Microbial Growth and Decay: A Commented Review of the Model

The paper reviews previous publications and reports some comments about a semi empirical model of the growth and decay process of a planktonic microbial culture. After summarizing and reshaping some fundamental mathematical expressions, the paper highlights the reasons for the choice of a suitable time origin that makes the parameters of the model self-consistent. Besides the potential applications to predictive microbiology studies and to effects of bactericidal drugs, the model allows a suitable proxy of the fitness of the microbial culture, which can be of interest for the studies on the evolution across some thousand generations of a Long Term Evolution Experiment.

Differential Calculus the Study of the Growth and Decay of an Entity’s Population

Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, i.e. when the resources are unlimited, a population P believes according to the following differential equation P’ = KP, with the application of the differential calculus we obtasin an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

Model simulations of the annual cycle of the landfast ice thickness in the East Siberian Sea

The annual cycle of the thickness and temperature of landfast sea ice in the East Siberian Sea has been examined using a one-dimensional thermodynamic model. The model was calibrated for the year August 2012-July 2013, forced using the data of the Russian weather station Kotel＇ny Island and ECMWF reanalyses. Thermal growth and decay of ice were reproduced well, and the maximum annual ice thickness and breakup day became 1.64 m and the end of July. Oceanic heat flux was 2 W.m^-2 in winter and raised to 25 W.m^-2 in summer, albedo was 0.3-0.8 depending on the surface type （snow/ice and wet/dry）. The model outcome showed sensitivity to the albedo, air temperature and oceanic heat flux. The modelled snow cover was less than 10 cm having a small influence on the ice thickness. In situ sea ice thickness in the East Siberian Sea is rarely available in publications. This study provides a method for quantitative ice thickness estimation by modelling. The result can be used as a proxy to understand the sea ice conditions on the Eurasian Arctic coast, which is important for shipping and high-resolution Arctic climate modelling.

Experiments and modelling of phenanthrene biodegradation in the aqueous phase by a mixed culture

Pollution by polycyclic aromatic hydrocarbons（PAHs） is widespread due to tmsuitable disposal of industrial waste. They are mostly defined as priority pollutants by environmental protection authorities worldwide. Phenanthrene, a typical PAH, was selected as the target in this paper. The PAH-degrading mixed culture, named ZM, was collected from a petroleum contaminated river bed. This culture was injected into phenanthrene solutions at different concentrations to quantify the biodegradation process. Results show near-complete removal of phenanthrene in three days of biodegradation if the initial phenanthrene concentration is low. When the initial concentration is high, the removal rate is increased but 20%-40% of the phenanthrene remains at the end of the experiment. The biomass shows a peak on the third day due to the combined effects of microbial growth and decay. Another peak is evident for cases with a high initial concentration, possibly due to production of an intermediate metabolite. The pH generally decreased during biodegradation because of the production of organic acid. Two phenomenological models were designed to simulate the phenanthrene biodegradation and biomass growth. A relatively simple model that does not consider the intermediate metabolite and its inhibition of phenanthrene biodegradation cannot fit the observed data. A modified Monod model that considered an intermediate metabolite （organic acid） and its inhibiting reversal effect reasonably depicts the experimental results.

Modeling and simulation of landfill gas production from pretreated MSW landfill simulator

The cumulative landfill gas （LFG） production and its rate were simulated for pretreated municipal solid waste （MSW） landfill using four models namely first order exponential model, modified Gompertz model, single component combined growth and decay model and Gaussian function. Considering the behavior of the pretreated MSW landfill, a new multi component model was based on biochemical processes that occurring in landfilled pretreated MSW. The model was developed on the basis of single component combined growth and decay model using an anaerobic landfill simulator reactor which treats the pretreated MSW. It includes three components of the degradation i.e. quickly degradable, moderately degradable and slowly degradable. Moreover, the devel- oped model was statistically analyzed for its goodness of fit. The results show that the multi components LFG production model is more suitable in comparison to the simulated models and can efficiently be used as a modeling tool for pretreated MSW landfills. The proposed model is likely to give assistance in sizing of LFG collection system, generates speedy results at lower cost, improves cost-benefit analysis and decreases LFG project risk. It also indicates the stabilization of the landfill and helps the managers in the reuse of the landfill space. The proposed model is limited to aerobically pretreated MSW landfill and also requires the values of delay times in LFG productions from moderately and slowly degradable fractions ofpretreated MSW.