Characteristic form of dynamics equations of Cosserat medium

In this paper, we construct the characteristic form of the equations of dynamics of the Cosserat medium and the Cosserat pseudocontinuum for bounded bodies. The method of matrix transformations proposed by the author is used for construction and allows obtaining the necessary relations using identical transformations. The obtained equations are compared with those for a symmetrically elastic isotropic homogeneous body. A method is proposed for selecting the necessary equations for computational schemes at the internal and boundary points of the body. A sequence of operations is proposed for iterative calculations of stresses, particle velocities, moment stresses, and angular velocities of particles in a coupled model of the Cosserat medium.

Comparison of Bayesian Methods for Recovering Sinusoids

In this paper, we study a problem of estimating parameters of sinusoids from noisy data within Bayesian inferential framework. In this context, three different computational schemes such as, Bretthorst’s integral method (BRETTHORST), Gibbs sampling (GIBBS) and parallel tempering (PT) are studied and modifications of their algorithms were tested on data generated from synthetic signals. In addition, our emphasis is given to a comparison of their performances with respect to Cramér-Rao lower bound (CRLB).

Forecasting Multivariate Chaotic Processes with Precedent Analysis

Predicting the state of a dynamic system influenced by a chaotic immersion environment is an extremely difficult task, in which the direct use of statistical extrapolation computational schemes is infeasible. This paper considers a version of precedent forecasting in which we use the aftereffects of retrospective observation segments that are similar to the current situation as a forecast. Furthermore, we employ the presence of relatively stable correlations between the parameters of the immersion environment as a regularizing factor. We pay special attention to the choice of similarity measures or distances used to find analog windows in arrays of retrospective multidimensional observations.

Diverse bistable dark novel explicit wave solutions of cubic–quintic nonlinear Helmholtz model

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

Scope

From the educational point of view, there are many textbooks on reactor physics used at various universities in the world. However, most of these textbooks focus either on application to Light Water Reactors (LWRs), or on the theory and mathematics, with a significant number of equations and computational schemes. Or else they were written more than 20, or even more than 60, years ago, and therefore they do not reflect the evolution of reactor concepts and engineering requirements since then. All those categories of books are either difficult to follow for non-physicists working in the nuclear industry, or else are of little value for those who are interested in special features of CANDU reactor physics.

Diverse solitary and Jacobian solutions in a continually laminated fluid with respect to shear flows through the Ostrovsky equation

In this paper, the generalized Jacobi elliptical functional (JEF) and modified Khater (MK) methods are employed to find the soliton, breather, kink, periodic kink, and lump wave solutions of the Ostrovsky equation. This model is considered as a mathematical modification model of the Korteweg-de Vries (KdV) equation with respect to the effects of background rotation. The solitary solutions of the well-known mathematical model (KdV equation) usually decay and are replaced by radiating inertia gravity waves. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Many distinct solutions are obtained through the employed computational schemes. Moreover, some solutions are sketched in 2D, 3D, and contour plots. The effective and powerful of the two used computational schemes are tested. Furthermore, the accuracy of the obtained solutions is examined through a comparison between them and that had been obtained in previously published research.

Evolutionary Optimization of Case-Based Forecasting Algorithms in Chaotic Environments

The problem of dynamic adaptation of prediction algorithms in chaotic environments based on identification of the situations-analogs in the database of retrospective observations is considered. Under conditions of symmetrical and unsymmetrical chaotic dynamics, traditional computational schemes of precedent prediction turn out to be ineffective. In this regard, a dynamic adaptation of precedent analysis algorithms based on the method of evolutionary modeling is proposed. Implementation of the computational precedent prediction scheme for chaotic processes as well as the evolutionary modeling method are described.