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POLYNOMIAL SPECTRAL F ACTORIZATION WITH COMPLEX COEFFICIENTS

IFAC Proceedings Volumes 2002年第1期35卷 13-18页

作者： Martin Hromčik Jan Jezek Michael Šebek Zdeněk Hurák Institute of Information Theory and Automation Prague CZ Centre of Applied Clg ernetics Czech Technic al University CZ

Conceptual and numerical issues related to the spectral factorization of polynomials and polynomial matrices with complex coefficients are studied in this report. Such investigation is motivated by the demand for reliable algorithms and CAD tools capable of solving latest signal processing problems involving complex polynomials (Ahlen and Sternad, 1993). Basic concepts of the real polynomial spectral facorization theory are inspected first, and their generalization and necessary modification for complex polynomials then follows. Efficient numerical methods which are known to work in the real case are then revisited and their applicability for complex coefficients is considered. As an immediate result of this research, the powerful algorithms proposed in this paper have given rise to several routines implemented in the Polynomial Toolbox for Matlab (Kwak ernaak and Sebek, 1999) and addressing the spectral factorization problem.

关键词： Algebraic design methods numerical algorithms signal processing

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Kalman—Type Filtering for Stochastic Systems with State—Dependent Noise and Markovian Jumps

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IFAC Proceedings Volumes 2009年第10期42卷 1375-1380页

作者： A.–M. Stoica V. Dragan I. Yaesh Faculty of Aerospace Engineering University “Politehnica” of Bucharest Bucharest Romania Institute of Mathematics of the Romanian Academy Bucharest Romania IMI Advanced Systems Div. Ramat-Hasharon Israel

The paper presents a Kalman–type filtering problem for linear stochastic systems subjected both to state–dependent white noise and to Markovian jumps. The results are derived using a unified approach for the continuous–time case and for the discrete-time models of the plant. It is proved that the optimal filters gains depend on the solutions of some specific Riccati-type systems which generalize the well–known equations from the classical Kalman filtering.

关键词： Kalman filters Stochastic systems Markov parameters Riccati equations numerical algorithms

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A Multi-Criteria Optimisation Algorithm for the Evaluation of Scientific Activity

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Procedia Computer Science 2023年 225卷 3987-3995页

作者： Aneta Olga Hapka Rafał Wojszczyk Tomasz Królikowski Faculty of Electronics and Computer Science Koszalin University of Technology 2 Sniadeckich 75-453 Koszalin Poland

The article discusses a multi-criteria optimization algorithm, developed for the estimation of the quality of scientific activity. The presented solution is based on a modified knapsack algorithm, the novelty of the approach relies on extended data sorting – with splitting apparently equivalent data blocks. The criteria of the algorithm are based on the regulations in force in Poland, but it is possible to easily adapt the methodology to the requirements for scientists in other countries and for other tasks requiring multi-criteria optimization

关键词： Data and knowledge management algorithms numerical algorithms optimization sorting/search

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CALCULATION OF THE MOLECULAR WEIGHT – LONG CHAIN BRANCHING DISTRIBUTION IN BRANCHED POLYMERS

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IFAC Proceedings Volumes 2006年第2期39卷 673-678页

作者： Krallis Apostolos Kiparissides Costas Department of Chemical Engineering and Chemical Process Engineering Research Institute Aristotle University of Thessaloniki P.O. Box 472 54006 Thessaloniki Greece

In the present study a population balance approach is described to follow the time evolution of molecular polymer properties in free-radical polymerizations. The model formulation is based on the fixed pivot technique (FPT) which was properly adapted to calculate the combined molecular weight - long chain branching distribution. At first the predictive capabilities of the proposed model were tested against experimental measurements and simulation results taken from the open literature, on molecular weight distribution (MWD) of branched polymers. Then the MWD calculated by the FPT was compared with the MWD calculated by the method of classes. However the FPT proved to be a faster method for the calculation of the MWD.

关键词： Computing elements Distributions Mathematical model numerical algorithms Polymerization

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Robust Stability Analysis of Uncertain Large-Scale Systems

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IFAC Proceedings Volumes 1995年第16期28卷 305-310页

作者： Liu Ximei Yu Fei QingLin. Wang Qing Dao Institute of Chemical Technology 266042 Beijing Institute of Technology Beijing 100081

In this paper, a new sufficient condition for robust stability of perturbed large-scale systems is presented. If the given matrix equations are solved, their solutions can be applied to obtain the bounds on the uncertain parameters to guarantee the stability of the system. Furthermore, we discuss the existence of the solutions of the matrix equations and numerical algorithms. The application of the proposed method is illustrated by an example.

关键词： large-scale systems robustenss numerical algorithms

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ANGLE-DEPENDENT SPECTRAL DISTORTION FOR AN INFINITE PLANAR FLUID FLUID INTERFACE

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1992年第5期92卷 2883-2899页

作者： OROFINO, DP PEDERSEN, PC Department of Electrical Engineering Worcester Polytechnic Institute Worcester Massachusetts 01609

Angle-dependent spectral distortion (ASD) refers to the change in complex spectrum of the signal from the receiving transducer due to change in angular orientation of the reflecting target, i.e., from normal incidence to some non-normal incidence. The ASD for a fluid-fluid infinite planar interface (IP-ASD) is numerically determined for the cases of a planar piston, spherically focused piston, and nondiffracting (J0-Bessel) transducer geometries. The numerical algorithm employed is based on an equivalent image transducer. Reception of the acoustic pulse is performed using discrete surface integration, based on 3-D surface mesh generation strategies. numerical simulations, together with experimental results, are presented for the above transducers for various geometries, reflector distances, and misalignment angles. The results indicate that the IP-ASD significantly alters the spectrum of the received acoustic pulse, and thus must be taken into consideration for quantitative ultrasonic measurements. Finally, the numerical simulations have revealed that the nondiffracting transducer produces distinct peaks in the magnitude IP-ASD that enable precise estimates of misalignment angle to be obtained.

关键词： Transducers Ultrasonic transducers Acoustical measurements numerical algorithms Ultrasonics

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On advantages of the Kelvin mapping in finite element implementations of deformation processes

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ENVIRONMENTAL EARTH SCIENCES 2016年第11期75卷 937-937页

作者： Nagel, Thomas Goerke, Uwe-Jens Moerman, Kevin M. Kolditz, Olaf UFZ Helmholtz Ctr Environm Res Leipzig Germany Trinity Coll Dublin Dublin Ireland MIT Media Lab Cambridge MA 02139 USA Tech Univ Dresden Dresden Germany

Classical continuum mechanical theories operate on three-dimensional Euclidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapping is that Kelvin's method preserves tensor character, and thus the numerical matrix notation directly corresponds to the original tensor notation. Further benefits in numerical implementations are that tensor norms are calculated identically without distinguishing stress-or strain-type quantities, and tensor equations can be directly transformed into matrix equations without additional considerations. The only implementational changes are related to a scalar factor in certain finite element matrices, and hence, harvesting the mentioned benefits comes at very little cost.

关键词： Kelvin mapping Voigt mapping Finite elements numerical algorithms OpenGeoSys

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Thermal contact resistance of nonconforming rough surfaces, part 1: Contact mechanics model

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2004年第2期18卷 209-217页

作者： Bahrami, A Culham, JR Yovanovich, MM Schneider, GE Univ Waterloo Dept Mech Engn Waterloo ON N2L 3G1 Canada Univ Waterloo Microelect Heat Transfer Lab Waterloo ON N2L 3G1 Canada

A new analytical model for spherical rough contacts, in the form of a set of relationships, is developed and solved numerically. It is shown that the maximum contact pressure is the parameter that specifies the contact pressure distribution. Simple correlations for calculating the maximum contact pressure and the radius of the macrocontact area as functions of the nondimensional parameters are proposed. A relationship for pressure distributions is derived where the load is higher than the critical load. A general pressure distribution is developed that covers the entire range of spherical contacts from the smooth Hertzian to the conforming rough contact. Finally, a criterion is derived to identify flat surfaces where the surface curvature has negligible effect on the contact pressure.

关键词： Contact Mechanics Surface Roughness Elastic Modulus Critical Loading Critical Pressure Computer Programs Elastic Deformation numerical algorithms Linear Interpolation Heat Transfer

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VARIABLE PRECISION EXPONENTIAL FUNCTION

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 1986年第2期12卷 79-91页

作者： HULL, TE ABRHAM, A Univ. of Toronto Toronto Ont. Canada Univ. of Toronto Toronto Ont. Canada

The exponential function presented here returns a result which differs from ex by less than one unit in the last place, for any representable value of x which is not too close to values for which ex would overflow or underflow. (For values of x which are not within this range, an error condition is raised.) It is a ?variable precision? function in that it returns a p-digit approximation for a p-digit argument, for any p = 0 (p-digit means p-decimal-digit). The program and analysis are valid for all p = 0, but current implementations place a restriction on p. The program is presented in a Pascal-like programming language called numerical Turing which has special facilities for scientific computing, including precision control, directed roundings, and built-in functions for getting and setting exponents.

关键词： Correctness proof error analysis numerical algorithms variable precision

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Study of the interplay between lower-order and higher-order energetic strain-gradient effects in polycrystal plasticity

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2022年 164卷

作者： Christodoulou, Paul G. Lebensohn, Ricardo A. Beyerlein, Irene J. Univ Calif Santa Barbara Mat Dept Santa Barbara CA 93117 USA Theoret Div Alamos Natl Lab Los Alamos NM 87845 USA

Strain-gradient (SG) plasticity refers to a class of non-local theories in which gradients of plastic slip determine the storage of geometrically necessary dislocations, introducing a length-scale dependence in the mechanical behavior of crystalline materials, which is otherwise lacking in local theories. In this work, we incorporate lower-order (LO) and higher-order energetic (HOE) strain-gradient effects into a crystal plasticity fast Fourier transform (FFT)-based formulation to investigate the interplay of the length scale that each strain-gradient term introduces at the microscale, and the mechanical properties that result at the macroscale. For an applicable range of length scales, we consider two systems: a 1-D two-phase face centered cubic (FCC) laminate and a 3-D FCC polycrystal, and two uniaxial deformation modes: monotonic tension and cyclic tension-compression. We show that increases in the individual LO and HOE length scales increase the hardening rate and strength of the material, respectively. When combined, the strong LO hardening is less pronounced than the effect alone due to the lowering of the gradients due to the HOE microstress. We demonstrate that the LO and HOE hardening manifest as "isotropic"(yield surface expansion) and "kinematic"(yield surface shift) effects, respectively, consistent with their theoretical origins. We show that in cyclic loading, the Bauschinger effect emerges in both local and non-local calculations and link its origins and severity to the behavior in the strain field, slip-system rates, and the HOE microforce.

关键词： A Dislocations Strain-gradient plasticity B Crystal plasticity Elastic-viscoplastic material C numerical algorithms

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