max, [HA]max, and Tmin was further investigated by fitting secondary growth models to the μmax data, including a modified secondary pH model. The fitting results showed that L. monocytogenes had an average pHmin of 4.5 (5-95% prediction interval (PI) 4.4-4.7), [NaCl]max of 2.0mM (PI 1.8-2.1), [HA]max of 5.1mM (PI 4.2-5.9), and Tmin of -2.2°C (PI (-3.3)-(-1.1)). The strain variability in cardinal growth parameters was benchmarked to available literature data, showing that the effect of strain variability explained around 1/3 or less of the variability found in literature. The cardinal growth parameters and their prediction intervals were used as input to illustrate the effect of strain variability on the growth of L. monocytogenes in food products with various characteristics, resulting in 2-4 logCFU/ml(g) difference in growth prediction between the most and least robust strains, depending on the type of food product. This underlined the importance
River water temperature and fish growth forecasting models
NASA Astrophysics Data System (ADS)
Danner, E.; Pike, A.; Lindley, S.; Mendelssohn, R.; Dewitt, L.; Melton, F. S.; Nemani, R. R.; Hashimoto, H.
2010-12-01
Water is a valuable, limited, and highly regulated resource throughout the United States. When making decisions about water allocations, state and federal water project managers must consider the short-term and long-term needs of agriculture, urban users, hydroelectric production, flood control, and the ecosystems downstream. In the Central Valley of California, river water temperature is a critical indicator of habitat quality for endangered salmonid species and affects re-licensing of major water projects and dam operations worth billions of dollars. There is consequently strong interest in modeling water temperature dynamics and the subsequent impacts on fish growth in such regulated rivers. However, the accuracy of current stream temperature models is limited by the lack of spatially detailed meteorological forecasts. To address these issues, we developed a high-resolution deterministic 1-dimensional stream temperature model (sub-hourly time step, sub-kilometer spatial resolution) in a state-space framework, and applied this model to Upper Sacramento River. We then adapted salmon bioenergetics models to incorporate the temperature data at sub-hourly time steps to provide more realistic estimates of salmon growth. The temperature model uses physically-based heat budgets to calculate the rate of heat transfer to/from the river. We use variables provided by the TOPS-WRF (Terrestrial Observation and Prediction System - Weather Research and Forecasting) model—a high-resolution assimilation of satellite-derived meteorological observations and numerical weather simulations—as inputs. The TOPS-WRF framework allows us to improve the spatial and temporal resolution of stream temperature predictions. The salmon growth models are adapted from the Wisconsin bioenergetics model. We have made the output from both models available on an interactive website so that water and fisheries managers can determine the past, current and three day forecasted water temperatures at
Error Growth Rate in the MM5 Model
NASA Astrophysics Data System (ADS)
Ivanov, S.; Palamarchuk, J.
2006-12-01
The goal of this work is to estimate model error growth rates in simulations of the atmospheric circulation by the MM5 model all the way from the short range to the medium range and beyond. The major topics are addressed to: (i) search the optimal set of parameterization schemes; (ii) evaluate the spatial structure and scales of the model error for various atmospheric fields; (iii) determine geographical regions where model errors are largest; (iv) define particular atmospheric patterns contributing to the fast and significant model error growth. Results are presented for geopotential, temperature, relative humidity and horizontal wind components fields on standard surfaces over the Atlantic-European region during winter 2002. Various combinations of parameterization schemes for cumulus, PBL, moisture and radiation are used to identify which one provides a lesser difference between the model state and analysis. The comparison of the model fields is carried out versus ERA-40 reanalysis of the ECMWF. Results show that the rate, at which the model error grows as well as its magnitude, varies depending on the forecast range, atmospheric variable and level. The typical spatial scale and structure of the model error also depends on the particular atmospheric variable. The distribution of the model error over the domain can be separated in two parts: the steady and transient. The first part is associated with a few high mountain regions including Greenland, where model error is larger. The transient model error mainly moves along with areas of high gradients in the atmospheric flow. Acknowledgement: This study has been supported by NATO Science for Peace grant #981044. The MM5 modelling system used in this study has been provided by UCAR. ERA-40 re-analysis data have been obtained from the ECMWF data server.
Assessing uncertainty in a stand growth model by Bayesian synthesis
Green, E.J.; MacFarlane, D.W.; Valentine, H.T.; Strawderman, W.E.
1999-11-01
The Bayesian synthesis method (BSYN) was used to bound the uncertainty in projections calculated with PIPESTEM, a mechanistic model of forest growth. The application furnished posterior distributions of (a) the values of the model's parameters, and (b) the values of three of the model's output variables--basal area per unit land area, average tree height, and tree density--at different points in time. Confidence or credible intervals for the output variables were obtained directly from the posterior distributions. The application also provides estimates of correlation among the parameters and output variables. BSYN, which originally was applied to a population dynamics model for bowhead whales, is generally applicable to deterministic models. Extension to two or more linked models is discussed. A simple worked example is included in an appendix.
Modelling the thermal effects of spherulite growth in rhyolitic lava
NASA Astrophysics Data System (ADS)
Tuffen, H.; Cordonnier, B.; Castro, J. M.
2012-12-01
Rhyolitic lava flows, sills and dykes commonly comprise a spherulitic interior enveloped by a glassy carapace. Spherulite crystallisation has long been assumed to be a "passive" process that occurs during cooling of the lava around and below its glass transition temperature (~600-700 °C). It has also been suggested to be self-limiting due to diffusion controlled growth, creating only a small proportion of spherulites embedded in glass (snowflake obsidian). However, textures in rhyolitic lava bodies at Hrafntinnuhryggur, Krafla, Iceland indicate that near-complete spherulite crystallisation can occur, and suggest that parts of the lava spatially associated with zones of spherulite and lithophysae growth may be significantly heated. Evidence for heating includes melting of parts of the glassy lava carapace by lower-viscosity, invading melt of identical composition. Additionally, spherulitic crystal morphologies have been grown experimentally at undercoolings of only 100 °C. As the liquidus temperature of dry rhyolite may approach 1200 °C, this means that spherulites could continue to grow in degassed magma at temperatures of >900 °C, well above the initial magma temperature. We use new constraints on spherulite growth rates to model the thermal effects of spherulite growth within rhyolitic lava bodies, using three growth laws (size- and temperature-dependent, diffusion controlled and linear) and a variety of initial temperatures, nucleation densities and seed nuclei sizes. Models consider both latent heat release due to crystallisation and conductive cooling. Model results indicate that, when lava bodies are sufficiently large, spherulite growth can cause considerable heating (possibly >150 °C), enabling parts of lava bodies to heat to above the initial eruption temperature. This heating can lead to a viscosity reduction of orders of magnitude and trigger vesiculation. Model results indicate that cooling rates of between 10-3 to 10-5 °C/s ought to mark the
On the Theory of Reactive Mixtures for Modeling Biological Growth
Ateshian, Gerard A.
2013-01-01
Mixture theory, which can combine continuum theories for the motion and deformation of solids and fluids with general principles of chemistry, is well suited for modeling the complex responses of biological tissues, including tissue growth and remodeling, tissue engineering, mechanobiology of cells and a variety of other active processes. A comprehensive presentation of the equations of reactive mixtures of charged solid and fluid constituents is lacking in the biomechanics literature. This study provides the conservation laws and entropy inequality, as well as interface jump conditions, for reactive mixtures consisting of a constrained solid mixture and multiple fluid constituents. The constituents are intrinsically incompressible and may carry an electrical charge. The interface jump condition on the mass flux of individual constituents is shown to define a surface growth equation, which predicts deposition or removal of material points from the solid matrix, complementing the description of volume growth described by the conservation of mass. A formu-lation is proposed for the reference configuration of a body whose material point set varies with time. State variables are defined which can account for solid matrix volume growth and remodeling. Constitutive constraints are provided on the stresses and momentum supplies of the various constituents, as well as the interface jump conditions for the electrochem cal potential of the fluids. Simplifications appropriate for biological tissues are also proposed, which help reduce the governing equations into a more practical format. It is shown that explicit mechanisms of growth-induced residual stresses can be predicted in this framework. PMID:17206407
Shao, Jie; Xiang, Jindong; Axner, Ove; Ying, Chaofu
2016-03-20
It is important to monitor and assess the growth of micro-organisms under various conditions. Yet, thus far there has been no technique to do this with the required speed and accuracy. This work demonstrates swift and accurate assessment of the concentration of carbon dioxide that is produced by use of a wavelength-modulated tunable diode-laser based absorption spectroscopy (WM-TDLAS). It is shown by experiments on two types of bacteria, Staphylococcus aureus and Candida albicans, that the technique can produce high signal-to-noise-ratio data from bacteria grown in confined spaces and exposed to limited amounts of nutrients that can be used for extraction of growth parameters by fitting of the Gompertz model. By applying the technique to S. aureus bacteria at various temperatures (in the 25°C to 42°C range), it is specifically shown that both the maximum growth rate and the so-called lag time have a strong temperature dependence (under the specific conditions with a maximum of the former at 37°C) that matches conventional models well for bacterial growth. Hence, it is demonstrated that WM-TDLAS monitoring CO_{2} is a user-friendly, non-intrusive, and label-free technique that swiftly, and with high signal-to-noise-ratio, can be used for rapid (on the Hz scale) and accurate assessment of bacterial growth. PMID:27140571
A mathematical model for pancreatic cancer growth and treatments.
Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B; Friedman, Avner
2014-06-21
Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer. PMID:24594371
Evolutionary model of the growth and size of firms
NASA Astrophysics Data System (ADS)
Kaldasch, Joachim
2012-07-01
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size-variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.
Bayesian Inference and Application of Robust Growth Curve Models Using Student's "t" Distribution
ERIC Educational Resources Information Center
Zhang, Zhiyong; Lai, Keke; Lu, Zhenqiu; Tong, Xin
2013-01-01
Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…
Analysis of Pdeudomonas aeruginosa Growth and Virulence in Modelled Microgravity
NASA Technical Reports Server (NTRS)
Guadarrama, Seratna; deL. Pulcini, Elinor; Broadaway, Susan C.; Pyle, Barry H.
2005-01-01
Stress, radiation and microgravity cause astronauts to experience secondary immunosuppression. Spaceflight conditions enhance bacterial growth and alter antimicrobial susceptibility. Clinostats are used to model microgravity effects at lxg. In controls rotated on the vertical axis, the g-vector acts on cells as in static cultures. Salmonella enterica serovar Typhimurium virulence genes are up-regulated in modelled microgravity (MMG); a MMG regulon has been postulated. We hypothesize that the virulence of P. aeruginosa (PA) may be affected similarly by microgravity, which could be observed in MMG. This study focused on regulation of the ETA protein by PA during growth in MMG. PA103 was grown in an ETA production medium at 37 C. One series of media was inoculated with frozen cultures and grown using horizontal (MMG) or static incubation. Another series inoculated with refrigerated cultures included vertical rotating controls. Analyses included optical density (OD), agar plate counts (PC) on R2A, ETA ELISA, and protein expression by 2-D gel analyses. Growth and ETA results differed depending on inoculum, with minor effects of MMG. Proteomic analysis of 2-D gels indicate differences in protein expression with MMG. Growth and ETA results show that consistent methodology is critical when studying environmental effects. This study provides information on the relationships between environmental changes and virulence regulation, especially for flight experiments, when ground experiments are used to predict potential spaceflight effects.
Orchestrated structure evolution: modeling growth-regulated nanomanufacturing.
Abbasi, Shaghayegh; Kitayaporn, Sathana; Schwartz, Daniel T; Böhringer, Karl F
2011-04-22
Orchestrated structure evolution (OSE) is a scalable manufacturing method that combines the advantages of top-down (tool-directed) and bottom-up (self-propagating) approaches. The method consists of a seed patterning step that defines where material nucleates, followed by a growth step that merges seeded islands into the final patterned thin film. We develop a model to predict the completed pattern based on a computationally efficient approximate Green's function solution of the diffusion equation plus a Voronoi diagram based approach that defines the final grain boundary structure. Experimental results rely on electron beam lithography to pattern the seeds, followed by the mass transfer limited growth of copper via electrodeposition. The seed growth model is compared with experimental results to quantify nearest neighbor seed-to-seed interactions as well as how seeds interact with the pattern boundary to impact the local growth rate. Seed-to-seed and seed-to-pattern interactions are shown to result in overgrowth of seeds on edges and corners of the shape, where seeds have fewer neighbors. We explore how local changes to the seed location can be used to improve the patterning quality without increasing the manufacturing cost. OSE is shown to enable a unique set of trade-offs between the cost, time, and quality of thin film patterning. PMID:21393828
Percolation model for growth rates of aggregates and its application for business firm growth
NASA Astrophysics Data System (ADS)
Fu, Dongfeng; Buldyrev, Sergey V.; Salinger, Michael A.; Stanley, H. Eugene
2006-09-01
Motivated by recent empirical studies of business firm growth, we develop a dynamic percolation model which captures some of the features of the economical system—i.e., merging and splitting of business firms—represented as aggregates on a d -dimensional lattice. We find the steady-state distribution of the aggregate size and explore how this distribution depends on the model parameters. We find that at the critical threshold, the standard deviation of the aggregate growth rates, σ , increases with aggregate size S as σ˜Sβ , where β can be explained in terms of the connectedness length exponent ν and the fractal dimension df , with β=1/(2νdf)≈0.20 for d=2 and 0.125 for d→∞ . The distributions of aggregate growth rates have a sharp peak at the center and pronounced wings extending over many standard deviations, giving the distribution a tent-shape form—the Laplace distribution. The distributions for different aggregate sizes scaled by their standard deviations collapse onto the same curve.
Microstructurally based model of fatigue initiation and growth
NASA Technical Reports Server (NTRS)
Brockenbrough, J. R.; Hinkle, A. J.; Magnusen, P. E.; Bucci, R. J.
1994-01-01
A model to calculate fatigue life is developed based on the assumption that fatigue life is entirely composed of crack growth from an initial microstructural inhomogeneity. Specifically, growth is considered to start from either an ellipsoidal void, a cracked particle, or a debonded particle. The capability of predicting fatigue life from material microstructure is based on linear elastic fracture mechanics principles, the sizes of the crack-initiating microstructural inhomogeneities, and an initiation parameter that is proportional to the cyclic plastic zone size. A key aspect of this modeling approach is that it is linked with a general purpose probability program to analyze the effect of the distribution of controlling microstructural features within the material. This enables prediction of fatigue stress versus life curves for various specimen geometries using distributional statistics obtained from characterizations of the microstructure. Results are compared to experimental fatigue data from an aluminum alloy.
Future Air Traffic Growth and Schedule Model User's Guide
NASA Technical Reports Server (NTRS)
Kimmel, William M. (Technical Monitor); Smith, Jeremy C.; Dollyhigh, Samuel M.
2004-01-01
The Future Air Traffic Growth and Schedule Model was developed as an implementation of the Fratar algorithm to project future traffic flow between airports in a system and of then scheduling the additional flights to reflect current passenger time-of-travel preferences. The methodology produces an unconstrained future schedule from a current (or baseline) schedule and the airport operations growth rates. As an example of the use of the model, future schedules are projected for 2010 and 2022 for all flights arriving at, departing from, or flying between all continental United States airports that had commercial scheduled service for May 17, 2002. Inter-continental US traffic and airports are included and the traffic is also grown with the Fratar methodology to account for their arrivals and departures to the continental US airports. Input data sets derived from the Official Airline Guide (OAG) data and FAA Terminal Area Forecast (TAF) are included in the examples of the computer code execution.
Future Air Traffic Growth and Schedule Model, Supplement
NASA Technical Reports Server (NTRS)
Kimmel, William M. (Technical Monitor); Smith, Jeremy C.; Dollyhigh, Samuel M.
2004-01-01
The Future Air Traffic Growth and Schedule Model was developed as an implementation of the Fratar algorithm to project future traffic flow between airports in a system and of then scheduling the additional flights to reflect current passenger time-of-travel preferences. The methodology produces an unconstrained future schedule from a current (or baseline) schedule and the airport operations growth rates. As an example of the use of the model, future schedules are projected for 2010 and 2022 for all flights arriving at, departing from, or flying between all continental United States airports that had commercial scheduled service for May 17, 2002. Inter-continental US traffic and airports are included and the traffic is also grown with the Fratar methodology to account for their arrivals and departures to the continental US airports. Input data sets derived from the Official Airline Guide (OAG) data and FAA Terminal Area Forecast (TAF) are included in the examples of the computer code execution.
Modeling urban growth with geographically weighted multinomial logistic regression
NASA Astrophysics Data System (ADS)
Luo, Jun; Kanala, Nagaraj Kapi
2008-10-01
Spatial heterogeneity is usually ignored in previous land use change studies. This paper presents a geographically weighted multinomial logistic regression model for investigating multiple land use conversion in the urban growth process. The proposed model makes estimation at each sample location and generates local coefficients of driving factors for land use conversion. A Gaussian function is used for determine the geographic weights guarantying that all other samples are involved in the calibration of the model for one location. A case study on Springfield metropolitan area is conducted. A set of independent variables are selected as driving factors. A traditional multinomial logistic regression model is set up and compared with the proposed model. Spatial variations of coefficients of independent variables are revealed by investigating the estimations at sample locations.
Modelling melt-solid interfaces in Bridgman growth
NASA Technical Reports Server (NTRS)
Barber, Patrick G.; Berry, Robert F.; Debnam, William J.; Fripp, Archibald F.; Huang, YU
1989-01-01
Doped epoxy models with abrupt interfaces were prepared to test radiographic and computer enhancement procedures used to study the images of melt-solid interfaces during crystal growth in Bridgman furnaces. A column averaging procedure resulted in improved images that faithfully reproduced the positions and shapes of interfaces even at very low density differences. These techniques were applied to lead tin telluride growing in Bridgman furnaces.
Dynamic Metabolic Modeling of Denitrifying Bacterial Growth: The Cybernetic Approach
Song, Hyun-Seob; Liu, Chongxuan
2015-06-29
Denitrification is a multistage reduction process converting nitrate ultimately to nitrogen gas, carried out mostly by facultative bacteria. Modeling of the denitrification process is challenging due to the complex metabolic regulation that modulates sequential formation and consumption of a series of nitrogen oxide intermediates, which serve as the final electron acceptors for denitrifying bacteria. In this work, we examined the effectiveness and accuracy of the cybernetic modeling framework in simulating the growth dynamics of denitrifying bacteria in comparison with kinetic models. In four different case studies using the literature data, we successfully simulated diauxic and triauxic growth patterns observed in anoxic and aerobic conditions, only by tuning two or three parameters. In order to understand the regulatory structure of the cybernetic model, we systematically analyzed the effect of cybernetic control variables on simulation accuracy. The results showed that the consideration of both enzyme synthesis and activity control through u- and v-variables is necessary and relevant and that uvariables are of greater importance in comparison to v-variables. In contrast, simple kinetic models were unable to accurately capture dynamic metabolic shifts across alternative electron acceptors, unless an inhibition term was additionally incorporated. Therefore, the denitrification process represents a reasonable example highlighting the criticality of considering dynamic regulation for successful metabolic modeling.
A population growth model forced by random, episodic disturbances
NASA Astrophysics Data System (ADS)
Peckham, S. D.
2011-12-01
As a first step to quantify and better understand the nature of thresholds in ecosystems, a prototype population dynamics model has been developed and analyzed for the case where a population is subjected to random, episodic disturbances. This model assumes that disturbances occur at random times (following a Poisson event process) and have random magnitudes that determine the fraction of the population that survives the disturbance. Disturbances may be events such as fire, drought, disease or infestation. Between disturbances, the model assumes that population growth is deterministic and can be modeled by an exponential or logistic equation. The model is characterized by time, t, and four other parameters: the initial population size, N0, the per capita growth rate, r, the expected number of disturbance events per unit time, λ , and μ = E(X), where X is the random fraction (between 0 and 1) of the population that survives a given disturbance. What is nice about this simple, stochastic model is that it is mathematically tractable and clearly exhibits threshold behavior that can be computed explicitly in terms of the model parameters. In particular, the long-term behavior of the model is characterized by an easily-computed indicator that is a function of the model parameters. Whenever the model parameters are such that this indicator is less than zero, the expected value of the random population size declines over time and is unsustainable. But whenever it is greater than zero, the expected population size grows, despite the random disturbances. The case where the indicator is zero therefore represents a type of critical threshold for this problem that determines whether or not the population is likely to survive the disturbances. A number of analytic results will be presented along with numerical results from a large number of simulations.
Modeling crack growth processes in fusion reactor materials
NASA Astrophysics Data System (ADS)
Jones, Russell H.; Wolfer, Wilhelm G.
1984-05-01
Models for the effect of the chemical environment on crack growth processes in austenitic and ferritic stainless were evaluated. The effect of impurity segregation, yield strength, and hydrogen on crack growth of HT-9 and radiation induced phosphorus segregation on the intergranular stress corrosion of 316SS have been evaluated. Moderate increases in impurity segregation and/or yield strength caused significant decreases in the K IC and K TH of HT-9, while less than a 10 fold increase in the intergranular stress corrosion crack growth rate of 316SS was predicted for a fluence of 100 dpa using the radiation induced phosphorus segregation data of Brimhall et al. and the stress corrosion model of Parkins. Therefore, while radiation induced impurity segregation is greater in 316SS than HT-9, the effect of impurity segregation may be more pronounced in HT-9. The effect of hydrogen on fatigue crack thresholds was evaluated using a model by Tien which describes the threshold as a function of surface energy. A reduction in the surface energy by hydrogen adsorption was found to cause a decrease in the fatigue threshold a small but comparable amount to that observed for 2-1/4Cr-lMo steel.
Santa Maria, Peter Luke; Weierich, Kendall; Kim, Sungwoo; Yang, Yunzhi Peter
2016-01-01
Hypothesis That heparin binding epidermal growth factor like growth factor (HB-EGF) heals chronic tympanic membrane (TM) perforations at higher rates than fibroblast growth factor 2 (FGF2) and epidermal growth factor (EGF) in an animal model. Background A non-surgical treatment for chronic TM perforation would benefit those unable to access surgery or those unable to have surgery, as well as reducing the cost of tympanoplasty. Growth factor (GF) treatments have been reported in the literature with variable success with the lack of a suitable animal providing a major obstacle. Methods The GFs were tested in a validated mouse model of chronic TM perforation. A bio absorbable hydrogel polymer was used to deliver the GF at a steady concentration as it dissolved over four weeks. A control (polymer only, n=18) was compared to polymer loaded with HB-EGF (5ug/ml, n=18), FGF2 (100ug/ml, n=19) and EGF (250ug/ml, n=19). Perforations were inspected at four weeks. Results The healing rates, as defined as one hundred percent perforation closure, were control (5/18, 27.8%), HB-EGF (15/18, 83.3%), FGF2 (6/19, 31.6%) and EGF (3/19, 15.8%). There were no differences between FGF2 (p=0.80) and EGF (p=0.31) with control healing rates. HB-EGF (p= 0.000001) showed a significant difference for healing. The HB-EGF healed TMs showed layers similar to a normal TM, whilst the other groups showed a lack of epithelial migration. Conclusion This study confirms the advantage of HB-EGF over two other commonly used growth factors and is a promising non-surgical treatment of chronic TM perforations. PMID:26075672
Kinetic model of impurity poisoning during growth of calcite
DeYoreo, J; Wasylenki, L; Dove, P; Wilson, D; Han, N
2004-05-18
The central role of the organic component in biologically controlled mineralization is widely recognized. These proteins are characterized by a high proportion of acidic amino acid residues, especially aspartate, Asp. At the same time, biomineralization takes place in the presence of a number of naturally-occurring, inorganic impurities, particularly Mg and Sr. In an attempt to decipher the controls on calcite growth imposed by both classes of modifiers, we have used in situ AFM to investigate the dependence of growth morphology and step kinetics on calcite in the presence of Sr{sup 2+}, as well as a wide suite of Aspartic acid-bearing polypeptides. In each case, we observe a distinct and step-specific modification. Most importantly, we find that the step speed exhibits a characteristic dependence on impurity concentration not predicted by existing crystal growth models. While all of the impurities clearly induce appearance of a 'dead zone,' neither the width of that dead zone nor the dependence of step speed on activity or impurity content can be explained by invoking the Gibbs-Thomson effect, which is the basis for the Cabrera-Vermilyea model of impurity poisoning. Common kink-blocking models also fail to explain the observed dependencies. Here we propose a kinetic model of inhibition based on a 'cooperative' effect of impurity adsorption at adjacent kink sites. The model is in qualitative agreement with the experimental results in that it predicts a non-linear dependence of dead zone width on impurity concentration, as well as a sharp drop in step speed above a certain impurity content. However, a detailed model of impurity adsorption kinetics that give quantitative agreement with the data has yet to be developed.
Relative growth rates of predator and prey dinosaurs reflect effects of predation
Cooper, Lisa Noelle; Lee, Andrew H; Taper, Mark L; Horner, John R
2008-01-01
Hadrosaurs grew rapidly, and quantifying their growth is key to understanding life-history interactions between predators and prey during the Late Cretaceous. In this study, we longitudinally sampled a sequence of lines of arrested growth (LAGs) from an essentially full-grown hadrosaur Hypacrosaurus stebingeri (MOR 549). Spatial locations of LAGs in the femoral and tibial transverse sections of MOR 549 were measured and circumferences were calculated. For each bone, a time series of circumference data was fitted to several stochastic, discrete growth models. Our results suggest that the femur and the tibia of this specimen of Hypacrosaurus probably followed a Gompertz curve and that LAGs reportedly missing from early ontogeny were obscured by perimedullary resorption. In this specimen, death occurred at 13 years and took approximately 10–12 years to reach 95 per cent asymptotic size. The age at growth inflection, which is a proxy for reproductive maturity, occurred at approximately 2–3 years. Comparisons with several small and large predatory theropods reveal that MOR 549 grew faster and matured sooner than they did. These results suggest that Hypacrosaurus was able to partly avoid predators by outgrowing them. PMID:18682367
Inhibitory effect of sodium fluoride and chlorhexidine on the growth of oral lactobacilli.
del Carmen Ahumada Ostengo, María; Wiese, Birgitt; Nader-Macias, María Elena
2005-02-01
The accumulation of microorganisms in dental plaque is related to the etiology of caries and periodontal disease, with a high prevalence worldwide. The prophylactic measures include the use of chemical agents as NaF and chlorhexidine. Lactic acid bacteria are members of the normal microbiota of the oral cavity being discussed with regard to their beneficial or detrimental effect in this environment. The present study was performed to determine the growth of some species of Lactobacillus at different concentrations of NaF and chlorhexidine. The strains were isolated from both caries-free and caries patients. Their growth parameters were evaluated by the application of the Gompertz model to the experimental data of optical density as a measurement of growth. The degree of inhibition of the growth of all of the lactobacilli studied was different, depending on each particular strain. NaF at 1 mmol x L(-1) inhibited between 5% and 46%, at 5 mmol x L(-1) between 13% and 65%, and at 20 mmol x L(-1) between 57% and 84%. CHX at higher concentrations (197 and 98 mmol x L(-1) showed a complete inhibition of some of the strains. The significance of the results was evaluated by the application of a multivariate analysis and also compared with the inhibition of pathogenic Streptococcus mutans and with lactobacilli strains from collection cultures. PMID:16091771
Prediction of Fatigue Crack Growth Using Regularized Numerical Models
NASA Technical Reports Server (NTRS)
Meade, Andrew J.
1999-01-01
Though it is known in the engineering community that successful analyses rest upon the proper balance of (1) theoretical analysis of mathematical models, (2) physical experimentation and (3) computational simulation, this balance is currently handled in sometimes unwieldy and inefficient manner. It is proposed to investigate and develop rigorous and computationally efficient method to effectively combine all available information, from both experimental measurements and mathematical models, in the emulation of physical systems. This will be specifically applied to fatigue crack growth in metallic structures of interest to NASA.
ERIC Educational Resources Information Center
Peugh, James; Fan, Xitao
2012-01-01
Growth mixture modeling (GMM) has become a more popular statistical method for modeling population heterogeneity in longitudinal data, but the performance characteristics of GMM enumeration indexes in correctly identifying heterogeneous growth trajectories are largely unknown. Few empirical studies have addressed this issue. This study considered…
Phase field model for growth of adatom islands
NASA Astrophysics Data System (ADS)
Yu, Yan-Mei; Liu, Bang-Gui
2005-03-01
We developed a phase-field model for epitaxial growth of 2D/3D adatom islands and self-organized formation of regular nanostripes. A local phase-field variable is introduced to describe adatom islands. The evolution of this phase field is determined by a time-dependent equation coupled to a diffusive transport equation of local adatom density. The limited interlayer diffusion and atomic detachment at steps are included in the model. Applied to real submonolayer epitaxial systems, we reproduce not only the scaling law of the island density but also the experimental size and spatial distribution of the islands. With large coverages of adatoms we obtain not only the 3D mounding islands but also their coarsening and roughening exponents. We explored the self-organized formation of regular arrays of Fe nanostripes on W(110) by the hybrid growth of islands and step flows during the post-deposition annealing. Compared with atomic models and mean-field models, this phase-field model can not only span larger space and time scales while containing the elemental atomic kinetic of epitaxy, but also provide a fine visualized morphology of epitaxial features in 2+1 dimensions. Y. M. Yu and B.-G. Liu, Phys. Rev. E 69, 021601 (2004); Phys. Rev. B 70, 051444 (2004).
Simulation model for plant growth in controlled environment systems
NASA Technical Reports Server (NTRS)
Raper, C. D., Jr.; Wann, M.
1986-01-01
The role of the mathematical model is to relate the individual processes to environmental conditions and the behavior of the whole plant. Using the controlled-environment facilities of the phytotron at North Carolina State University for experimentation at the whole-plant level and methods for handling complex models, researchers developed a plant growth model to describe the relationships between hierarchial levels of the crop production system. The fundamental processes that are considered are: (1) interception of photosynthetically active radiation by leaves, (2) absorption of photosynthetically active radiation, (3) photosynthetic transformation of absorbed radiation into chemical energy of carbon bonding in solube carbohydrates in the leaves, (4) translocation between carbohydrate pools in leaves, stems, and roots, (5) flow of energy from carbohydrate pools for respiration, (6) flow from carbohydrate pools for growth, and (7) aging of tissues. These processes are described at the level of organ structure and of elementary function processes. The driving variables of incident photosynthetically active radiation and ambient temperature as inputs pertain to characterization at the whole-plant level. The output of the model is accumulated dry matter partitioned among leaves, stems, and roots; thus, the elementary processes clearly operate under the constraints of the plant structure which is itself the output of the model.
Models of lipid droplets growth and fission in adipocyte cells
Boschi, Federico; Rizzatti, Vanni; Zamboni, Mauro; Sbarbati, Andrea
2015-08-15
(fission and the decrease through neutral lipid exit from pre-existing droplets) to reproduce their size reduction observed in lipolytic conditions. The results suggest that each single process, considered alone, can not be considered the only responsible for the size variation observed, but more than one of them, playing together, can quite well reproduce the experimental data. - Highlights: The growth and fission of the lipid droplets (LDs) were computationally simulated. To write and test the growth and fission models more than 110,000 LDs were measured. The usual processes considered alone, are not able to justify the experimental data. Some processes, playing together, can explain the growth and fission.
A new 'Jackson Hunt' model for monotectic composite growth
NASA Astrophysics Data System (ADS)
Stöcker, C.; Ratke, L.
1999-06-01
Directional solidification of monotectic alloys can lead under certain conditions of growth velocity and temperature gradient in the melt to composite microstructures with a rodlike appearance. For a theoretical description most researchers applied the Jackson and Hunt model of rod eutectic growth and predicted a relation between the mean rod distance R and the solidification velocity v0, as v0R2=const. similar to eutectics. The comparison between theory and experiments always led to discrepancies not yet resolved. In the approach presented here we propose an additional mode of mass transport in front of the zone coupled growth, since in our mind the main difference between monotectic and eutectic solidification is the liquid phase state of the (rod) L2 phase growing simultaneously within a nearly perfectly pure solid matrix. We assume that the thermocapillary effect causes convection at the surface of the liquid L2 phase. This Marangoni convection induces a flow field in front of the solidification front and has a strong influence on the solute transport, depending on the local temperature gradient and the Peclet number. We find a new relation between R and v0 in the case of small Peclet numbers and discuss some consequences on the stability of composite growth.
Airway smooth muscle growth from the perspective of animal models.
Martin, James G; Ramos-Barbón, David
2003-09-16
Airway smooth muscle maintains airway tone and may assist in adjusting ventilation distribution within the normal lung. Alterations in the properties or the quantity of ASM are likely responsible for some instances of airways hyperresponsiveness to bronchoconstrictive stimuli that is a characteristic of diseases such as asthma. Morphometric studies have shown an increase in the mass of ASM in human asthmatic airways. Animal models have been developed that confirm that ASM can be induced to grow by allergic sensitization and challenge. Growth is in large part by hyperplasia as measured by incorporation of bromodeoxyuridine as a marker of the S-phase of the cell cycle. T cells, in particular CD4+ cells, may participate in the stimulation of growth of ASM by allergen challenge. The growth factors responsible for the increase in ASM are as yet unidentified but two mediators associated with allergic airway responses, cysteinyl leukotrienes and endothelin, have been implicated using specific receptor antagonists. The links between T cells and the biochemical mediators of growth have not been established. PMID:14516730
Fault growth by linkage: observations and implications from analogue models
NASA Astrophysics Data System (ADS)
Mansfield, Chris; Cartwright, Joe
2001-05-01
Using time sequence analyses of extensional fault models we demonstrate the pivotal role played by fault segmentation in the accumulation of displacement and length during the growth of faults. Experiments are described in which incremental steps during the development of individual faults have been reconstructed from time-lapse photographs taken during model deformation. These records confirm the composite segment hierarchy of fault structure, a pattern that is frequently recognised in many natural arrays. They reveal the progressive enlargement of individual faults to be the product of a repetitive cycle of tip-line propagation, overlap and linkage between nearest neighbours. By contrasting the displacement patterns of successive increments during growth convincing evidence is also presented to suggest that individual segments of faults may remain kinematically independent once they are physically linked. This behaviour is shown to be responsible for the characteristic saw-tooth patterns often recognised in strike-parallel fault displacement profiles. Such patterns are believed to arise where relict segment boundaries remain preserved as asperities to slip, so that displacement is confined to discrete parts of a fault plane surface. Growth in this way also causes the maximum displacement (D) and surface length (L) of faults to continually change by different proportions. Incremental displacement records presented here corroborate field evidence which shows that linkage between fault segments during growth is responsible for a significant component of the spread of values often recorded in D versus L compilations. Finally, we speculate that linkage between fault segments also accounts for transient irregularities recorded in the frequency distribution of the fault length populations of each model.
Travelling wave analysis of a mathematical model of glioblastoma growth.
Gerlee, Philip; Nelander, Sven
2016-06-01
In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered. PMID:27021919
The Unified Plant Growth Model (UPGM): software framework overview and model application
Technology Transfer Automated Retrieval System (TEKTRAN)
Since the Environmental Policy Integrated Climate (EPIC) model was developed in 1989, the EPIC plant growth component has been incorporated into other erosion and crop management models (e.g., WEPS, WEPP, SWAT, ALMANAC, and APEX) and modified to meet model developer research objectives. This has re...
Evaluating Model Fit for Growth Curve Models: Integration of Fit Indices from SEM and MLM Frameworks
ERIC Educational Resources Information Center
Wu, Wei; West, Stephen G.; Taylor, Aaron B.
2009-01-01
Evaluating overall model fit for growth curve models involves 3 challenging issues. (a) Three types of longitudinal data with different implications for model fit may be distinguished: balanced on time with complete data, balanced on time with data missing at random, and unbalanced on time. (b) Traditional work on fit from the structural equation…
Mechanistic models of biofilm growth in porous media
NASA Astrophysics Data System (ADS)
Jaiswal, Priyank; Al-Hadrami, Fathiya; Atekwana, Estella A.; Atekwana, Eliot A.
2014-07-01
Nondestructive acoustics methods can be used to monitor in situ biofilm growth in porous media. In practice, however, acoustic methods remain underutilized due to the lack of models that can translate acoustic data into rock properties in the context of biofilm. In this paper we present mechanistic models of biofilm growth in porous media. The models are used to quantitatively interpret arrival times and amplitudes recorded in the 29 day long Davis et al. (2010) physical scale biostimulation experiment in terms of biofilm morphologies and saturation. The model pivots on addressing the sediment elastic behavior using the lower Hashin-Shtrikman bounds for grain mixing and Gassmann substitution for fluid saturation. The time-lapse P wave velocity (VP; a function of arrival times) is explained by a combination of two rock models (morphologies); "load bearing" which assumes the biofilm as an additional mineral in the rock matrix and "pore filling" which assumes the biofilm as an additional fluid phase in the pores. The time-lapse attenuation (QP-1; a function of amplitudes), on the other hand, can be explained adequately in two ways; first, through squirt flow where energy is lost from relative motion between rock matrix and pore fluid, and second, through an empirical function of porosity (φ), permeability (κ), and grain size. The squirt flow model-fitting results in higher internal φ (7% versus 5%) and more oblate pores (0.33 versus 0.67 aspect ratio) for the load-bearing morphology versus the pore-filling morphology. The empirical model-fitting results in up to 10% increase in κ at the initial stages of the load-bearing morphology. The two morphologies which exhibit distinct mechanical and hydraulic behavior could be a function of pore throat size. The biofilm mechanistic models developed in this study can be used for the interpretation of seismic data critical for the evaluation of biobarriers in bioremediation, microbial enhanced oil recovery, and CO2
Concentration-Driven Growth of Model Protocell Membranes
2012-01-01
The first protocell membranes may have assembled from fatty acids and related single-chain lipids available in the prebiotic environment. Prior to the evolution of complex cellular machinery, spontaneous protocell membrane growth and division had to result from the intrinsic physicochemical properties of these molecules, in the context of specific environmental conditions. Depending on the nature of the chemical and physical environment, fatty acids can partition between several different phases, including soluble monomers, micelles, and lamellar vesicles. Here we address the concentration dependence of fatty acid aggregation, which is dominated by entropic considerations. We quantitatively distinguish between fatty acid phases using a combination of physical and spectroscopic techniques, including the use of the fluorescent fatty acid analogue Laurdan, whose emission spectrum is sensitive to structural differences between micellar and lamellar aggregates. We find that the monomer–aggregate transition largely follows a characteristic pseudophase model of molecular aggregation but that the composition of the aggregate phase is also concentration dependent. At low amphiphile concentrations above the critical aggregate concentration, vesicles coexist with a significant proportion of micelles, while more concentrated solutions favor the lamellar vesicle phase. We subsequently show that the micelle–vesicle equilibrium can be used to drive the growth of pre-existing vesicles upon an increase in amphiphile concentration either through solvent evaporation or following the addition of excess lipids. We propose a simple model for a primitive environmentally driven cell cycle, in which protocell membrane growth results from evaporative concentration, followed by shear force or photochemically induced division. PMID:23198690
The growth of structure in interacting dark energy models
Caldera-Cabral, Gabriela; Maartens, Roy; Schaefer, Bjoern Malte E-mail: roy.maartens@port.ac.uk
2009-07-01
If dark energy interacts with dark matter, there is a change in the background evolution of the universe, since the dark matter density no longer evolves as a{sup −3}. In addition, the non-gravitational interaction affects the growth of structure. In principle, these changes allow us to detect and constrain an interaction in the dark sector. Here we investigate the growth factor and the weak lensing signal for a new class of interacting dark energy models. In these models, the interaction generalises the simple cases where one dark fluid decays into the other. In order to calculate the effect on structure formation, we perform a careful analysis of the perturbed interaction and its effect on peculiar velocities. Assuming a normalization to today's values of dark matter density and overdensity, the signal of the interaction is an enhancement (suppression) of both the growth factor and the lensing power, when the energy transfer in the background is from dark matter to dark energy (dark energy to dark matter)
Concentration-driven growth of model protocell membranes.
Budin, Itay; Debnath, Anik; Szostak, Jack W
2012-12-26
The first protocell membranes may have assembled from fatty acids and related single-chain lipids available in the prebiotic environment. Prior to the evolution of complex cellular machinery, spontaneous protocell membrane growth and division had to result from the intrinsic physicochemical properties of these molecules, in the context of specific environmental conditions. Depending on the nature of the chemical and physical environment, fatty acids can partition between several different phases, including soluble monomers, micelles, and lamellar vesicles. Here we address the concentration dependence of fatty acid aggregation, which is dominated by entropic considerations. We quantitatively distinguish between fatty acid phases using a combination of physical and spectroscopic techniques, including the use of the fluorescent fatty acid analogue Laurdan, whose emission spectrum is sensitive to structural differences between micellar and lamellar aggregates. We find that the monomer-aggregate transition largely follows a characteristic pseudophase model of molecular aggregation but that the composition of the aggregate phase is also concentration dependent. At low amphiphile concentrations above the critical aggregate concentration, vesicles coexist with a significant proportion of micelles, while more concentrated solutions favor the lamellar vesicle phase. We subsequently show that the micelle-vesicle equilibrium can be used to drive the growth of pre-existing vesicles upon an increase in amphiphile concentration either through solvent evaporation or following the addition of excess lipids. We propose a simple model for a primitive environmentally driven cell cycle, in which protocell membrane growth results from evaporative concentration, followed by shear force or photochemically induced division. PMID:23198690
A simple model for dislocation emission mediated dynamic nanovoid growth
NASA Astrophysics Data System (ADS)
Wilkerson, Justin; Ramesh, K. T.
2015-06-01
Failure of ductile metals has long been attributed to the microscopic processes of void nucleation, growth, and finally coalescence leading to fracture. Our traditional view of void nucleation is associated with interface debonding at second-phase particles. However, much of this understanding has been gleaned from observations of quasi-static fracture surfaces. Under more extreme dynamic loading conditions second-phase particles may not necessarily be the dominant source of void nucleating material defects, and a few key experimental observations of laser spall surfaces seem to support this assertion. Here, we motivate an alternative mechanism to the traditional view, namely shock-induced vacancy generation and clustering followed by nanovoid growth mediated by dislocation emission. This mechanism only becomes active at very large stresses, and thus it is desirable to establish a closed-form criterion for the macroscopic stress required to activate dislocation emission in porous materials. Following an approach similar to Lubarda and co-workers, we make use of stability arguments applied to the analytic solutions of the elastic interactions of dislocations and voids to derive the desired criterion. We then propose a dynamic nanovoid growth law that is motivated by the kinetics of dislocation emission. The resulting failure model is validated against a number of molecular dynamics simulations with favorable agreement. Lastly, we make use of our simple model to predict some interesting anomalous behaviors associated with high surface energies and nonlinear elasticity.
Interfacial properties in a discrete model for tumor growth
NASA Astrophysics Data System (ADS)
Moglia, Belén; Guisoni, Nara; Albano, Ezequiel V.
2013-03-01
We propose and study, by means of Monte Carlo numerical simulations, a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent β=0.32(2) that governs the early time regime, (ii) the roughness exponent α=0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z=α/β≃1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g., ξ∝t1/z, where ξ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang universality class, in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture or tumor.
Modeling of microbiological growth in the capillary fringe
NASA Astrophysics Data System (ADS)
Hron, Pavel; Bastian, Peter; Ippisch, Olaf; Jost, Daniel
2013-04-01
The capillary fringe (CF) is a highly dynamic soil zone, which is located above the groundwater level. It results from the capillary water rise into the unsaturated soil zone and therewith offers a broad range of growth conditions for microorganisms. These conditions change from aerobic (good oxygen supply) at the top of the CF to anaerobic (no available oxygen) at the bottom of the CF and under the water table. In recent years, a lot of earth scientists and microbiologists worked together to deepen the understanding of the physical, geochemical and biological processes in the CF. But there is still a lack in knowledge on both sides, since the water content changes in the CF from saturated to almost unsaturated which hampers determination of biological parameters as well as modeling. In the DFG-project "Dynamic Capillary Fringes - A Multidisciplinary Approach (DyCap)" researchers started to simulate growth of microorganisms in the CF. The biological parameters like growth rates, saturation constants for substrate and oxygen, yield coefficients and maintenance rate were determined in batch assays using parameter estimation. A flow through cell filled with fine sand was used to establish a CF and to investigate the growth of microorganisms in this zone. In order to allow non-invasive visualization and quantification, facultative anaerobic Escherichia coli) cells which can grow under aerobic and anaerobic conditions and which produce a green fluorescent protein were used. We developed a numerical simulator for multiphase multicomponent reactive flow in porous media, which is able to consider simultaneously multiphase flow, component transport, phase exchange and microbiological processes. This tool was used to simulate the E. coli growth in the CF with nutrient supply under steady-state condition and the results are finally compared to the experimental data.
Dynamic model for predicting growth of salmonella spp. in ground sterile pork
Technology Transfer Automated Retrieval System (TEKTRAN)
Predictive model for Salmonella spp. growth in ground pork was developed and validated using kinetic growth data. Salmonella spp. kinetic growth data in ground pork was collected at several isothermal conditions (between 10 and 45C) and Baranyi model was fitted to describe the growth at each temper...
Growth index of matter perturbations in running vacuum models
NASA Astrophysics Data System (ADS)
Basilakos, Spyros; Solà, Joan
2015-12-01
We derive for the first time the growth index of matter perturbations of the Friedmann-Lemaître-Robertson-Walker (FLRW) flat cosmological models in which the vacuum energy depends on redshift. A particularly well-motivated model of this type is the so-called quantum field vacuum, in which, apart from a leading constant term Λ0 , there is also an H2 dependence in the functional form of the vacuum, namely, Λ (H )=Λ0+3 ν (H2-H02) . Since |ν |≪1 , this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at the perturbation level, we find that the growth index of the running vacuum cosmological model is γΛH≈6/+3 ν 11 -12 ν , and thus it nicely extends analytically the result of the Λ CDM model, γΛ≈6 /11 .
A two-phase mixture model of avascular tumor growth
NASA Astrophysics Data System (ADS)
Ozturk, Deniz; Burcin Unlu, M.; Yonucu, Sirin; Cetiner, Ugur
2012-02-01
Interactions with biological environment surrounding a growing tumor have major influence on tumor invasion. By recognizing that mechanical behavior of tumor cells could be described by biophysical laws, the research on physical oncology aims to investigate the inner workings of cancer invasion. In this study, we introduce a mathematical model of avascular tumor growth using the continuum theory of mixtures. Mechanical behavior of the tumor and physical interactions between the tumor and host tissue are represented by biophysically founded relationships. In this model, a solid tumor is embedded in inviscid interstitial fluid. The tumor has viscous mechanical properties. Interstitial fluid exhibits properties of flow through porous medium. Associated with the mixture saturation constraint, we introduce a Lagrange multiplier which represents hydrostatic pressure of the interstitial fluid. We solved the equations using Finite Element Method in two-dimensions. As a result, we have introduced a two-phase mixture model of avascular tumor growth that provided a flexible mathematical framework to include cells' response to mechanical aspects of the tumor microenvironment. The model could be extended to capture tumor-ECM interactions which would have profound influence on tumor invasion.
Micromechanical model of crack growth in fiber reinforced brittle materials
NASA Technical Reports Server (NTRS)
Rubinstein, Asher A.; Xu, Kang
1990-01-01
A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution.
Modeling the initiation and growth of delaminations in composite structures
Reedy, E.D. Jr.; Mello, F.J.; Guess, T.R.
1996-01-01
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 4-noded quadrilateral shell elements. A special, 8-noded hex constraint element connects the sublaminates and makes them act as a single laminate until a prescribed failure criterion is attained. When the failure criterion is reached, the connection is broken, and a discrete delamination is initiated or grows. This approach has been implemented in a three-dimensional, finite element code. This code uses explicit time integration, and can analyze shell-like structures subjected to large deformations and complex contact conditions. Tensile, compressive, and shear laminate failures are also modeled. This paper describes the 8-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. In addition, calculated 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 reproduce observed behavior. Results are also presented for a diametrally compressed ring to demonstrate the capacity to analyze progressive failure in a highly deformed composite structure.
Micromechanical model of crack growth in fiber reinforced ceramics
NASA Technical Reports Server (NTRS)
Rubinstein, Asher A.; Xu, Kang
1990-01-01
A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution.
Dynamic density functional theory of solid tumor growth: Preliminary models.
Chauviere, Arnaud; Hatzikirou, Haralambos; Kevrekidis, Ioannis G; Lowengrub, John S; Cristini, Vittorio
2012-03-01
Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT) extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth. PMID:22489279
Existence of Periodic Solutions for a Modified Growth Solow Model
NASA Astrophysics Data System (ADS)
Fabião, Fátima; Borges, Maria João
2010-10-01
In this paper we analyze the dynamic of the Solow growth model with a Cobb-Douglas production function. For this purpose, we consider that the labour growth rate, L'(t)/L(t), is a T-periodic function, for a fixed positive real number T. We obtain the closed form solutions for the fundamental Solow equation with the new description of L(t). Using notions of the qualitative theory of ordinary differential equations and nonlinear functional analysis, we prove that there exists one T-periodic solution for the Solow equation. From the economic point of view this is a new result which allows a more realistic interpretation of the stylized facts.
A model of northern pintail productivity and population growth rate
Flint, P.L.; Grand, J.B.; Rockwell, R.F.
1998-01-01
Our objective was to synthesize individual components of reproductive ecology into a single estimate of productivity and to assess the relative effects of survival and productivity on population dynamics. We used information on nesting ecology, renesting potential, and duckling survival of northern pintails (Anas acuta) collected on the Yukon-Kuskokvim Delta (Y-K Delta), Alaska, 1991-95, to model the number of ducklings produced under a range of nest success and duckling survival probabilities. Using average values of 25% nest success, 11% duckling survival, and 56% renesting probability from our study population, we calculated that all young in our population were produced by 13% of the breeding females, and that early-nesting females produced more young than later-nesting females. Further, we calculated, on average, that each female produced only 0.16 young females/nesting season. We combined these results with estimates of first-year and adult survival to examine the growth rate (??) of the population and the relative contributions of these demographic parameters to that growth rate. Contrary to aerial survey data, the population projection model suggests our study population is declining rapidly (?? = 0.6969). The relative effects on population growth rate were 0.1175 for reproductive success, 0.1175 for first-year survival, and 0.8825 for adult survival. Adult survival had the greatest influence on ?? for our population, and this conclusion was robust over a range of survival and productivity estimates. Given published estimates of annual survival for adult females (61%), our model suggested nest success and duckling survival need to increase to approximately 40% to achieve population stability. We discuss reasons for the apparent discrepancy in population trends between our model and aerial surveys in terms of bias in productivity and survival estimates.
Modeling and control of the Czochralski crystal growth process
NASA Astrophysics Data System (ADS)
Martinez, Denise Marie
The Czochralski process is a method of pulling crystal from the melt that is widely used by the semiconductor industry. The current breadth of this industry makes the method indespensible. The International Technology Roadmap for Semiconductors forecasts the use of 35 nm technology on 64 Gbit DRAM and 10 GHz processor speeds by the end of this decade. This implies the need for higher quality crystals, and therefore improved growth systems. Furthermore, industry has noted a problem with rapid pull rate variation contributing to structural defects in the grown crystals. It was proposed by industry to investigate elimination of the pull rate as a control input. The current state of the system as well as the predicted path of the industry served to motivate development of a new control scheme. The first objective of this work was to develop or enhance a first-principles based model of the process. This model must be kept at a manageable order to accommodate online simulation while still capturing the dominant process physics. The model must also be formulated as a time differential equation in order to apply the desired control theories. The second objective of this work was to answer industry's question regarding elimination of pull rate as a manipulated input. The final objective of this work was to use the model to design a new control algorithm. The control development includes consideration of the time delay between heater and the crystal. The work is based on silicon growth, but the developments are kept as generic as possible for future application to other materials. Data from industry crystal growths as well as experimental results reported in literature will be used to gauge the effectiveness of the new designs.
A multiphase model for three-dimensional tumor growth
Sciumè, G; Shelton, S; Gray, WG; Miller, CT; Hussain, F; Ferrari, M; Decuzzi, P; Schrefler, BA
2014-01-01
Several mathematical formulations have analyzed the time-dependent behaviour of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the Thermodynamically Constrained Averaging Theory (TCAT). A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TC), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HC); and an interstitial fluid (IF) for the transport of nutrients. The equations are solved by a Finite Element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTS) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behaviour: initially, the rapidly growing tumor cells tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable tumor cells whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case – mostly due to the relative adhesion of the tumor and healthy cells to the ECM, and the less favourable transport of nutrients. In particular, for tumor cells adhering less avidly to the ECM, the healthy tissue is progressively displaced
A multiphase model for three-dimensional tumor growth
NASA Astrophysics Data System (ADS)
Sciumè, G.; Shelton, S.; Gray, W. G.; Miller, C. T.; Hussain, F.; Ferrari, M.; Decuzzi, P.; Schrefler, B. A.
2013-01-01
Several mathematical formulations have analyzed the time-dependent behavior of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the thermodynamically constrained averaging theory. A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TCs), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HCs); and an interstitial fluid for the transport of nutrients. The equations are solved by a finite element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTSs) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behavior: initially, the rapidly growing TCs tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable TCs whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case—mostly due to the relative adhesion of the TCs and HCs to the ECM, and the less favorable transport of nutrients. In particular, for HCs adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas TC
An overview of reliability growth models and their potential use for NASA applications
NASA Technical Reports Server (NTRS)
Taneja, V. S.; Safie, F. M.
1992-01-01
An overview is provided of reliability growth literature over the past 25 years. This includes a thorough literature review of different areas of the application of reliability growth such as design, prediction, tracking/management, and demonstration. Various reliability growth models use different bases on how they characterize growth. Different models are discussed. Also, the use is addressed of reliability growth models to NASA applications. This includes the application of these models to the space shuttle main engine. For potential NASA applications, we classify growth models in two groups, which are characterized.
Stochastic resonance in a generalized Von Foerster population growth model
Lumi, N.; Mankin, R.
2014-11-12
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
Stoichiometric growth model for riboflavin-producing Bacillus subtilis.
Dauner, M; Sauer, U
2001-09-01
Rate equations for measured extracellular rates and macromolecular composition data were combined with a stoichiometric model to describe riboflavin production with an industrial Bacillus subtilis strain using errors in variables regression analysis. On the basis of this combined stoichiometric growth model, we explored the topological features of the B. subtilis metabolic reaction network that was assembled from a large amount of literature. More specifically, we simulated maximum theoretical yields of biomass and riboflavin, including the associated flux regimes. Based on the developed model, the importance of experimental data on building block requirements for maximum yield and flux calculations were investigated. These analyses clearly show that verification of macromolecular composition data is important for optimum flux calculations. PMID:11505383
Modeling of Intermetallic Compounds Growth Between Dissimilar Metals
NASA Astrophysics Data System (ADS)
Wang, Li; Wang, Yin; Prangnell, Philip; Robson, Joseph
2015-09-01
A model has been developed to predict growth kinetics of the intermetallic phases (IMCs) formed in a reactive diffusion couple between two metals for the case where multiple IMC phases are observed. The model explicitly accounts for the effect of grain boundary diffusion through the IMC layer, and can thus be used to explore the effect of IMC grain size on the thickening of the reaction layer. The model has been applied to the industrially important case of aluminum to magnesium alloy diffusion couples in which several different IMC phases are possible. It is demonstrated that there is a transition from grain boundary-dominated diffusion to lattice-dominated diffusion at a critical grain size, which is different for each IMC phase. The varying contribution of grain boundary diffusion to the overall thickening kinetics with changing grain size helps explain the large scatter in thickening kinetics reported for diffusion couples produced under different conditions.
Application of constraint modelling to evaluation of crack growth experiments
Faleskog, J.; Nilsson, F.; Shehu, S.; Oeberg, H.
1997-12-01
A large number of fracture mechanics experiments were carried out using a variety of specimens in order to investigate the applicability of the J-Q approach to initiation and growth of cracks. The study was performed at different temperatures spanning the transition interval of a pressure vessel steel. A comparison of the cleavage initiation levels with the model by Ritchie et al. (RKR) was also conducted. The experiments did not show, although the scatter was large, any systematic geometry effects that could not be explained within the framework of the J-Q concept. This was also the case for surface-cracked plates subjected to nonproportional loading. The trends of the dependence of the initiation on constraint are in qualitative agreement with the RKR model, although this model seems to underestimate this dependence for the current material. The ductile initiation level seems to be fairly independent of constraint but showed a tendency of variation with temperature.
Stochastic resonance in a generalized Von Foerster population growth model
NASA Astrophysics Data System (ADS)
Lumi, N.; Mankin, R.
2014-11-01
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
A simple unforced oscillatory growth model in the chemostat.
Lemesle, V; Gouzé, J L
2008-02-01
In a chemostat, transient oscillations in cell number density are often experimentally observed during cell growth. The aim of this paper is to propose a simple autonomous model which is able to generate these oscillations, and to investigate it analytically. Our point of view is based on a simplification of the cell cycle in which there are two states (mature and immature) with the transfer between the two dependent on the available resources. We use the mathematical global properties of competitive differential systems to prove the existence of a limit cycle. A comparison between our model and a more complex model consisting of partial differential equations is made with the help of numerical simulations, giving qualitatively similar results. PMID:17912591
Technology Transfer Automated Retrieval System (TEKTRAN)
A new mechanistic growth model was developed to describe microbial growth under isothermal conditions. The new mathematical model was derived from the basic observation of bacterial growth that may include lag, exponential, and stationary phases. With this model, the lag phase duration and exponen...
Jenkins, P; Poulos, P G; Cole, M B; Vandeven, M H; Legan, J D
2000-02-01
Models to predict days to growth and probability of growth of Zygosaccharomyces bailii in high-acid foods were developed, and the equations are presented here. The models were constructed from measurements of growth of Z. bailii using automated turbidimetry over a 29-day period at various pH, NaCl, fructose, and acetic acid levels. Statistical analyses were carried out using Statistical Analysis Systems LIFEREG procedures, and the data were fitted to log-logistic models. Model 1 predicts days to growth based on two factors, combined molar concentration of salt plus sugar and undissociated acetic acid. This model allows a growth/no-growth boundary to be visualized. The boundary is comparable with that established by G. Tuynenburg Muys (Process Biochem. 6:25-28, 1971), which still forms the basis of industry assumptions about the stability of acidic foods. Model 2 predicts days to growth based on the four independent factors of salt, sugar, acetic acid, and pH levels and is, therefore, much more useful for product development. Validation data derived from challenge studies in retail products from the U.S. market are presented for Model 2, showing that the model gives reliable, fail-safe predictions and is suitable for use in predicting growth responses of Z. bailii in high-acid foods. Model 3 predicts probability of growth of Z. bailii in 29 days. This model is most useful for spoilage risk assessment. All three models showed good agreement between predictions and observed values for the underlying data. PMID:10678428
Kristjansson, Sean D; Kircher, John C; Webb, Andrea K
2007-09-01
Psychophysiologists often use repeated measures analysis of variance (RMANOVA) and multivariate analysis of variance (MANOVA) to analyze data collected in repeated measures research designs. ANOVA and MANOVA are nomothetic approaches that focus on group means. Newer multilevel modeling techniques are more informative than ANOVA because they characterize both group-level (nomothetic) and individual-level (idiographic) effects, yielding a more complete understanding of the phenomena under study. This article was written as an introduction to growth curve modeling for applied researchers. A growth model is defined that can be used in place of RMANOVAs and MANOVAs for single-group and mixed repeated measures designs. The model is expanded to test and control for the effects of baseline levels of physiological activity on stimulus-specific responses. Practical, conceptual, and statistical advantages of growth curve modeling are discussed. PMID:17596179
Modelling the interaction between flooding events and economic growth
NASA Astrophysics Data System (ADS)
Grames, Johanna; Fürnkranz-Prskawetz, Alexia; Grass, Dieter; Viglione, Alberto; Blöschl, Günter
2016-04-01
Recently socio-hydrology models have been proposed to analyze the interplay of community risk-coping culture, flooding damage and economic growth. These models descriptively explain the feedbacks between socio-economic development and natural disasters such as floods. Complementary to these descriptive models, we develop a dynamic optimization model, where the inter-temporal decision of an economic agent interacts with the hydrological system. This interdisciplinary approach matches with the goals of Panta Rhei i.e. to understand feedbacks between hydrology and society. It enables new perspectives but also shows limitations of each discipline. Young scientists need mentors from various scientific backgrounds to learn their different research approaches and how to best combine them such that interdisciplinary scientific work is also accepted by different science communities. In our socio-hydrology model we apply a macro-economic decision framework to a long-term flood-scenario. We assume a standard macro-economic growth model where agents derive utility from consumption and output depends on physical capital that can be accumulated through investment. To this framework we add the occurrence of flooding events which will destroy part of the capital. We identify two specific periodic long term solutions and denote them rich and poor economies. Whereas rich economies can afford to invest in flood defense and therefore avoid flood damage and develop high living standards, poor economies prefer consumption instead of investing in flood defense capital and end up facing flood damages every time the water level rises. Nevertheless, they manage to sustain at least a low level of physical capital. We identify optimal investment strategies and compare simulations with more frequent and more intense high water level events.
Modeling fatigue crack growth in cross ply titanium matrix composites
NASA Technical Reports Server (NTRS)
Bakuckas, J. G., Jr.; Johnson, W. S.
1993-01-01
In this study, the fatigue crack growth behavior of fiber bridging matrix cracks in cross-ply SCS-6/Ti-15-3 and SCS-6/Timetal-21S laminates containing center holes was investigated. Experimental observations revealed that matrix cracking was far more extensive and wide spread in the SCS-6/Ti-15-3 laminates compared to that in the SCS-6/Timetal-21S laminates. In addition, the fatigue life of the SCS-6/Ti-15-3 laminates was significantly longer than that of the SCS-6/Timetal-21S laminates. The matrix cracking observed in both material systems was analyzed using a fiber bridging (FB) model which was formulated using the boundary correction factors and weight functions for center hole specimen configurations. A frictional shear stress is assumed in the FB model and was used as a curve fitting parameter to model matrix crack growth data. The higher frictional shear stresses calculated in the SCS-6/Timetal-21S laminates resulted in lower stress intensity factors in the matrix and higher axial stresses in the fibers compared to those in the SCS-6/Ti-15-3 laminates at the same applied stress levels.
A Big Bang model of human colorectal tumor growth
Sottoriva, Andrea; Kang, Haeyoun; Ma, Zhicheng; Graham, Trevor A.; Salomon, Matthew P.; Zhao, Junsong; Marjoram, Paul; Siegmund, Kimberly; Press, Michael F.; Shibata, Darryl; Curtis, Christina
2015-01-01
What happens in the early, still undetectable human malignancy is unknown because direct observations are impractical. Here we present and validate a “Big Bang” model, whereby tumors grow predominantly as a single expansion producing numerous intermixed sub-clones that are not subject to stringent selection, and where both public (clonal) and most detectable private (subclonal) alterations arise early during growth. Genomic profiling of 349 individual glands from 15 colorectal tumors revealed the absence of selective sweeps, uniformly high intra-tumor heterogeneity (ITH), and sub-clone mixing in distant regions, as postulated by our model. We also verified the prediction that most detectable ITH originates from early private alterations, and not from later clonal expansions, thus exposing the profile of the primordial tumor. Moreover, some tumors appear born-to-be-bad, with sub-clone mixing indicative of early malignant potential. This new model provides a quantitative framework to interpret tumor growth dynamics and the origins of ITH with significant clinical implications. PMID:25665006
Konstorum, Anna; Sprowl, Stephanie A.; Waterman, Marian L.; Lander, Arthur D.; Lowengrub, John S.
2014-01-01
A large number of growth factors and drugs are known to act in a biphasic manner: at lower concentrations they cause increased division of target cells, whereas at higher concentrations the mitogenic effect is inhibited. Often, the molecular details of the mitogenic effect of the growth factor are known, whereas the inhibitory effect is not. Hepatoctyte Growth Factor, HGF, has recently been recognized as a strong mitogen that is present in the microenvironment of solid tumors. Recent evidence suggests that HGF acts in a biphasic manner on tumor growth. We build a multi-species model of HGF action on tumor cells using different hypotheses for high dose-HGF activation of a growth inhibitor and show that the shape of the dose-response curve is directly related to the mechanism of inhibitor activation. We thus hypothesize that the shape of a dose-response curve is informative of the molecular action of the growth factor on the growth inhibitor. PMID:25075381
Modelling the solution growth of TGS crystals in low gravity
NASA Technical Reports Server (NTRS)
Nadarajah, Arunan; Rosenberger, Franz; Alexander, J. Iwan D.
1990-01-01
The experimental growth of triglycine sulfate (TGS) crystals from aqueous solution is modeled here in two dimensions using the PHOENICS finite volume code. Simulations are carried out for steady, impulsive, and periodic accelerations in order to determine tolerable acceleration levels. Scaling arguments are used to estimate the times required for thermal and solutal variations from the initial equilibrium state to be diffusively transported throughout the system, and to obtain order of magnitude information on the relative magnitudes of diffusive and convective transport. The computed concentration fields reflect the features of the concentration distributions found experimentally during experiments conducted aboard Spacelab 3 in 1985.
Stable Algorithms for Modeling Thin-Film Epitaxial Growth
NASA Astrophysics Data System (ADS)
Seyfarth, Greg; Vollmayr-Lee, Benjamin
2013-03-01
We search for stable time-stepping schemes for a phase-field model of thin film epitaxial growth. In particular, we consider a class of linear semi-implicit schemes which ensure the free energy decreases with time, a property called gradient stability. System dynamics slow at late times, so gradient stable schemes which allow adaptive time stepping are highly desirable. We perform a linear stability analysis and support it with numerical testing, revealing a region in parameter space of gradient stable semi-implicit schemes. Funded by NSF REU Grant #PHY-1156964.
Stochastic contribution to the growth factor in the LCDM model
Ribeiro, A. L.B.; Andrade, A. P.A.; Letelier, P. S.
2009-01-01
We study the effect of noise on the evolution of the growth factor of density perturbations in the context of the LCDM model. Stochasticity is introduced as a Wiener process amplified by an intensity parameter alpha. By comparing the evolution of deterministic and stochastic cases for different values of alpha we estimate the intensity level necessary to make noise relevant for cosmological tests based on large-scale structure data. Our results indicate that the presence of random forces underlying the fluid description can lead to significant deviations from the nonstochastic solution at late times for alpha>0.001.
Modeling growth paths of interacting crack pairs in elastic media.
Ghelichi, Ramin; Kamrin, Ken
2015-10-28
The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the 'En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, linear elastic fracture mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps. PMID:26330342
Percentile growth charts for biomedical studies using a porcine model.
Corson, A M; Laws, J; Laws, A; Litten, J C; Lean, I J; Clarke, L
2008-12-01
Increasing rates of obesity and heart disease are compromising quality of life for a growing number of people. There is much research linking adult disease with the growth and development both in utero and during the first year of life. The pig is an ideal model for studying the origins of developmental programming. The objective of this paper was to construct percentile growth curves for the pig for use in biomedical studies. The body weight (BW) of pigs was recorded from birth to 150 days of age and their crown-to-rump length was measured over the neonatal period to enable the ponderal index (PI; kg/m3) to be calculated. Data were normalised and percentile curves were constructed using Cole's lambda-mu-sigma (LMS) method for BW and PI. The construction of these percentile charts for use in biomedical research will allow a more detailed and precise tracking of growth and development of individual pigs under experimental conditions. PMID:22444086
Causes of growth failure in growth failure in a model of neonatal zinc (Zn) deficiency
Technology Transfer Automated Retrieval System (TEKTRAN)
Zn deficiency is a common cause of growth failure in children in developing countrie,s and Zn supplementation can significantly improve growth of at-risk populations. Although Zn deficiency leads to anorexia and poor growth, it is unclear whether anorexia is the sole cause of poor growth. Our object...
BGFit: management and automated fitting of biological growth curves
2013-01-01
Background Existing tools to model cell growth curves do not offer a flexible integrative approach to manage large datasets and automatically estimate parameters. Due to the increase of experimental time-series from microbiology and oncology, the need for a software that allows researchers to easily organize experimental data and simultaneously extract relevant parameters in an efficient way is crucial. Results BGFit provides a web-based unified platform, where a rich set of dynamic models can be fitted to experimental time-series data, further allowing to efficiently manage the results in a structured and hierarchical way. The data managing system allows to organize projects, experiments and measurements data and also to define teams with different editing and viewing permission. Several dynamic and algebraic models are already implemented, such as polynomial regression, Gompertz, Baranyi, Logistic and Live Cell Fraction models and the user can add easily new models thus expanding current ones. Conclusions BGFit allows users to easily manage their data and models in an integrated way, even if they are not familiar with databases or existing computational tools for parameter estimation. BGFit is designed with a flexible architecture that focus on extensibility and leverages free software with existing tools and methods, allowing to compare and evaluate different data modeling techniques. The application is described in the context of bacterial and tumor cells growth data fitting, but it is also applicable to any type of two-dimensional data, e.g. physical chemistry and macroeconomic time series, being fully scalable to high number of projects, data and model complexity. PMID:24067087
Modeling the growth of an altered layer in mineral weathering
NASA Astrophysics Data System (ADS)
Reis, Fábio D. A. Aarão
2015-10-01
A stochastic reaction-diffusion model on a lattice is introduced to describe the growth kinetics of an altered layer in the weathering of a mineral. Particles R represent H2O that permanently fills the outer surface and diffuse on M (mineral) and A (altered) sites with coefficients DM and DA , respectively. The transformation M + R → A occurs with rate r, representing the irreversible formation of the altered material in a region of molecular size, viz. the lattice site of size a. These assumptions agree with predictions of the interfacial dissolution-reprecipitation mechanism, although the model does not describe the chemistry of dissolution reactions or precipitation processes. Scaling concepts are used to distinguish kinetic regimes and their crossovers, and are supported by simulation results. In the short time reactive regime, the thickness of the altered layer increases linearly in time and filling of that layer by particles R is high. In the long time diffusive regime, the altered layer thickness grows as (DA t) 1 / 2 . Modeling of single crystals require very small values of DM , which produces atomically narrow interfaces between the altered material and the mineral and absence of R in the latter, in agreement with recent experimental results. If r
Modeling dust growth in protoplanetary disks: The breakthrough case
NASA Astrophysics Data System (ADS)
Drążkowska, J.; Windmark, F.; Dullemond, C. P.
2014-07-01
Context. Dust coagulation in protoplanetary disks is one of the initial steps toward planet formation. Simple toy models are often not sufficient to cover the complexity of the coagulation process, and a number of numerical approaches are therefore used, among which integration of the Smoluchowski equation and various versions of the Monte Carlo algorithm are the most popular. Aims: Recent progress in understanding the processes involved in dust coagulation have caused a need for benchmarking and comparison of various physical aspects of the coagulation process. In this paper, we directly compare the Smoluchowski and Monte Carlo approaches to show their advantages and disadvantages. Methods: We focus on the mechanism of planetesimal formation via sweep-up growth, which is a new and important aspect of the current planet formation theory. We use realistic test cases that implement a distribution in dust collision velocities. This allows a single collision between two grains to have a wide range of possible outcomes but also requires a very high numerical accuracy. Results: For most coagulation problems, we find a general agreement between the two approaches. However, for the sweep-up growth driven by the "lucky" breakthrough mechanism, the methods exhibit very different resolution dependencies. With too few mass bins, the Smoluchowski algorithm tends to overestimate the growth rate and the probability of breakthrough. The Monte Carlo method is less dependent on the number of particles in the growth timescale aspect but tends to underestimate the breakthrough chance due to its limited dynamic mass range. Conclusions: We find that the Smoluchowski approach, which is generally better for the breakthrough studies, is sensitive to low mass resolutions in the high-mass, low-number tail that is important in this scenario. To study the low number density features, a new modulation function has to be introduced to the interaction probabilities. As the minimum resolution
The Biasing Effects of Unmodeled ARMA Time Series Processes on Latent Growth Curve Model Estimates
ERIC Educational Resources Information Center
Sivo, Stephen; Fan, Xitao; Witta, Lea
2005-01-01
The purpose of this study was to evaluate the robustness of estimated growth curve models when there is stationary autocorrelation among manifest variable errors. The results suggest that when, in practice, growth curve models are fitted to longitudinal data, alternative rival hypotheses to consider would include growth models that also specify…
ERIC Educational Resources Information Center
Kim, Su-Young
2012-01-01
Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the…
A Proposed Model for Protein Crystal Nucleation and Growth
NASA Technical Reports Server (NTRS)
Pusey, Marc; Curreri, Peter A. (Technical Monitor)
2002-01-01
How does one take a molecule, strongly asymmetric in both shape and charge distribution, and assemble it into a crystal? We propose a model for the nucleation and crystal growth process for tetragonal lysozyme, based upon fluorescence, light, neutron, and X-ray scattering data, size exclusion chromatography experiments, dialysis kinetics, AFM, and modeling of growth rate data, from this and other laboratories. The first species formed is postulated to be a 'head to side' dimer. Through repeating associations involving the same intermolecular interactions this grows to a 4(sub 3) helix structure, that in turn serves as the basic unit for nucleation and subsequent crystal growth. High salt attenuates surface charges while promoting hydrophobic interactions. Symmetry facilitates subsequent helix-helix self-association. Assembly stability is enhanced when a four helix structure is obtained, with each bound to two neighbors. Only two unique interactions are required. The first are those for helix formation, where the dominant interaction is the intermolecular bridging anion. The second is the anti-parallel side-by-side helix-helix interaction, guided by alternating pairs of symmetry related salt bridges along each side. At this stage all eight unique positions of the P4(sub3)2(sub 1),2(sub 1) unit cell are filled. The process is one of a) attenuating the most strongly interacting groups, such that b) the molecules begin to self-associate in defined patterns, so that c) symmetry is obtained, which d) propagates as a growing crystal. Simple and conceptually obvious in hindsight, this tells much about what we are empirically doing when we crystallize macromolecules. By adjusting the growth parameters we are empirically balancing the intermolecular interactions, preferentially attenuating the dominant strong (for lysozyme the charged groups) while strengthening the lesser strong (hydrophobic) interactions. In the general case for proteins the lack of a singularly defined
ERIC Educational Resources Information Center
Cassano, Christina Marie
2013-01-01
The present study used individual growth modeling to examine the role of specific forms (i.e., receptive, expressive, and definitional vocabulary and grammatical skill) and levels of oral vocabulary skill (i.e., 25th, 50th, or 75th percentile) in phonological awareness growth during the preschool and kindergarten years. Sixty-one,…
ERIC Educational Resources Information Center
Lash, Andrea; Makkonen, Reino; Tran, Loan; Huang, Min
2016-01-01
This study, undertaken at the request of the Nevada Department of Education, examined the stability over years of teacher-level growth scores from the Student Growth Percentile (SGP) model, which many states and districts have selected as a measure of effectiveness in their teacher evaluation systems. The authors conducted a generalizability study…
A simple growth model constructs critical avalanche networks.
Abbott, L F; Rohrkemper, R
2007-01-01
Neurons recorded from electrode arrays show a remarkable scaling property in their bursts of spontaneous activity, referred to as "avalanches" (Beggs and Plenz, 2003, 2004). Such scaling suggests a critical property in the coupling of these circuits. We show that similar scaling laws can arise in a simple model for the growth of neuronal processes. In the model (Van Ooyen and Van Pelt, 1994, 1996), the spatial range of the processes extending from each neuron is represented by a circle that grows or shrinks as a function of the average intracellular calcium concentration. Neurons interact when the circles corresponding to their processes intersect, with a strength proportional to the area of overlap. PMID:17925237
Information models of software productivity - Limits on productivity growth
NASA Technical Reports Server (NTRS)
Tausworthe, Robert C.
1992-01-01
Research into generalized information-metric models of software process productivity establishes quantifiable behavior and theoretical bounds. The models establish a fundamental mathematical relationship between software productivity and the human capacity for information traffic, the software product yield (system size), information efficiency, and tool and process efficiencies. An upper bound is derived that quantifies average software productivity and the maximum rate at which it may grow. This bound reveals that ultimately, when tools, methodologies, and automated assistants have reached their maximum effective state, further improvement in productivity can only be achieved through increasing software reuse. The reuse advantage is shown not to increase faster than logarithmically in the number of reusable features available. The reuse bound is further shown to be somewhat dependent on the reuse policy: a general 'reuse everything' policy can lead to a somewhat slower productivity growth than a specialized reuse policy.
A mathematical model of pre-diagnostic glioma growth.
Sturrock, Marc; Hao, Wenrui; Schwartzbaum, Judith; Rempala, Grzegorz A
2015-09-01
Due to their location, the malignant gliomas of the brain in humans are very difficult to treat in advanced stages. Blood-based biomarkers for glioma are needed for more accurate evaluation of treatment response as well as early diagnosis. However, biomarker research in primary brain tumors is challenging given their relative rarity and genetic diversity. It is further complicated by variations in the permeability of the blood brain barrier that affects the amount of marker released into the bloodstream. Inspired by recent temporal data indicating a possible decrease in serum glucose levels in patients with gliomas yet to be diagnosed, we present an ordinary differential equation model to capture early stage glioma growth. The model contains glioma-glucose-immune interactions and poses a potential mechanism by which this glucose drop can be explained. We present numerical simulations, parameter sensitivity analysis, linear stability analysis and a numerical experiment whereby we show how a dormant glioma can become malignant. PMID:26073722
Elasticity-based targeted growth models of morphogenesis.
Alford, Patrick W
2015-01-01
Embryonic tissue mechanics play an important role in regulating morphogenesis during organ formation, both in a bottom-up sense, where changes in gene expression drive mechanical shape changes, and in a top-down sense, where perturbations in tissue mechanics feed back to drive changes in gene expression. In growing tissues that can generate internal forces and have complex geometries, like those in the embryo, it can often be difficult to empirically determine the mechanical state of the tissue, let alone the relationships between gene expression and mechanical behavior. Mathematical models can be used to fill this gap. Here, we discuss elasticity-based models for growing tissues with a specific focus on targeted growth in embryonic tissues. PMID:25245704
An Evolutionary Hybrid Cellular Automaton Model of Solid Tumour Growth
Gerlee, P.; Anderson, A.R.A.
2007-01-01
We propose a cellular automaton model of solid tumour growth, in which each cell is equipped with a micro-environment response network. This network is modelled using a feed-forward artificial neural network, that takes environmental variables as an input and from these determines the cellular behaviour as the output. The response of the network is determined by connection weights and thresholds in the network, which are subject to mutations when the cells divide. As both available space and nutrients are limited resources for the tumour this gives rise to clonal evolution where only the fittest cells survive. Using this approach we have investigated the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. The results show that the oxygen concentration affects the selection pressure, cell population diversity and morphology of the tumour. A low oxygen concentration in the tissue gives rise to a tumour with a fingered morphology that contains aggressive phenotypes with a small apoptotic potential, while a high oxygen concentration in the tissue gives rise to a tumour with a round morphology containing less evolved phenotypes. The tissue oxygen concentration thus affects the tumour at both the morphological level and on the phenotype level. PMID:17374383
Network-based model of the growth of termite nests
NASA Astrophysics Data System (ADS)
Eom, Young-Ho; Perna, Andrea; Fortunato, Santo; Darrouzet, Eric; Theraulaz, Guy; Jost, Christian
2015-12-01
We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general.
Integrative models of vascular remodeling during tumor growth
Rieger, Heiko; Welter, Michael
2015-01-01
Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature that is in many respects different from the hierarchically organized arterio-venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. © 2015 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. PMID:25808551
Network-based model of the growth of termite nests.
Eom, Young-Ho; Perna, Andrea; Fortunato, Santo; Darrouzet, Eric; Theraulaz, Guy; Jost, Christian
2015-12-01
We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general. PMID:26764747
Modelling the interaction between flooding events and economic growth
NASA Astrophysics Data System (ADS)
Grames, Johanna; Grass, Dieter; Prskawetz, Alexia; Blöschl, Günther
2015-04-01
Socio-hydrology describes the interaction between the socio-economy, water and population dynamics. Recent models analyze the interplay of community risk-coping culture, flooding damage and economic growth (Di Baldassarre, 2013, Viglione, 2014). These models descriptively explain the feedbacks between socio-economic development and natural disasters like floods. Contrary to these descriptive models, our approach develops an optimization model, where the intertemporal decision of an economic agent interacts with the hydrological system. This is the first economic growth model describing the interaction between the consumption and investment decisions of an economic agent and the occurrence of flooding events: Investments in defense capital can avoid floods even when the water level is high, but on the other hand such investment competes with investment in productive capital and hence may reduce the level of consumption. When floods occur, the flood damage therefore depends on the existing defense capital. The aim is to find an optimal tradeoff between investments in productive versus defense capital such as to optimize the stream of consumption in the long-term. We assume a non-autonomous exogenous periodic rainfall function (Yevjevich et.al. 1990, Zakaria 2001) which implies that the long-term equilibrium will be periodic . With our model we aim to derive mechanisms that allow consumption smoothing in the long term, and at the same time allow for optimal investment in flood defense to maximize economic output. We choose an aggregate welfare function that depends on the consumption level of the society as the objective function. I.e. we assume a social planer with perfect foresight that maximizes the aggregate welfare function. Within our model framework we can also study whether the path and level of defense capital (that protects people from floods) is related to the time preference rate of the social planner. Our model also allows to investigate how the frequency
Modelling spatial patterns of urban growth in Africa.
Linard, Catherine; Tatem, Andrew J; Gilbert, Marius
2013-10-01
The population of Africa is predicted to double over the next 40 years, driving exceptionally high urban expansion rates that will induce significant socio-economic, environmental and health changes. In order to prepare for these changes, it is important to better understand urban growth dynamics in Africa and better predict the spatial pattern of rural-urban conversions. Previous work on urban expansion has been carried out at the city level or at the global level with a relatively coarse 5-10 km resolution. The main objective of the present paper was to develop a modelling approach at an intermediate scale in order to identify factors that influence spatial patterns of urban expansion in Africa. Boosted Regression Tree models were developed to predict the spatial pattern of rural-urban conversions in every large African city. Urban change data between circa 1990 and circa 2000 available for 20 large cities across Africa were used as training data. Results showed that the urban land in a 1 km neighbourhood and the accessibility to the city centre were the most influential variables. Results obtained were generally more accurate than results obtained using a distance-based urban expansion model and showed that the spatial pattern of small, compact and fast growing cities were easier to simulate than cities with lower population densities and a lower growth rate. The simulation method developed here will allow the production of spatially detailed urban expansion forecasts for 2020 and 2025 for Africa, data that are increasingly required by global change modellers. PMID:25152552
Modelling spatial patterns of urban growth in Africa
Linard, Catherine; Tatem, Andrew J.; Gilbert, Marius
2013-01-01
The population of Africa is predicted to double over the next 40 years, driving exceptionally high urban expansion rates that will induce significant socio-economic, environmental and health changes. In order to prepare for these changes, it is important to better understand urban growth dynamics in Africa and better predict the spatial pattern of rural-urban conversions. Previous work on urban expansion has been carried out at the city level or at the global level with a relatively coarse 5–10 km resolution. The main objective of the present paper was to develop a modelling approach at an intermediate scale in order to identify factors that influence spatial patterns of urban expansion in Africa. Boosted Regression Tree models were developed to predict the spatial pattern of rural-urban conversions in every large African city. Urban change data between circa 1990 and circa 2000 available for 20 large cities across Africa were used as training data. Results showed that the urban land in a 1 km neighbourhood and the accessibility to the city centre were the most influential variables. Results obtained were generally more accurate than results obtained using a distance-based urban expansion model and showed that the spatial pattern of small, compact and fast growing cities were easier to simulate than cities with lower population densities and a lower growth rate. The simulation method developed here will allow the production of spatially detailed urban expansion forecasts for 2020 and 2025 for Africa, data that are increasingly required by global change modellers. PMID:25152552
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J.; Tierz, Miguel
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Nutrient-controlled growth of Skeletonema costatum: an applied model
NASA Astrophysics Data System (ADS)
Sun, Ke; Qiu, Zhongfeng; He, Yijun; Yin, Baoshu
2014-05-01
To model Skeletonema costatum blooms and their relationship with environmental parameters in situ, a S. costatum-specific zero-dimensional box model based on the mechanistic model Eco3M was established using physiological features. The parameters were calibrated using experimental counterparts, and simulations were compared with published laboratory findings. The resulting normalized objective function (NOF) values are less than 1.0 (and in most cases less than 0.58) and the values for the slope γ (between 0.656 7-1.127 4) and R 2 (between 0.806 8-0.971) are close to 1.0 for most of the sub-figures. This indicates good agreement between simulated and measured data and suggests that the model reproduces the general characteristics of S. costatum growth and use of nutrients under different N- or P-limiting conditions. The model is appropriate for further applications and can be used to test more scenarios using other nutrients.
Collective mechanochemical growth of carbon nanotubes
NASA Astrophysics Data System (ADS)
Bedewy, Mostafa M. K. M. A.
Hierarchically ordered carbon nanotubes (CNTs) are promising for integration in high-performance structural composites, electrical interconnects, thermal interfaces, and filtration membranes. These and other applications require CNTs that are monodisperse, well aligned, and densely packed. Moreover, because more than 1 billion CNTs per square centimeter grow simultaneously in a typical chemical vapor deposition (CVD) process, understanding the collective chemical and mechanical effects of growth is key to engineering the properties of CNT-based materials. This dissertation presents tailored synthesis processes, characterization techniques, and mathematical models that enable improved control of the morphology of as-grown CNT "forests.". First, a comprehensive characterization methodology, combining synchrotron X-ray scattering and attenuation with real-time height kinetics, enabled mapping the spatiotemporal evolution of CNT diameter distribution, alignment and density. By this method, the forest mass kinetics were measured and found to follow the S-shaped Gompertz curve of population growth. Dividing a forest into subpopulations revealed size-dependent activation-deactivation competition. Additionally, in situ transmission electron microscopy (TEM) showed that the kinetics of CNT nucleation are S-shaped. Based on these findings, a collective growth model is proposed, wherein randomly oriented CNTs first nucleate then self-organize and lift-off during a crowding stage, followed by a density decay stage until self-termination when the density drops below the self-supporting threshold. Next, further X-ray data analysis enabled modeling the mechanics of entangled CNTs and proved that mechanical coupling is not only responsible for the self-organization into the aligned morphology, but is also an important limiting mechanism as significant forces ensue from diameter-dependent CNT growth rates. A custom-built CVD system was used for mechanical manipulation of growing
Fernández-Navarro, Francisco; Valero, Antonio; Hervás-Martínez, César; Gutiérrez, Pedro A; García-Gimeno, Rosa M; Zurera-Cosano, Gonzalo
2010-07-15
Boundary models have been recognized as useful tools to predict the ability of microorganisms to grow at limiting conditions. However, at these conditions, microbial behaviour can vary, being difficult to distinguish between growth or no growth. In this paper, the data from the study of Valero et al. [Valero, A., Pérez-Rodríguez, F., Carrasco, E., Fuentes-Alventosa, J.M., García-Gimeno, R.M., Zurera, G., 2009. Modelling the growth boundaries of Staphylococcus aureus: Effect of temperature, pH and water activity. International Journal of Food Microbiology 133 (1-2), 186-194] belonging to growth/no growth conditions of Staphylococcus aureus against temperature, pH and a(w) were divided into three categorical classes: growth (G), growth transition (GT) and no growth (NG). Subsequently, they were modelled by using a Radial Basis Function Neural Network (RBFNN) in order to create a multi-classification model that was able to predict the probability of belonging at one of the three mentioned classes. The model was developed through an over sampling procedure using a memetic algorithm (MA) in order to balance in part the size of the classes and to improve the accuracy of the classifier. The multi-classification model, named Smote Memetic Radial Basis Function (SMRBF) provided a quite good adjustment to data observed, being able to correctly classify the 86.30% of training data and the 82.26% of generalization data for the three observed classes in the best model. Besides, the high number of replicates per condition tested (n=30) produced a smooth transition between growth and no growth. At the most stringent conditions, the probability of belonging to class GT was higher, thus justifying the inclusion of the class in the new model. The SMRBF model presented in this study can be used to better define microbial growth/no growth interface and the variability associated to these conditions so as to apply this knowledge to a food safety in a decision-making process. PMID
Growth Mixture Modeling: Application to Reading Achievement Data from a Large-Scale Assessment
ERIC Educational Resources Information Center
Bilir, Mustafa Kuzey; Binici, Salih; Kamata, Akihito
2008-01-01
The popularity of growth modeling has increased in psychological and cognitive development research as a means to investigate patterns of changes and differences between observation units over time. Random coefficient modeling, such as multilevel modeling and latent growth curve modeling as a special application of structural equation modeling are…
Avalanche dynamics in evolution, growth, and depinning models
NASA Astrophysics Data System (ADS)
Paczuski, Maya; Maslov, Sergei; Bak, Per
1996-01-01
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of 1/f noise, diffusion with anomalous Hurst exponents, Lévy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in d spatial plus one temporal dimension. The complex state can be reached either by tuning a parameter, or it can be self-organized. We present two exact equations for the avalanche behavior in the latter case. (1) The slow approach to the critical attractor, i.e., the process of self-organization, is governed by a ``gap'' equation for the divergence of avalanche sizes. (2) The hierarchical structure of avalanches is described by an equation for the average number of sites covered by an avalanche. The exponent γ governing the approach to the critical state appears as a constant rather than as a critical exponent. In addition, the conservation of activity in the stationary state manifests itself through the superuniversal result η=0. The exponent π for the Lévy flight jumps between subsequent active sites can be related to other critical exponents through a study of ``backward avalanches.'' We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with
Gysemans, K P M; Bernaerts, K; Vermeulen, A; Geeraerd, A H; Debevere, J; Devlieghere, F; Van Impe, J F
2007-03-20
Several model types have already been developed to describe the boundary between growth and no growth conditions. In this article two types were thoroughly studied and compared, namely (i) the ordinary (linear) logistic regression model, i.e., with a polynomial on the right-hand side of the model equation (type I) and (ii) the (nonlinear) logistic regression model derived from a square root-type kinetic model (type II). The examination was carried out on the basis of the data described in Vermeulen et al. [Vermeulen, A., Gysemans, K.P.M., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2006-this issue. Influence of pH, water activity and acetic acid concentration on Listeria monocytogenes at 7 degrees C: data collection for the development of a growth/no growth model. International Journal of Food Microbiology. .]. These data sets consist of growth/no growth data for Listeria monocytogenes as a function of water activity (0.960-0.990), pH (5.0-6.0) and acetic acid percentage (0-0.8% (w/w)), both for a monoculture and a mixed strain culture. Numerous replicates, namely twenty, were performed at closely spaced conditions. In this way detailed information was obtained about the position of the interface and the transition zone between growth and no growth. The main questions investigated were (i) which model type performs best on the monoculture and the mixed strain data, (ii) are there differences between the growth/no growth interfaces of monocultures and mixed strain cultures, (iii) which parameter estimation approach works best for the type II models, and (iv) how sensitive is the performance of these models to the values of their nonlinear-appearing parameters. The results showed that both type I and II models performed well on the monoculture data with respect to goodness-of-fit and predictive power. The type I models were, however, more sensitive to anomalous data points. The situation was different for the mixed strain culture. In
A Morpho-Elastic Model of Hyphal Tip Growth in Filamentous Organisms
NASA Astrophysics Data System (ADS)
Goriely, A.; Tabor, M.; Tongen, A.
The growth of filamentous cells is modeled through the use of exact, nonlinear, elasticity theory for shells and membranes. The biomechanical model is able to capture the generic features of growth of a broad array of cells including actinomycetes, fungi, and root hairs. It also provides the means of studying the effects of external surface stresses. The growth mechanism is modeled by a process of incremental elastic growth in which the cell wall responds elastically to the continuous addition of new material.
Modelling of frost formation and growth on microstuctured surface
NASA Astrophysics Data System (ADS)
Muntaha, Md. Ali; Haider, Md. Mushfique; Rahman, Md. Ashiqur
2016-07-01
Frost formation on heat exchangers is an undesirable phenomenon often encountered in different applications where the cold surface with a temperature below freezing point of water is exposed to humid air. The formation of frost on the heat transfer surface results in an increase in pressure drop and reduction in heat transfer, resulting in a reduction of the system efficiency. Many factors, including the temperature and moisture content of air, cold plate temperature, surface wettability etc., are known to affect frost formation and growth. In our present study, a model for frost growth on rectangular, periodic microgroove surfaces for a range of microgroove dimension (ten to hundreds of micron) is presented. The mathematical model is developed analytically by solving the governing heat and mass transfer equations with appropriate boundary conditions using the EES (Engineering Equation Solver) software. For temperature, a convective boundary condition at frost-air interface and a fixed cold plate surface temperature is used. Instead of considering the saturation or super-saturation models, density gradient at the surface is obtained by considering experimentally-found specified heat flux. The effect of surface wettability is incorporated by considering the distribution of condensed water droplets at the early stage of frost formation. Thickness, density and thermal conductivity of frost layer on the micro-grooved surfaces are found to vary with the dimension of the grooves. The variation of density and thickness of the frost layer on these micro-grooved surfaces under natural convection is numerally determined for a range of plate temperature and air temperature conditions and is compared with experimental results found in the open literature.
Formation of algae growth constitutive relations for improved algae modeling.
Gharagozloo, Patricia E.; Drewry, Jessica L.
2013-01-01
This SAND report summarizes research conducted as a part of a two year Laboratory Directed Research and Development (LDRD) project to improve our abilities to model algal cultivation. Algae-based biofuels have generated much excitement due to their potentially large oil yield from relatively small land use and without interfering with the food or water supply. Algae mitigate atmospheric CO2 through metabolism. Efficient production of algal biofuels could reduce dependence on foreign oil by providing a domestic renewable energy source. Important factors controlling algal productivity include temperature, nutrient concentrations, salinity, pH, and the light-to-biomass conversion rate. Computational models allow for inexpensive predictions of algae growth kinetics in these non-ideal conditions for various bioreactor sizes and geometries without the need for multiple expensive measurement setups. However, these models need to be calibrated for each algal strain. In this work, we conduct a parametric study of key marine algae strains and apply the findings to a computational model.
Modeling microalgal growth in an airlift-driven raceway reactor.
Ketheesan, Balachandran; Nirmalakhandan, Nagamany
2013-05-01
In previous proof-of-concept studies, feasibility of a new airlift-raceway configuration and its energetic advantage and improved CO2 utilization efficiency over the traditional raceways and photobioreactors have been documented. In the current study, a mathematical model for predicting biomass growth in the airlift-raceway reactor is presented, which includes supply and transfer of CO2 and the synergetic effects of light, CO2, nitrogen, and temperature. The model was calibrated and validated with data from prototype scale versions of the reactor on two test species: Nannochloropsis salina and Scenedesmus sp., cultivated under indoor and outdoor conditions. Predictions of biomass concentrations by the proposed model agreed well with the temporal trend of the experimental data, with r(2) ranging from 0.96 to 0.98, p<0.001. A sensitivity analysis of the 10 model parameters used in this study revealed that only three of them were significant, with sensitivity coefficients ranging from 0.08 to 0.13. PMID:23603218
Growth, efficiency, and yield of commercial broilers from 1957, 1978, and 20051
Zuidhof, M. J.; Schneider, B. L.; Carney, V. L.; Korver, D. R.; Robinson, F. E.
2014-01-01
The effect of commercial selection on the growth, efficiency, and yield of broilers was studied using 2 University of Alberta Meat Control strains unselected since 1957 and 1978, and a commercial Ross 308 strain (2005). Mixed-sex chicks (n = 180 per strain) were placed into 4 replicate pens per strain, and grown on a current nutritional program to 56 d of age. Weekly front and side profile photographs of 8 birds per strain were collected. Growth rate, feed intake, and measures of feed efficiency including feed conversion ratio, residual feed intake, and residual maintenance energy requirements were characterized. A nonlinear mixed Gompertz growth model was used to predict BW and BW variation, useful for subsequent stochastic growth simulation. Dissections were conducted on 8 birds per strain semiweekly from 21 to 56 d of age to characterize allometric growth of pectoralis muscles, leg meat, abdominal fat pad, liver, gut, and heart. A novel nonlinear analysis of covariance was used to test the hypothesis that allometric growth patterns have changed as a result of commercial selection pressure. From 1957 to 2005, broiler growth increased by over 400%, with a concurrent 50% reduction in feed conversion ratio, corresponding to a compound annual rate of increase in 42 d live BW of 3.30%. Forty-two-day FCR decreased by 2.55% each year over the same 48-yr period. Pectoralis major growth potential increased, whereas abdominal fat decreased due to genetic selection pressure over the same time period. From 1957 to 2005, pectoralis minor yield at 42 d of age was 30% higher in males and 37% higher in females; pectoralis major yield increased by 79% in males and 85% in females. Over almost 50 yr of commercial quantitative genetic selection pressure, intended beneficial changes have been achieved. Unintended changes such as enhanced sexual dimorphism are likely inconsequential, though musculoskeletal, immune function, and parent stock management challenges may require additional
Habitat and density-dependent growth of the sea urchin Paracentrotus lividus in Galicia (NW Spain)
NASA Astrophysics Data System (ADS)
Ouréns, Rosana; Flores, Luis; Fernández, Luis; Freire, Juan
2013-02-01
We studied the small-scale spatial variability in the growth of Paracentrotus lividus in two populations in Galicia (NW Spain) by reading growth rings. A tetracycline marking experiment was carried out to verify that the rings form annually. The growth rings were read by two independent readers in order to estimate the uncertainty involved in assigning the age. Of the six growth models evaluated (Tanaka, von Bertalanffy, Gompertz, Richards, logistic and Jolicoeur) the Tanaka function obtained the best fit to the data. This function predicts unlimited growth and a maximum growth rate of 15.00 (± 0.97 SE) mm·year- 1 at 3.09 ± 0.10 years old, which progressively decreases at older ages. However, habitat characteristics lead to intrapopulation variations in this general function. Recruitment seems to occur mainly in shallow waters (≤ 4 m) and when the sea urchins reach 50 mm (approximately 4 years old) they migrate to deeper areas. Sea urchins larger than 50 mm that stayed in shallow waters grew at a rate between 0.41 and 0.43 mm·year- 1 less than the sea urchins that moved to depths of 8 and 12 m. The population density also influenced the growth, and individuals older than 4 years had higher growth rates in high-density patches than in low-density areas. This could be due to the better environmental conditions in aggregation areas, that is, better protection against waves and predators and/or more abundant food.
Ignition and Growth Modeling of LX-17 Hockey Puck Experiments
Tarver, C M
2004-04-19
Detonating solid plastic bonded explosives (PBX) formulated with the insensitive molecule triaminotrinitrobenzene (TATB) exhibit measurable reaction zone lengths, curved shock fronts, and regions of failing chemical reaction at abrupt changes in the charge geometry. A recent set of ''hockey puck'' experiments measured the breakout times of diverging detonation waves in ambient temperature LX-17 (92.5 % TATB plus 7.5% Kel-F binder) and the breakout times at the lower surfaces of 15 mm thick LX-17 discs placed below the detonator-booster plane. The LX-17 detonation waves in these discs grow outward from the initial wave leaving regions of unreacted or partially reacted TATB in the corners of these charges. This new experimental data is accurately simulated for the first time using the Ignition and Growth reactive flow model for LX-17, which is normalized to a great deal of detonation reaction zone, failure diameter and diverging detonation data. A pressure cubed dependence for the main growth of reaction rate yields excellent agreement with experiment, while a pressure squared rate diverges too quickly and a pressure quadrupled rate diverges too slowly in the LX-17 below the booster equatorial plane.
Genomic Heritability of Bovine Growth Using a Mixed Model
Ryu, Jihye; Lee, Chaeyoung
2014-01-01
This study investigated heritability for bovine growth estimated with genomewide single nucleotide polymorphism (SNP) information obtained from a DNA microarray chip. Three hundred sixty seven Korean cattle were genotyped with the Illumina BovineSNP50 BeadChip, and 39,112 SNPs of 364 animals filtered by quality assurance were analyzed to estimate heritability of body weights at 6, 9, 12, 15, 18, 21, and 24 months of age. Restricted maximum likelihood estimate of heritability was obtained using covariance structure of genomic relationships among animals in a mixed model framework. Heritability estimates ranged from 0.58 to 0.76 for body weights at different ages. The heritability estimates using genomic information in this study were larger than those which had been estimated previously using pedigree information. The results revealed a trend that the heritability for body weight increased at a younger age (6 months). This suggests an early genetic evaluation for bovine growth using genomic information to increase genetic merits of animals. PMID:25358309
A biological model for controlling interface growth and morphology.
Hoyt, Jeffrey John; Holm, Elizabeth Ann
2004-01-01
Biological systems create proteins that perform tasks more efficiently and precisely than conventional chemicals. For example, many plants and animals produce proteins to control the freezing of water. Biological antifreeze proteins (AFPs) inhibit the solidification process, even below the freezing point. These molecules bond to specific sites at the ice/water interface and are theorized to suppress solidification chemically or geometrically. In this project, we investigated the theoretical and experimental data on AFPs and performed analyses to understand the unique physics of AFPs. The experimental literature was analyzed to determine chemical mechanisms and effects of protein bonding at ice surfaces, specifically thermodynamic freezing point depression, suppression of ice nucleation, decrease in dendrite growth kinetics, solute drag on the moving solid/liquid interface, and stearic pinning of the ice interface. Stearic pinning was found to be the most likely candidate to explain experimental results, including freezing point depression, growth morphologies, and thermal hysteresis. A new stearic pinning model was developed and applied to AFPs, with excellent quantitative results. Understanding biological antifreeze mechanisms could enable important medical and engineering applications, but considerable future work will be necessary.
Mejlholm, Ole; Dalgaard, Paw
2013-10-15
A new and extensive growth and growth boundary model for psychrotolerant Lactobacillus spp. was developed and validated for processed and unprocessed products of seafood and meat. The new model was developed by refitting and expanding an existing cardinal parameter model for growth and the growth boundary of lactic acid bacteria (LAB) in processed seafood (O. Mejlholm and P. Dalgaard, J. Food Prot. 70. 2485-2497, 2007). Initially, to estimate values for the maximum specific growth rate at the reference temperature of 25 °C (μref) and the theoretical minimum temperature that prevents growth of psychrotolerant LAB (T(min)), the existing LAB model was refitted to data from experiments with seafood and meat products reported not to include nitrite or any of the four organic acids evaluated in the present study. Next, dimensionless terms modelling the antimicrobial effect of nitrite, and acetic, benzoic, citric and sorbic acids on growth of Lactobacillus sakei were added to the refitted model, together with minimum inhibitory concentrations determined for the five environmental parameters. The new model including the effect of 12 environmental parameters, as well as their interactive effects, was successfully validated using 229 growth rates (μ(max) values) for psychrotolerant Lactobacillus spp. in seafood and meat products. Average bias and accuracy factor values of 1.08 and 1.27, respectively, were obtained when observed and predicted μ(max) values of psychrotolerant Lactobacillus spp. were compared. Thus, on average μ(max) values were only overestimated by 8%. The performance of the new model was equally good for seafood and meat products, and the importance of including the effect of acetic, benzoic, citric and sorbic acids and to a lesser extent nitrite in order to accurately predict growth of psychrotolerant Lactobacillus spp. was clearly demonstrated. The new model can be used to predict growth of psychrotolerant Lactobacillus spp. in seafood and meat
NE Ohio Urban Growth Monitoring and Modeling Prototype. Revised
NASA Technical Reports Server (NTRS)
Siebert, Loren; Klosterman, Richard E.
2001-01-01
At the University of Akron, Dr. Loren Siebert, Dr. Richard Klosterman, and their graduate research assistants (Jung-Wook Kim, Mohammed Hoque, Aziza Parveen, and Ben Stabler) worked on the integration of remote sensing and GIs-based planning support systems. The primary goal of the project was to develop methods that use remote sensing land cover mapping and GIs-based modeling to monitor and project urban growth and farmland loss in northeast Ohio. Another research goal has been to use only GIS data that are accessible via the World Wide Web, to determine whether Ohio's small counties and townships that do not currently have parcel-level GIS systems can apply these techniques. The project was jointly funded by NASA and USGS OhioView grants during the 2000-2001 academic year; the work is now being continued under a USGS grant.
Growth of transition metals on cerium tungstate model catalyst layers.
Skála, T; Tsud, N; Stetsovych, V; Mysliveček, J; Matolín, V
2016-10-01
Two model catalytic metal/oxide systems were investigated by photoelectron spectroscopy and scanning tunneling microscopy. The mixed-oxide support was a cerium tungstate epitaxial thin layer grown in situ on the W(1 1 0) single crystal. Active particles consisted of palladium and platinum 3D islands deposited on the tungstate surface at 300 K. Both metals were found to interact weakly with the oxide support and the original chemical state of both support and metals was mostly preserved. Electronic and morphological changes are discussed during the metal growth and after post-annealing at temperatures up to 700 K. Partial transition-metal coalescence and self-cleaning from the CO and carbon impurities were observed. PMID:27494195
A model for pore growth in anodically etched gallium phosphide
NASA Astrophysics Data System (ADS)
Ricci, P. C.; Salis, M.; Anedda, A.
2005-06-01
The electrochemical etching process of porous gallium phosphide was studied by means of the characteristic current-potential (I-V) curves. Measurements were performed in H2SO4 0.5-M aqueous solution both in the dark and by illuminating the samples with the 351-nm line of an argon laser. Raman spectroscopy was applied to investigate the surface morphology of the samples prepared under different anodizing conditions within the potentiostatic regime. Based on a few reasonable assumptions, a simple model of pore growth is proposed. The enhancing effect in current intensity due to the branching of pores and the opposite effect due to a concomitant decrease in the effective cross area available for carrier transport are accounted for to explain the main features of the recorded I -V curves.
Mirzaei, H R; Pitchford, W S; Verbyla, A P
2011-01-01
Two analyses, cubic and piecewise random regression, were conducted to model growth of crossbred cattle from birth to about two years of age, investigating the ability of a piecewise procedure to fit growth traits without the complications of the cubic model. During a four-year period (1994-1997) of the Australian "Southern Crossbreeding Project", mature Hereford cows (N = 581) were mated to 97 sires of Angus, Belgian Blue, Hereford, Jersey, Limousin, South Devon, and Wagyu breeds, resulting in 1141 steers and heifers born over four years. Data included 13 (for steers) and eight (for heifers) live body weight measurements, made approximately every 50 days from birth until slaughter. The mixed model included fixed effects of sex, sire breed, age (linear, quadratic and cubic), and their interactions between sex and sire breed with age. Random effects were sire, dam, management (birth location, year, post-weaning groups), and permanent environmental effects and for each of these when possible, their interactions with linear, quadratic and cubic growth. In both models, body weights of all breeds increased over pre-weaning period, held fairly steady (slightly flattening) over the dry season then increased again towards the end of the feedlot period. The number of estimated parameters for the cubic model was 22 while for the piecewise model it was 32. It was concluded that the piecewise model was very similar to the cubic model in the fit to the data; with the piecewise model being marginally better. The piecewise model seems to fit the data better at the end of the growth period. PMID:21968730
Overview: early history of crop growth and photosynthesis modeling.
El-Sharkawy, Mabrouk A
2011-02-01
As in industrial and engineering systems, there is a need to quantitatively study and analyze the many constituents of complex natural biological systems as well as agro-ecosystems via research-based mechanistic modeling. This objective is normally addressed by developing mathematically built descriptions of multilevel biological processes to provide biologists a means to integrate quantitatively experimental research findings that might lead to a better understanding of the whole systems and their interactions with surrounding environments. Aided with the power of computational capacities associated with computer technology then available, pioneering cropping systems simulations took place in the second half of the 20th century by several research groups across continents. This overview summarizes that initial pioneering effort made to simulate plant growth and photosynthesis of crop canopies, focusing on the discovery of gaps that exist in the current scientific knowledge. Examples are given for those gaps where experimental research was needed to improve the validity and application of the constructed models, so that their benefit to mankind was enhanced. Such research necessitates close collaboration among experimentalists and model builders while adopting a multidisciplinary/inter-institutional approach. PMID:20826195
Growth and Division in a Dynamic Protocell Model
Villani, Marco; Filisetti, Alessandro; Graudenzi, Alex; Damiani, Chiara; Carletti, Timoteo; Serra, Roberto
2014-01-01
In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of “genetic memory molecules” (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells. PMID:25479130
Growth and division in a dynamic protocell model.
Villani, Marco; Filisetti, Alessandro; Graudenzi, Alex; Damiani, Chiara; Carletti, Timoteo; Serra, Roberto
2014-01-01
In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of "genetic memory molecules" (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells. PMID:25479130
A statistical model of diurnal variation in human growth hormone
NASA Technical Reports Server (NTRS)
Klerman, Elizabeth B.; Adler, Gail K.; Jin, Moonsoo; Maliszewski, Anne M.; Brown, Emery N.
2003-01-01
The diurnal pattern of growth hormone (GH) serum levels depends on the frequency and amplitude of GH secretory events, the kinetics of GH infusion into and clearance from the circulation, and the feedback of GH on its secretion. We present a two-dimensional linear differential equation model based on these physiological principles to describe GH diurnal patterns. The model characterizes the onset times of the secretory events, the secretory event amplitudes, as well as the infusion, clearance, and feedback half-lives of GH. We illustrate the model by using maximum likelihood methods to fit it to GH measurements collected in 12 normal, healthy women during 8 h of scheduled sleep and a 16-h circadian constant-routine protocol. We assess the importance of the model components by using parameter standard error estimates and Akaike's Information Criterion. During sleep, both the median infusion and clearance half-life estimates were 13.8 min, and the median number of secretory events was 2. During the constant routine, the median infusion half-life estimate was 12.6 min, the median clearance half-life estimate was 11.7 min, and the median number of secretory events was 5. The infusion and clearance half-life estimates and the number of secretory events are consistent with current published reports. Our model gave an excellent fit to each GH data series. Our analysis paradigm suggests an approach to decomposing GH diurnal patterns that can be used to characterize the physiological properties of this hormone under normal and pathological conditions.
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth
Armstrong, Michelle Hine; Buganza Tepole, Adrián; Kuhl, Ellen; Simon, Bruce R.; Vande Geest, Jonathan P.
2016-01-01
The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues. PMID:27078495
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.
Armstrong, Michelle Hine; Buganza Tepole, Adrián; Kuhl, Ellen; Simon, Bruce R; Vande Geest, Jonathan P
2016-01-01
The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues. PMID:27078495
Analysis of growth curves of fowl. I. Chickens.
Knízetová, H; Hyánek, J; Kníze, B; Roubícek, J
1991-12-01
1. The Richards function was used to describe the growth curves (n = 989) of 9 broiler lines. Chickens were fed ad libitum and body weight was recorded every second week from hatching to 26 weeks of age. 2. The accuracy of curve fit measured by the coefficient of determination (R2) was better for males than for females (0.9986-0.9995 vs 0.9972-0.9988, respectively). 3. The estimation of the asymptotic final weight (A) for different lines enabled the degree of maturity (ut = yt/A) to be determined at any fixed point of the curve. At the age of 7 weeks this had a value of 0.318-0.369 for cockerels and 0.325-0.377 for pullets and represented the slaughter maturity of individual lines. The ratio of inflection/asymptotic weight (y+/A = 0.370-0.388) indicated that in some cases chicken growth can be described approximately by the Gompertz function (y+/A = 0.368). 4. It was found that the age at the inflection point of curves (t+ 48.2-55.7 d for cockerels and t+ = 47.8-52.8 d for pullets) roughly corresponds to the slaughter age of the chickens. 5. The interline differences in the parameters of maturation rate for weight (y+/A, k, t+, u7) are low in comparison with the differences in body weight (A, y+, y7) and absolute growth rate (v, v+). 6. The intragroup phenotypic correlation among growth parameters and the importance of the mathematical models are discussed. PMID:1786568
Investigating Stage-Sequential Growth Mixture Models with Multiphase Longitudinal Data
ERIC Educational Resources Information Center
Kim, Su-Young; Kim, Jee-Seon
2012-01-01
This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand…
Specification Search for Identifying the Correct Mean Trajectory in Polynomial Latent Growth Models
ERIC Educational Resources Information Center
Kim, Minjung; Kwok, Oi-Man; Yoon, Myeongsun; Willson, Victor; Lai, Mark H. C.
2016-01-01
This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting…
Comparison of Primary Models to Predict Microbial Growth by the Plate Count and Absorbance Methods
Pla, María-Leonor; Oltra, Sandra; Esteban, María-Dolores; Andreu, Santiago; Palop, Alfredo
2015-01-01
The selection of a primary model to describe microbial growth in predictive food microbiology often appears to be subjective. The objective of this research was to check the performance of different mathematical models in predicting growth parameters, both by absorbance and plate count methods. For this purpose, growth curves of three different microorganisms (Bacillus cereus, Listeria monocytogenes, and Escherichia coli) grown under the same conditions, but with different initial concentrations each, were analysed. When measuring the microbial growth of each microorganism by optical density, almost all models provided quite high goodness of fit (r2 > 0.93) for all growth curves. The growth rate remained approximately constant for all growth curves of each microorganism, when considering one growth model, but differences were found among models. Three-phase linear model provided the lowest variation for growth rate values for all three microorganisms. Baranyi model gave a variation marginally higher, despite a much better overall fitting. When measuring the microbial growth by plate count, similar results were obtained. These results provide insight into predictive microbiology and will help food microbiologists and researchers to choose the proper primary growth predictive model. PMID:26539483
Comparison of Primary Models to Predict Microbial Growth by the Plate Count and Absorbance Methods.
Pla, María-Leonor; Oltra, Sandra; Esteban, María-Dolores; Andreu, Santiago; Palop, Alfredo
2015-01-01
The selection of a primary model to describe microbial growth in predictive food microbiology often appears to be subjective. The objective of this research was to check the performance of different mathematical models in predicting growth parameters, both by absorbance and plate count methods. For this purpose, growth curves of three different microorganisms (Bacillus cereus, Listeria monocytogenes, and Escherichia coli) grown under the same conditions, but with different initial concentrations each, were analysed. When measuring the microbial growth of each microorganism by optical density, almost all models provided quite high goodness of fit (r(2) > 0.93) for all growth curves. The growth rate remained approximately constant for all growth curves of each microorganism, when considering one growth model, but differences were found among models. Three-phase linear model provided the lowest variation for growth rate values for all three microorganisms. Baranyi model gave a variation marginally higher, despite a much better overall fitting. When measuring the microbial growth by plate count, similar results were obtained. These results provide insight into predictive microbiology and will help food microbiologists and researchers to choose the proper primary growth predictive model. PMID:26539483
Micro/macro solidification modeling of columnar eutectic growth
NASA Astrophysics Data System (ADS)
Judson, Ward Michael
2000-11-01
A general multidimensional model of alloy solidification is presented in which a velocity-dependent freezing temperature is coupled with the macroscale energy equation. The velocity dependence of the freezing temperature ( Tf˜v ) results from the microscale species diffusion for microstructures with coupled eutectic growth. At solidification rates ( ˜ 1--10 mm/s) that are representative of gravity permanent mold and die casting processes, consideration of the nonequilibrium conditions at the interface affects the prediction of the macroscale thermal field. Near-eutectic alloys freeze with a macroscopically discrete solid-liquid interface at a temperature below the equilibrium eutectic temperature. The model is illustrated with unidirectional solidification of a near-eutectic alloy in a finite domain and solved numerically with a fixed-grid Galerkin finite element method. The numerical algorithm includes inexpensive steps to compute the interface speed explicitly. By nondimensionalizing the governing equations the effect of coupled eutectic growth on heat transport is clearly identified so that the model's sensitivity to important parameters can be investigated. Additionally, the average eutectic spacing can be determined with the temperature field, rather than post-determination from a standard, uncoupled solution of the energy equation. The eutectic coupling results indicate that the predicted solid-liquid interface location lags behind the uncoupled solution; therefore, decreasing the amount of solid formed, increasing the total solidification time, and increasing the average eutectic spacing. A procedure is also illustrated for computing mechanical properties using experimental correlations and the computed interface velocity history. The effect of the eutectic undercooling is then studied in a square domain and a realistic three-dimensional production casting geometry. In order to address the multidimensional cases, a phase-field formulation is developed
Growth kinetics in a phase field model with continuous symmetry
NASA Astrophysics Data System (ADS)
Marini Bettolo Marconi, Umberto; Crisanti, Andrea
1996-07-01
We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric O(N) model recently introduced [U. Marini Bettolo Marconi and A. Crisanti, Phys. Rev. Lett. 75, 2168 (1995)] in order to generalize the so-called phase field model of Langer [Rev. Mod. Phys. 52, 1 (1980); Science 243, 1150 (1989)]. The Hamiltonian contains two O(N) invariant fields φ and U bilinearly coupled. The order parameter field φ evolves according to a nonconserved dynamics, whereas the diffusive field U follows a conserved dynamics. In the limit N-->∞ we obtain an exact solution, which displays an interesting kinetic behavior characterized by three different growth regimes. In the early regime the system displays normal scaling and the average domain size grows as t1/2; in the intermediate regime one observes a finite wave-vector instability, which is related to the Mullins-Sekerka instability; finally, in the late stage the structure function has a multiscaling behavior, while the domain size grows as t1/4.
Lubricating bacteria model for branching growth of bacterial colonies
NASA Astrophysics Data System (ADS)
Kozlovsky, Yonathan; Cohen, Inon; Golding, Ido; Ben-Jacob, Eshel
1999-06-01
Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serratia, and Salmonella) exhibit colonial branching patterns during growth on poor semisolid substrates. These patterns reflect the bacterial cooperative self-organization. A central part of the cooperation is the collective formation of a lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by a nonlinear diffusion coefficient, branching patterns evolve. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.
Zwintscher, Nathan P.; Shah, Puja M.; Salgar, Shashikumar K.; Newton, Christopher R.; Maykel, Justin A.; Samy, Ahmed; Jabir, Murad; Steele, Scott R.
2016-01-01
Introduction Dextran sodium sulfate (DSS) is commonly used to induce a murine fulminant colitis model. Hepatocyte growth factor (HGF) has been shown to decrease the symptoms of inflammatory bowel disease (IBD) but the effect of its activator, HGFA, is not well characterized. Arginine reduces effects of oxidative stress but its effect on IBD is not well known. The primary aim is to determine whether HGF and HGFA, or arginine will decrease IBD symptoms such as pain and diarrhea in a DSS-induced fulminant colitis murine model. Methods A severe colitis was induced in young, male Fischer 344 rats with 4% (w/v) DSS oral solution for seven days; rats were sacrificed on day 10. Rats were divided into five groups of 8 animals: control, HGF (700 mcg/kg/dose), HGF and HGFA (10 mcg/dose), HGF and arginine, and high dose HGF (2800 mcg/kg/dose). Main clinical outcomes were pain, diarrhea and weight loss. Blinded pathologists scored the terminal ileum and distal colon. Results DSS reliably induced severe active colitis in 90% of animals (n = 36/40). There were no differences in injury scores between control and treatment animals. HGF led to 1.38 fewer days in pain (p = 0.036), while arginine led to 1.88 fewer days of diarrhea (P = 0.017) compared to controls. 88% of HGFA-treated rats started regaining weight (P < 0.001). Discussion/Conclusion Although treatment was unable to reverse fulminant disease, HGF and arginine were associated with decreased days of pain and diarrhea. These clinical interventions may reduce associated symptoms for severe IBD patients, even when urgent surgical intervention remains the only viable option. PMID:27144006
Matrix population models are often used to extrapolate from life stage-specific stressor effects on survival and reproduction to population-level effects. Demographic elasticity analysis of a matrix model allows an evaluation of the relative sensitivity of population growth rate ...
Morphology and growth of murine cell lines on model biomaterials.
Godek, Marisha L; Duchsherer, Nichole L; McElwee, Quinn; Grainger, David W
2004-01-01
All biomaterial implants are assaulted by the host "foreign body" immune response. Understanding the complex, dynamic relationship between cells, biomaterials and milieu is an important first step towards controlling this reaction. Material surface chemistry dictates protein adsorption, and thus subsequent cell interactions. The cell-implant is a microenvironment involving 1) proteins that coat the surface and 2) cells that interact with these proteins. Macrophages and fibroblasts are two cell types that interact with proteins on biomaterials surfaces and play different related, but equally important, roles in biomaterials rejection and implant failure. Growth characteristics of four murine cell lines on model biomaterials surfaces were examined. Murine monocyte-macrophages (RAW 264.7 and J774A.1), murine macrophage (IC-21) and murine fibroblast (NIH 3T3) cell lines were tested to determine whether differences exist in adhesion, proliferation, differentiation, spreading, and fusion (macrophage lineages only) on these surfaces. Differences were observed in the ability of cells to adhere to and subsequently proliferate on polymer surfaces. (Monocyte-) macrophages grew well on all surfaces tested and growth rates were measured on three representative polymer biomaterials surfaces: tissue culture polystyrene (TCPS), polystyrene, and Teflon-AF. J774A.1 cultures grown on TCPS and treated with exogenous cytokines IL-4 and GM-CSF were observed to contain multinucleate cells with unusual morphologies. Thus, (monocyte-) macrophage cell lines were found to effectively attach to and interrogate each surface presented, with evidence of extensive spreading on Teflon-AF surfaces, particularly in the IC-21 cultures. The J774A.1 line was able to proliferate and/or differentiate to more specialized cell types (multinucleate/dendritic-like cells) in the presence of soluble chemokine cues. PMID:15133927
MODELING THE RED SEQUENCE: HIERARCHICAL GROWTH YET SLOW LUMINOSITY EVOLUTION
Skelton, Rosalind E.; Bell, Eric F.; Somerville, Rachel S.
2012-07-01
We explore the effects of mergers on the evolution of massive early-type galaxies by modeling the evolution of their stellar populations in a hierarchical context. We investigate how a realistic red sequence population set up by z {approx} 1 evolves under different assumptions for the merger and star formation histories, comparing changes in color, luminosity, and mass. The purely passive fading of existing red sequence galaxies, with no further mergers or star formation, results in dramatic changes at the bright end of the luminosity function and color-magnitude relation. Without mergers there is too much evolution in luminosity at a fixed space density compared to observations. The change in color and magnitude at a fixed mass resembles that of a passively evolving population that formed relatively recently, at z {approx} 2. Mergers among the red sequence population ('dry mergers') occurring after z = 1 build up mass, counteracting the fading of the existing stellar populations to give smaller changes in both color and luminosity for massive galaxies. By allowing some galaxies to migrate from the blue cloud onto the red sequence after z = 1 through gas-rich mergers, younger stellar populations are added to the red sequence. This manifestation of the progenitor bias increases the scatter in age and results in even smaller changes in color and luminosity between z = 1 and z = 0 at a fixed mass. The resultant evolution appears much slower, resembling the passive evolution of a population that formed at high redshift (z {approx} 3-5), and is in closer agreement with observations. We conclude that measurements of the luminosity and color evolution alone are not sufficient to distinguish between the purely passive evolution of an old population and cosmologically motivated hierarchical growth, although these scenarios have very different implications for the mass growth of early-type galaxies over the last half of cosmic history.
NASA Astrophysics Data System (ADS)
Woeger, Julia; Kinoshita, Shunichi; Wolfgang, Eder; Briguglio, Antonino; Hohenegger, Johann
2016-04-01
Operculina complanata was collected in 20 and 50 m depth around the Island of Sesoko belonging to Japans southernmost prefecture Okinawa in a series of monthly sampling over a period of 16 months (Apr.2014-July2015). A minimum of 8 specimens (4 among the smallest and 4 among the largest) per sampling were cultured in a long term experiment that was set up to approximate conditions in the field as closely as possible. A set up allowing recognition of individual specimens enabled consistent documentation of chamber formation, which in combination with μ-CT-scanning after the investigation period permitted the assignment of growth steps to specific time periods. These data were used to fit various mathematical models to describe growth (exponential-, logistic-, generalized logistic-, Gompertz-function) and chamber building rate (Michaelis-Menten-, Bertalanffy- function) of Operculina complanata. The mathematically retrieved maximum lifespan and mean chamber building rate found in cultured Operculina complanata were further compared to first results obtained by the simultaneously conducted "natural laboratory approach". Even though these comparisons hint at a somewhat stunted growth and truncated life spans of Operculina complanata in culture, they represent a possibility to assess and improve the quality of further cultivation set ups, opening new prospects to a better understanding of the their theoretical niches.
NASA Astrophysics Data System (ADS)
Lalanne-Aulet, David; Piacentini, Adalberto; Guillot, Pierre; Marchal, Philippe; Moreau, Gilles; Colin, Annie
2015-11-01
Using a millifluidics and macroscale setup, we study quantitatively the impact of gas exchange on bacterial growth. In millifluidic environments, the permeability of the incubator materials allows an unlimited oxygen supply by diffusion. Moreover, the efficiency of diffusion at small scales makes the supply instantaneous in comparison with the cell division time. In hermetic closed vials, the amount of available oxygen is low. The growth curve has the same trend but is quantitatively different from the millifluidic situation. The analysis of all the data allows us to write a quantitative modeling enabling us to capture the entire growth process.
ERIC Educational Resources Information Center
Colorado Department of Education, 2013
2013-01-01
This report examines the relationship between socioeconomic status, as defined by a free-and-reduced lunch proxy variable, and student growth percentiles by elementary, middle, and high school grade levels for math, reading, and writing. Comparisons were made between median growth percentiles for each educational level by free and reduced lunch…
A computational model that predicts reverse growth in response to mechanical unloading
Genet, M.; Acevedo-Bolton, G.; Ordovas, K.; Guccione, J. M.; Kuhl, E.
2014-01-01
Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure–volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry. PMID:24888270
Assessment of improved root growth representation in a 1-D, field scale crop model
NASA Astrophysics Data System (ADS)
Miltin Mboh, Cho; Gaiser, Thomas; Ewert, Frank
2015-04-01
Many 1-D, field scale crop models over-simplify root growth. The over-simplification of this "hidden half" of the crop may have significant consequences on simulated root water and nutrient uptake with a corresponding reflection on the simulated crop yields. Poor representation of root growth in crop models may therefore constitute a major source of uncertainty propagation. In this study we assess the effect of an improved representation of root growth in a model solution of the model framework SIMPLACE (Scientific Impact assessment and Modeling PLatform for Advanced Crop and Ecosystem management) compared to conventional 1-D approaches. The LINTUL5 crop growth model is coupled to the Hillflow soil water balance model within the SIMPLACE modeling framework (Gaiser et al, 2013). Root water uptake scenarios in the soil hydrological simulator Hillflow (Bronstert, 1995) together with an improved representation of root growth is compared to scenarios for which root growth is simplified. The improvement of root growth is achieved by integrating root growth solutions from R-SWMS (Javaux et al., 2008) into the SIMPLACE model solution. R-SWMS is a three dimensional model for simultaneous modeling of root growth, soil water fluxes and solute transport and uptake. These scenarios are tested by comparing how well the simulated water contents match with the observed soil water dynamics. The impacts of the scenarios on above ground biomass and wheat grain are assessed
A bifactor model of the Posttraumatic Growth Inventory
Konkolÿ Thege, Barna; Kovács, Éva; Balog, Piroska
2014-01-01
Purpose: The Posttraumatic Growth Inventory (PTGI) is a self-administered measurement instrument designed to provide information concerning positive psychological changes after a traumatic life event. The aim of the present study was to examine the psychometric properties of the PTGI in a Hungarian sample. By examining a bifactor model of the instrument, we also wanted to contribute to the establishment of an evidence-based practice concerning the use of different score types (total score versus subscale scores). Methods: Altogether, 691 Hungarian respondents (82.2% female; M age = 33.0 ± 13.4 years), who experienced some kind of trauma or loss, participated in this study. Results: A series of confirmatory factor analyses revealed that among the tested first- and second-order models, a bifactor model provided the best-fit to our data (χ 2/df = 4.32, Comparative Fit Index = .91, root mean square error of approximation = .07, standardized root mean square residual = .04). Further, the Hungarian version of the PTGI showed high internal consistency (Cronbach's alpha = .93, omega total = .95, omega hierarchical = .87) and test–retest reliability (r = .90; p < .01) coefficients. However, omega hierarchical coefficients (.14–.40) and explained variance values (.05–.10) for the subscales were low. Conclusions: The present study provided empirical support for the psychometric adequacy of the Hungarian adaptation of the PTGI and suggests that only the total and not the subscale scores of the inventory should be used. PMID:25750800
Fissore, Eliana N; Santo Domingo, Cinthia; Gerschenson, Lía N; Giannuzzi, Leda
2015-05-01
The effect of different fractions enriched in soluble fiber obtained from artichoke using citric acid or citric acid/hemicellulase on the selective growth of Lactobacillus plantarum 8114 and Bifidobacterium bifidum ATCC 11863 was evaluated. Gompertz modeling of Lactobacillus plantarum 8114 growth showed a higher specific growth rate (μ: 0.16 h(-1)) in the presence of fractions isolated from stems using hemicellulase (fraction A) than in the presence of glucose (μ: 0.09 h(-1)). In the case of Bifidobacterium bifidum 11863, the highest μ was obtained for the microorganism grown in the presence of fraction A and for the fraction isolated from stems without hemicellulase, their rate being twice that observed for glucose (0.04 h(-1)). The positive prebiotic activity scores observed with respect to Escherichia coli 25922 indicated that fibers assayed are metabolized as well as glucose by Lactobacillus plantarum 8114 and Bifidobacterium bifidum ATCC 11863 and that they are selectively metabolized by these microorganisms. The potential capacity to selectively stimulate the growth of intestinal bacteria associated with health shown by fraction A can be ascribed to its high inulin and low methylation degree pectin contents. PMID:25904284
NASA Astrophysics Data System (ADS)
Troy, Tara J.; Ines, Amor V. M.; Lall, Upmanu; Robertson, Andrew W.
2013-04-01
Large-scale hydrologic models, such as the Variable Infiltration Capacity (VIC) model, are used for a variety of studies, from drought monitoring to projecting the potential impact of climate change on the hydrologic cycle decades in advance. The majority of these models simulates the natural hydrological cycle and neglects the effects of human activities such as irrigation, which can result in streamflow withdrawals and increased evapotranspiration. In some parts of the world, these activities do not significantly affect the hydrologic cycle, but this is not the case in south Asia where irrigated agriculture has a large water footprint. To address this gap, we incorporate a crop growth model and irrigation model into the VIC model in order to simulate the impacts of irrigated and rainfed agriculture on the hydrologic cycle over south Asia (Indus, Ganges, and Brahmaputra basin and peninsular India). The crop growth model responds to climate signals, including temperature and water stress, to simulate the growth of maize, wheat, rice, and millet. For the primarily rainfed maize crop, the crop growth model shows good correlation with observed All-India yields (0.7) with lower correlations for the irrigated wheat and rice crops (0.4). The difference in correlation is because irrigation provides a buffer against climate conditions, so that rainfed crop growth is more tied to climate than irrigated crop growth. The irrigation water demands induce hydrologic water stress in significant parts of the region, particularly in the Indus, with the streamflow unable to meet the irrigation demands. Although rainfall can vary significantly in south Asia, we find that water scarcity is largely chronic due to the irrigation demands rather than being intermittent due to climate variability.
Predicting bacterial growth in raw, salted, and cooked chicken breast fillets during storage.
Galarz, Liane Aldrighi; Fonseca, Gustavo Graciano; Prentice, Carlos
2016-09-01
Growth curves were evaluated for aerobic mesophilic and psychrotrophic bacteria, Pseudomonas spp. and Staphylococcus spp., grown in raw, salted, and cooked chicken breast at 2, 4, 7, 10, 15, and 20 ℃, respectively, using the modified Gompertz and modified logistic models. Shelf life was determined based on microbiological counts and sensory analysis. Temperature increase reduced the shelf life, which varied from 10 to 26 days at 2 ℃, from nine to 21 days at 4 ℃, from six to 12 days at 7 ℃, from four to eight days at 10 ℃, from two to four days at 15 ℃, and from one to two days at 20 ℃. In most cases, cooked chicken breast showed the highest microbial count, followed by raw breast and lastly salted breast. The data obtained here were useful for the generation of mathematical models and parameters. The models presented high correlation and can be used for predictive purposes in the poultry meat supply chain. PMID:26683484
A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.
Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M
2014-04-01
A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications. PMID:24491334
A mathematical model for crop spectral-temporal trajectories based on a plant growth model
NASA Technical Reports Server (NTRS)
Woolford, T. L.
1983-01-01
The Kubelka-Munk radiative transfer model is combined with an approximation of Kauth-Thomas greeness and brightness transforms to derive approximate closed form expressions for crop greeness and brightness surrogates in terms of canopy biomass. The greeness relation derived resembles an existing empirical relation between leaf area index and greeness. A simple growth model based on interception and utilization of photosynthetically active radiation is developed and used to describe the time evolution of greeness and brightness. The model developed does not yet yield definitive profile calculations but suggests a conceptual framework which may be found useful for further profile analysis.
Two models for phosphorus and phytoplankton growth were field verified along a marked gradient in trophic conditions in Green Bay (Lake Michigan): one, the Monod model, relates growth rate to external (dissolved) phosphorus concentration, and the other, the Droop model, describes...
Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots
ERIC Educational Resources Information Center
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
2013-01-01
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
Growth Curve Models for Zero-Inflated Count Data: An Application to Smoking Behavior
ERIC Educational Resources Information Center
Liu, Hui; Powers, Daniel A.
2007-01-01
This article applies growth curve models to longitudinal count data characterized by an excess of zero counts. We discuss a zero-inflated Poisson regression model for longitudinal data in which the impact of covariates on the initial counts and the rate of change in counts over time is the focus of inference. Basic growth curve models using a…
Power and Bias in Hierarchical Linear Growth Models: More Measurements of Fewer People
ERIC Educational Resources Information Center
Haardoerfer, Regine
2010-01-01
Hierarchical Linear Modeling (HLM) sample size recommendations are mostly made with traditional group-design research in mind, as HLM as been used almost exclusively in group-design studies. Single-case research can benefit from utilizing hierarchical linear growth modeling, but sample size recommendations for growth modeling with HLM are scarce…
Large-Scale Numerical Modeling of Melt and Solution Crystal Growth
NASA Astrophysics Data System (ADS)
Derby, Jeffrey J.; Chelikowsky, James R.; Sinno, Talid; Dai, Bing; Kwon, Yong-Il; Lun, Lisa; Pandy, Arun; Yeckel, Andrew
2007-06-01
We present an overview of mathematical models and their large-scale numerical solution for simulating different phenomena and scales in melt and solution crystal growth. Samples of both classical analyses and state-of-the-art computations are presented. It is argued that the fundamental multi-scale nature of crystal growth precludes any one approach for modeling, rather successful crystal growth modeling relies on an artful blend of rigor and practicality.
Modeling and bulk crystal growth processes: What is to be learned?
NASA Astrophysics Data System (ADS)
Derby, Jeffrey J.
2010-07-01
Modeling is an important tool to better understand crystal growth. This assertion is discussed via examples of classical models that have proven to be enlightening. The discussion continues with a brief primer on the mathematical governing equations of continuum and interfacial phenomena important in crystal growth processes and several techniques that can be applied to these equations for analysis, including scaling and numerical methods. Finally, some examples of modeling a melt growth system are presented to illustrate modern applications.
NASA Astrophysics Data System (ADS)
McBeck, Jessica A.; Madden, Elizabeth H.; Cooke, Michele L.
2016-03-01
Growth by Optimization of Work (GROW) is a new modeling tool that automates fracture initiation, propagation, interaction, and linkage. GROW predicts fracture growth by finding the propagation path and fracture geometry that optimizes the global external work of the system. This implementation of work optimization is able to simulate more complex paths of fracture growth than energy release rate methods. In addition, whereas a Coulomb stress analysis determines two conjugate planes of potential failure, GROW identifies a single failure surface for each increment of growth. GROW also eliminates ambiguity in determining whether shear or tensile failure will occur at a fracture tip by assessing both modes of failure by the same propagation criterion. Here we describe the underlying algorithm of the program and present GROW models of two propagating faults separated by a releasing step. The discretization error of these models demonstrates that GROW can predict fault propagation paths within the numerical uncertainty produced by discretization. Model element size moderately influences the propagation paths, however, the final fault geometry remains similar between models with significantly different element sizes. The propagation power of the fault system, calculated from the change in work due to fault propagation, indicates when model faults interact through both soft- and hard-linkage.
ERIC Educational Resources Information Center
Kashy, Deborah A.; Donnellan, M. Brent; Burt, S. Alexandra; McGue, Matt
2008-01-01
Growth modeling is a useful tool for studying change over time, and it is becoming increasingly popular with developmental researchers. There is a considerable methodological literature surrounding growth modeling for individuals; however, far less attention has been focused on growth models for pairs of related individuals (i.e., dyads). In this…
Using colloids to model atomic thin film growth
NASA Astrophysics Data System (ADS)
Ganapathy, Rajesh; Buckley, Mark; Cohen, Itai
2009-03-01
We epitaxially grow colloidal thin films by sedimenting micron sized colloidal particles on a microfabricated substrate. The attractive interaction between the colloids, induced by a depletant polymer, leads to the nucleation of islands that grow and coalesce with one another. We use confocal microscopy and particle tracking to study the dynamics of the colloidal particles as they diffuse, aggregate and rearrange configurations during deposition. The saturation island density is estimated as a function of the deposition rate and depletant concentration. We find that our results are in excellent agreement with those obtained from atomic deposition experiments suggesting that our system can be used to model various phenomena that occur in atomic thin film growth. Furthermore, we quantify the Ehrlich-Schwoebel step edge barrier by using holographic optical tweezers to create artificial islands and study the dynamics of colloidal monomers placed on the edge of these islands. Owing to the short-range of the attractive interaction in our system, the origin of the step edge barrier in colloids is strikingly different from atoms.
Modeling of Melt Growth During Carbothermal Processing of Lunar Regolith
NASA Technical Reports Server (NTRS)
Balasubramaniam, R.; Gokoglu S.; Hegde, U.
2012-01-01
The carbothermal processing of lunar regolith has been proposed as a means to produce carbon monoxide and ultimately oxygen to support human exploration of the moon. In this process, gaseous methane is pyrolyzed as it flows over the hot surface of a molten zone of lunar regolith and is converted to carbon and hydrogen. Carbon gets deposited on the surface of the melt, and mixes and reacts with the metal oxides in it to produce carbon monoxide that bubbles out of the melt. Carbon monoxide is further processed in other reactors downstream to ultimately produce oxygen. The amount of oxygen produced crucially depends on the amount of regolith that is molten. In this paper we develop a model of the heat transfer in carbothermal processing. Regolith in a suitable container is heated by a heat flux at its surface such as by continuously shining a beam of solar energy or a laser on it. The regolith on the surface absorbs the energy and its temperature rises until it attains the melting point. The energy from the heat flux is then used for the latent heat necessary to change phase from solid to liquid, after which the temperature continues to rise. Thus a small melt pool appears under the heated zone shortly after the heat flux is turned on. As time progresses, the pool absorbs more heat and supplies the energy required to melt more of the regolith, and the size of the molten zone increases. Ultimately, a steady-state is achieved when the heat flux absorbed by the melt is balanced by radiative losses from the surface. In this paper, we model the melting and the growth of the melt zone with time in a bed of regolith when a portion of its surface is subjected to a constant heat flux. The heat flux is assumed to impinge on a circular area. Our model is based on an axisymmetric three-dimensional variation of the temperature field in the domain. Heat transfer occurs only by conduction, and effects of convective heat transport are assumed negligible. Radiative heat loss from the
Growth mixture modelling in families of the Framingham Heart Study
2009-01-01
Growth mixture modelling, a less explored method in genetic research, addresses unobserved heterogeneity in population samples. We applied this technique to longitudinal data of the Framingham Heart Study. We examined systolic blood pressure (BP) measures in 1060 males from 692 families and detected three subclasses, which varied significantly in their developmental trajectories over time. The first class consisted of 60 high-risk individuals with elevated BP early in life and a steep increase over time. The second group of 131 individuals displayed first normal BP, but showed a significant increase over time and reached high BP values late in their life time. The largest group of 869 individuals could be considered a normative group with normal BP on all exams. To identify genetic modulators for this phenotype, we tested 2,340 single-nucleotide polymorphisms on chromosome 8 for association with the class membership probabilities of our model. The probability of being in Class 1 was significantly associated with a very rare variant (rs1445404) present in only four individuals from four different families located in the coding region of the gene EYA (eyes absent homolog 1 in Drosophila) (p = 1.39 × 10-13). Mutations in EYA are known to cause brachio-oto-renal syndrome, as well as isolated renal malformations. Renal malformations could cause high BP early in life. This result awaits replication; however, it suggests that analyzing genetic data stratified for high-risk subgroups defined by a unique development over time could be useful for the detection of rare mutations in common multi-factorial diseases. PMID:20017979
Using Spreadsheets To Model Population Growth, Competition and Predation in Nature.
ERIC Educational Resources Information Center
Carter, Ashley J. R.
1999-01-01
Describes how to place mathematical equations modeling population growth into a spreadsheet that performs calculations quickly and easily. Suggests experiments that can be performed with the spreadsheets. (WRM)
Revisiting a model of ontogenetic growth: estimating model parameters from theory and data.
Moses, Melanie E; Hou, Chen; Woodruff, William H; West, Geoffrey B; Nekola, Jeffery C; Zuo, Wenyun; Brown, James H
2008-05-01
The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the M(1/4) scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the M(3/4) scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research. PMID:18419571
NASA Astrophysics Data System (ADS)
Franck, Carl; Zhou, Xaio-Qiao S.; Deshmukh, Amrish; Bogart, Elijah; Lau, Sharon; Daie, Kayvon; Bae, Albert
2010-03-01
In recent work we explored the notion that the transition between slow and fast growth, the lag-log transition, with increasing density seen in shaken cell culture represents a collective effect. (Phys. Rev. E 77, 041905 (2008)). We reported preliminary observations in which the lag phase was apparently missing. Here, we present significantly more measurements than in our original work as well as increased sensitivity at low densities. We confirm that instances of nearly exponential (``log'') growth do in fact appear, but more frequently, we find evidence of lagging. The degree of lagging fluctuates significantly from run to run, in contrast to our earlier observations and theory, but in all cases exponential growth is established with increasing density once the range of 10^4 to 10^5 cells/ml is reached. We present evidence against two natural explanations for these fluctuations: 1) a mixture of strains which have different growth phenotypes or 2) a single strain variation due to an epigenetic switch which can be set to the low growth state by subjecting cells to high density environments. The appearance of such growth variations has considerable practical significance and suggests that there is an additional dynamical variable besides density in play.
A model for the growth of cdte by metal organic chemical vapor deposition
NASA Astrophysics Data System (ADS)
Nemirovsky, Y.; Goren, D.; Ruzin, A.
1991-10-01
A kinetic model for the metalorganic chemical vapor deposition (MOCVD) growth of CdTe over a wide temperature range is presented. The model yields the growth rate as a function of the gas-phase concentrations of the constituents. The model is corroborated with experimental results obtained by the MOCVD growth of CdTe at 380° C. The major features of the model are the observed two-step surface-controlled pyrolysis and surface saturation, leading initially to a growth rate that increases with the square root of the concentrations of the reacting species and subsequently to a decrease of the growth rate as the concentrations increase. At even higher concentrations, an additional increase of growth rate is observed and modeled.
Hypothesis Generation in Latent Growth Curve Modeling Using Principal Components
ERIC Educational Resources Information Center
Davison, Mark L.
2008-01-01
While confirmatory latent growth curve analyses provide procedures for testing hypotheses about latent growth curves underlying data, one must first derive hypotheses to be tested. It is argued that such hypotheses should be generated from a combination of theory and exploratory data analyses. An exploratory components analysis is described and…
NASA Astrophysics Data System (ADS)
Lattuca, M. E.; Lozano, I. E.; Brown, D. R.; Renzi, M.; Luizon, C. A.
2015-12-01
Age and growth, otolith shape and diet of Odontesthes nigricans were analysed in order to provide an insight into the life history of the species and furthermore, to assess their possible use as a tool for discriminating silverside populations from the South Atlantic Ocean (Punta María) and Beagle Channel waters (Varela Bay). The age and growth analysis was performed by counting daily increments and annual marks in sagittae otoliths. Length-at-age data of individuals <65 mm standard length (SL) were fitted to the Laird-Gompertz model (SLt = 6.22 exp 2.45 [1-exp (-0.02t)]), which provided an excellent description of the pattern of daily growth for O. nigricans juveniles from Varela Bay. The spawning period was also assessed through back-calculation of hatching dates and it extended from November to February. The count of annual marks in larger individuals identified 7 year classes (0+ to 6+) in Varela Bay and 6 year classes (0+ to 5+) in Punta María. The von Bertalanffy growth model explained more than 95% of the growth patterns observed in O. nigricans from Varela Bay (SLt = 245.49 [1 - exp -0.24(t+0.46)]) and Punta María (SLt = 345.09 [1 - exp -0.15(t+0.31)]). Particularly, k and SL∞ varied significantly between sampling sites; reaching Punta María a larger SL∞ value with a lower k. Otolith shape variation was also explored using elliptical Fourier analysis and it showed significant differences between Varela Bay and Punta María populations. Furthermore, gut content analysis characterized O. nigricans as an invertebrate predator, being benthic organisms the most important components of its diet, which also showed significant site dependence. The use of all these analyses contributed to a holistic approach which maximized the likelihood of correctly identifying both O. nigricans populations in the southernmost limit of the species distribution.
Oberhuber, Walter; Gruber, Andreas; Kofler, Werner; Swidrak, Irene
2014-05-01
Dendroclimatological studies in a dry inner Alpine environment (750 m a.s.l.) revealed different growth response of co-occurring coniferous species to climate, which is assumed to be caused by a temporal shift in wood formation among species. The main focus of this study therefore was to monitor intra-annual dynamics of radial increment growth of mature deciduous and evergreen coniferous species (Pinus sylvestris, Larix decidua and Picea abies) during two consecutive years with contrasting climatic conditions. Radial stem growth was continuously followed by band dendrometers and modelled using Gompertz functions to determine time of maximum growth. Histological analyses of tree ring formation allowed determination of temporal dynamics of cambial activity and xylem cell development. Daily fluctuations in stem radius and radial stem increments were extracted from dendrometer traces, and correlations with environmental variables were performed. While a shift in temporal dynamics of radial growth onset and cessation was detected among co-occurring species, intra-annual radial growth peaked synchronously in late May 2011 and early June 2012. Moist atmospheric conditions, i.e. high relative air humidity, low vapour pressure deficit and low air temperature during the main growing period, favoured radial stem increment of all species. Soil water content and soil temperature were not significantly related to radial growth. Although a temporal shift in onset and cessation of wood formation was detected among species, synchronous culmination of radial growth indicates homogenous exogenous and/or endogenous control. The close coupling of radial growth to atmospheric conditions points to the importance of stem water status for intra-annual growth of drought-prone conifers. PMID:24883053
Oberhuber, Walter; Gruber, Andreas; Kofler, Werner; Swidrak, Irene
2014-01-01
Dendroclimatological studies in a dry inner Alpine environment (750 m a.s.l.) revealed different growth response of co-occurring coniferous species to climate, which is assumed to be caused by a temporal shift in wood formation among species. The main focus of this study therefore was to monitor intra-annual dynamics of radial increment growth of mature deciduous and evergreen coniferous species (Pinus sylvestris, Larix decidua and Picea abies) during two consecutive years with contrasting climatic conditions. Radial stem growth was continuously followed by band dendrometers and modelled using Gompertz functions to determine time of maximum growth. Histological analyses of tree ring formation allowed determination of temporal dynamics of cambial activity and xylem cell development. Daily fluctuations in stem radius and radial stem increments were extracted from dendrometer traces, and correlations with environmental variables were performed. While a shift in temporal dynamics of radial growth onset and cessation was detected among co-occurring species, intra-annual radial growth peaked synchronously in late May 2011 and early June 2012. Moist atmospheric conditions, i.e. high relative air humidity, low vapour pressure deficit and low air temperature during the main growing period, favoured radial stem increment of all species. Soil water content and soil temperature were not significantly related to radial growth. Although a temporal shift in onset and cessation of wood formation was detected among species, synchronous culmination of radial growth indicates homogenous exogenous and/or endogenous control. The close coupling of radial growth to atmospheric conditions points to the importance of stem water status for intra-annual growth of drought-prone conifers. PMID:24883053
Kidney Tumor Growth Prediction by Coupling Reaction-Diffusion and Biomechanical Model
Chen, Xinjian; Summers, Ronald M.; Yao, Jianhua
2014-01-01
It is desirable to predict the tumor growth rate so that appropriate treatment can be planned in the early stage. Previously, we proposed a finite element method (FEM)-based 3D kidney tumor growth prediction system using longitudinal images. A reaction-diffusion model was applied as the tumor growth model. In this paper, we not only improve the tumor growth model by coupling the reaction-diffusion model with a biomechanical model, but also take the surrounding tissues into account. Different diffusion and biomechanical properties are applied for different tissue types. FEM is employed to simulate the coupled tumor growth model. Model parameters are estimated by optimizing an objective function of overlap accuracy using a hybrid optimization parallel search package (HOPSPACK). The proposed method was tested with kidney CT images of eight tumors from five patients with seven time points. The experimental results showed the performance of the proposed method improved greatly compared to our previous work. PMID:23047857
Development of a competition model for microbial growth in mixed culture.
Fujikawa, Hiroshi; Munakata, Kanako; Sakha, Mohammad Z
2014-01-01
A novel competition model for describing bacterial growth in mixed culture was developed in this study. Several model candidates were made with our logistic growth model that precisely describes the growth of a monoculture of bacteria. These candidates were then evaluated for the usefulness in describing growth of two competing species in mixed culture using Staphylococcus aureus, Escherichia coli, and Salmonella. Bacterial cells of two species grew at initial doses of 10(3), 10(4), and 10(5) CFU/g at 28ºC. Among the candidates, a model where the Lotka-Volterra model, a general competition model in ecology, was incorporated as a new term in our growth model was the best for describing all types of growth of two competitors in mixed culture. Moreover, the values for the competition coefficient in the model were stable at various combinations of the initial populations of the species. The Baranyi model could also successfully describe the above types of growth in mixed culture when it was coupled with the Gimenez and Dalgaard model. However, the values for the competition coefficients in the competition model varied with the conditions. The present study suggested that our model could be a basic model for describing microbial competition. PMID:24975409
A plant-growth stress model: Conceptual model and development plan
Chen, C.W. )
1989-12-01
This report begins with a literature review of existing models for crops and forest trees. The models were analyzed for their assumptions, formulations, inputs, outputs, calibrations and verifications. The formulations of crop models (e.g. corn, sugar beet, soybean, and red radish) included detailed hypotheses of carbon uptake, light attenuation through leaves, photosynthesis, chemical synthesis of organics, material transport between plant parts and production of havestable dry matter. Most crop models performed simulations with a time step of 15 minutes to an hour for a total period of 100 to 150 days. Tree models were developed, mostly without verification, for forest management practices, ecological studies of species succession, and assessment of air pollution effects. None are physiologically based models that can simulate mechanistically tree responses to interacting natural and anthropogenic stresses. A new generation tree model was formulated. The model incorporated subroutines from an existing model (ILWAS) to calculate daily soil temperature, soil moisture, cations (including aluminum species) and anion concentrations in the soil solution at the root zone. It also includes a new plant module to simulate daily physiological and growth responses of trees, subjected to the dynamic impacts of air pollution, aluminum toxicity, nutrient deficiency, and drought. Model coefficient will be calibrated with data from exposure experiments where environmental conditions are controlled. The model can then be extended to the field where environmental conditions change dynamically. 90 refs., 11 figs.
Sipkema, E.M.; Koning, W. de; Ganzeveld, K.J.; Janssen, D.B.; Beenackers, A.A.C.M.
2000-04-01
Chlorinated ethenes, such as the environmental pollutant trichloroethene, can be converted aerobically only via cometabolism. In this process, conversion results from the nonspecificity of oxygenating enzymes. Expression of these enzymes occurs during growth on compounds such as alkanes, aromatics, and ammonia. A biochemical model is presented that described growth of Methylosinus trichosporium OB3b on methane. The model, which was developed to compare strategies to alleviate NADH limitation resulting from cometabolic contaminant conversion, includes (1) catabolism of methane via methanol, formaldehyde, and formate to carbon dioxide; (2) growth as formaldehyde assimilation; and (3) storage material (poly-{beta}-hydroxy-butyric acid, PHB) metabolism. To integrate the three processes, the cofactor NADH is used as central intermediate and controlling factor--instead of the commonly applied energy carrier ATP. This way a stable and well-regulated growth model is obtained that gives a realistic description of a variety of steady-state and transient-state experimental data. An analysis of the cells' physiological properties is given to illustrate the applicability of the model. Steady-state model calculations showed that in strain OB3b flux control is located primarily at the first enzyme of the metabolic pathway. Since no adaptation in V{sub MAX} values is necessary to describe growth at different dilution rates, the organism seems to have a ``rigid enzyme system,'' the activity of which is not regulated in response to continued growth at low rates. During transient periods of excess carbon and energy source availability, PHB is found to accumulate, serving as a sink for transiently available excess reducing power.
NASA Astrophysics Data System (ADS)
Waag, Andreas
This chapter is devoted to the growth of ZnO. It starts with various techniques to grow bulk samples and presents in some detail the growth of epitaxial layers by metal organic chemical vapor deposition (MOCVD), molecular beam epitaxy (MBE), and pulsed laser deposition (PLD). The last section is devoted to the growth of nanorods. Some properties of the resulting samples are also presented. If a comparison between GaN and ZnO is made, very often the huge variety of different growth techniques available to fabricate ZnO is said to be an advantage of this material system. Indeed, growth techniques range from low cost wet chemical growth at almost room temperature to high quality MOCVD growth at temperatures above 1, 000∘C. In most cases, there is a very strong tendency of c-axis oriented growth, with a much higher growth rate in c-direction as compared to other crystal directions. This often leads to columnar structures, even at relatively low temperatures. However, it is, in general, not straight forward to fabricate smooth ZnO thin films with flat surfaces. Another advantage of a potential ZnO technology is said to be the possibility to grow thin films homoepitaxially on ZnO substrates. ZnO substrates are mostly fabricated by vapor phase transport (VPT) or hydrothermal growth. These techniques are enabling high volume manufacturing at reasonable cost, at least in principle. The availability of homoepitaxial substrates should be beneficial to the development of ZnO technology and devices and is in contrast to the situation of GaN. However, even though a number of companies are developing ZnO substrates, only recently good quality substrates have been demonstrated. However, these substrates are not yet widely available. Still, the situation concerning ZnO substrates seems to be far from low-cost, high-volume production. The fabrication of dense, single crystal thin films is, in general, surprisingly difficult, even when ZnO is grown on a ZnO substrate. However
Fatigue Crack Growth Analysis Models for Functionally Graded Materials
Dag, Serkan; Yildirim, Bora; Sabuncuoglu, Baris
2008-02-15
The objective of this study is to develop crack growth analysis methods for functionally graded materials (FGMs) subjected to mode I cyclic loading. The study presents finite elements based computational procedures for both two and three dimensional problems to examine fatigue crack growth in functionally graded materials. Developed methods allow the computation of crack length and generation of crack front profile for a graded medium subjected to fluctuating stresses. The results presented for an elliptical crack embedded in a functionally graded medium, illustrate the competing effects of ellipse aspect ratio and material property gradation on the fatigue crack growth behavior.
Growth, characterization, modeling and device applications of semiconductor nanowire networks
NASA Astrophysics Data System (ADS)
Lohn, Andrew J.
Semiconducting nanowire networks composed specifically of indium phosphide or silicon are developed with the goal of understanding their electrical, thermal and optoelectronic properties while developing scalable, manufacturable solutions to a number of problems of contemporary interest to society, with particular emphasis on direct conversion of heat to electricity. Nanowire networks are grown by metal organic chemical vapor deposition on non-single crystalline surfaces leading to highly interconnected networks of nanowires capable of long-range three-dimensional transport while retaining many of the unique properties of highly conned nanowire structures and displaying advantageous and unique properties such as mechanical flexibility. Growth of semiconducting nanowire networks is discussed in depth, especially relating to the role of the non-single crystalline surfaces from which they grow and morphological changes associated with doping. Finite element simulations suggest that the physical intersections present within a nanowire network are found to play a complex and potentially useful role in thermal transport and in electrical transport through experiment, demonstrating quantized conductance for the first time at room temperature. Electrical transport over distances far in excess of the dimensions of the individual nanowires is also studied experimentally by applying surface photovoltage techniques for the first time to nanowire networks. The theoretical model developed to analyze data from this, first of its type, experiment reveals insights that can aid in developing improved thermoelectric devices. Such thermoelectric devices were fabricated using a highly scalable and very low cost approach. Thermoelectric testing displays large series electrical resistance but Seebeck voltages comparable to its bulk counterpart. The preliminary results clearly indicate that if series electrical resistance can be decreased, nanowire networks will be an excellent candidate
ERIC Educational Resources Information Center
Brooks, Rechele; Meltzoff, Andrew N.
2008-01-01
We found that infant gaze following and pointing predicts subsequent language development. At ages 0 ; 10 or 0 ; 11, infants saw an adult turn to look at an object in an experimental setting. Productive vocabulary was assessed longitudinally through two years of age. Growth curve modeling showed that infants who gaze followed and looked longer at…
ERIC Educational Resources Information Center
Wimmers, Paul F.; Lee, Ming
2015-01-01
To determine the direction and extent to which medical student scores (as observed by small-group tutors) on four problem-based-learning-related domains change over nine consecutive blocks during a two-year period (Domains: Problem Solving/Use of Information/Group Process/Professionalism). Latent growth curve modeling is used to analyze…
ERIC Educational Resources Information Center
Hong, Sehee; You, Sukkyung
2012-01-01
Addressing the academic needs of a growing student population with culturally and linguistically diverse characteristics is one of the challenges facing educators. This study used data from the Early Childhood Longitudinal Study to test for differences in patterns of mathematics growth (e.g., high, middle, and low performance groups) in Latino…
A Validity Agenda for Growth Models: One Size Doesn't Fit All!
ERIC Educational Resources Information Center
Patelis, Thanos
2012-01-01
This is a keynote presentation given at AERA on developing a validity agenda for growth models in a large scale (e.g., state) setting. The emphasis of this presentation was to indicate that growth models and the validity agenda designed to provide evidence in supporting the claims to be made need to be personalized to meet the local or…
Modeling Nonlinear Growth with Three Data Points: Illustration with Benchmarking Data
ERIC Educational Resources Information Center
Kamata, Akihito; Nese, Joseph F. T.; Patarapichayatham, Chalie; Lai, Cheng-Fei
2013-01-01
The purpose of this article is to demonstrate ways to model nonlinear growth using three testing occasions. We demonstrate our growth models in the context of curriculum-based measurement using the fall, winter, and spring passage reading fluency benchmark assessments. We present a brief technical overview that includes the limitations of a growth…
A comparison of two models to evaluate soil compaction effects on corn root growth
Technology Transfer Automated Retrieval System (TEKTRAN)
Several complex interactions among soil physical properties influence root growth of common crops. Models are used to combine limitations of temperature, aeration, water availability and soil strength to determine the zonal suitability for root growth. Two models are compared in this study, the Jone...
Predictive model for growth of Clostridium perfringens during cooling of cooked ground chicken
Technology Transfer Automated Retrieval System (TEKTRAN)
Traditional methodologies for development of microbial growth models under dynamic temperature conditions do not take into account the organism’s prior history. Such models were shown to be inadequate in predicting growth of the organisms under dynamic conditions commonly encountered in the food ind...
Using Design-Based Latent Growth Curve Modeling with Cluster-Level Predictor to Address Dependency
ERIC Educational Resources Information Center
Wu, Jiun-Yu; Kwok, Oi-Man; Willson, Victor L.
2014-01-01
The authors compared the effects of using the true Multilevel Latent Growth Curve Model (MLGCM) with single-level regular and design-based Latent Growth Curve Models (LGCM) with or without the higher-level predictor on various criterion variables for multilevel longitudinal data. They found that random effect estimates were biased when the…
Discussion of the Special Issue on Growth Models for Longitudinal Data in Educational Research
ERIC Educational Resources Information Center
Molenaar, Peter C. M.; Campbell, Cynthia G.
2008-01-01
In his introduction to this special issue, Roger Millsap has given an excellent summary of its contents. This eases our task considerably. In what follows, we first present some general observations about growth curve modeling of longitudinal data. Among other things, we will address the criticism that the popular latent growth curve model may…
The Role of Coding Time in Estimating and Interpreting Growth Curve Models.
ERIC Educational Resources Information Center
Biesanz, Jeremy C.; Deeb-Sossa, Natalia; Papadakis, Alison A.; Bollen, Kenneth A.; Curran, Patrick J.
2004-01-01
The coding of time in growth curve models has important implications for the interpretation of the resulting model that are sometimes not transparent. The authors develop a general framework that includes predictors of growth curve components to illustrate how parameter estimates and their standard errors are exactly determined as a function of…
Evaluating the MaizSim model in simulating potential corn growth
Technology Transfer Automated Retrieval System (TEKTRAN)
Models that simply calculate crop growth rate as the product of intercepted light and radiation use efficiency may not be able to adequately simulate plant growth under stress conditions. We developed a new corn model MaizSim. In MaizSim, photosynthesis is mechanistically related to environmental co...
PREDICTIVE MODEL FOR GROWTH OF CLOSTRIDIUM PERFRINGENS DURING COOLING OF COOKED GROUND CHICKEN
Technology Transfer Automated Retrieval System (TEKTRAN)
Traditional methodologies for development of microbial growth models under dynamic temperature conditions do not take adequate account for the organism’s history. Such models were shown to be inadequate in predicting growth of the organisms under dynamic conditions commonly encountered in the food i...
Final Report on the Evaluation of the Growth Model Pilot Project
ERIC Educational Resources Information Center
Hoffer, Thomas B.; Hedberg, E. C.; Brown, Kevin L.; Halverson, Marie L.; Reid-Brossard, Paki; Ho, Andrew D.; Furgol, Katherine
2011-01-01
The U.S. Department of Education (ED) initiated the Growth Model Pilot Project (GMPP) in November 2005 with the goal of approving up to ten states to incorporate growth models in school adequate yearly progress (AYP) determinations under the "Elementary and Secondary Education Act" ("ESEA"). After extensive reviews, nine states were fully approved…
Modelling the growth of Populus species using Ecosystem Demography (ED) model
NASA Astrophysics Data System (ADS)
Wang, D.; Lebauer, D. S.; Feng, X.; Dietze, M. C.
2010-12-01
Hybrid poplar plantations are an important source being evaluated for biomass production. Effective management of such plantations requires adequate growth and yield models. The Ecosystem Demography model (ED) makes predictions about the large scales of interest in above- and belowground ecosystem structure and the fluxes of carbon and water from a description of the fine-scale physiological processes. In this study, we used a workflow management tool, the Predictive Ecophysiological Carbon flux Analyzer (PECAn), to integrate literature data, field measurement and the ED model to provide predictions of ecosystem functioning. Parameters for the ED ensemble runs were sampled from the posterior distribution of ecophysiological traits of Populus species compiled from the literature using a Bayesian meta-analysis approach. Sensitivity analysis was performed to identify the parameters which contribute the most to the uncertainties of the ED model output. Model emulation techniques were used to update parameter posterior distributions using field-observed data in northern Wisconsin hybrid poplar plantations. Model results were evaluated with 5-year field-observed data in a hybrid poplar plantation at New Franklin, MO. ED was then used to predict the spatial variability of poplar yield in the coterminous United States (United States minus Alaska and Hawaii). Sensitivity analysis showed that root respiration, dark respiration, growth respiration, stomatal slope and specific leaf area contribute the most to the uncertainty, which suggests that our field measurements and data collection should focus on these parameters. The ED model successfully captured the inter-annual and spatial variability of the yield of poplar. Analyses in progress with the ED model focus on evaluating the ecosystem services of short-rotation woody plantations, such as impacts on soil carbon storage, water use, and nutrient retention.
NASA Astrophysics Data System (ADS)
Spangler, J.; Schulz, C. J.; Childers, G. W.
2009-12-01
Modeling microbial respiration and growth is an important tool for understanding many geochemical systems. The estimation of growth parameters relies on fitting experimental data to a selected model, such as the Monod equation or some variation, most often under batch or continuous culture conditions. While continuous culture conditions can be analogous to some natural environments, it often isn’t the case. More often, microorganisms are subject to fluctuating temperature, substrate concentrations, pH, water activity, and inhibitory compounds, to name a few. Microbial growth estimation under non-isothermal conditions has been possible through use of numerical solutions and has seen use in the field of food microbiology. In this study, numerical solutions were used to extend growth models under more non-isostatic conditions using momentary growth rate estimates. Using a model organism common in wastewater (Paracoccus denitrificans), growth and respiration rate parameters were estimated under varying static conditions (temperature, pH, electron donor/acceptor concentrations) and used to construct a non-isostatic growth model. After construction of the model, additional experiments were conducted to validate the model. These non-isostatic models hold the potential for allowing the prediction of cell biomass and respiration rates under a diverse array of conditions. By not restricting models to constant environmental conditions, the general applicability of the model can be greatly improved.
Identification and automatic segmentation of multiphasic cell growth using a linear hybrid model.
Hartmann, András; Neves, Ana Rute; Lemos, João M; Vinga, Susana
2016-09-01
This article considers a new mathematical model for the description of multiphasic cell growth. A linear hybrid model is proposed and it is shown that the two-parameter logistic model with switching parameters can be represented by a Switched affine AutoRegressive model with eXogenous inputs (SARX). The growth phases are modeled as continuous processes, while the switches between the phases are considered to be discrete events triggering a change in growth parameters. This framework provides an easily interpretable model, because the intrinsic behavior is the same along all the phases but with a different parameterization. Another advantage of the hybrid model is that it offers a simpler alternative to recent more complex nonlinear models. The growth phases and parameters from datasets of different microorganisms exhibiting multiphasic growth behavior such as Lactococcus lactis, Streptococcus pneumoniae, and Saccharomyces cerevisiae, were inferred. The segments and parameters obtained from the growth data are close to the ones determined by the experts. The fact that the model could explain the data from three different microorganisms and experiments demonstrates the strength of this modeling approach for multiphasic growth, and presumably other processes consisting of multiple phases. PMID:27424949
Calibration of the Sleuth Model Based on the Historic Growth of Houston
NASA Astrophysics Data System (ADS)
Hakan, O.; Klein, A. G.; Srinivasan, R.
The SLEUTH cellular automaton urban growth model was calibrated against historical growth in the Houston-Galveston-Brazoria Consolidated Metropolitan Statistical Area (Houston CMSA) from 1974-2002. The Houston CMSA presents an interesting case study of modeling urban growth using SLEUTH. Houston is perhaps the archetypal Sunbelt city and experienced rapid population growth over the calibration period. Compared to many other United States cities, Houstonxs local governments have a laissez-faire approach to development; in fact Houston is the only major US metropolitan area with no zoning regulations. Calibration of SLEUTH reveals that over the study period urban growth in the Houston CMSA was dominated organic growth, with urban expansion occurring at the urban edges of existing urban centers. Lack of zoning regulations is thought to play an important role on the outward growth of urbanization in Houston.
Exploring growth kinetics of carbon nanotube arrays by in situ optical diagnostics and modeling
Puretzky, Alexander A; Geohegan, David B; Pannala, Sreekanth; Rouleau, Christopher
2014-01-01
Simple kinetic models of carbon nanotube growth have been able to successfully link together many experimental parameters involved in the growth of carbon nanotubes for practical applications including the prediction of growth rates, terminal lengths, number of walls, activation energies, and their dependences on the growth environment. The implications of recent experiments utilizing in situ monitoring of carbon nanotube growth on our past kinetic model are first reviewed. Then, sub-second pulsed feedstock gas introduction is discussed to explore the nucleation and initial growth of carbon nanotubes in the context of the kinetic model. Moreover, kinetic effects in "pulsed CVD" - using repeated pulsed gas introduction to stop and restart nanotube growth - are explored to understand renucleation, the origin of alignment in nanotube arrays, and incremental growth. Time-resolved reflectivity of the surface is used to remotely understand the kinetics of nucleation and the coordinated growth of arrays. This approach demonstrates that continuous vertically aligned single wall carbon nanotubes can be grown incrementally by pulsed CVD, and that the first exposure of fresh catalyst to feedstock gas is critical to nanotubes site density required for coordinated growth. Aligned nanotube arrays (as short as 60 nm) are shown to nucleate and grow within single, sub-second gas pulses. The multiple-pulse growth experiments (> 100 pulses) show that a high fraction of nanotubes renucleate on subsequent gas pulses.
Keren, Leeat; Segal, Eran; Milo, Ron
2016-01-01
Most proteins show changes in level across growth conditions. Many of these changes seem to be coordinated with the specific growth rate rather than the growth environment or the protein function. Although cellular growth rates, gene expression levels and gene regulation have been at the center of biological research for decades, there are only a few models giving a base line prediction of the dependence of the proteome fraction occupied by a gene with the specific growth rate. We present a simple model that predicts a widely coordinated increase in the fraction of many proteins out of the proteome, proportionally with the growth rate. The model reveals how passive redistribution of resources, due to active regulation of only a few proteins, can have proteome wide effects that are quantitatively predictable. Our model provides a potential explanation for why and how such a coordinated response of a large fraction of the proteome to the specific growth rate arises under different environmental conditions. The simplicity of our model can also be useful by serving as a baseline null hypothesis in the search for active regulation. We exemplify the usage of the model by analyzing the relationship between growth rate and proteome composition for the model microorganism E.coli as reflected in recent proteomics data sets spanning various growth conditions. We find that the fraction out of the proteome of a large number of proteins, and from different cellular processes, increases proportionally with the growth rate. Notably, ribosomal proteins, which have been previously reported to increase in fraction with growth rate, are only a small part of this group of proteins. We suggest that, although the fractions of many proteins change with the growth rate, such changes may be partially driven by a global effect, not necessarily requiring specific cellular control mechanisms. PMID:27073913
Barenholz, Uri; Keren, Leeat; Segal, Eran; Milo, Ron
2016-01-01
Most proteins show changes in level across growth conditions. Many of these changes seem to be coordinated with the specific growth rate rather than the growth environment or the protein function. Although cellular growth rates, gene expression levels and gene regulation have been at the center of biological research for decades, there are only a few models giving a base line prediction of the dependence of the proteome fraction occupied by a gene with the specific growth rate. We present a simple model that predicts a widely coordinated increase in the fraction of many proteins out of the proteome, proportionally with the growth rate. The model reveals how passive redistribution of resources, due to active regulation of only a few proteins, can have proteome wide effects that are quantitatively predictable. Our model provides a potential explanation for why and how such a coordinated response of a large fraction of the proteome to the specific growth rate arises under different environmental conditions. The simplicity of our model can also be useful by serving as a baseline null hypothesis in the search for active regulation. We exemplify the usage of the model by analyzing the relationship between growth rate and proteome composition for the model microorganism E.coli as reflected in recent proteomics data sets spanning various growth conditions. We find that the fraction out of the proteome of a large number of proteins, and from different cellular processes, increases proportionally with the growth rate. Notably, ribosomal proteins, which have been previously reported to increase in fraction with growth rate, are only a small part of this group of proteins. We suggest that, although the fractions of many proteins change with the growth rate, such changes may be partially driven by a global effect, not necessarily requiring specific cellular control mechanisms. PMID:27073913
Creep crack growth predictions in INCO 718 using a continuum damage model
NASA Technical Reports Server (NTRS)
Walker, K. P.; Wilson, D. A.
1985-01-01
Creep crack growth tests have been carried out in compact type specimens of INCO 718 at 1200 F (649 C). Theoretical creep crack growth predictions have been carried out by incorporating a unified viscoplastic constitutive model and a continuum damage model into the ARAQUS nonlinear finite element program. Material constants for both the viscoplastic model and the creep continuum damage model were determined from tests carried out on uniaxial bar specimens of INCO 718 at 1200 F (649 C). A comparison of the theoretical creep crack growth rates obtained from the finite element predictions with the experimentally observed creep crack growth rates indicates that the viscoplastic/continuum damage model can be used to successfully predict creep crack growth in compact type specimens using material constants obtained from uniaxial bar specimens of INCO 718 at 1200 F (649 C).
A stress driven growth model for soft tissue considering biological availability
NASA Astrophysics Data System (ADS)
Oller, S.; Bellomo, F. J.; Armero, F.; Nallim, L. G.
2010-06-01
Some of the key factors that regulate growth and remodeling of tissues are fundamentally mechanical. However, it is important to take into account the role of bioavailability together with the stresses and strains in the processes of normal or pathological growth. In this sense, the model presented in this work is oriented to describe the growth of soft biological tissue under "stress driven growth" and depending on the biological availability of the organism. The general theoretical framework is given by a kinematic formulation in large strain combined with the thermodynamic basis of open systems. The formulation uses a multiplicative decomposition of deformation gradient, splitting it in a growth part and visco-elastic part. The strains due to growth are incompatible and are controlled by an unbalanced stresses related to a homeostatic state. Growth implies a volume change with an increase of mass maintaining constant the density. One of the most interesting features of the proposed model is the generation of new tissue taking into account the contribution of mass to the system controlled through biological availability. Because soft biological tissues in general have a hierarchical structure with several components (usually a soft matrix reinforced with collagen fibers), the developed growth model is suitable for the characterization of the growth of each component. This allows considering a different behavior for each of them in the context of a generalized theory of mixtures. Finally, we illustrate the response of the model in case of growth and atrophy with an application example.
Niemi, J K; Sevón-Aimonen, M-L; Stygar, A H; Partanen, K
2015-08-01
The selection of animals for improved performance affects the profitability of pig fattening and has environmental consequences. The goal of this paper was to examine how changes in genetic and market parameters impact the biophysical (feeding patterns, timing of slaughter, nitrogen excretion) and economic (return per pig space unit) results describing pig fattening in a Finnish farm. The analysis can be viewed as focusing on terminal line breeding goals. An integrated model using recursive stochastic dynamic programming and a biological pig growth model was used to estimate biophysical results and economic values. Combining these models allowed us to provide more accurate estimates for the value of genetic improvement and, thus, provide better feedback to animal breeding programs than the traditional approach, which is based on fixed management patterns. Besides the benchmark scenario, the results were simulated for 5 other scenarios. In each scenario, genotype was improved regarding daily growth potential, carcass lean meat content, or the parameters of the Gompertz growth curve (maturing rate [], adult weight of protein [α], and adult weight of lipid mass []). The change in each parameter was equal to approximately 1 SD genetic improvement (ceteris paribus). Increasing , , daily growth potential, or carcass lean meat content increased the return on pig space unit by €12.60, €7.60, €4.10, or €2.90 per year, respectively, whereas an increase in decreased the return by €3.10. The genetic improvement in and resulted in the highest decrease in nitrogen excretion calculated in total or per kilogram of carcass gain but only under the optimal feeding pattern. Simulated changes in the Gompertz growth function parameters imply greater changes in ADG and lean meat content than changes in scenarios focusing on improving ADG and lean meat content directly. The economic value of genetic improvements as well as the quantity of nitrogen excreted during the fattening
A dynamic void growth model governed by dislocation kinetics
NASA Astrophysics Data System (ADS)
Wilkerson, J. W.; Ramesh, K. T.
2014-10-01
Here we examine the role of dislocation kinetics and substructure evolution on the dynamic growth of voids under very high strain rates, and develop a methodology for accounting for these effects in a computationally efficient manner. In particular, we account for the combined effects of relativistic dislocation drag and an evolving mobile dislocation density on the dynamics of void growth. We compare these effects to the constraints imposed by micro-inertia and discuss the conditions under which each mechanism governs the rate of void growth. The consequences of these constraints may be seen in a number of experimental observations associated with dynamic tensile failure, including the extreme rate-sensitivity of spall strength observed in laser shock experiments, an apparent anomalous temperate dependence of spall strength, and some particular features of void size distributions on spall surfaces.