An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions.     

Boundary element analysis of uncoupled transient thermo-elastic problems with time- and space-dependent heat sources

A boundary element method (BEM) for the analysis of two- and three-dimensional uncoupled transient thermo-elastic problems involving time- and space-dependent heat sources is presented. The domain integrals are efficiently treated using the Cartesian transformation and the radial integration methods without considering any internal cells. Similar to the dual reciprocity method (DRM), some internal points without any connectivity are considered; however, in contrast to the DRM, any arbitrary mesh-free interpolation method can be used in the present formulation. There is no need to find any particular solutions and the shape functions in the mesh-free interpolation method can be arbitrary and sufficiently complicated. Unlike the DRM, the generated system of equations contains the unknowns only on the boundary. After finding the primary unknowns on the boundary, the temperature, displacement, and stress components at all internal points can directly be found without solving any system of equations. Three examples with different forms of heat sources are presented to demonstrate the efficiency and accuracy of the proposed method. Although the proposed BEM is mathematically more complicated than domain methods, such as the finite element method (FEM), it is more efficient from a modelling viewpoint since only the surface mesh has to be generated in the presented method.     

Regenerative cascade homotopies for solving polynomial systems

A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods.     

Synchronization of a growing chaotic network model

Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon, which is helpful for the understanding of working mechanisms in neuronal networks, social network, etc. In this paper, we will investigate the synchronization phenomenon in a network model. A feedback control scheme is proposed for the synchronization of the given complex networks. The obtained result indicates that synchronization can be achieved for growing chaotic network model. Method enhance the synchronizability of the given model are given at the same time. Finally, numerical simulations are given to show the effectiveness of obtained results.     

A contact problem in generalized thermoelasticity

In this work we study a one-dimensional contact problem in generalized thermoelasticity under the Green-Lindsay theory. Unilateral contact with an elastic obstacle is assumed. We consider the quasi-static and the fully dynamic situations. We prove existence and uniqueness results and propose finite element approximations in space with backward Euler discretization in time. Stability results are given and some numerical experiments reported. The second sound effect of heat conduction is observed in the simulations.     

Quantum-inspired space search algorithm (QSSA) for global numerical optimization

This work presents the evolutionary quantum-inspired space search algorithm (QSSA) for solving numerical optimization problems. In the proposed algorithm, the feasible solution space is decomposed into regions in terms of quantum representation. As the search progresses from one generation to the next, the quantum bits evolve gradually to increase the probability of selecting the regions that render good fitness values. Through the inherent probabilistic mechanism, the QSSA initially behaves as a global search algorithm and gradually evolves into a local search algorithm, yielding a good balance between exploration and exploitation. To prevent a premature convergence and to speed up the overall search speed, an overlapping strategy is also proposed. The QSSA is applied to a series of numerical optimization problems. The experiments show that the results obtained by the QSSA are quite competitive compared to those obtained using state-of-the-art IPOP-CMA-ES and QEA.     

The construction of numerical integration rules of degree three for product regions

Numerical integration formulas in n-dimensional Euclidean space of degree three are discussed. In this paper, for the product regions a method is presented to construct numerical integration formulas of degree three with 2n real points and positive weights. The presented problem is a little different from those dealt with by other authors. All the corresponding one-dimensional integrals can be different from each other and they are also nonsymmetrical. In this paper an n-dimensional numerical integration problem is turned into n one-dimensional moment problems, which simplifies the construction process. Some explicit numerical formulas are given. Furthermore, a more generalized numerical integration problem is considered, which will shed light on the final solution to the third degree numerical integration problem.     

Convergence of numerical solutions to stochastic age-structured system of three species

In general, most of stochastic age-structured system of three species do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age-structured system of three species.     

Prediction error sampling procedure based on dominant Schur decomposition. Application to state estimation in high dimensional oceanic model

Iterative procedure is described to generate patterns of dominant Schur vectors of the system dynamics. Their roles in estimating the filter gain is study. These patterns are produced by several integrations of the model from a set of perturbations. This approach is motivated by a number of interesting results on stability of the filter whose gain is approximated in a subspace of dominant Schur vectors. A simple method for the filter design is presented which is aimed at overcoming the most serious drawback of advanced filtering algorithms for high dimensional systems related to very high computational cost in evaluation of the filter gain.The resulting filter will be compared with the existing ones, showing its relevance from a practical point of view. In order to demonstrate its efficiency, the new filter is tested on various experiments. These experiments include the much studied problem of estimating the solution of the Lorenz system as well as that of assimilating sea surface height observations in a high dimensional oceanic model. It is shown that significant increases in efficiency can be obtained by using this filter and that the proposed filter is very promising for solving realistic assimilation problems in meteorology and oceanography.     

Numerical approximation for a Baer-Nunziato model of two-phase flows

We present a well-balanced numerical scheme for approximating the solution of the Baer-Nunziato model of two-phase flows by balancing the source terms and discretizing the compaction dynamics equation. First, the system is transformed into a new one of three subsystems: the first subsystem consists of the balance laws in the gas phase, the second subsystem consists of the conservation law of the mass in the solid phase and the conservation law of the momentum of the mixture, and the compaction dynamic equation is considered as the third subsystem. In the first subsystem, stationary waves are used to build up a well-balanced scheme which can capture equilibrium states. The second subsystem is of conservative form and thus can be numerically treated in a standard way. For the third subsystem, the fact that the solid velocity is constant across the solid contact suggests us to compose the technique of the Engquist-Osher scheme. We show that our scheme is capable of capturing exactly equilibrium states. Moreover, numerical tests show the convergence of approximate solutions to the exact solution.