Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle

Experiments of continuous alcoholic fermentation of sugarcane juice with flocculating yeast recycle were conducted in a system of two 0.22-L tower bioreactors in series, operated at a range of dilution rates (D (1) = D (2) = 0.27-0.95 h(-1)), constant recycle ratio (alpha = F (R) /F = 4.0) and a sugar concentration in the feed stream (S (0)) around 150 g/L. The data obtained in these experimental conditions were used to adjust the parameters of a mathematical model previously developed for the single-stage process. This model considers each of the tower bioreactors as a perfectly mixed continuous reactor and the kinetics of cell growth and product formation takes into account the limitation by substrate and the inhibition by ethanol and biomass, as well as the substrate consumption for cellular maintenance. The model predictions agreed satisfactorily with the measurements taken in both stages of the cascade. The major differences with respect to the kinetic parameters previously estimated for a single-stage system were observed for the maximum specific growth rate, for the inhibition constants of cell growth and for the specific rate of substrate consumption for cell maintenance. Mathematical models were validated and used to simulate alternative operating conditions as well as to analyze the performance of the two-stage process against that of the single-stage process.

A mathematical view of water table fluctuations in a shallow aquifer in Brazil

Detailed monitoring of the groundwater table can provide important data about both short- and long-term aquifer processes, including information useful for estimating recharge and facilitating groundwater modeling and remediation efforts. In this paper, we presents results of 4 years (2002 to 2005) of monitoring groundwater water levels in the Rio Claro Aquifer using observation wells drilled at the Rio Claro campus of São Paulo State University in Brazil. The data were used to follow natural periodic fluctuations in the water table, specifically those resulting from earth tides and seasonal recharge cycles. Statistical analyses included methods of time-series analysis using Fourier analysis, cross-correlation, and R/S analysis. Relationships could be established between rainfall and well recovery, as well as the persistence and degree of autocorrelation of the water table variations. We further used numerical solutions of the Richards equation to obtain estimates of the recharge rate and seasonable groundwater fluctuations. Seasonable soil moisture transit times through the vadose zone obtained with the numerical solution were very close to those obtained with the cross-correlation analysis. We also employed a little-used deep drainage boundary condition to obtain estimates of seasonable water table fluctuations, which were found to be consistent with observed transient groundwater levels during the period of study.

Theoretical approaches to forensic entomology: I. Mathematical model of postfeeding larval dispersal

An overall theoretical approach to model phenomena of interest for forensic entomology is advanced. Efforts are concentrated in identifying biological attributes at the individual, population and community of the arthropod fauna associated with decomposing human corpses and then incorporating these attributes into mathematical models. In particular in this paper a diffusion model of dispersal of post feeding larvae is described for blowflies, which are the most common insects associated with corpses.