scholarly journals Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions

2021 ◽  
Vol 41 (1) ◽  
pp. 277-296
Author(s):  
João Marcos do Ó ◽  
◽  
Bruno Ribeiro ◽  
Bernhard Ruf ◽  
Keyword(s):  
Exponential Growth ◽  
Elliptic Systems ◽  
Growth Conditions ◽  
Double Exponential

scholarly journals The interplay of phenotypic variability and fitness in finite microbial populations

2020 ◽  
Vol 17 (166) ◽  
pp. 20190827 ◽  
Author(s):  
Ethan Levien ◽  
Jane Kondev ◽  
Ariel Amir
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Finite Population ◽  
Microbial Population ◽  
Phenotypic Variability ◽  
Growth Conditions ◽  
Microbial Populations ◽  
Steady State Distribution ◽  
State Distribution ◽  
History Of

In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler–Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler–Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

scholarly journals EXISTENCE OF SOLUTIONS FOR CRITICAL SYSTEMS WITH VARIABLE EXPONENTS

2018 ◽  
Vol 23 (4) ◽  
pp. 596-610 ◽  
Author(s):  
Hadjira Lalilia ◽  
Saadia Tas ◽  
Ali Djellit
Keyword(s):  
Existence Result ◽  
Existence Of Solutions ◽  
Elliptic Systems ◽  
Growth Conditions ◽  
Critical Growth ◽  
Concentration Compactness ◽  
Variable Exponents ◽  
Critical Systems ◽  
Concentration Compactness Principle ◽  
Compactness Principle

In this work, we deal with elliptic systems under critical growth conditions on the nonlinearities. Using a variant of concentration-compactness principle, we prove an existence result.

scholarly journals Hamiltonian elliptic systems with critical polynomial-exponential growth

2022 ◽  
Vol 214 ◽  
pp. 112579
Author(s):  
João Marcos do Ó ◽  
Abiel Macedo ◽  
Bruno Ribeiro
Keyword(s):  
Exponential Growth ◽  
Elliptic Systems

Controls on Domoic Acid Production by the Diatom Nitzschia pungens f. multiseries in Culture: Nutrients and Irradïance

1991 ◽  
Vol 48 (7) ◽  
pp. 1136-1144 ◽  
Author(s):  
S. S. Bates ◽  
A. S. W. de Freitas ◽  
J. E. Milley ◽  
R. Pocklington ◽  
M. A. Quilliam ◽  
...  
Keyword(s):  
Cell Division ◽  
Stationary Phase ◽  
Exponential Growth ◽  
Domoic Acid ◽  
Culture Medium ◽  
Dark Period ◽  
Growth Conditions ◽  
Dark Cycle ◽  
Division Rate ◽  
Nitzschia Pungens

Nitzschia pungens f. multiseries (clone NPARL) was grown in nonaxenic batch culture under a range of growth conditions. Domoic acid (DA) was not detected during exponential growth, but production promptly started at a rate of approximately 1 pg DA∙cell−1∙d−1 at the onset of the stationary phase, in this case induced by silicate limitation. Cellular DA reached a maximum of 7 pg∙cell−1; thereafter, DA production continued at the same rate, with cellular levels remaining relatively constant due to concurrent release of DA into the culture medium. DA production ceased in the absence of nitrogen during the stationary phase, but resumed when nitrate was added back to the medium. Low irradiance slowed the division rate and consequently delayed the attainment of the stationary phase, but DA production rates were comparable with the control once stationary phase was reached. Cells during the dark period of a light–dark cycle, or placed into darkness, or in the presence of the photosynthetic inhibitor DCMU promptly ceased DA production. We conclude that at least three conditions are required for DA production by clone NPARL: cessation of cell division, availability of nitrogen during the stationary phase, and the presence of light. Growth in medium f/2 fulfils these requirements.

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