971 resultados para Exponential equation


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The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

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The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

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Pratylenchus thornei is a major pathogen of wheat in Australia. Two glasshouse experiments with four wheat cultivars that had different final populations (Pf) of P. thornei in the field were used to optimise conditions for assessing resistance. With different initial populations (Pi) ranging up to 5250 P. thornei/kg soil, Pf of P. thornei increased to 16 weeks after sowing, and then decreased at 20 weeks in some cultivar x Pi combinations. The population dynamics of P. thornei up to 16 weeks were best described by a modified exponential equation P f (t) = aP i e kt where P f (t) is the final population density at time t, P i is the initial population density, a is the proportion of P i that initiates population development, and k is the intrinsic rate of increase of the population. The cultivar GS50a had very low k values at Pi of 5250 and 1050 indicating its resistance, Suneca and Potam had high k values indicating susceptibility, whereas intolerant Gatcher had a low value at the higher Pi and a high value at the lower Pi. Nitrate fertiliser increased plant growth and Pf values of susceptible cultivars, but in unplanted soil it decreased Pf. Nematicide (aldicarb 5 mg/kg soil) killed P. thornei more effectively in planted than in unplanted soil and increased plant growth particularly in the presence of N fertiliser. In both experiments, the wheat cultivars Suneca and Potam were more susceptible than the cultivar GS50a reflecting field results. The method chosen to discriminate wheat cultivars was to assess Pf after growth for 16 weeks in soil with Pi ~1050–5250 P. thornei/kg soil and fertilised with 200 mg NO3–N/kg soil.

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分析了陕北黄土高原典型流域生物结皮的形成和发育对土壤养分的积累效应,同时对生物结皮条件下土壤养分的流失风险进行评价.结果表明:生物结皮生长发育后能够迅速增加结皮层及2cm土层的养分含量,但对深层土壤影响较小;退耕0~20年间结皮层的养分含量与退耕年限之间的关系可用指数函数(y=a[b-exp(-cx)])拟合,其中有机质、全氮和碱解氮在退耕20年间的增加速度变化不大,而全磷、速效磷和速效钾在退耕初期增加迅速,后期增加缓慢;自然发育生物结皮对土壤养分的年均净贡献量为:有机质50.15g.m-2、全氮1.95g.m-2、全磷0.44g.m-2、碱解氮164.33mg.m-2、速效磷9.64mg.m-2和速效钾126.21mg.m-2,人工培育条件下生物结皮发育更快,对养分尤其是速效养分的贡献速率更高;生物结皮条件下养分含量的提高增加了养分流失风险,尤其是养分随泥沙流失大幅度增加,生物结皮增加的养分中平均有39.06%随泥沙流失,仅有60.94%得以保留.总之,生物结皮可迅速、全面增加表层土壤养分,但同时会加大养分流失风险.尽管如此,土壤养分的净增加量仍相当可观,显示生物结皮具有较好的土壤养分积累效应.

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BACKGROUND: The alcohol purchase task (APT), which presents a scenario and asks participants how many drinks they would purchase and consume at different prices, has been used among students and small clinical samples to obtain measures of alcohol demand but not in large, general population samples. METHODS: We administered the APT to a large sample of young men from the general population (Cohort Study on Substance Use Risk Factors). Participants who reported drinking in the past year (n=4790), reported on past 12 months alcohol use, on DSM-5 alcohol use disorder (AUD) criteria and on alcohol related consequences were included. RESULTS: Among the APT's demand parameters, intensity was 8.7 (SD=6.5) indicating that, when drinks are free, participants report a planned consumption of almost 9 drinks. The maximum alcohol expenditure (Omax) was over 35CHF (1CHF=1.1USD) and the demand became elastic (Pmax) at 8.4CHF (SD=5.6). The mean price at which the consumption was suppressed was 15.6CHF (SD=5.4). Exponential equation provided a satisfactory fit to individual responses (mean R(2): 0.8, median: 0.8). Demand intensity was correlated with alcohol use, number of AUD criteria and number of consequences (all r≥0.3, p<0.0001). Omax was correlated with alcohol use (p<0.0001). The elasticity parameter was weakly correlated with alcohol use in the expected direction. CONCLUSION: The APT measures are useful in characterizing demand for alcohol in young men in the general population. Demand may provide a clinically useful index of strength of motivation for alcohol use in general population samples.

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A new synthetic pathway to analogues of the aglucones of naturally occurring cyclic hydroxamic acids (2,4-dihydroxy-l,4-benzoxazin-3-ones) has been developed. The new pathway involves the coupling of substituted nitrophenols wdth /-propyl-abromo- O-methoxymethylglycolate. These materials were reductively cyclised to reveal the hydroxamic acid functionality. Removal of the C-2 0-methoxymethyl protecting group was achieved chemoselectively using boron trichloride. The analogue 7-methoxy-2,4-dihydroxy-l,4-benzoxazin-3-one (DIMBOA) was assayed with papain and a semilog plot of activity of papain in the presence of excess DIMBOA was found to be linear. A single exponential equation was suggested as the model for kinetic analysis. '^ Nuclear magnetic resonance (NMR) spectra of a couple of hydroxamates were acquired as reference standards for future mechanistic studies of these compounds as thiol protease inhibitors. A 10% '^-labeled sample ofDIMBOA was also prepared for future mechanistic studies using NMR techniques.

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In the present environment, industry should provide the products of high quality. Quality of products is judged by the period of time they can successfully perform their intended functions without failure. The cause of the failures can be ascertained through life testing experiments and the times to failure due to different cause are likely to follow different distributions. Knowledge of this distribution is essential to eliminate causes of failures and thereby to improve the quality and the reliability of products. The main accomplishment expected to the study is to develop statistical tools that could facilitate solution to lifetime data arising in such and similar contexts

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Three goats provided with oesophageal and ruminal cannulae were used to determine variations in dry matter (DM) and neutral-detergent fibre (NDF) degradability of the forage consumed when grazing thorn scrubland in the semi-arid region of north Mexico, during two consecutive dry and wet periods. Ingesta samples were incubated intraruminally, the data were fitted to the exponential equation P = a + b (1-e(-ct)) and statistically analysed using a randomized-block design. Organic matter and crude protein (CP) contents were higher (P < 0.05) in the wet seasons. Values of NDF were similar in dry and wet season of both years whereas higher numerical values of acid-detergent fibre (ADF), lignin and cellulose were registered in the dry seasons. DM and NDF degradabilities after 24 and 48 h of ruminal incubation were higher (P < 0.05) in the wet seasons. Higher values (P < 0.05) in DM and NDF bag losses at zero time (A fraction) were registered in the two wet seasons. The insoluble but fermentable DM and NDF (B fractions) were higher (P < 0.05) in the 1999 wet season and variable in the rest of the studied period. Numerically higher values of DM and NDF c fraction were found in wet periods, whereas DM and NDF potential degradabilities were higher (P < 0.05) in the wet season in 1999 and similar across seasons in 2000. Lowest (P < 0.05) contents of CP in grazed forage, DM and NDF degradabilities after 48 h of ruminal incubation, and A, and B, and c fractions were observed in the dry seasons. Thus, these results may be related to both the lower feeding value of forage consumed by the animals and lower performance of livestock during this period. Then, the DM and NDF degradability after 48 h, together with the insoluble but fermentable matter and the c fraction permit the nutritive value of the forage consumed by grazing goats to be accurately described.

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A estimativa da curva de resistência do solo à penetração (CRP) a partir de variáveis de fácil obtenção, como o conteúdo de água, representa uma medida útil não só para a quantificação do estado de compactação, mas também para facilitar a interpretação da resistência do solo à penetração obtida em diferentes condições de campo. O objetivo deste trabalho foi estimar a CRP em solos de diferentes granulometrias e densidades, a partir de dados obtidos com o penetrômetro de impacto. O experimento foi realizado no laboratório de Pedologia da Faculdade de Ciências Agrárias e Veterinárias (UNESP), Jaboticabal, SP. Foram utilizadas quatro classes de solos: Neossolo Quartzarênico, Argissolo Vermelho-Amarelo, Latossolo Vermelho distrófico e Latossolo Vermelho acriférrico, os quais foram coletados na camada de 0-0,20 m. Colunas de PVC, com dimensões de 0,25 m de diâmetro e 0,6 m de altura, foram preenchidas de forma a obter duas condições de compactação: menor densidade e maior densidade do solo. O conteúdo de água nos solos, inicialmente elevado até o ponto de saturação, foi monitorado diariamente por meio de um medidor eletrônico tipo TDR (Profile Probe PR2 acoplado ao Moisture Meter HH2). A resistência do solo à penetração foi mensurada por meio de um penetrômetro de impacto adaptado para vaso. Os pares de dados entre a resistência do solo à penetração e o conteúdo de água foram ajustados, e as CRP foram submetidas ao teste de significância. A relação entre a resistência do solo à penetração e o conteúdo de água foi descrita pelo modelo exponencial decrescente: em que RP representa a resistência do solo à penetração (MPa); Ug é o conteúdo de água (kg kg-1); e A, B e C são os coeficientes da equação. Foram obtidos coeficientes de determinação que variaram de 0,79 a 0,96.

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The static and cyclic assays are common to test materials in structures.. For cycling assays to assess the fatigue behavior of the material and thereby obtain the S-N curves and these are used to construct the diagrams of living constant. However, these diagrams, when constructed with small amounts of S-N curves underestimate or overestimate the actual behavior of the composite, there is increasing need for more testing to obtain more accurate results. Therewith, , a way of reducing costs is the statistical analysis of the fatigue behavior. The aim of this research was evaluate the probabilistic fatigue behavior of composite materials. The research was conducted in three parts. The first part consists of associating the equation of probability Weilbull equations commonly used in modeling of composite materials S-N curve, namely the exponential equation and power law and their generalizations. The second part was used the results obtained by the equation which best represents the S-N curves of probability and trained a network to the modular 5% failure. In the third part, we carried out a comparative study of the results obtained using the nonlinear model by parts (PNL) with the results of a modular network architecture (MN) in the analysis of fatigue behavior. For this we used a database of ten materials obtained from the literature to assess the ability of generalization of the modular network as well as its robustness. From the results it was found that the power law of probability generalized probabilistic behavior better represents the fatigue and composites that although the generalization ability of the MN that was not robust training with 5% failure rate, but for values mean the MN showed more accurate results than the PNL model

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Several researches have been developed in order to verify the porosity effect over the ceramic material properties. The starch consolidation casting (SCC) allows to obtain porous ceramics by using starch as a binder and pore forming element. This work is intended to describe the porous mathematical behavior and the mechanical resistance at different commercial starch concentration. Ceramic samples were made with alumina and potato and corn starches. The slips were prepared with 10 to 50 wt% of starch. The specimens were characterized by apparent density measurements and three-point flexural test associated to Weibull statistics. Results indicated that the porosity showed a first-order exponential equation e(-x/c) increasing in both kinds of starches, so it was confirmed that the alumina ceramic porosity is related to the kind of starch used. The mechanical resistance is represented by a logarithmic expression R = A + B/1+10((Log(x0)-P)C).

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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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.