Pre- and post-processing for the finite element method

The finite element method provides a powerful procedure to mathematically model physical phenomena. The technique is numerically formulated and is effectively used on a broad range of computers. The method has increased in both popularity and functionality with the development of user friendly pre- and post-processing software. Pre-processing software is used to create the model, generate an appropriate finite element grid, apply the appropriate boundary conditions, and view the total model. Post-processing provides visualization of the computed results. This paper addresses the pertinent issues of pre- and post-processing for finite element analysis. It reviews the capabilities that are provided by pre- and post-processors and suggests enhancements and new features that will likely be developed in the near future.     

Combinatorial and robust optimisation models and algorithms for railway applications

The following is a summary of the author??s Ph.D. thesis supervised by Alberto Caprara and Paolo Toth and defended on April 16, 2009?at the Università di Bologna. The thesis is written in English and is available from the author upon request. Railway systems represent a challenging area for operations research, especially when highly-complex and data-intensive applications, such as large-scale transportation networks, are at stake. One of the main issues concerns imperfect information. The classic notion of Robust Optimisation, as a way to represent and handle mathematically systems with not precisely known data, did not prove to be successfully applicable in the railway setting. For this reason a new paradigm has been defined recently in Liebchen et?al. (2007): Recoverable robustness. Here we present our research on recoverable robust optimisation models for two important railway problems: Train platforming and Rolling stock planning.     

Applied optimal shape design

This paper is a short survey of optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, correct discretization are important theoretical issues. Practical implementation issues for airplane designs are critical too.The paper is also a summary of the material covered in our recent book, Applied Optimal Shape Design, Oxford University Press, 2001.     

Nonlinear system identification and adaptive control using polynomial networks

This work introduces a new nonlinear computational model called polynomial network for identification and adaptive control of nonlinear dynamical systems. The network approximates the Volterra systems or recursive polynomial systems. The approximation properties of this network are compared with the sigmoid networks. The results show that the polynomial network constructs a simpler and smaller model and requires less training data. Also, the model realized by the polynomial network is mathematically tractable. The feasibility of using this model for direct model reference adaptive control of a class of nonlinear systems is demonstrated.     

A Lagrangian heuristic for determining the speed and bunkering port of a ship

This study addresses the problem of determining the ship speed and bunkering ports in a ship route. All of the previous research has investigated the ship speed optimization issues by assuming that the ship navigates at constant speed or by ignoring the bunkering port decision. In this study, the problem of determining the variable speed and bunkering port is formulated mathematically with a nonlinear program in order to minimize the bunker fuel, ship time costs, and carbon tax imposed on greenhouse gas emissions. This study then provides a Lagrangian heuristic by deriving a property for a relaxed problem. The performance of the heuristic is evaluated and analysed using the data obtained from the literature, real practice and random generation.     

Effects of the killing rate on global bifurcation in an oncolytic-virus system with tumors

Oncologists and virologist are quite concerned about many kinds of issues related to tumor-virus dynamics in different virus models. Since the virus invasive behavior emerges from combined effects of tumor cell proliferation, migration and cell-microenvironment interactions, it has been recognized as a complex process and usually simulated by nonlinear differential systems. In this paper, a nonlinear differential model for tumor-virus dynamics is investigated mathematically. We first give a priori estimates for positive steady-states and analyze the stability of the positive constant solution. And then, based on these, we mainly discuss effects of the rate of killing infected cells on the bifurcation solution emanating from the positive constant solution by taking the killing rate as the bifurcation parameter.     

Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.     

Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.     

冲突分析的一种改进方法

本文分析了冲突分析所存在的问题并提出了解决方法，为此引入了势函数．用势函数代替偏好值进行冲突分析，所得结论更合理更精确．     

About a numerical method of successive interpolations for functional Hammerstein integral equations

A new and robust numerical method for Hammerstein functional integral equations is proposed. The convergence and the numerical stability of the method are mathematically proved and tested on some examples.     

Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.     

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.     

Analysis of stable two-dimensional patterns in contractile cytogel

Summary Contractile actomyosin systems play a central role in the generation of intracellular patterns. Models for pattern formation have benefited greatly from the application of mechanochemical theory. However, investigations of the patterns have been primarily qualitative in nature; the two-dimensional nature of the evolving patterns has not yet been addressed mathematically, nor has the evolution of stable heterogeneous steady-state solutions. We consider these issues, supporting our analytical predictions with numerical simulations in one and two spatial dimensions. We show how, for certain gels, the two and three-dimensional tensor equation which describes a balance of forces can be reduced to a reaction-diffusion equation.     

Neurocontrol of nonlinear systems via local memory neurons

In this report, we consider the part of our work which concerns the approximation of nonlinear dynamic systems using neural networks. Based on a new paradigm of neurons with local memory (NNLM), we discuss the representation of control systems by neural networks. Using this formulation, the basic issues of controllability and observability for the dynamic system are addressed. A separation principle of learning and control is presented for NNLM, showing that the weights of the network do not affect its dynamics. Theoretical issues concerning local linearization via a coordinate transformation and nonlinear feedback are discussed. For illustration of the approach simulation results for nonlinear control of an aircraft encountering wind shear on take-off is presented.     

A new metaheuristic algorithm based on shark smell optimization

In this article, a new metaheuristic optimization algorithm is introduced. This algorithm is based on the ability of shark, as a superior hunter in the nature, for finding prey, which is taken from the smell sense of shark and its movement to the odor source. Various behaviors of shark within the search environment, that is, sea water, are mathematically modeled within the proposed optimization approach. The effectiveness of the suggested approach is compared with many other heuristic optimization methods based on standard benchmark functions. Also, to illustrate the efficiency of the proposed optimization method for solving real‐world engineering problems, it is applied for the solution of load frequency control problem in electrical power systems. The obtained results confirm the validity of the proposed metaheuristic optimization algorithm. © 2014 Wiley Periodicals, Inc. Complexity 21: 97–116, 2016     

Numerical Method for Damping String Vibrations with Unknown Initial State in the Class of Weak Generalized Solutions

The problem of positional boundary control is considered for the spatially one-dimensional wave equation. The objective of control is to transfer the system from an unknown initial state into the state of rest in finite time. A specific feature of the statement of the problem is the weakening of the requirements on the regularity of generalized solutions, observations, and control. The smoothing procedure is used to transfer the problem into the class of strong generalized solutions, where the method previously developed by the authors can be used. The procedure is mathematically justified, and the corresponding results of numerical experiments are given.     

Operations planning with VERT

The Venture Evaluation and Review Technique (VERT) is a computerized, mathematically oriented network-based simulation technique designed to analyze risk existing in three parameters of most concern to managers in new projects or ventures--time, cost, and performance. As such, the VERT technique is more powerful than techniques such as GERT, which are basically time and cost oriented. VERT has been successfully utilized to assess the risks involved in new ventures and projects, in the estimation of future capital requirements, in control monitoring, and in the overall evaluation of ongoing projects, programs, and systems. It has been helpful to management in cases where there is a requirement to make decisions with incomplete or inadequate information about the alternatives. An example describing the application of VERT to an operational planning problem--the evaluation of electric power generating methods--is illustrated.     

Robust D-stability analysis for linear uncertain discrete singular systems with state delay

In this work, by using the maximum modulus principle and the spectral radii of matrices, a new robust D-stability (i.e., robust eigenvalue clustering in a specified circular region) condition is proposed to ensure that, for all admissible structured parameter uncertainties, the linear discrete singular system with state delay is regular, causal and D-stable. The proposed criterion is mathematically proved to be less conservative than the existing one reported very recently.     

Residual scaling techniques in multigrid, II: Practical applications

This paper focuses on the practical applications of the multigrid residual scaling techniques and is the continuation of a companion paper: Residual scaling techniques in multigrid, I: Equivalence proof [Appl. Math. Comput. 86:283–303 (1997)]. We discuss the computational issues of some residual scaling techniques which have been proven mathematically equivalent. A heuristic residual analysis technique, based on the geometry of the grid points and the relaxation pattern, is introduced to estimate the optimal residual scaling factor for a high-order multigrid method. We compare the performance of a typical pre-optimization (pre-acceleration) technique with a typical post-optimization (post-acceleration) technique and show that the pre-optimization is preferable in both convergence and efficiency. Our numerical results support the theoretical conclusions made in the companion paper and demonstrate the full advantage of the pre-optimization technique over the post-optimization technique.