LOCAL GROWTH MODELS

1989 ◽  
pp. 101-133
Keyword(s):  
2020 ◽  
Author(s):  
Nabil T. Fadai ◽  
Matthew J. Simpson

AbstractThe Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.


Author(s):  
T. S. Kuan

Recent electron diffraction studies have found ordered phases in AlxGa1-xAs, GaAsxSb1-x, and InxGa1-xAs alloy systems, and these ordered phases are likely to be found in many other III-V ternary alloys as well. The presence of ordered phases in these alloys was detected in the diffraction patterns through the appearance of superstructure reflections between the Bragg peaks (Fig. 1). The ordered phase observed in the AlxGa1-xAs and InxGa1-xAs systems is of the CuAu-I type, whereas in GaAsxSb1-x this phase and a chalcopyrite type ordered phase can be present simultaneously. The degree of order in these alloys is strongly dependent on the growth conditions, and during the growth of these alloys, high surface mobility of the depositing species is essential for the onset of ordering. Thus, the growth on atomically flat (110) surfaces usually produces much stronger ordering than the growth on (100) surfaces. The degree of order is also affected by the presence of antiphase boundaries (APBs) in the ordered phase. As shown in Fig. 2(a), a perfectly ordered In0.5Ga0.5As structure grown along the <110> direction consists of alternating InAs and GaAs monolayers, but due to local growth fluctuations, two types of APBs can occur: one involves two consecutive InAs monolayers and the other involves two consecutive GaAs monolayers.


2008 ◽  
Author(s):  
Stephen Tse ◽  
Fusheng Xu ◽  
Cassandra D'Esposito ◽  
Xiaofei Liu ◽  
Bernard Kear

Author(s):  
Mario Lesina ◽  
Lovorka Gotal Dmitrovic

The paper shows the relation among the number of small, medium and large companies in the leather and footwear industry in Croatia, as well as the relation among the number of their employees by means of the Spearman and Pearson correlation coefficient. The data were collected during 21 years. The warning zone and the risk zone were determined by means of the Statistical Process Control (SPC) for a certain number of small, medium and large companies in the leather and footwear industry in Croatia. Growth models, based on externalities, models based on research and development and the AK models were applied for the analysis of the obtained research results. The paper shows using the correlation coefficients that The relation between the number of large companies and their number of employees is the strongest, i.e. large companies have the best structured work places. The relation between the number of medium companies and the number of their employees is a bit weaker, while there is no relation in small companies. This is best described by growth models based on externalities, in which growth generates the increase in human capital, i.e. the growth of the level of knowledge and skills in the entire economy, but also deductively in companies on microeconomic level. These models also recognize the limit of accumulated knowledge after which growth may be expected. The absence of growth in small companies results from an insufficient level of human capital and failure to reach its limit level which could generate growth. According to Statistical Process Control (SPC), control charts, as well as regression models, it is clear that the most cost-effective investment is the investment into medium companies. The paper demonstrates the disadvantages in small, medium and large companies in the leather and footwear industry in Croatia. Small companies often emerge too quickly and disappear too easily owing to the employment of administrative staff instead of professional production staff. As the models emphasize, companies need to invest into their employees and employ good production staff. Investment and support to the medium companies not only strengthens the companies which have a well-arranged technological process and a good systematization of work places, but this also helps large companies, as there is a strong correlation between the number of medium and large companies.


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