Zonal modeling of radiative heat transfer in industrial furnaces using simplified model for exchange area calculation

The zonal analysis of industrial furnaces is considered with three-dimensional radiative heat transfer, incorporated with the mathematical zone method. In this method exchange areas are determined by simplified numerical integration in three dimensions for surface-surface, surface-gas and gas–gas zones for absorbing and emitting media. By focusing on new strategies to overcome the drawbacks of evaluating direct exchange areas, it is shown that the zone method is an effective numerical method for modeling three-dimensional thermal performance of gas-filled enclosures. Also the developed method for evaluating of exchange area is presented and compared with other methods in both sides of CPU time and accuracy. The method can decrease about 70% in error of calculation of some exchange areas as compared with the other numerical methods.     

An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model

An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖_∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.     

An introduction to Minkowski geometries

The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students’ understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.     

Effective optimization-based approach for designing active noise control systems in enclosures

An efficient constrained optimization-based prototype program OPTANC is developed to expedite the optimum design of active noise control systems in enclosures. The boundary element method is used to model the sound field of enclosures in which the walls provide complex impedance and point noise sources may exist at arbitrary locations. A sequential quadratic programming algorithm is selected as the optimizer for the deisgn because of its accuracy, efficiency, and reliability. The program is coded in C with portability on micro, mini, and mainframe computers, and is also modularized for future expansion. Simulations show that the software can effectively and efficiently produce the optimal locations and sound strengths of the control sources for active noise control problems.     

Interval methods for verifying structural optimality of circle packing configurations in the unit square

The paper is dealing with the problem of finding the densest packings of equal circles in the unit square. Recently, a global optimization method based exclusively on interval arithmetic calculations has been designed for this problem. With this method it became possible to solve the previously open problems of packing 28, 29, and 30 circles in the numerical sense: tight guaranteed enclosures were given for all the optimal solutions and for the optimum value. The present paper completes the optimality proofs for these cases by determining all the optimal solutions in the geometric sense. Namely, it is proved that the currently best-known packing structures result in optimal packings, and moreover, apart from symmetric configurations and the movement of well-identified free circles, these are the only optimal packings. The required statements are verified with mathematical rigor using interval arithmetic tools.     

Taylor-model-based enclosure of invariant manifolds for planar diffeomorphisms and applications

Fundamental questions in the study of interesting dynamics of planar diffeomorphisms like the Hénon map involve homoclinic phenomena, topological entropy and strange attractors. Inherently, answering these questions requires knowledge about the stable and unstable manifolds, which in the typical case in the plane are smooth curves. We present a method to find highly accurate Taylor Model enclosures of the invariant curves near hyperbolic fixed points. Successive iteration of these local enclosures yields similarly accurate enclosures of pieces of the global manifold tangle. Applications presented include the automatic computation of rigorous enclosures of all homoclinic points up to finite iterates. This allows to find symbolic dynamics in the original system and consequently compute rigorous lower bounds for its topological entropy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semi-partial geometries and spreads of classical polar spaces

A new construction method for semi-partial geometries is given and new examples of semi-partial geometries are deduced. Further, several constructions of spreads of the quadratic Q^?(5, q) are given.     

Weierstrass formula and zero-finding methods

Summary. Classical Weierstrass' formula [29] has been often the subject of investigation of many authors. In this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions. We are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros. Conditions for the safe convergence of Weierstrass' method, depending only on initial approximations, are given. In particular, we study polynomials with interval coefficients. Using an interval version of Weierstrass' method enclosures in the form of disks for the complex-valued set containing all zeros of a polynomial with varying coefficients are obtained. We also present Weierstrass-like algorithm for approximating, simultaneously, all zeros of a class of analytic functions in a given closed region. To demonstrate the proposed algorithms, three numerical examples are included. Received September 13, 1993     

Determination of the characteristics of concentrated heat sources in a half-space under prescribed conditions for the heat exchange and temperature distribution on its surface

A method is given for solving the inverse problem for determining the intensity and location of concentrated heat sources in a half-space under prescribed conditions on the heat exchange with the external medium and a distribution of surface temperature with error. Using methods of the variational calculus, we obtain a system of nonlinear equations for the characteristics of subsurface heat sources, leading to a temperature function on the surface which is closest to the given distribution. Several individual examples are solved.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 46–51, 1989.     

等周问题的一个初等证明

本文把欧氏平面，半球面和非欧面之中，不含给定边界，含有给定边界和含有边界而且在其上给定端点这样三种等周问题、给以初等、统一的证明。其要点在于把它们的存在性和唯一性简明扼要地归结到下述初等引理，即一个给定凹边边长的四边形的面积以四顶共圆时为其唯一的极大     

Finite element modeling of the nonlinear oscillations in axisymmetric acoustic resonators

Oscillation of a gas in closed resonators has gained considerable interest in the past years. In this paper, the nonlinear equations governing the behavior of the gas oscillations inside the resonator are formulated in a weak form and then modeled using the finite element method. The pressure ratios, predicted by the proposed model, are in close agreement with the exact solutions available for simple geometries such as cylindrical, exponential and linearly varying area resonators. The presented comparisons validate the accuracy of the finite element model and emphasize its potential for predicting the performance or resonators of more complex geometries which are necessary for generating high pressures from the standing waves. Also, gas flow through the boundaries of the resonator is implemented in the proposed model. The presented finite element model presents an invaluable tool for designing a new class of acoustic compressors which can be used, for example, in refrigeration and vibration control applications.     

A hierarchical method for obtaining eigenvalue enclosures

We introduce a new method of obtaining guaranteed enclosures of the eigenvalues of a variety of self-adjoint differential and difference operators with discrete spectrum. The method is based upon subdividing the region into a number of simpler regions for which eigenvalue enclosures are already available.

     

The Transit Route Arc-Node Service Maximization problem

This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the route. The mathematical formulation modifies and exploits the structure of linear programming problems designed for the traveling salesman problem. An innovative divide-and-conquer solution procedure is presented that not only makes the transit routing problem tractable, but also provides a range of high-quality alternate routes for consideration, some of which have substantially varying geometries. Variant formulations are provided for several common transit route types. The model is tested through its application to an existing street network in Richardson, TX. Optimal numeric results are obtained for several problem instances, and these results demonstrate that increased route cost is not correlated with increased service provision.     

A new theorem discovered by computer prover

Concerning Pappus lines and Leisenring lines there is a set of interesting theorems given in [1]. In this paper, we show that these theorems can be easily proved by our computer prover which is implemented on the basis of Wu's method for mechanical theorem proving in geometries. Using this prover we discovered, furthermore, a new theorem: The six intersection points of every Pappus line and its corresponding Leisenring line are collinear.     

Truncations of principal geometries

We investigate the class of principal pregeometries (free simplicial geometries with spanning simplex) which form an important subclass of the class of transversal pregeometries (free simplicial geometries). We give a coordinate-free method for imbedding a transversal pregeometry on a simplex as a free simplicial pregeometry which makes use only of the set-theoretic properties of a presentation of the transversal pregeometry. We introduce the notion of an (r, k)-principal set as a generalization of principal basis and prove the collection of (r, k)-principal sets of a rank k pregeometry, if non-empty, are the bases of another pregeometry whose structure is determined. An algorithm for constructing principal sets is given. We then characterize truncations of principal geometries in terms of the existence of a principal set. We do this by erecting a given pregeometry to a free simplicial pregeometry with spanning simplex. The erection is the freest of all erections of the given pregeometry.     

Improved boundary treatment for the smoothed particle hydrodynamics method using implicit surfaces

The boundary treatment for modeling complex geometries in smoothed particle hydrodynamics (SPH) methods is always challenging, especially for objects with sharp corners. In this paper, we propose an improved boundary treatment technique to handle boundary conditions in the SPH method where objects are represented as implicit surfaces. The improved boundary treatment technique provides a full treatment for complicated geometries and can handle sharp edges without any special treatment. The boundary particles are uniformly distributed in compliance with the curvature of the objects, therefore taking into consideration the effect of the boundary. Several simulations are presented to validate and demonstrate the applicability and versatility of the proposed technique.     

基于双因子定价模型的投资组合风险价值的多分辨率特征研究

为了识别金融市场投资风险的多分辨率特征及优化投资组合,以资本市场风险和汇率市场风险为双因子定价模型的风险因子,利用小波方差及协方差无偏估计量,给出了单个资产风险因子敏感度多分辨率计算方法,以此为基础还得到了投资组合的风险值(VaR)及其边际风险值(MVaR)的多分辨率分解公式.对上证A股市场的实证分析表明投资组合的风险价值及边际风险价值依赖于投资时限,短线投资潜在的损失比长线投资要大;进一步分析表明中国股市存在多分辨率风险特征,这种风险特点可能是由市场系统风险和汇率风险以及异质性投资活动共同作用的结果.研究还发现多分辨率边际风险价值是确定多分辨率投资组合优化模型求解的重要条件之一.     

Mathematically modelling surface EMG signals

Comprehension and correct interpretation of EMG signals and their generation could still be well improved. Computational models that can predict the EMG signal resulting from realistic motor unit recruitment as well as the underlying biophysical processes of single skeletal muscle fibres are therefore highly desirable. Having such a model available, one can test, verify and improve algorithms determining motor unit recruitment. Here, we present a three-dimensional, continuum-based, forward model that is able to produce a virtual EMG signal based on the underlying biophysical principles of skeletal muscle fibre activation. The result is a virtual EMG signal for complex and realistic geometries that may even undergo deformations as in the case of dynamic contractions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extensions of ValEncIA-IVP for reduction of overestimation,for simulation of differential algebraic systems,and for dynamical optimization

Simulation techniques are commonly used to analyze the influence of uncertainties of initial conditions and systemparameters on the trajectories of the state variables of dynamical systems. In this context, interval arithmetic approaches are of interest. They are capable of determining guaranteed bounds of all reachable states if worst-case bounds of the above-mentioned uncertainties are known. Furthermore, interval algorithms ensure the correctness of numerical results in spite of rounding errors which inevitably arise if floating point operations are carried out on a computer. However, naive implementations of interval algorithms often lead to overestimation, i.e., too conservative enclosures which can make the results meaningless. In this contribution, we summarize the basic routines of ValEncIA-IVP which computes interval enclosures of all reachable states of dynamical systems described by ordinary differential equations ODEs. ValEncIA-IVP , VAL idation of state ENC losures using I nterval A rithmetic for I nitial V alue P roblems, can be applied to the simulation of systems with both uncertain parameters and uncertain initial conditions. Advanced techniques for reduction of overestimation are demonstrated for a simplified catalytic reactor. Afirst approach to using VanEncIA-IVP for the simulation of sets of differential algebraic equations is outlined. Finally, an outlook on the integration of ValEncIA-IVP in an interval arithmetic framework for computation of optimal and robust control strategies for continuous-time processes is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)