Authors:Vivian Martins Gomes; Cristiano Fiorilo de Mello; Elbert E. N. Macau; Antonio Fernando Bertachini de Alme Prado; Othon Cabo Winter Pages: 1463 - 1469 Abstract: Abstract Studies related to Celestial Mechanics started long ago, and it is one of the oldest fields in Astronomy. It started to try to explain the motions of the stars in the sky, in particular the irregular motion of some of those of then, which were really the planets of the Solar System. In the 20th century, with the arrival of the “Space Age”, many applications related to the motion of artificial spacecrafts appeared. This new field was called “Astrodynamics”, to designate the use of Celestial Mechanics in man-made objects. Several aspects, like orbit determination, maneuvers to change the orbit of the spacecraft, etc., are covered by this topic. The present Focus Issue in Celestial Mechanics publishes a list of papers in topics related to applications in Celestial Mechanics to both situations: natural and artificial satellites. PubDate: 2017-12-01 DOI: 10.1007/s40314-017-0499-9 Issue No:Vol. 36, No. 4 (2017)

Authors:Saeed Emami; Ghasem Moslehi; Mohammad Sabbagh Pages: 1471 - 1515 Abstract: Abstract In this paper, we consider a simultaneous order acceptance and scheduling problem in a non-identical parallel machines environment. The orders are defined by their due dates, revenues, tardiness penalties, different processing times on the machines, and sequence-dependent setup times. We present an MILP formulation to maximize the profit. Furthermore, we assume that the revenue from an accepted order and the processing times are uncertain and accordingly, develop the robust counterpart of the proposed MILP model. The problem is computationally intractable; therefore, we develop a Benders decomposition approach to solve it. We introduce some valid cuts to accelerate the convergence of the classical Benders algorithm and a heuristic method to obtain the feasible solutions. Through numerical experiments on randomly generated large instances with up to 40 orders and 6 machines, we demonstrate that the proposed Benders decomposition approach outperforms the MILP model. PubDate: 2017-12-01 DOI: 10.1007/s40314-015-0302-8 Issue No:Vol. 36, No. 4 (2017)

Authors:Elaine Cristina Catapani Poletti; João Frederico da Costa Azevedo Meyer Pages: 1517 - 1528 Abstract: Abstract This paper proposes to analyze the dispersion of pollutants in aquatic systems, solving the advection–diffusion equation using numerical methods and fuzzy sets. For solution, numerical approximations were adopted, based on the finite element method for the spatial discretization and Crank–Nicolson for the time variable. The parameters of the equation were modeled taking into account aspects of multiple varieties of natural phenomena, based on fuzzy sets. The two-dimensional model resulted in the value of pollutant dispersion taking into account the flow velocity, in situations of prevailing winds in the region of a reservoir of Sao Paulo. According to the results, it was observed that the integration of the numerical methods and the fuzzy parameters is a potential instrument for environmental process analysis. The rule-based systems allowed a better design of the local natural phenomena. The spread of the plumes of pollutants was well defined by the model and the simulated scenarios are in agreement, from a qualitative point of view, with the local reality. PubDate: 2017-12-01 DOI: 10.1007/s40314-015-0299-z Issue No:Vol. 36, No. 4 (2017)

Authors:N. Karimi; H. Davoudpour Pages: 1529 - 1544 Abstract: Abstract This paper will introduce a new scheduling problem in the supply chain. This is an integrated scheduling and transportation problem where stage-dependent holding cost is taken into consideration. This supply chain consists of a number of serial factories joined together. The objective is minimizing the whole system’s criteria which are the sum of the transportation cost and stage-dependent holding costs. Transporting and delivering a number of jobs in the form of batches are also allowed. In scheduling systems with delivery, a job can be delivered when its processing is completed. The processed job should remain in the system until its batch’s completion time. On the other hand, on receiving at a factory, jobs should wait until their process has started. These would impose the WIP inventory cost. The other holding cost imposed on the system is finished-goods holding cost which is incurred on the jobs that are delivered to the customer before their due dates. Thus, the objective of this study is to find a schedule with trade-off among holding costs and delivery cost. A time-indexed formulation of the problem is also presented. Computational studies are performed to check the performance of the proposed models. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0305-0 Issue No:Vol. 36, No. 4 (2017)

Authors:Mantas Landauskas; Zenonas Navickas; Alfonsas Vainoras; Minvydas Ragulskis Pages: 1545 - 1558 Abstract: Abstract An algebraic approach for the selection of weight coefficients for weighted moving averaging is proposed in this paper. The algebraic complexity of the sequence transformed by weighted moving averaging is set as a target criterion for the optimization problem of weight coefficients. A special computational setup is constructed in order to tackle the inevitable additive noise for real-world time series. Computational experiments prove that the proposed approach can outperform time series predictors based on classical moving averaging. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0309-9 Issue No:Vol. 36, No. 4 (2017)

Authors:Wenwen Zeng; Xiaopin Zhong; Jingzhen Li; Yupeng Fan Pages: 1559 - 1575 Abstract: Abstract Tomographic reconstruction from a small number of projections is still a challenging problem. In the paper, we formulate this problem as a statistical graphical model by the smooth assumption that the image has a structure where neighbor pixels have a larger probability to take a closer value. This Markov random filed framework allows easily integrating other prior information. Reasoning in the model can be solved using belief propagation algorithm. However, one projection line involves multiple pixels. This leads to high order cliques and exponential computation in the message passing procedure. A variable-change strategy is used to largely reduce the computation and forms an efficient sum-product reasoning algorithm. Numerical simulation examples show that the proposed method greatly surpasses traditional methods, such as FBP, EM and ART. Our method is suitable not only for the case of a very small amount of projection, but also for the multi-pixel-value case. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0313-0 Issue No:Vol. 36, No. 4 (2017)

Authors:Wang Fangzong; Liao Xiaobing Pages: 1577 - 1590 Abstract: Abstract The differential quadrature method (DQM) has been widely used for structural dynamics problems computation. Traditional DQM usually adopts simultaneous discretization in multi-grid points, and then all variables are solved simultaneously. Obviously, this will result in the curse of dimensionality problem for large-scale systems. In this paper, on the basis of the multi-stage high-order time domain DQM, a fast numerical calculation method for large-scale structural dynamics problems based on \({\varvec{V}}\) -transformation is proposed. Using the \({\varvec{V}}\) -transformation possessed by the weighting coefficient matrix of DQM, the whole Jacobian matrix equations involved in the traditional approach of DQM can be decoupled into blocks; thus, the multi-stage block recursive method is derived. Numerical experiments show that: even using 2s times step size of the Newmark method, the computational accuracy of DQM is about 2–3 orders of magnitude higher than that of the Newmark method. Furthermore, three different scale systems are used for time test and the results show that the multi-stage block recursive method can obtain high speedup ratio, which can significantly improve the computational efficiency of large-scale structural dynamics problems. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0310-3 Issue No:Vol. 36, No. 4 (2017)

Authors:Mehdi Dehghan; Reza Mohammadi-Arani Pages: 1591 - 1606 Abstract: Abstract GPBiCG is a generalization of a class of product-type methods where the residual polynomials can be factored by the residual polynomial of BiCG and other polynomials with standard three-term recurrence relations. Actually this method generalizes CGS and BiCGStab methods. In this paper we use GPBiCG to present a new method for solving shifted linear systems. GPBiCG is faster than BiCGStab and its convergence is smoother than CGS. So here we are expecting to develop a method which is faster and its convergence is smoother than shifted BiCGStab and shifted CGS methods for solving shifted linear systems. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0315-y Issue No:Vol. 36, No. 4 (2017)

Authors:Mujahid Abbas; Talat Nazir; Tatjana Aleksić Lampert; Stojan Radenović Pages: 1607 - 1622 Abstract: Abstract The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0314-z Issue No:Vol. 36, No. 4 (2017)

Authors:Qilong Liu; Chaoqian Li; Yaotang Li Pages: 1623 - 1635 Abstract: Abstract Strong \(\mathcal {H}\) -tensors play an important role in identifying the positive definiteness of even-order real symmetric tensor. An iterative algorithm for identifying strong \(\mathcal {H}\) -tensors was given in Li et al. (J Comput Appl Math 255:1–14, 2014), where the method does not stop in finite iterative steps when the tensor is not a strong \(\mathcal {H}\) -tensor. In this paper, to overcome this drawback, we present a new algorithm which always terminates after finite iterative steps and needs fewer iterations than the earlier one for a general tensor. Numerical examples are given to show the effectiveness of the proposed method. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0311-2 Issue No:Vol. 36, No. 4 (2017)

Authors:Jien Deng; Zhenzhen Tao; Tong Zhang Pages: 1637 - 1657 Abstract: Abstract In the paper we consider the one-level and two-level iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem based on the iteration of pressure with a factor of penalty parameter. Firstly, the \(\mathbf {H}^1\) and \(\mathbf {L}^2\) error estimates of numerical solutions of one-level iterative penalty finite element method are provided. Secondly, the stability and convergence of two-level iterative penalty finite element method are analyzed. Finally, some numerical results are provided to verify the effectiveness of the developed numerical schemes. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0323-y Issue No:Vol. 36, No. 4 (2017)

Authors:Xiangkui Zhang; Chunning Jin; Ping Hu; Xuefeng Zhu; Wenbin Hou; Jinting Xu; Changsheng Wang; Yuewei Zhang; Zheng-Dong Ma; Holly Smith Pages: 1659 - 1679 Abstract: Abstract We present an approach to construct NURBS (Non-Uniform Rational B-Splines) surfaces for tubular engineering structures. Isogeometric shell analysis using degenerated NURBS elements for tubular structures is also presented. We developed an automatic and simple algorithm to reconstruct multiple \(C^0\) continuous NURBS surfaces using the skeleton withdrawn from the trimmed CAD model. Isogeometric shell analysis based on Reissner–Mindlin theory was applied to the reconstructed model. To verify the efficiency of the present method, we constructed the CAD model of the car body of an electric car and simulate the deformation of an electric car using isogeometric shell analysis. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0312-1 Issue No:Vol. 36, No. 4 (2017)

Authors:M. S. Cecconello; Jefferson Leite; R. C. Bassanezi Pages: 1681 - 1697 Abstract: Abstract In this work, we analyze the asymptotic behavior of fuzzy solutions using recent results on equilibrium and periodic points. We apply this analysis in some examples to investigate interesting properties of fuzzy solutions. As we show, the fuzzy solutions considered can present a more complex behavior than the deterministic ones. In addition, we show a new interpretation to the membership function of such fuzzy solutions as well as explore some properties of projections of fuzzy solutions. Computational simulations are done to illustrate these asymptotic behaviors. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0326-8 Issue No:Vol. 36, No. 4 (2017)

Authors:Miglena N. Koleva; Lubin G. Vulkov Pages: 1699 - 1715 Abstract: Abstract In this paper we present a numerical method for a time-fractional Black–Scholes equation, which is used for modeling the fractional structure of the financial market. The method is based on—first, discretization in time and then the weighted finite difference spatial approximation. Some properties of the spatial discretization are studied. The main difficulty (that originates from the non-local structure of the differential operator) of the algorithm is the impossibility to advance layer by layer in time. Numerical experiments are discussed. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0330-z Issue No:Vol. 36, No. 4 (2017)

Authors:Khang Jie Liew; Ahmad Ramli; Ahmad Abd. Majid Pages: 1717 - 1732 Abstract: Abstract This paper examines the bootstrap test error estimation of radial basis functions, specifically thin plate spline fitting in surface reconstruction. In the presence of noisy data, instead of an interpolation scheme, the approximation scheme for a thin plate spline is used; therefore, an appropriate value for the smoothing parameter is needed to control the quality of fitting using a set of data points. To find a better smoothing parameter, bootstrap-based test error estimation (the bootstrap leave-one-out error estimator) is applied in searching for the smoothing parameter for a point set model with features. Experimental results demonstrate that the proposed bootstrap leave-one-out error is able to yield the optimum value for the smoothing parameter, which will produce good data approximation and visually pleasing results. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0332-x Issue No:Vol. 36, No. 4 (2017)

Authors:Bogdan Nita; Peter Nolan; Ashwin Vaidya Pages: 1733 - 1746 Abstract: Abstract In this paper, we numerically investigate the impact of body shape and wing orientation upon the flow induced drag forces experienced by a body in its steady state. The current study focuses on simple toy models but derives its motivations from previous reported work on wind-induced drag on birds in flight most of which are experimental in nature. Our numerical results show that body shape/eccentricites, wing length and orientation are all important in determining the forces experienced by a body in a flow. Their geometries and specific features are key to determining the optimal mode of locomotion which is determined by looking at the relationship between drag force, bending behavior versus flow and geometric parameters. PubDate: 2017-12-01 DOI: 10.1007/s40314-016-0333-9 Issue No:Vol. 36, No. 4 (2017)

Authors:Wendi Bao; Yongzhong Song; Hongmei Shao Pages: 1747 - 1782 Abstract: Abstract In this paper, we obtain a sinc discretization method for solving the boundary value problems of differential-algebraic equations (DAEs) and prove that the discrete solutions converge to the true solutions of the DAEs exponentially. In the process of presenting the solution, we find that the discrete solution is determined by a large and ill-conditioned linear system. To efficiently solve the linear system, we construct block-tridiagonal preconditioners for the iterative methods. Moreover, we derive the bounds for the eigenvalues of the preconditioned matrices. Numerical experiments are given to illustrate the effective performance and applicability of our method. PubDate: 2017-12-01 DOI: 10.1007/s40314-017-0498-x Issue No:Vol. 36, No. 4 (2017)

Authors:Mohammad Rezaiee-Pajand; Mahdi Karimi-Rad Abstract: Abstract A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method. PubDate: 2017-10-16 DOI: 10.1007/s40314-017-0520-3

Authors:Renato Candido; Magno T. M. Silva; Marcio Eisencraft Abstract: Abstract Many communication systems based on the synchronization of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, due to the lack of robustness of complete chaotic synchronization, even minor channel impairments are enough to hinder communication. In this paper, we propose a communication system that includes an adaptive equalizer and a switching scheme to alter between a chaos-based modulation and a conventional one, depending on the communication channel conditions. Simulation results show that the switching and equalization algorithms can successfully recover the transmitted sequence in different nonideal scenarios. PubDate: 2017-10-12 DOI: 10.1007/s40314-017-0519-9

Authors:R. H. Lopez; J. E. Souza Cursi; A. G. Carlon Abstract: Abstract This paper presents a new approach for state estimation problems. It is based on the representation of random variables using stochastic functions. Its main idea is to expand the state variables in terms of the noise variables of the system, and then estimate the unnoisy value of the state variables by taking the mean value of the stochastic expansion. Moreover, it was shown that in some situations, the proposed approach may be adapted to the determination of the probability distribution of the state noise. For the determination of the coefficients of the expansions, we present three approaches: moment matching (MM), collocation (COL) and variational (VAR). In the numerical analysis section, three examples are analyzed including a discrete linear system, the Influenza in a boarding school and the state estimation problem in the Hodgkin–Huxley’s model. In all these examples, the proposed approach was able to estimate the values of the state variables with precision, i.e., with very low RMS values. PubDate: 2017-10-11 DOI: 10.1007/s40314-017-0515-0