Journal of Computational Methods in Sciences and Engineering - Volume 4, issue 1-2

Authors: Hoppe, Ronald H.W. | Petrova, Svetozara I.

Article Type: Research Article

Abstract: A structural optimization method based on the homogenization approach (the homogenization design method) has been applied to the modeling of the recently produced biomorphic composite materials. The design itself involves a structural optimization problem which is solved under a set of equality and inequality constraints on the state variables (displacements) and design parameters (lengths of the layers in the microstructure and angle of cell rotation). Primal-dual Newton-type interior-point method with proper optimality criteria is applied to the resulting nonconvex nonlinear optimization problem.

Keywords: biomorphic microcellular ceramics from wood, structural optimization, elasticity problems, homogenization technique, primal-dual interior-point methods

DOI: 10.3233/JCM-2004-41-211

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 87-96, 2004

Authors: Villarroel, Javier

Article Type: Research Article

Abstract: We determine the class of one-dimensional stochastic differential equations with a strong solution that can be represented as a functional of Brownian motion. For this class we detail the corresponding solution and transition density. Sharp conditions for explosion to occur are determined.

Keywords: Ito's equation, stochastic ordinary differential equations

DOI: 10.3233/JCM-2004-41-212

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 97-103, 2004

Authors: Miletics, E. | Molnárka, G.

Article Type: Research Article

Abstract: The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations. In some cases such algorithms will be much more complicated than a R-K methods, because it will require more function evaluation than well-known classical algorithms. However these evaluations can be accomplished fully parallel and the coefficients of truncated Taylor series can be calculated with matrix-vector operations. For large systems these operations suit …for the parallel computers. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval and the local error of this solution at the interior points of the subinterval is less than that one at the end point. This property offers different facility for adaptive error control. This paper describes several above-mentioned algorithms and examines its consistency and stability properties. It demonstrates some numerical test results for stiff systems herewith we attempt to prove the efficiency of these new-old algorithms. Show more

Keywords: Taylor series algorithm, numerical derivatives, parallel algorithms

DOI: 10.3233/JCM-2004-41-213

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 105-114, 2004

Authors: Valverde, Jose C. | Pelayo, Fernando L. | Martinez, Juan A. | Miralles, Juan J.

Article Type: Research Article

Abstract: In this paper we present a specific software package to bifurcation analysis. Specifically for locating fixed points of maps defined on R and their variation with respect to parameters. Also this program allows both detecting and analyzing bifurcations under higher order conditions. We deal mainly with discrete-time systems and give only brief remarks on the continuous time case.

Keywords: Computational engineering, computational mathematics, symbolic mathematical computing, bifurcations, dynamical systems, mathematica

DOI: 10.3233/JCM-2004-41-214

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 115-123, 2004

Authors: Valverde, Jose C. | Pelayo, Fernando L. | Martinez, Juan A. | Miralles, Juan J.

Article Type: Research Article

Abstract: Nowadays, one of the main topics in Engineering is, undoubtedly, the Automatic Control of Systems. Probably, the most important problem in this area is how to guarantee the stability of a closed loop control system. The Routh-Hurwith Criterion, RHC, provides one of the most powerful algorithm for analyzing the mentioned stability, even when it depends on an adjustable parameter. It has been developed a computational system in Mathematica, which, applying this Criterion, is able to analyze the stability of every Continuous System which can be modelled by transfer functions in the way of quotient of real coefficients polynomials.

Keywords: computational engineering, computational mathematics, industrial mathematics, automatic control, stability, mathematica

DOI: 10.3233/JCM-2004-41-215

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 125-134, 2004

Authors: Larsson, B. | Levitina, T. | Brändas, E.J.

Article Type: Research Article

Abstract: A new powerful approach to compute the eigenfunctions of the finite two-dimensional Fourier transform is developed and analysed. The numerical technique is a generalization of an earlier method developed for ordinary prolate spheroidal wave functions. Special considerations are given to the problem of singularities and the procedure to locate the eigenvalues. It is demonstrated that the computations are fundamentally improved by the introduction of appropriate auxiliary differential equations.

DOI: 10.3233/JCM-2004-41-216

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 135-148, 2004

Authors: Theron, R. | Moreno, V. | Curto, B. | Blanco, F.J.

Article Type: Research Article

Abstract: In this abstract it is presented the assesment of two different methods devoted to the evaluation of the configuration space for planar revolute manipulators. The formalism proposed in [3] for the evaluation of the C-space, when applied to planar revolute manipulators, is compared to a new method, which provides both better results and a way to generalize the evaluation for any kind of robotic structure.

DOI: 10.3233/JCM-2004-41-217

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 149-156, 2004

Authors: Belkić, Karen | Belkić, Dževad

Article Type: Research Article

Abstract: In the very recent period Magnetic Resonance Spectroscopy (MRS) and Spectroscopic Imaging (MRSI) have become key diagnostic modalities for neuro-oncology. MRS and MRSI are now applied extensively for initial detection of brain tumours, for histopathologic classification, tumour localization and grading, as well as for assessment of response to therapy and for follow-up surveillance, striving, in particular, for earlier identification of recurrence. In this paper we review the current state of the art of MRS and MRSI for brain tumour diagnostics, highlighting the achievements, as well as remaining dilemmas. Clearly, MRS and MRSI represent an important advance for the detection …and characterisation of tumours of the brain. However, there are still important shortcomings of the present applications of MRS and MRSI in neuro-oncology. First of all, very few of the currently assessed metabolite concentrations or ratios unequivocally distinguish intra-cerebral tumours from normal brain tissue. Moreover, changes in each of the metabolite concentrations and ratios are non-specific for cancer of the brain. In other words, non-neoplastic processes such as infection, stroke, demyelinating disorders, inter alia, frequently show spectral changes that are identical to those seen in brain tumours. Histopathological characterization and tumour grading, both crucial for clinical decision-making, have been greatly aided by MRS and MRSI. However, there are numerous contradictory findings in the literature. We demonstrate in this paper that many of the shortcomings of MRS and MRSI for neuro-oncology are directly related to the reliance upon the conventional Fourier-based framework for data analysis. We review the distinct advantages of the Fast Padé Transform (FPT) relative to the Fast Fourier Transform (FFT). Our focus is on those salient features of the FPT that are of critical clinical relevance for achieving an overall improved diagnostic performance of MRS and MRSI. These features are extremely stable and rapid convergence, as well as highly accurate quantification estimates of spectra from in vivo MRS time signals, as presently illustrated for data from the brain of a healthy volunteer. The next, and urgently needed step, is to more widely apply the FPT to in vivo MRS and MRSI signals from patients with brain tumours with the aim of tackling, in actual practice, the diagnostic dilemmas still plaguing neuro-oncology. Show more

Keywords: brain tumours, metastatic disease, biomedical imaging, magnetic resonance spectroscopy, magnetic resonance spectroscopic imaging

DOI: 10.3233/JCM-2004-41-218

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 157-207, 2004

Authors: Didenko, V. | Pittaluga, G. | Sacripante, L. | Venturino, E.

Article Type: Research Article

Abstract: In this paper we consider simple methods for the numerical solution of Cauchy singular integral equations with conjugation based on quadratures. They use collocation at a set of nodes which is graded toward the endpoints, to accomodate for the presence of the singularity. Our numerical experience reveals that the theoretical stability findings are indeed of practical applicability, as the empirical condition number is seen very often to reach a plateau, whose asymptotic value is indeed very low.

DOI: 10.3233/JCM-2004-41-219

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 209-233, 2004