応用および計算数学ジャーナル

Linear stability conditions for a first order 4-dimensional discrete dynamic are derived in terms of the trace, sum of minors, sum of their minors, and the determinant of the Jacobian evaluated at the equilibrium.

Following the critical review of Seaman et al., we react on an essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian data analysis remains stable under different choices of noninformative prior distributions. However, as discussed by Seaman et al., there may also be unintended consequences of a choice of noninformative prior and, according to these authors, this is a problem often ignored in applications of Bayesian inference". They focused on four examples, analyzing each for several choices of prior. Here, we reassess these examples and their Bayesian processing via different prior choices for fixed data sets. The conclusion is to infer the overall stability of the posterior distributions and to consider that the effect of reasonable noninformative priors is mostly negligible.

The paper is focused on a new perspective in solving dynamics inverse problems, by considering recurrent equations based on Metabolic P (MP) grammars. MP grammars are a particular type of multiset rewriting grammars, introduced in 2004 for modeling metabolic systems, which express dynamics in terms of finite difference equations. Regression algorithms, based on MP grammars, were introduced since 2008 for algorithmically solving dynamics inverse problems in the context of biological phenomena. This paper shows that, when MP regression is applied to time series of circular functions (where time is replaced by rotation angle), the dynamics that is found turns out to coincide with recurrent equations derivable from classical analytical definitions of these functions. This validates the MP regression as a general methodology to discover deep logics underlying observed dynamics. At the end of the paper some applications are also discussed, which exploit the regression capabilities of the MP framework for the analysis of periodical signals and for the implementation of sequential circuits providing periodical oscillators.

This paper presents a mixed finite volume and finite difference solver with results showing the solitary wave interactions and shoaling process by solving a set of conservative forms of Boussinesq equations. A second order accurate finite volume scheme is applied to the conservative terms of the governing equations while up to the second order finite difference formulations are used to discretize the dispersive source terms with higher order derivatives. The limiters and surface gradient method are implemented in the model to remove the unwanted spurious oscillations and preserve the still water condition without introducing errors at the interfaces. The performance of the present numerical solver is tested with results of head on collisions and shoaling of solitary waves compared against those from finite element models that were developed based on fully nonlinear weakly dispersive and weakly nonlinear weakly dispersive forms of the Boussinesq equations as well as analytical solutions and experimental observations.

The present work deals the development of a nonlinear numerical model for structural analysis of solids composed by multi-domains considering cohesive discontinuities along its interfaces. The numerical method adopted is the boundary element method (BEM), through its singular and hyper–singular integral equations. Due to the mesh dimensionality reduction provided by BEM, this numerical method is robust and accurate for analyzing the fracture process in solids, as well as physical nonlinearities that occurs along the body’s boundaries. Multi-domain structures are modelled considering the sub-region technique, in which both equilibrium of forces and compatibility of displacements are enforced along all interfaces. The crack propagation process is simulated by the fictitious crack model, in which the residual resistance of the region ahead the crack tip is represented by cohesive tractions. It leads to a nonlinear problem relating the tractions at cohesive interface cracks to its crack opening displacements. The implemented formulation is applied to analysis of three examples. The numerical responses achieved are compared to numerical and experimental solutions available in literature in order to show the robustness and accuracy of the formulation.