Journal of Computational Methods in Sciences and Engineering - Volume 10, issue 1-2

Authors: Pavlou, D.G. | Mavrothanasis, F.I. | Tsitouras, Ch. | Pavlou, M.G. | Avlonitis, S. | Vlachakis, V.N.

Article Type: Research Article

Abstract: Common characteristic of the structure of the crystalic or amorphous materials is the existence of micro-cracks. Reasons of the existence of micro-cracks are (a) the chemical composition of the material, (b) the kinetic mechanisms of the atoms or grains or atomic chains or dislocations or other structural elements during the solidification or forming or loading of a macroscopic material part. The dramatic effect of sub-critical crack growth on the mechanical integrity of structures was clearly brought to light by the often structural failures. As the micro-crack growth is the result of atomic bonds de-boding, the understanding of mechanisms and analysis …of cracks is a useful tool for the chemistry to improve the chemical composition and the resulted micro-structure of materials in order to achieve better macroscopic fracture toughness. Due to the progress of the nanomechanics and the microelectronics, it is recognized today that the existence and growth of micro-cracks in the interface between thin layers such as thin films in electronic devices, sensors and actuators in smart materials or ceramic coating in machine components for wear or corrosion resistance, cause changes in the prescribed material properties and reduction of the material quality. In the present work, a mathematical analysis to determine the stress concentration areas in order strong particles to be inserted there (using chemical methods) for the material strengthening is attempted. To this scope, the equations describing the stress fields around interfacial micro-cracks in materials under internal singular loading sources are formulated. Numerical examples are included. Show more

DOI: 10.3233/JCM-2010-0287

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 3-12, 2010

Authors: Zebbiche, Toufik

Article Type: Research Article

Abstract: When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented …in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air. Show more

Keywords: Supersonic flow, high temperature, Prandtl Meyer function, Gauss Legendre quadrature, relative error

DOI: 10.3233/JCM-2010-0284

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 13-22, 2010

Authors: Vonikakis, Vassilios | Andreadis, Ioannis | Gasteratos, Antonios

Article Type: Research Article

Abstract: This paper presents a new method suitable for shape recognition, inspired by the Primary Visual Cortex of the Human Visual System. It extracts a description for 2-dimensional shapes with a closed contour, regardless of their size, rotation and position, with low computational cost. The paper introduces a new computational approach to the modeling of the hypercolumns of the Primary Visual Cortex, which requires significantly less computational burden and which is highly parallel. A new shape descriptor based on the relative angles of an object is also proposed. It produces close results for different shapes of the same object, it is …proportion-flexible and it can identify distorted shapes correctly. Experimental results prove that the method is adequate for shape-based image retrieval and classification, as well as for efficiently storage of edges and line drawings. Show more

DOI: 10.3233/JCM-2010-0288

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 23-35, 2010

Authors: Drakopoulos, V.

Article Type: Research Article

Abstract: Sequential visualisation methods for the most widely used methods for the graphical representation of the Mandelbrot set are compared. Two groups of methods are presented. In the first, the Mandelbrot set (or its border) is rendered and, in the second, its complement is rendered. Examples of two-dimensional images obtained using these methods are also given.

Keywords: Attractor, Mandelbrot set, rendering methods

DOI: 10.3233/JCM-2010-0286

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 37-45, 2010

Authors: Mestechkin, M.

Article Type: Research Article

Abstract: A method for direct construction of continued fraction elements, presenting a square root from a natural number, is proposed. This technique resembles the usual division process. Derivation of the computing procedures is based on the Euclidean algorithm, Fermat's and Euler's theorems on a sum of two squares, and formulation of the basic equation for the continued fraction elements as Diophantine equation. The solution of Pell equation is presented explicitly through the same functions, which describe the Euclidean algorithm and solutions to linear Diophantine equations. It is supposed that similar procedures could be used by Fermat when he challenged to solve …the quadratic Diophantine equation for special difficult cases found by him. Show more

Keywords: Continued fraction, Pell Equation, Euclidean algorithm, Diophantine equation

DOI: 10.3233/JCM-2010-0261

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 49-66, 2010

Authors: Huber, Alfred

Article Type: Research Article

Abstract: The classical Lie group formalism as well as the nonclassical procedure is applied to study a nonlinear partial differential equation of the second order. It is important to stress that until now no symmetry calculation is available. Therefore it seems indispensable to apply this method yielding a deeper insight into the behaviour of the solution manifold. Firstly we determine the classical Lie point symmetries including algebraic properties. Similarity solutions in a most general form and nonlinear transformations are obtained. Also a statement relating to potential symmetries is performed. Then we show how the equation leads …to approximate symmetries and we apply the method for the first time. Secondly some important hints relating to different alge braic solution techniques are given in order to construct further closed-form solutions. We finally show how this less-studied equation admits solitary and peakon classes of solutions of practical relevance. Show more

Keywords: Classical Lie group formalism, similarity solutions, nonclassical symmetries

DOI: 10.3233/JCM-2010-0283

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 67-78, 2010

Authors: Huber, Alfred

Article Type: Research Article

Abstract: The classical Lie group formalism is applied to deduce classes of solutions of a special nonlinear partial differential equation, the so called Short-Pulse-Equation important in physical applications. We determine the Lie point symmetries and their algebraic properties. Similarity solutions are given as well as nonlinear transformations. In addition we discuss approximate symmetries for the first time. This analysis allows one to deduce wider classes of new unknown solutions either of practical or theoretical use.

Keywords: Nonlinear partial differential equations, evolution equations, Short-Pulse-Equation, similarity solutions, approximate symmetries

DOI: 10.3233/JCM-2010-0262

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 79-87, 2010

Article Type: Correction

DOI: 10.3233/JCM-2010-0285

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 89-89, 2010