Non-linear growth models for bullfrog tadpoles

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

Continuous pasteurization of egg yolk: Thermophysical properties and process simulation

This article presents empirical correlations to predict the density, specific heat, thermal conductivity and rheological power-law parameters of liquid egg yolk over a temperature range compatible with its industrial thermal processing (0-61 C). Moreover, a mathematical model for a pasteurizer that takes into account the spatial variation of the overall heat transfer coefficient throughout the plate heat exchanger is presented, as are two of its simplified forms. The obtained correlations of thermophysical properties are applied for the simulation of the egg yolk pasteurization, and the obtained temperature profiles are used for evaluating the extent of thermal inactivation. A detailed simulation example shows that there is a considerable deviation between the designed level of heat treatment and that this is predicted through process simulation. It is shown that a reliable mathematical model, combined with specialized thermophysical property correlations, provide a more accurate design of the pasteurization equipment that ensures effective inactivation, while preserving nutritional and sensorial characteristics.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Avaliação do peso à desmama e do ganho médio de peso de bezerros cruzados, no estado do Mato Grosso do Sul

O objetivo deste trabalho foi comparar o desempenho de bezerros mestiços de diferentes grupos genéticos até a desmama. Informações de 3631 bezerros F1 filhos de vacas Nelore com touros Aberdeen Angus, Brangus, Brangus (pelagem vermelha), Canchim, Gelbvieh, Nelore e Simental foram usadas (Grupo 1). Foram usadas também informações de 1896 bezerros de fêmeas Nelore com touros das raças supracitadas e de fêmeas F1 retrocruzadas com touros Gelbvieh e Nelore (Grupo 2). Os pesos à desmama foram ajustados aos 230 dias (PD230) e aos 240 dias (PD240), para os grupos 1 e 2, respectivamente, e o ganho médio diário até a desmama (GMD), para ambos os grupos, foi determinado. O modelo matemático usado nas análises pelo método de quadrados mínimos incluiu os efeitos fixos de grupo contemporâneo (GC), grupo genético do bezerro (GG) e idade do bezerro e idade da vaca. GC e GG influenciaram as características estudadas em ambos os grupos. A idade do bezerro não influiu significativamente no PD230 e GMD no Grupo 1, mas no Grupo 2 foi significativa para PD240 e GMD. A idade da vaca ao parto influenciou as características estudadas tanto no Grupo 1 como no Grupo 2. Os animais cruzados foram superiores aos puros Nelore em ambos os grupos. Foi obtido, a partir do Grupo 2, um terceiro conjunto de dados, Grupo 3, contendo os produtos do retrocruzamento de fêmeas F1, Nelore-Gelbvieh, com touros Gelbvieh e Nelore, contendo 722 informações de PD240 e GMD. Nesse arquivo foram estimados os efeitos aditivos direto e materno e heterótico individual. Apenas o efeito heterótico individual foi significativo.

Non-local interactions and the dynamics of dispersal in immature insects

A simple mathematical model is developed to explain the appearance of oscillations in the dispersal of larvae from the food source in experimental populations of certain species of blowflies. The life history of the immature stage in these flies, and in a number of other insects, is a system with two populations, one of larvae dispersing on the soil and the other of larvae that burrow in the soil to pupate. The observed oscillations in the horizontal distribution of buried pupae at the end of the dispersal process are hypothesized to be a consequence of larval crowding at a given point in the pupation substrate. It is assumed that dispersing larvae are capable of perceiving variations in density of larvae buried at a given point in the substrate of pupation, and that pupal density may influence pupation of dispersing larvae. The assumed interaction between dispersing larvae and the larvae that are burrowing to pupate is modeled using the concept of non-local effects. Numerical solutions of integro-partial differential equations developed to model density-dependent immature dispersal demonstrate that variation in the parameter that governs the non-local interaction between dispersing and buried larvae induces oscillations in the final horizontal distribution of pupae. (C) 1997 Academic Press Limited.

Transmission network expansion planning with security constraints

A mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints are presented. The methodology allows one to find an optimal and reliable transmission network expansion plan using a DC model to represent the electrical network. The security (n-1) criterion is used. The model presented is solved using a genetic algorithm designed to solve the reliable expansion planning in an efficient way. The results obtained for several known systems from literature show the excellent performance of the proposed methodology. A comparative analysis of the results obtained with the proposed methodology is also presented.

Application of rotor response analysis to fault detection in hydro powerplants.

In this article some considerations obtained during the utilization of rotor response analysis techniques in hydraulic powerplants are discussed. An applied research work was carried out in two hydraulic turbines analysing the rotor response both theoretically and experimentally. A developed mathematical model was used to simulate the rotordynamic behaviour of Francis and Kaplan turbines. The main dynamical effects that appear during the operation of the machines are discussed too. A series of measurements were carried out in the turbines using impact hammers to determine the modal behaviour of the units. The tests were carried out with the machine still and in operation. Some results and the comparison with the theory is presented in this article. The improved theoretical model was used for a sensitivity analysis of the different bearings to the main excitations that fake place during the machine operation. From this analysis, the best measuring points for condition monitoring were determined.

Energy balance optimization of sugarcane crop residual biomass

This work presents a mathematical model for helping mills choose sugarcane varieties for planting. It maximizes crop residual biomass energy balance by considering the difference between generated and consumed energy in the process of transferring this biomass from the field to the processing center; it takes into account enterprise demand restrictions and cane planting area. For this full zero-one linear programming techniques were proposed. The model is viable for choosing sugarcane varieties that would benefit sugarcane production and industrial systems, by reducing crop residue and increasing final energy production. (c) 2006 Published by Elsevier Ltd.

Modelling and optimization of the cephalosporin C production bioprocess in a fed-batch bioreactor with invert sugar as substrate

Cephalosporin C production process optimization was studied based on four experiments carried out in an agitated and aerated tank fermenter operated as a fed-batch reactor. The microorganism Cephalosporium acremonium ATCC 48272 (C-10) was cultivated in a synthetic medium containing glucose as major carbon and energy source. The additional medium contained a hydrolyzed sucrose solution as the main carbon and energy source and it was added after the glucose depletion. By manipulating the supplementary feed rate, it was possible to increase antibiotic production. A mathematical model to represent the fed-batch production process was developed. It was observed that the model was applicable under different operation conditions, showing that optimization studies can be made based on this model. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Rotor support stiffness estimation by sensitivity analysis

In the present work, a method for rotor support stiffness estimation via a model updating process using the sensitivity analysis is presented. This method consists in using the eigenvalues sensitivity analysis, relating to the rotor support stiffnesses variation to perform the adjustment of the model based on the minimization of the difference between eigenvalues of reference and eigenvalues obtained via mathematical model from previously adopted support bearing stiffness values. The mathematical model is developed by the finite element method and the method of adjustment should converge employing an iterative process. The performance and robustness of the method have been analyzed through a numerical example.

On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Modeling and simulation of cephalosporin C production in a fed-batch tower-type bioreactor

Immobilized cell utilization in tower-type bioreactor is one of the main alternatives being studied to improve the industrial bioprocess. Other alternatives for the production of beta -lactam antibiotics, such as a cephalosporin C fed-batch p recess in an aerated stirred-tank bioreactor with free cells of Cepha-losporium acremonium or a tower-type bioreactor with immobilized cells of this fungus, have proven to be more efficient than the batch profess. In the fed-batch process, it is possible to minimize the catabolite repression exerted by the rapidly utilization of carbon sources (such as glucose) in the synthesis of antibiotics by utilizing a suitable flow rate of supplementary medium. In this study, several runs for cephalosporin C production, each lasting 200 h, were conducted in a fed-batch tower-type bioreactor using different hydrolyzed sucrose concentrations, For this study's model, modifications were introduced to take into account the influence of supplementary medium flow rate. The balance equations considered the effect of oxygen limitation inside the bioparticles. In the Monod-type rate equations, eel concentrations, substrate concentrations, and dissolved oxygen were included as reactants affecting the bioreaction rate. The set of differential equations was solved by the numerical method, and the values of the parameters were estimated by the classic nonlinear regression method following Marquardt's procedure with a 95% confidence interval. The simulation results showed that the proposed model fit well with the experimental data,and based on the experimental data and the mathematical model an optimal mass flow rate to maximize the bioprocess productivity could be proposed.

Influence of solid wastes in the mycelium growth of Lentinula edodes (berk.) Pegler

In Brazil there was little research related to Shiitake axenic culture. The aim of this research was to understand the substratum effects in the kinetics of the Shiitake mycelium growth. It was used two Shiitake strains and two different base substrate (eucalyptus sawdust and sugar cane bagasse) varying in three proportions of the supplements. The supplements, a blend of rice and wheat brans, were added in the proportion of 0, 10 and 20% of the base substrate. The experiment was composed of six treatments. The mycelium growth kinetics in volume had no effect relation to the strains and substrate and it followed a mathematical model represented by logarithmic equation. Beta, gamma and delta parameters didn't show any correlation with the growth velocity in volume. The strain L55 was better adapted than L17.

Concentration profiles and effective diffusion coefficients of sucrose and water in osmo-dehydrated apples

The spatial distribution of water and sugars in half-fresh apples dehydrated in sucrose solutions (30% and 50% w/w, 27 degrees C) for 2, 4 and 8 h, was determined. Each half was sliced as from the exposed surface. The density, water and sugar contents were determined for each piece. A mathematical model was fitted to the experimental data of the water and sucrose contents considering the overall flux and tissue shrinkage. A numerical method of finite differences permitted the calculation of the effective diffusion coefficients as a function of concentration, using material coordinates and integrating the two differential equations (for water and sucrose) simultaneously. The coefficients obtained were one or even two orders of magnitude lower than those for pure solutions and presented unusual concentration dependence. The behaviour of the apple tissue was also studied using light microscopy techniques to obtain images of the osmotically treated pieces (20%, 30% and 50% w/w sucrose solutions for 2, 4 and 8 h). (c) 2006 Elsevier Ltd. All rights reserved.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).