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Circle-circle intersection. A universal method for solving typical surveying problems

APPLIED GEOMATICS 2024年第4期16卷 1047-1056页

作者： Gargula, Tadeusz Agr Univ Krakow Dept Land Surveying Balicka 253A PL-30198 Krakow Poland

The research problem of the article is to devise a universal mathematical procedure for calculating point coordinates from typical planar surveying measurements. The proposed solution involves calculating the intersection points of two circles with radii equal to the measured distances (the distance-distance intersection problem). The author demonstrates a straightforward method for reducing every typical surveying problem to the distance-distance intersection form. The procedure also verifies the accuracy of the calculated coordinates. The derived equations were tested numerically using practical examples. The devised procedure will be integrated into an exhaustive numerical algorithm for diverse surveying problems regardless of the geometric approach during measurements.

关键词： Field measurements Distance-distance intersection Circle-circle intersection numerical algorithm

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New concept of the discrete sources method in electromagnetic scattering problems

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Mathematical Models and Computer Simulations 2016年第2期8卷 175-182页

作者： Grishina, N.V. Eremin, Yu. A. Sveshnikov, A.G. Moscow State University Moscow 119991 Russian Federation Moscow State University Moscow 119991 Russian Federation

We propose and implement a new concept of the discrete sources method;by applying this concept, one can investigate dielectric scatterers with large wave numbers. It is shown that the total scattering cross section can be determined analytically by using the amplitudes of discrete sources. The numerical results are presented;they demonstrate a considerable gain obtained by using the new concept in comparison with the conventional concept. © 2016, Pleiades Publishing, Ltd.

关键词： dielectric particles of large sizes discrete sources method electromagnetic scattering numerical algorithm

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A Coupled Model of Controlled Synthesis, of a Composite on a Substrate

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2022年第7期43卷 1878-1893页

作者： Knyazeva, A. G. Kryukova, O. N. Russian Acad Sci Siberian Branch Inst Strength Phys & Mat Sci Tomsk 634055 Russia

A mathematical model of the process of composite synthesis from a mixture of powders is formulated. It is assumed that the synthesis is performed on a substrate and is controlled by a scanning laser beam. The stress-strain state is described in quasi-static approximation. The model takes into account two phenomena that are neglected in traditional surface treatment and 3D models: the mutual influence of the heat transfer process and deformation and the heat sources and sinks that result from chemical reactions. The formation of the composition is described by a total reaction scheme that includes a strengthening particle formation stage and a matrix formation stage. The nonlinear model is reduced to a dimensionless form and investigated numerically using an implicit difference scheme for the thermal conductivity equation, the semi-implicit Euler method for the kinetic equations, and the iteration procedure for the mechanical equilibrium problem. As a result of the calculations, we have the fields of temperature, concentrations, stresses, and strains at an arbitrary moment of time, as well as the final composition of the composite. It is shown that the coupling of processes of different physical nature is important both for determining the composition of the composite and for estimating the residual stresses and strains.

关键词： coupled model composite synthesis reaction rates residual stresses controlled mode numerical algorithm

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Modern anti-windup synthesis : control augmentation for actuator saturation /

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2011年

作者： Zaccarian Luca.

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algorithm of event detection for hybrid power system simulation

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3rd International Conference on Electric Utility Deregulation, Restructuring and Power Technologies

作者： Zhao, Hong-shan Hu, Yan-bin N China Elect Power Univ Dept Elect Engn Baoding 071003 Hebei Peoples R China

ISBN: (纸本)9787564112493

The power system is a large-scale nonlinear system, and presents the hybrid characteristic of continuous dynamics and discrete event dynamics. Hence power system is considered as a classic hybrid system. This paper proposed a numerical calculating approach which system control theory is applied for evaluation of stepsize. A solution algorithm used to detect and locate events occurred in process of power system numerical simulation is studied, i.e. this algorithm is taken as a feedback controller, controller input is system guard functions, and controller output is the stepsize of numerical calculation. This output stepsize then combined with traditional stepsize choice techniques and an appropriate stepsize is finally determined for numerical simulation. The proposed algorithm can exactly detect and locate events occurred in power system. Finaly, a simple example of power system is given, the results of numerical evaluation show that the proposed approach is reasonable and feasible.

关键词： event detection feedback control numerical algorithm power system

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On the selection of active slip systems in rate independent crystal plasticity

On the selection of active slip systems in rate independent ...

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16th ESAFORM Conference on Material Forming (ESAFORM 2013)

作者： Orthaber, Markus Antretter, Thomas Gaenser, Hans-Peter Mat Ctr Leoben Forsch GmbH A-8700 Leoben Austria

ISBN: (纸本)9783037857199

Non-uniqueness in the set of active slip systems is a crucial issue in crystal plasticity. To avoid this problem one may perform viscoplastic regularization. This introduces a certain rate dependency, while many crystals are known to behave rate independently. This is sometimes approximated using ver low viscosity parameters in the regularized model, however at the cost of numerical difficulties. Hence, to adequately treat rate independent crystal plasticity an alternative method is needed. The proposed method, Maximum Dissipation Crystal Plasticity (MDCP), achieves uniqueness by selecting the set of active slip systems according to its dissipation. In a finite element calculation, a system of coupled quadratic equations is solved at every integration point to define the material behaviour. This approach is formally equal to the method of incremental energy minimization recently proposed by H. Petryk and M. Kursa (Book of Abstracts of the 8th European Solid Mechanics Conference, Graz, G.A. Holzapfel and R.W. Ogden (eds.)). It can be shown that a viscoplastically regularized model is a limiting case of MDCP, giving similar results when cross hardening becomes negligible. Nevertheless, recent 3D dislocation dynamics calculations by Devincre et al. (Mat. Sci. Eng. A, 400-401 (2005), 182-185) show that cross hardening in face centered cubic crystals is far more important than self hardening. In such cases MDCP gives results distinctly different from its rate dependent counterpart. The proposed method is numerically implemented as user material subroutine into the finite element package ABAQUS within the small as well as large deformation framework, called MDCP and FinDMDCP respectively, such that the simulation of arbitrary load cases is possible.

关键词： crystal plasticity selection of slip systems numerical algorithm finite element method

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algorithm and software for defining the distribution of eigenvalues of random symmetric matrices via simulation

Algorithm and software for defining the distribution of eige...

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8th International Conference of Computational and Mathematical Methods in Science and Engineering (CMMSE 2008)

作者： Shmerling, E. Ariel Univ Ctr Samaria Dept Comp Sci & Math IL-44837 Ariel Israel

A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.

关键词： eigenvalues distribution Monte Carlo simulation random symmetric matrices matlab numerical algorithm

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State Estimation by Continuous-Time Observations in Multiplicative Noise

State Estimation by Continuous-Time Observations in Multipli...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Borisov, Andrey V. Semenikhin, Konstantin V. Russian Acad Sci Fed Res Ctr Comp Sci & Control Moscow Russia Natl Res Univ Moscow Aviat Inst Moscow Russia

The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is a function of the estimated vector, hence the traditional optimal filtering framework fails in this case. The estimate is obtained both in the explicit integral form and as the solution to a stochastic differential system with some jump processes in the right hand side. The presence of the multiplicative noise gives a possibility to raise the estimation quality up to the exact value restoration. The numerical procedure for the estimate calculation is accompanied with the accuracy analysis. An example illustrating the performance of the proposed estimate is also presented. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Optimal estimation multiplicative noise continuous time filter local smoothing numerical algorithm

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New Theory and algorithm of Optimal Control Based on Natural Computation 11

New Theory and Algorithm of Optimal Control Based on Natural...

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11th International Conference on Natural Computation (ICNC) / 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

作者： Yang, Yi Nan, Ying Chen, Haoxiang Nanjing Univ Aeronaut & Astronaut Coll Astronaut Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781467376792

This paper presents a new theory and algorithm regarding on optimal control based on natural computation. This natural algorithm simulates the survival and competition of multi-races and multi-individuals in the astrospace which consists of all races and individuals. This super-intelligent natural algorithm covers most of current optimization algorithms for dynamic and static parameters, and is applicable to a variety of fields and disciplines. In the natural running process, all races and individuals can compete for its own interests, and the final results must be optimal for the overall situation. Some numerical simulation results show that this new theory and algorithm of optimal control are correct and feasible, as well as superior for the multilateral confrontations problem.

关键词： nature computation natural running optimal control global integrative optimization numerical algorithm multilateral confrontations

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An inverse eigenvalue problem of the theory of optical waveguides

An inverse eigenvalue problem of the theory of optical waveg...

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International Conference on Days on Diffraction (DD)

作者： Karchevskii, E. M. Spiridonov, A. O. Kazan Fed Univ Dept Appl Math Kazan Russia

ISBN: (纸本)9781479966998

We present a new method for calculation of permittivities of dielectric materials using optical fiber's propagation constants measurements. Our numerical algorithm is based on approximate solution of a nonlinear nonselfadjoint inverse eigenvalue problem for a system of weakly singular integral equations. We prove that it is enough to measure propagation constants of fundamental eigenmode only at two frequencies for reconstruction of dielectric constants of core and cladding of a waveguide.

关键词： approximation theory eigenvalues and eigenfunctions integral equations inverse problems optical fibre cladding optical fibre testing permittivity approximate solution dielectric constants dielectric materials fundamental eigenmode nonlinear nonselfadjoint inverse eigenvalue problem numerical algorithm optical fiber propagation constant measurements optical waveguide theory singular integral equations waveguide cladding waveguide core Eigenvalues and eigenfunctions Nonlinear optics Optical waveguide theory Permittivity Propagation constant Splines (mathematics) Dielectric constant Optical waveguide theory Eigenfunctions Propagation constant singular integral equations dielectric materials Optical fiber testing optical fibre cladding Approximation Theory Nonlinear optics Integral equations Inverse method dielectric properties

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