977 resultados para Asymptotic Formulas
Resumo:
En este trabajo se observo las respuestas de tres caracteres, rendimientos, diámetro del bulbo y altura de tallo, de la cebolla Cristal WhiteWax, a las aplicaciones de 13 formulas de fertilizantes. Para este trabajo se uso el diseño de parcelas al azar con seis repeticiones. De acuerdo a los resultados obtenidos las formulas 150-100-0 y 100-200-0, son iguales estadisticamente y superiores al testigo 0-0-. Se encontraron tendencias ascendentes de rendimiento correspondientes a sucesivos incrementos de nitrógeno solo (50, 100 y 150 lbs/mza) pero estas diferencias no fueron significativas. Así mismo se encontró este mismo tipo de tendencia para el fósforo solo (100 y 200 lbs/mza.) Los resultados obtenidos para esta características están de acuerdo con algunos de los mencionados en la revisión de literatura. Para la característica diámetro del bulbo no se encontró diferencias estadísticas entre las formulas usadas, aunque como el caso anterior se observo una tendencia ascendente a los incrementos sucesivos de nitrógeno solo aplicado en los niveles de 50, 100 y 150 lbs/mza. El análisis estadístico de los resultados para altura de tallo demostró diferencias altamente significativas entre los tratamientos usados, observándose ademas que para las aplicaciones de nitrógeno solo, nitrógeno y fósforo juntos, fósforo solo y formula completas algunas de las respuestas obtenidas podrían considerarse como ilógica. En ninguno de los casos se observo una tendencia ascendente al aumento de las cantidades de fertilizantes usados. Se hace constar que los resultados obtenidos no se consideran suficientes para emitir conclusiones ni para soportar una recomendación de fertilización en cebolla.
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Con el fin de determinar la prevalencia e incidencia de huevos de nematodos parásitos en heces de vacunos jóvenes del departamento de Chontales. Se realizo una investigación para conocer el grado de infestacion, que se inicio el 13 de junio y finalizo el 3 de agosto de 1972. El diseño de muestreo bietapico, se adopto para este tipo de investigación. Se estudiaron todos los municipios del departamento, dentro de cada municipio se tomaron 2 fincas al azar que corresponde a la Etapa 1, y 13 muestras por finca que corresponde a la Etapa 2. Se tomaron 208 muestras extraídas de animales menores de 15 meses sin distingo de sexos, anotándose la consistencia de las heces. Para análisis de las muestras se uso la técnica de dilucion de Stoll. Los datos obtenidos en laboratorio se sometieron a un análisis de varianza entre fincas y dentro de fincas por medio de los valores esperados de los cuadrados medios para cada genero encontrado, con los fines de conocer el error dentro de las muestras y comprobar si la cantidad tomada de muestras por finca eran las suficientes, de no ser así había que completar hasta lo adecuado. La prevalencia e incidencia de huevos por gramo de nematodos fue intensa en todo el departamento y estaba formada por ocho géneros que en orden de importancia son: Strongyloides sp., Sosophagostomun sp., Haemonchus sp., Toxocara sp., Trichiuris sp., Nocascaris sp., Ascaris sp., y Dictyocaulus sp. El municipio de la Libertad mostró la mayor incidencia de huevos por gramo del genero Strongyloides sp., y Juigalpa el que mostró la menor incidencia. No se encontró en el municipio de La Libertad, prevalencia de Necascaris sp., Ascaris sp., y Dictyocaulus sp., encontrnadose en Juigalpa Necascaris sp., y Dictyocaulus sp. Las distancias entre los municipios son variables, desde 250 kilómetros (Santo Domingo), hasta 20 kilómetros (Juigalpa), a partir de esta ciudad que es la cabecera departamental. Los tiempos de ida y regreso varían de acuerdo a las distancias, lo que influye directamente al estimar los costos promedios entre municipios que varían desde C76,50 (Santo Domingo), hasta C 11,00 (Juigalpa), debido a que las vías de comunicación entre ciertos municipios son caminos de herradura. Los costos promedios por finca dentro del municipio y por muestra dentro de cada finca son constantes. La cantidad tomada de muestras por finca fueron calculadas en base a las formulas de optimizacion de Cochran, obteniéndose como resultados k=2, numero de animales por finca, y r=10, numero de fincas por municipios.
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This paper proposes criteria for predicting the tendency of looping in tropical cyclone tracks using the approach of vortex dynamics. We model the asymmetric structure of a cyclone by a system of vortex patches. The evolution of such system of vortices is simulated by the method of contour dynamics. A new set of exact analytic formulas for contour dynamics calculations is derived, which is shown to be more computationally effective. Based on point-vortex models, we derive analytic formulas for the criteria of looping in a cyclone track. From numerical experiments, the simulated trajectories obtained from the point-vortex system and vortex patch system agree quite well. Hence, the looping criteria obtained from the point-vortex system can be applied by forecasters to stay alert for tendency of looping in a cyclone track. To demonstrate the applicability of the proposed criteria, the trajectory of Typhoon Yancy (9012), whose field data are available from ''TCM-90'', is simulated. The case study shows that the asymmetric structure similar to the pattern of a beta gyre is responsible for its recurvature when Yancy landed Fujian Province, China on 20 August 1990.
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A new method is presented for calculating the values of K-I and K-II in the elasticity solution at the tip of an interface crack. The method is based on an evaluation of the J-integral by the virtual crack extension method. Expressions for calculating K-I and K-II by using the displacements and the stiffness derivative of the finite element solution and asymptotic crack tip displacements are derived. The method is shown to produce very accurate solutions even with coarse element mesh.
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In this paper, we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain, Mode I. A four- or five-term asymptotic series of the solutions is derived. It is found that when 1.6 < n less-than-or-equal-to 2.8 (here, n is the hardening exponent), the elastic effect enters the third-order stress field; but when 2.8< n less-than-or-equal-to 3.7 this effect turns to enter the fourth-order field, with the fifth-order field independent. Moreover, if n>3.7, the elasticity only affects the fields whose order is higher than 4. In this case, the fourth-order field remains independent. Our investigation also shows that as long as n is larger than 1.6, the third-order field is always not independent, whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields, respectively). Firmly, good agreement is found between our results and O'Dowd and Shih's numerical ones[8] by comparison.
Resumo:
A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation. A set of the singular integral equations for the distribution function of the dislocation density is developed. Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals. The role of the stress parallel to the interface, sigma0 is taken into account in these formulas. The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness. Throughout the paper, the influences of the inplane stress sigma0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.
Resumo:
A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.
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This paper presents a micromechanics analysis of the elastic solids weakened by a large number of microcracks in a plane problem. A new cell model is proposed. Each cell is an ellipse subregion and contains a microcrack. The effective moduli and the stress intensity factors for an ellipse cell are obtained. The analytic closed formulas of concentration factor tensor for an isotropic matrix containing an anisotropic inclusion are derived. Based on a self-consistent method, the effective elastic moduli of the solids weakened by randomly oriented microcracks are obtained.
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This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.
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Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.
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A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.
Resumo:
The simplified governing equations and corresponding boundary conditions of flexural vibration of viscoelastically damped unsymmetrical sandwich plates are given. The asymptotic solution of the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the Modal Strain Energy (MSE) Method. As more terms of the asymptotic solution are taken, the successive calculations show improved accuracy. With the natural frequencies and the modal loss factors of a damped sandwich plate known, one can calculate the response of the plate to various loads providing a reliable basis for engineering design.
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Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.
Resumo:
By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.
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The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.