A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot-Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna´s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information

Mathematical modelling of neural processes within the oculomotor system

It is presented a mathematical model of the oculomotor plant, based on experimental data in cats. The system that generates, from the neuronal processes at the motoneuron, the control signals to the eye muscles that moves the eye. In contrast with previous models, that base the eye movement related motoneuron behavior on a first order linear differential equation, non-linear effects are described: A dependency on the eye angular position of the model parameters.