Schemes For Solution Of Problems Research Articles

Content of ontology for solving compute-intensive problems of the cosmic plasma hydrodynamics

Modern mathematical modeling on supercomputer systems requires that researchers have both a view of the main aspects of a studied phenomena and a knowledge base of numerical methods and supercomputer technologies for solving natural science problems. Development of intelligent support systems for solving such problems can greatly facilitate the researcher work by providing convenient tools for constructing an efficient scheme of problem solution on a target computational architecture and, if possible, implementing it using already developed program codes.This paper describes an implementation of this idea for the compute-intensive problems of the cosmic plasma hydrodynamics. A knowledge base has been developed, including ontological descriptions of studied astrophysical phenomena, their mathematical representations, numerical methods for solving set problems and supercomputer architectures that can be used for calculations. The paper presents patterns describing the main classes of the constructed ontology and their instances. The ontology can be expanded by a generation system of computational codes for the selected schemes of a problem solution.

An Inverse Problem Solution Scheme for Solving the Optimization Problem of Drug-Controlled Release from Multilaminated Devices.

The optimization problem of drug release based on the multilaminated drug-controlled release devices has been solved in this paper under the inverse problem solution scheme. From the viewpoint of inverse problem, the solution of optimization problem can be regarded as the solution problem of a Fredholm integral equation of first kind. The solution of the Fredholm integral equation of first kind is a well-known ill-posed problem. In order to solve the severe ill-posedness, a modified regularization method is presented based on the Tikhonov regularization method and the truncated singular value decomposition method. The convergence analysis of the modified regularization method is also given. The optimization results of the initial drug concentration distribution obtained by the modified regularization method demonstrate that the inverse problem solution scheme proposed in this paper has the advantages of the numerical accuracy and antinoise property.

Critical Sociocybernetics: Developing the Concept of Dispositif for an Analysis of Steering Processes Between Social Systems

Sociocybernetics is particularly interested in investigating how societies steer their social systems. According to Hornung (2006), sociocybernetic studies have predominantly followed three main strategies: a problem–solution scheme, a structural analysis and a normative proposal. We consider that, to have an integral constructivist foundation, sociocybernetics needs to also take a critical perspective into account. Critical theory used to be circumscribed to the first school of Frankfurt, but now it includes a wide range of approaches —such as Michel Foucault’s genealogical and archaeological project, psychoanalytical perspectives (e.g. Slavoj Žižek), schizoid-analysis (e.g. Gilles Deleuze and Felix Guattari), feminist perspectives (e.g. Judith Butler), and de–colonialist proposals (e.g. Boaventura De Sousa Santos)— offering very diverse notions of power, ethics and transformation. Nevertheless, some key concepts, such as dispositif, event, subject, cultural industry and antagonism, link many of these critical theorists. In this article, we explore how sociocybernetics can develop a critical perspective and some of the challenges of bringing together concepts pertaining to different theories. Specifically, we develop the concept of dispositif originally used by Foucault, Agamben and Deleuze for an analysis of asymmetrical dynamics of power and steering processes between social systems. Thus, we put forth a sociocybernetical understanding of dispositifs as second–order steering mechanisms which intervene strategically between systems and couple them conditionally. Ultimately, we seek to demonstrate that sociocybernetics can benefit from critical theory and vice versa.

A new modal-based approach for modelling the bump foil structure in the simultaneous solution of foil-air bearing rotor dynamic problems

Recently-proposed techniques for the simultaneous solution of foil-air bearing (FAB) rotor dynamic problems have been limited to a simple bump foil model in which the individual bumps were modelled as independent spring-damper (ISD) subsystems. The present paper addresses this limitation by introducing a modal model of the bump foil structure into the simultaneous solution scheme. The dynamics of the corrugated bump foil structure are first studied using the finite element (FE) technique. This study is experimentally validated using a purpose-made corrugated foil structure. Based on the findings of this study, it is proposed that the dynamics of the full foil structure, including bump interaction and foil inertia, can be represented by a modal model comprising a limited number of modes. This full foil structure modal model (FFSMM) is then adapted into the rotordynamic FAB problem solution scheme, instead of the ISD model. Preliminary results using the FFSMM under static and unbalance excitation conditions are proven to be reliable by comparison against the corresponding ISD foil model results and by cross-correlating different methods for computing the deflection of the full foil structure. The rotor-bearing model is also validated against experimental and theoretical results in the literature.

Erratum: A technique for time integration analysis with steps larger than the excitation steps

Commun. Numer. Meth. Engng. 2008; 24(12):2087–2111 There was an error in the definition of the h in Equations (5). The correct definition is as follows: h is the maximum step size, appropriate for preserving convergence (numerical stability and consistency) [9, 19, 26]. There was an error in the fonts of the texts in Figure 13(b). The correct figure is as follows: The spelling of the author surname in reference [38] was incorrect. The reference should be as follows: McNamara JF. Solution schemes for problems of nonlinear structural dynamics. Journal of Pressure Vessels 1974; 96:147–155.

Application of Genetic Algorithms in Texture Analysis and Optimization

The genetic algorithms method (GAM) is a modern computer technique based on some ideas taken from biological evolution theory. The GAM is especially useful in a study of problems being not completely determined. They are, e.g., problems having a few but not very different solutions or problems without a strict (exact) solution. The last situation may occur if it is enough to find a good enough solution but not necessarily the best one. In GAM approach, it is not necessary to know a priori a general scheme of problem solution; however, it is important to have a procedure estimating the quality of a solution. This procedure is necessary to eliminate some solutions and to accept another ones. In the last years, GAM was applied with success in different areas of science (e.g., sociology, construction engineering, artificial intelligence and many others). The present authors have applied GAM in crystallographic texture analysis: the orientation distribution function (ODF) was calculated from a set of measured pole figures. The quality of obtained results was very good; however, the calculation time and memory space were relatively high. The main reason of this situation was the use of spherical harmonic function series for the ODF representation. An important simplification of the calculation scheme (and of calculation time and memory space) can be obtained if ODF is represented by a sum of a few Gauss-type functions. The quality of solutions in this new approach is still very correct. The above-mentioned improved GAM scheme was also used to find an optimal crystallographic texture that optimizes the elastic properties of material. By using this approach the Young modulus can be maximised or minimised along a given sample direction.

Optimum Design of a Ceramic Tensile Creep Specimen Using a Finite Element Method.

An optimization procedure for designing a ceramic tensile creep specimen to minimize stress concentration is carried out using a finite element method. The effect of pin loading and the specimen geometry are considered in the stress distribution calculations. A growing contact zone between the pin and the specimen has been incorporated into the problem solution scheme as the load is increased to its full value. The optimization procedures are performed for the specimen, and all design variables including pinhole location and pinhole diameter, head width, neck radius, and gauge length are determined based on a set of constraints imposed on the problem. In addition, for the purpose of assessing the possibility of delayed failure outside the gage section, power-law creep in the tensile specimen is considered in the analysis. Using a particular grade of advanced ceramics as an example, it is found that if the specimen is not designed properly, significant creep deformation and stress redistribution may occur in the head of the specimen resulting in undesirable (delayed) head failure of the specimen during the creep test.

Nonlinear stability and convergence of finite-difference methods for the ?good? Boussinesq equation

The "good" Boussinesq equationu tt =?u xxxx +u xx +(u 2) xx has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the "good" Boussinesq equation. Numerical experimentas are also reported.

Solution Schemes for Problems of Nonlinear Structural Dynamics

A number of alternative solution schemes for problems of dynamic structural analysis involving large displacements and plastic deformations are compared. The equations of motion, derived from the finite element approximation, are integrated directly using a number of well-known time integration operators; namely, the Houbolt, Newmark, Wilson, and central difference operators. This latter operator serves as a basis for a comparison of accuracy and economy with all methods. Numerical results for nonlinear systems are used to indicate the true worth of integration operators whose properties have been determined theoretically by studying their behavior with linear systems only.

ON THE APPROXIMATE AND NUMERICAL SOLUTION OF ORR-SOMMERFELD PROBLEMS

Two computer-oriented schemes for solution of problems in hydrodynamic stability theory are outlined. The first is a variational approach, which allows the eigenvalue problem to be reduced to an algebraic problem of matrix eigenvalue determination. Choosing relatively simple families of approximating functions, surprisingly accurate results can be obtained using only a few terms. Moreover, the matrix representation allows a portion of the eigenvalue spectrum to be found. The second scheme involves numerical integration, which is inherently difficult because of the high singularity of the Orr-Sommerfeld equation at large Reynolds number. Kaplan has suggested a method for extraction of rapidly growing solutions, and this idea has been used in a variety of recent calculations with remarkable success. The integrations are repeated with successively improved eigenvalues, starting from an initial guess. Experience has shown that the initial guess must be relatively good, and a few-term variational approximation provides a speedy means for selecting the initial value. Together the variational and integration scheme provide a powerful package for solution of linearized stability problems.

Computing schemes for solution of problems in scheduling theory

Computing schemes for solution of problems in scheduling theory