Home About us Contact
|
Home About us Contact | ||
|
|
||
Perturbation Methods (perturbation + methods)
Selected AbstractsBoundary Perturbation Methods for Water WavesGAMM - MITTEILUNGEN, Issue 1 2007David P. Nicholls Abstract The most successful equations for the modeling of ocean wave phenomena are the free,surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open,ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, "Boundary Perturbation" methods for the analysis and numerical simulation of this "water wave problem". Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A generalized dimension-reduction method for multidimensional integration in stochastic mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2004H. Xu Abstract A new, generalized, multivariate dimension-reduction method is presented for calculating statistical moments of the response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of an N -dimensional response function into at most S -dimensional functions, where S,N; an approximation of response moments by moments of input random variables; and a moment-based quadrature rule for numerical integration. A new theorem is presented, which provides a convenient means to represent the Taylor series up to a specific dimension without involving any partial derivatives. A complete proof of the theorem is given using two lemmas, also proved in this paper. The proposed method requires neither the calculation of partial derivatives of response, as in commonly used Taylor expansion/perturbation methods, nor the inversion of random matrices, as in the Neumann expansion method. Eight numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the proposed method. Results indicate that the multivariate dimension-reduction method generates convergent solutions and provides more accurate estimates of statistical moments or multidimensional integration than existing methods, such as first- and second-order Taylor expansion methods, statistically equivalent solutions, quasi-Monte Carlo simulation, and the fully symmetric interpolatory rule. While the accuracy of the dimension-reduction method is comparable to that of the fourth-order Neumann expansion method, a comparison of CPU time suggests that the former is computationally far more efficient than the latter. Copyright © 2004 John Wiley & Sons, Ltd. [source] Random perturbation methods applied to multivariate spatial sampling designENVIRONMETRICS, Issue 7 2001J. M. Angulo Abstract The problem of estimating a multivariate spatial random process from observations obtained by sampling a related multivariate spatial random process is considered. A method based on additive perturbation of the variables of interest is proposed for the assignment of degrees of relative importance to the variables and/or locations of interest in the design of sampling strategies. In the case where the variables involved have a multivariate Gaussian distribution, some theoretical results are provided to justify the method proposed; in particular, it is proved that the amount of information contained in the data on the perturbed variables of interest is never higher than that contained in the original variables of interest. These results and the application of the method are illustrated with an empirical study, showing the variation of the effects of perturbation on spatial sampling design configurations and related ratios of information for different degrees of dependence according to the model specifications. Copyright © 2001 John Wiley & Sons, Ltd. [source] A method for analysing the transient and the steady-state oscillations in third-order oscillators with shifting biasINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2001A. Buonomo Abstract We provide an asymptotic method for systematically analysing the transient and the steady-state oscillations in third-order oscillators with shifting bias. The method allows us to construct the general solution of the weakly non-linear differential equation describing these oscillators through an iteration procedure of successive approximations typical of perturbation methods. The approximation to first order is obtained solving a system of two first-order non-linear differential equations in the leading terms of solution (dc component and fundamental harmonic), whereby the dominant dynamics, the stationary states and their stability can be easily analysed. Unlike existing approaches, our method also enables us to determine the higher harmonics as well as the frequency shift from the system's natural frequency in the exact solution through analytical formulae. In addition, formulae for higher-order approximations of the above quantities are determined. The proposed method is applied to a practical circuit to show its usefulness in both analysis and design problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] ON AXISYMMETRIC TRAVELING WAVES AND RADIAL SOLUTIONS OF SEMI-LINEAR ELLIPTIC EQUATIONSNATURAL RESOURCE MODELING, Issue 3 2000THOMAS P. WITELSKI ABSTRACT. Combining analytical techniques from perturbation methods and dynamical systems theory, we present an elementaryapproach to the detailed construction of axisymmetric diffusive interfaces in semi-linear elliptic equations. Solutions of the resulting non-autonomous radial differential equations can be expressed in terms of a slowlyvarying phase plane system. Special analytical results for the phase plane system are used to produce closed-form solutions for the asymptotic forms of the curved front solutions. These axisym-metric solutions are fundamental examples of more general curved fronts that arise in a wide variety of scientific fields, and we extensivelydiscuss a number of them, with a particular emphasis on connections to geometric models for the motion of interfaces. Related classical results for traveling waves in one-dimensional problems are also reviewed briefly. Manyof the results contained in this article are known, and in presenting known results, it is intended that this article be expositoryin nature, providing elementarydemonstrations of some of the central dynamical phenomena and mathematical techniques. It is hoped that the article serves as one possible avenue of entree to the literature on radiallysymmetric solutions of semilinear elliptic problems, especiallyto those articles in which more advanced mathematical theoryis developed. [source] | |||||||||||||