Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

El sentimiento partidista presente en el inicio de la Conquista del Perú : supervivencia medieval en los conflictos entre Pizarro y Almagro

El siglo XVI americano fue escenario de la lucha de partidos entre los españoles que defendieron con vigorosa fidelidad a sus respectivos líderes. En la Conquista del Perú se encuentra el caso que mejor demuestra el nivel de violencia que alcanzaron las rivalidades partidarias. Fue en la singular, difícil y posteriormente violenta relación entre Diego de Almagro y Francisco Pizarro desde la salida de Panamá en 1524 hasta la lucha por la dominación de la ciudad del Cuzco en 1538.

El federalismo en el origen, consolidación, desarrollo y superación del constitucionalismo

Resumen: Los poderes territoriales predominaron en el nacimiento de los Estados en Europa occidental, en los que se advierten contrapesos entre órganos, de sustento consuetudinario y reconocimiento escrito de derechos. En la aparición y el afianzamiento del constitucionalismo escrito tienen singular importancia la transformación de confederaciones en Estados federales, en Estados Unidos, Suiza y Alemania; así como los procesos de Venezuela, Colombia, México, Brasil y Argentina. Su consolidación resulta de los sistemas de control de constitucionalidad: el difuso, que nace en Estados Unidos; y el concentrado, que comienza en Austria; ambos países federales. En la actualidad los Estados semicontinentales y las regiones de similares dimensiones pueden entenderse como superación del constitucionalismo, pues se ha modificado sustancialmente su ámbito geográfico, el cual resulta esencial para que la representación posea una inmediación suficiente y puedan funcionar los frenos y contrapesos que aseguran la moderación del poder. Una gran autonomía y fortaleza de las instituciones locales, es decir un auténtico federalismo, puede configurar un reaseguro suficiente para los objetivos iniciales del constitucionalismo: que el reconocimiento de los derechos y los equilibrios entre los titulares de poderes locales y centrales tengan la oportunidad de lograrse.

Peregrinación a la cibdat de gygantes : configuración del imaginario geográfico bíblico en La fazienda de Ultramar

Resumen: Dado que la imaginación medieval del mundo se nutre de ideas directamente heredadas de la Biblia, a menudo en contienda con la exploración empírica del globo terrestre, el estudio de los relatos de viajes en general, y de las guías de peregrinos a Tierra Santa en particular, nos permite comprender el modo en que el hombre de letras medieval se apropiaba del imaginario bíblico para darle forma a un mundo cuyos límites exóticos cobraban familiaridad por ser el escenario de las historias más apreciadas por los lectores de la época. Dentro del repertorio de literatura de viajes hispánica, La fazienda de Ultramar, cuya redacción se habría llevado a cabo a comienzos del siglo XIII, es un texto de singular importancia, por ser una de las más antiguas versiones en romance de la Biblia. No solo es un texto fundacional para una tradición que cambió la forma en que el hombre medieval se acercaba a las Sagradas Escrituras, sino que, debido a su carácter de itinerarium, nos permite conocer el modo en que la Biblia afectaba la imaginación del lector medieval acerca de la geografía de Tierra Santa. Es por ello que el propósito de esta comunicación será analizar el modo en que la estructura de itinerarium incide sobre el tratamiento del texto sagrado y la forma en que la lógica narrativa de los episodios bíblicos se subordina a la geográfica. De esta forma, se intentará echar luz sobre algunas cuestiones que han limitado el estudio de esta obra.

Computation of stress intensity factors by the sub-region mixed finite element method of lines

Based on the sub-region generalized variational principle, a sub-region mixed version of the newly-developed semi-analytical 'finite element method of lines' (FEMOL) is proposed in this paper for accurate and efficient computation of stress intensity factors (SIFs) of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations (ODEs) and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

Para pensar es necesario entender

El entendimiento es la principal potencia del alma, la que primero emana de ella, la más perfecta de todas y la característica distintiva de la naturaleza humana. A través de ella el hombre participa en algo de los seres superiores, Dios y los ángeles. Como las demás potencias, el entendimiento no puede ser directamente conocido por nosotros, sino sólo por medio de sus actos propios. A diferencia de los sentidos, cuyo conocimiento se limita a los accidentes, el entendimiento penetra hasta la esencia de la realidad; más aún, la esencia de las cosas materiales constituye el objeto propio del entendimiento humano. El nombre con que se le designa (intellectus = intus-legere = leer dentro) quiere expresar precisamente esta índole peculiar. Penetrando en las esencias, el entendimiento humano es capaz de abstraer (extraer lo universal de lo particular o singular) y concebir ideas o conceptos. Estos actos y objetos, eminentemente espirituales, demuestran que su sujeto, el entendimiento, también lo es; y si el entendimiento es una potencia o energía espiritual, necesariamente debe serlo también el principio del cual fluye, o sea, el alma humana...

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

Kinking of an interface crack between 2 dissimilar anisotropic elastic solids

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.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

A new formulated method of a quasi-compatible finite-element and its application in fracture-mechanics

Based on the local properties of a singular field, the displacement pattern of an isoparametric element is improved and a new formulated method of a quasi-compatible finite element is proposed in this paper. This method can be used to solve various engineering problems containing singular distribution, especially, the singular field existing at the tip of cracks. The singular quasi-compatible element (SQCE) is constructed. The characteristics of the elements are analysed from various angles and many examples of calculations are performed. The results show that this method has many significant advantages, by which, the numerical analysis of brittle fracture problems can be solved.

Prediction of mixed-mode cracking direction in random, short-fibre composite-materials

The prediction of cracking direction in composite materials is of significance to the design of composite structures. This paper presents several methods for predicting the cracking direction in the double grooved tension-shear specimen which gives mixed-mode cracking. Five different criteria are used in this analysis: two of them have been used by other investigators and the others are proposed by the present authors. The strain energy density criterion proposed by G.C. Sih is modified to take account of the influence of the anisotropy of the strength on the direction of crack. The two failure criteria of Tsai-Hill and Norris are extended to predict the crack orientation. The stress distributions in the near-notch zone are calculated by using the 8-node quadrilateral isoparametric finite element method. The predictions of all the criteria except one are in good agreement with the experimental measurement. In addition, on the basis of the FEM results, the size of the zone in which the singular term is dominant is estimated.

Singularity criteria for perturbation series

This paper is concerned with some mathematical aspects of the Van Dyke method inperturbation theory, i.e. the singularity criteria of perturbation series. The author suggestsa sign criterion and a Domb-syke plot for the cases with complex conjugate singularities, thussucceeding in extending the conclusions of Van Dyke's. Subsequently. effects of singularitiesof the lower order upon the criteria are taken into account. In addition, a method of locat-ing singular points is developed by analysing the new perturbation series derived by the Eulertransformation.