56 resultados para Logistic growth equation


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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.

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Experimental programs in constant and variable amplitude loading were performed to obtain a x N curves and to study retardation in fatigue crack growth due to overloads. The main aim of this research program was to analyse the effect of overload ratio and number of overload peaks. The effect of underloads, before and after the overload blocks was also studied. The generalised equation of Paris-Erdogan type was used for modelling of obtained data on crack propagation under constant amplitude load.

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The adsorption process in layer-by-layer (LBL) films of poly(o-methoxyaniline) alternated with poly(vinyl sulfonic acid) is explained using the Avrami equation. This equation was used due to its mathematical simplicity and adequate description of experimental data in real polymer systems. The Avrami parameters are a convenient means to represent empirical data of crystallization, and if microscopic knowledge is available these parameters can also be associated with adsorption mechanisms. The growth of spherulites in the LBL films was studied as a function of time using atomic force microscopy and the data were used to estimate the number and radii of aggregates, from which the Avrami parameters were determined. We find that the adsorption mechanism may correspond to a tri dimensional, diffusion-controlled growth, with increasing nucleation rate, consistent with results from kinetics of adsorption.

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

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This paper presents the theoretical and experimental results for oxide thin film growth on titanium films previously deposited over glass substrate. Ti films of thickness 0.1 μm were heated by Nd:YAG laser pulses in air. The oxide tracks were created by moving the samples with a constant speed of 2 mm/s, under the laser action. The micro-topographic analysis of the tracks was performed by a microprofiler. The results taken along a straight line perpendicular to the track axis revealed a Gaussian profile that closely matches the laser's spatial mode profile, indicating the effectiveness of the surface temperature gradient on the film's growth process. The sample's micro-Raman spectra showed two strong bands at 447 and 612 cm -1 associated with the TiO 2 structure. This is a strong indication that thermo-oxidation reactions took place at the Ti film surface that reached an estimated temperature of 1160 K just due to the action of the first pulse. The results obtained from the numerical integration of the analytical equation which describes the oxidation rate (Wagner equation) are in agreement with the experimental data for film thickness in the high laser intensity region. This shows the partial accuracy of the one-dimensional model adopted for describing the film growth rate. © 2001 Elsevier Science B.V.

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The growth of the mouse parotid glands during 7 and 35 days of postnatal life was studied by morphometric methods. The mass of the gland, the volume of each morphological compartment, and the cell number in each compartment were evaluated. The data obtained for each evaluated dimension were adjusted by an exponential equation, of the type Y = a.e KX, thus permitting the calculation of their mean duplication time (T D), i.e., an estimation of their growth rate. Analysis of the results showed a marked 1,424% increase in the gland mass during the whole studied period, with T D = 7.10 days. This growth occurred by increases in absolute volume of acini, intercalated ducts, striated ducts, excretory ducts and stroma, with percentual increases of 3,048%, 417%, 2,662%, 2,594% and 367%, respectively, and T Ds of 5.62, 11.71, 5.55, 5.47 and 14.45 days, respectively. Analysis of the cell number growth in each compartment showed increases of 1,904%, 285%, 1,228%, 1,090% and 286%, respectively, and T Ds of 6.62, 20.40, 7.19, 7.26 and 14.51 days, respectively. Based on the present results, we concluded that the growth of the mouse parotid glands from day 7 to day 35 of age occurred by intense cell accumulation, mainly in the acini, striated ducts and excretory ducts, with a growth rate sensibly higher than that of the intercalated ducts and stroma.

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Thermal transformations on microalloyed steels can produce multiphase microstructures with different amounts of ferrite, martensite, bainite and retained austenite. These different phases, with distinct morphologies, are determinant of the mechanical behavior of the steel and can, for instance, affect the crack path or promote crack shielding, thus resulting in changes on its propagation rate under cyclic loading. The aim of the present work is to evaluate the effects of microstructure on the tensile strength and fatigue crack growth (FCG) behaviour of a 0.08%C-1,5%Mn (wt. pct.) microalloyed steel, recently developed by a Brazilian steel maker under the designation of RD480. This steel is being considered as a promising alternative to replace low carbon steel in wheel components for the automotive industry. Various microstructural conditions were obtained by means of heat treatments followed by water quench, in which the material samples were kept at the temperatures of 800, 950 and 1200 °C. In order to describe the FCG behavior, two models were tested: the conventional Paris equation and a new exponential equation developed for materials showing non-linear FCG behavior. The results allowed correlating the tensile properties and crack growth resistance to the microstructural features. It is also shown that the Region II FCG curves of the dual and multiphase microstructural conditions present crack growth transitions that are better modeled by dividing them in two parts. The fracture surfaces of the fatigued samples were observed via scanning electron microscopy in order to reveal the fracture mechanisms presented by the various material conditions. © 2010 Published by Elsevier Ltd.

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The aluminum alloy 2524 (Al-Cu-Mg) was developed during the 90s mainly to be employed in aircraft fuselage panels, replacing the standard Al 2024. In the present analysis the fatigue crack growth (FCG) behavior of 2524-T3 was investigated, regarding the influence of three parameters: load ratio, pre strain and crack plane orientation of the material. The pre strain of aluminum alloys is usually performed in order to obtain a more homogeneous precipitates distribution, accompanied by an increase in the yield strength. In this work, it was evaluated the resistance of Al 2524-T3 sheet samples to the fatigue crack growth, having L-T and T-L crack orientations. FCG tests were performed under constant amplitude loading at three distinct positive load ratios. The three material conditions were tested: as received(AR), pre strained longitudinally (SL) and transversally (ST) in relation to rolling direction. In order to describe FCG behavior, two-parameter kinetic equations were compared: a Paris-type potential model and a new exponential equation introduced in a previous work conducted by our research group. It was observed that the exponential model, which takes into account the deviations from linearity presented by da/dN versus AK data, describes more adequately the FCG behavior of Al 224-T3 in relation to load ratio, pre strain effects and crack plane orientation. © 2011 Published by Elsevier Ltd.

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We evaluated the population dynamics of Acetes americanus Ortmann, 1893 focusing on sex ratio, individual growth, longevity, and the juvenile recruitment period. Samples were collected monthly from January 2006 to June 2007 in the bay of Ubatuba, Brazil. Specimen growth was identified for each gender, and the chosen cohorts were fitted in a von Bertalanffy Growth Model (VBGM); longevity was estimated by the von Bertalanffy inverse equation, considering 99% of the asymptotic length. A total of 6881 individuals (2343 males and 4538 females) were captured. On average the body size (total length) was greater in females (14.64 ± 3.34 mm) than in males (12.27 ± 1.86 mm). The mean growth curves (obtained by grouping the cohorts for each sex), provided estimates of TL∞ = 19.33 mm, k = 0.02 and t0 = -0.12 days for females and TL∞ = 15.13 mm, k = 0.03 and to = -0.07 days for males, where TL∞ is the asymptotic length, k is coefficient of growth and to is the theorical age when the size is equal to 0. Longevity was estimated at 0.61 years for females and 0.50 years for males. The sex ratio tended to favor females, which corroborates with others studies of sergestids. Our finding that males of A. americanus have higher values of k and therefore achieve a smaller size relative to females has been observed in other penaeids. We concluded that this differential growth pattern between the sexes is found across Dendrobranchiata. The life cycles of penaeids have an average duration of approximately 1-2 years, but our results corroborate other studies that estimate a shorter longevity for Acetes, as species of this genus are typically smaller in size. We found continuous recruitment with two main peaks observed during the study period, corroborating previous studies of Acetes. © The Crustacean Society, 2013. Published by Brill NV, Leiden.

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The main purpose of this study was to provide an estimate for the onset of morphological sexual maturity in the freshwater crab Trichodactylus fluviatilis, from a population located in south-eastern Brazil, based on the relative growth relationships, as well as the characterization of ''handedness''. Monthly collections were carried out at night, from January 2006 to January 2007, in a small water body. In the laboratory, the crabs were sexed; the following body structures were measured and the estimate of onset of sexual maturity was given by the logistic function, as y a/(1\+becx), for 50% of the population to reach the adult phase (CW50carapace width). Right propodus length and abdomen width were the best-fit relationships to represent the onset of sexual maturity for males and females, respectively. Based on the logistic function, the onset of sexual maturity was estimated to occur at around 18mm CW for both sexes. The relative growth recorded for this species is consistent with the model for brachyuran crabs (Hartnoll RG. 1982, Growth. In: Bliss, DE, editor. The biology of Crustacea: embryology, morphology and genetics. New York: Academic Press. p. 111-196), except for the abdomen growth, which is likely to be an adaptive condition related to protection of the newly hatched young. © 2013 Taylor & Francis.

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This investigation aimed to study the relative growth, morphological sexual maturity and fecundity of the swimming crab Achelous spinicarpus in a tropical region, on the south-eastern continental shelf of Brazil (25°S). Biometry of all specimens was conducted, including measurements of the cephalothorax, cheliped, abdomen and gonopods. Relative growth was described based on the equation for allometry (y = axb), and size at sexual maturity was determined from inflections in relations involving the cheliped, gonopods (males), and abdomen (females), as dependent variables, related to the cephalothorax width (independent variable). Fecundity was estimated by the gravimetric method. The relations of the length of the chelar propodus and carpal spine to the carapace width without the lateral spines (CW) showed positive allometry in both sexes, with a significant variation in the constant 'b' for males between the developmental stages (juvenile and adult) and the size at maturity estimated at 37 mm CW. In females, the abdomen was most appropriate for the estimate of morphological maturity, which occurred at a smaller size (32 mm CW), with a change in the growth pattern between the stages, passing from isometric (juveniles) to positive allometric (adults). The gonopods also showed different growth rates between developmental stages, in synchrony with the variables of the cheliped. Mean fecundity for the species was 53,984 eggs, with a positive correlation between the number of eggs exteriorized and the size of the female; the equations allowed interconversion between these variables, due to the adjustment of the power function (r2 ≥ 86%). © 2012 Marine Biological Association of the United Kingdom.

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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.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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PURPOSE: To measure fetal renal volume in normoglycemic and hyperglycemic pregnancies. METHODS: A longitudinal prospective study was conducted and included 92 hyperglycemic and 339 normoglycemic pregnant women attended at the prenatal service of a hospital from Rio de Janeiro State. Ultrasound examinations were performed to estimate gestational age at baseline and the kidney volume was estimated using the prolate ellipsoid volume equation. RESULTS: Fetal kidney volume growth between normoglycemic and hyperglycemic pregnancies are significantly different. The fetal kidney volume growth in pregnancy is positively correlated with gestational age explained by these predictor equations, by group: normal renal volume = exp (6.186+0.09×gestational week); hyperglycemic renal volume = exp (6.978+0.071×gestational week) and an excessive growth pattern for hyperglycemic pregnancies may be established according to gestational age. CONCLUSION: This is important for early detection of abnormalities in pregnancy, particularly in diabetic mothers.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)