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.

Mathematical modeling of the ester oil-refrigerant R134A mixture two-phase flow with foam formation through a small diameter tube

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

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.

Simulação de modelagem qualitativa para avaliação preliminar da qualidade da água na Bacia do Ribeirão das Perdizes em Campos do Jordão/SP, como subsídio ao enquadramento

The purpose of this research was to present the principles for the implementation of a future water body classification program at the UGRHI-1 (Management Unit of Water Resources-1/São Paulo, Brazil) using qualitative and quantitative water modeling. Our study area was in Campos do Jordão, a city in the state of São Paulo, specifically in the Perdizes river watershed, which is included in the UGRHI-1. The water quality assessment used a modeling mehtodology that can support a future study for the classification of water bodies in the region. The behavior of DO and BOD parameters was assessed in the water quality scenarios, considering the variations of flows, loads, reductions in withdrawals and different efficiencies in sewage treatment. The model used was QUAL2E developed by USEPA (United States Environmental Protection Agency) that received a new graphic interface named QUAL2R model. The reference flows Q7,10, Q95% and Qm used were obtained through the DAEE (Department of Water and Electric Energy) hydrologic regionalization method. It was noted that of the 9 proposed scenarios, only scenario 6 that was predicted in the flow regime Qm with the existence of a treatment system capable of removing 93% of the BOD, in the Perdizes River remained 67.5% of the time in class 2. Scenario 8 predicted a 50% reduction in In scenario 8 a reduction of 50% in the flow captured in CA-04, associated with the efficiency of 93% of BOD removal keeping the river in class 2. In scenario 9 the minimum required efficiency in sewage treatment in the flow regime Q95% for keeping the river in class 2 was also calculated and the value of 94.7% was obtained.

Water quality index as a simple indicator of aquaculture effects on aquatic bodies

This paper proposes a water quality index (WQI) to subsidize management actions in the Medio Paranapanema Watershed in São Paulo State, Brazil, as a simple pollution indicator for aquaculture activity. Water quality of the Macuco and Queixada rivers was investigated for 2 years (from May 2003 to May 2005). The index proposed in this work is composed of three measurable environmental parameters-turbidity, total phosphorus and dissolved oxygen. Concentrations of these three variables were normalized on a scale from 0 to 100 and translated into statements of water quality (excellent, good, regular, fair and poor). The index was applied to seventeen monitoring points in the aquatic bodies described above and compared to others, one being that used by the Environmental Protection Agency of United States and proposed for the National Sanitation Foundation, other employing minimal index and the last one considering the minimum operator concept. The results show that the degradation in this watershed from aquaculture activity can be easily inferred with this index, which is more restricted than the others routinely used to infer water quality. (C) 2007 Elsevier Ltd. All rights reserved.

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Spatial and temporal quality of water in the Itupararanga Reservoir, Alto Sorocaba basin (SP), Brazil

Considering the great importance of the Itupararanga Reservoir, Upper Alto Sorocaba basin/SP, this study aimed to report the variations of some parameters of water quality in the spatial and temporal gradients in this multipurpose res- ervoir. The eutrophication of this reservoir was checked using the Carlson Index Modified and the results indicate that the surface water were classified as eutrophic and mesotrophic in wet and dry periods, being characterized the better quality of water in wet period. In the vertical gradient the results showed a stratiphication in all parameters analyzed, except for the electrical conductivity, with good correlation between total phosphorous and chlorophyll-a, indicating that eutrophication of the reservoir changes the conditions of algal growth, mainly in its initial area. Immediate inter- ventions are needed, which must be directed to planning of land use, domestic effluents treatment, taking to an inte- grated management of this important watershed located in the São Paulo State.

Water quality and plankton populations in an earthen polyculture pond

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fuzzy Index for Public Supply Water Quality

Human population growth and increased industrial activity in recent decades have contributed to a range of environmental problems, including the contamination of groundwater and surface water. In order to help in the management of these resources, water quality indices are used as tools to summarize multiple parameters and express them in the form of a single number. The ability to provide both an integrated assessment of changes in environmental variables, as well as performance tracking, has resulted in such indices being increasingly employed in surface water monitoring programs. The aim of this study was to develop an Index for Public Supply Water Quality (IPS) using a fuzzy inference methodology. Linguistic systems generally provide satisfactory tools for qualitative purposes, enabling the inclusion of descriptive variables with reduced loss of individual information. Validation of the technique was achieved by analysis of measurement data obtained for the Sorocaba River, provided by CETESB. The new procedure proved more rigorous, compared to classical IPS. It could be readily applied in the evaluation of other water bodies, or be adjusted to incorporate additional parameters also considered important for the assessment of water quality.

Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K (a) and K (b). Typical values for these parameters were used, i. e., K (a) = 3.68 x 10(-5)-1.83 x 10(-4) and K (b) = 1.83 x 10(-7)-2.30 x 10(-7) s(-1). The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20-60 s(-1) and flocculation efficiencies of 50-90 % were adopted.

Water quality and zooplankton in tanks with larvae of Brycon Orbignyanus (Valenciennes, 1949)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of rainfall on water quality in six sequentially disposed fishponds with continuous water flow

O estudo foi efetuado durante o período de chuva (dezembro-fevereiro) em seis viveiros de produção semi-intensiva de peixes, a fim de avaliar o efeito da chuva na qualidade da água de viveiros que apresentam fluxo contínuo de água, a qual é passada de um viveiro para outro sem tratamento prévio. Foram amostrados oito pontos de coleta nas saídas dos viveiros. O viveiro P1 (próximo à nascente) apresentou as menores concentrações físicas e químicas da água e as maiores no viveiro P4 (considerado um ponto crítico recebendo material alóctone proveniente de outros viveiros e do escoamento do setor de criação de rãs). A disposição seqüencial dos viveiros estudados promoveu aumento nas concentrações dos nutrientes, clorofila-a e condutividade. As chuvas características desta época do ano aumentaram o fluxo de água nos viveiros e conseqüentemente, carreando material particulado e dissolvido de um viveiro para outro e, promovendo um aumento das variáveis limnológicas em direção do P3 ao P6. Os resultados sugerem que a chuva no período de estudo afetou positivamente a qualidade da água dos viveiros estudados, porém, como os sistemas analisados estão dispostos em distribuição seqüencial e escoamento constante da água de viveiros e tanques paralelos sem tratamento prévio, cuidados devem ser averiguados para que o aumento do fluxo de água provocado pelas chuvas não tenha efeito adverso nos viveiros estudados.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

Effect of the litter material on drinking water quality in broiler production

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)