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Efficient Implementation of a Transport Model in Periodic Layered Structures

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第6期58卷 967-975页

作者： Muradyan, M. G. Armenian State Univ Econ Yerevan 0025 Armenia

An analytical representation of the general solution to a finite-difference system describing transport in a periodic medium is found. On the basis of this representation, an efficient numerical algorithm is developed... 详细信息

关键词： transport in periodic media reflection and transmission operators dissipative and conservative transport analogue of the Milne problem numerical algorithm

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Discrete State Event-Driven Approach for High-Power Converter Simulations

Discrete State Event-Driven Approach for High-Power Converte...

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IEEE Energy Conversion Congress and Exposition

作者： Bochen Shi Zhengming Zhao Yicheng Zhu Zhujun Yu Jiahe Ju Liqiang Yuan Kainan Chen State Key Laboratory of Control and Simulation of Power System and Generation Equipment Tsinghua University Beijing China

Demands for high-power converters are increasing rapidly. Nevertheless, due to their complex structures and multi-time-scale features, accurate and efficient simulation of such systems has long been a huge obstacle. Aiming at improving the unacceptably slow simulation speed of high-power converters, this paper improves Discrete State Event-Driven (DSED) approach by implementing a decoupling method. Taking a 10kV 1MW electric energy router as an example, this paper evaluates the effectiveness of DSED with the proposed decoupling method in high-power applications. In the studied case, compared with commercially available tool for power electronics simulation, PLECS, DSED can achieve an up to 1000-fold improvement in simulation speed under the same accuracy: PLECS takes 6 hours while DSED only takes 18 seconds. DSED provides a powerful simulation tool for analysis, design and control of high-power converters.

关键词： event-driven simulation numerical algorithm circuit partitioning high-power converter electric energy router solid-state transformer

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Mathematical Modeling and Computational Simulation of the Diffusive Behavior of Adenocarcinoma Biomarker Particles 5th

Mathematical Modeling and Computational Simulation of the Di...

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5th Workshop on Engineering Applications (WEA)

作者： Vallejo, Esteban Suarez, Gustavo Torres, William Uribe, Adolfo Univ Pontificia Bolivariana Math Grp GMAT Cir 1 70-01 Medellin 050031 Colombia Clin Las Amer Video Endoscopy Unit Dg 75B 2A-80-140 Medellin 050025 Colombia

ISBN: (纸本)9783030003500;9783030003494

Colorectal adenocarcinoma is one of the carcinogenic diseases that most affects the health of the world population. This disease is manifested biologically by the segregation of biomarker substances in the human system. This paper presents the development of a numerical-mathematical model for the study of the diffuse behavior of particles segregated by this type of cancer. Flow conditions, characteristics and properties of the diffusive medium are determined, and the study domain is defined. A mathematical description is elaborated to represent the behavior of the phenomenon by means of constitutive laws of the biosystem. A numerical-computational algorithm is constructed that makes possible the analysis of the different behavioral conditions;in this paper one of the multiples settings is showed. The computational implementation is done using Taylor series defined by finite differences with a refinement of the grid that can be controlled by the user. In addition, a structural element is incorporated with which it is intended to evaluate the level of concentration in the structure-substance contact zone. As a platform for the implementation of the algorithm, Matlab program is used. The results have been plotted by surface curves. Concentration levels are obtained at three points of interest, including concentrations at the structure-substance contact point, with concentration values of 1 * 10(-6) kg/m(3). The research is oriented in the search of an alternative that allows the detection of colorectal cancer in its early phase.

关键词： Colorectal adenocarcinoma Mathematical modeling numerical algorithm Simulation Diffusive behavior

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numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms

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ADVANCES IN ENGINEERING SOFTWARE 2017年 113卷 120-129页

作者： Adamek, Vitezslav Vales, Frantisek Cerv, Jan Univ West Bohemia NTIS Univ 8 Plzen 30614 Czech Republic AS CR Inst Thermomech Vvi Veleslavinova 11 Plzen 30114 Czech Republic AS CR Inst Thermomech Vvi Dolejskova 1402-5 Prague 18200 8 Czech Republic

The objective of this work is to find a suitable algorithm for numerical Laplace inversion which could be used for effective and precise solution of elastodynamic problems. For this purpose, the capabilities of four algorithms are studied using three transforms resulted from analytical solutions of longitudinal waves in a thin rod, flexural waves in a thin beam and plane waves in a strip. In particular, the Gaver-Stehfest algorithm, the Gaver-Wynn's rho algorithm, the Fixed-Talbot algorithm and the FFT algorithm combined with Wynn's epsilon accelerator are tested. The codes written in Maple 16 employing multi-precision computations are presented for each method. Given the results obtained, the last mentioned algorithm proves to be the best. It is most efficient and it gives results of reasonable accuracy nearly for all tested times ranging from 3 x 10(-7) s to 3 x 10(3) s. (C) 2016 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.

关键词： Inverse Laplace transform numerical algorithm Wave propagation Multi-precision computation Maple code

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Collatz Conjecture for 2¹⁰⁰⁰⁰⁰-1 is True - algorithms for Verifying Extremely Large Numbers 4

Collatz Conjecture for 2<SUP>100000</SUP>-1 is True - Algori...

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IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI)

作者： Ren, Wei Li, Simin Xiao, Ruiyang Bi, Wei China Univ Geosci Hubei Key Lab Intelligent Geoinformat Proc Sch Comp Sci Wuhan 430074 Peoples R China Guizhou Univ Guizhou Prov Key Lab Publ Big Data Guizhou Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China China Univ Geosci Sch Comp Sci Sch Math & Phys Wuhan 430074 Peoples R China SeeleTech Corp San Francisco CA 94107 USA

ISBN: (纸本)9781538693803

Collatz conjecture (or 3x+1 problem) has been explored for about 80 years. By now the largest number that has been verified for Collatz conjecture is about 60 bits. In this paper, we propose new algorithms that can verify much greater numbers than known algorithms, i.e., about 100000 bits (30000 digits) on whether they can return 1 after 3*x+1 and x/2 computations. The proposed algorithms change numerical computation to bit computation (or logical computation), and change inner memory data representation to hard disk file manipulation. We make it possible to verify extremely large numbers without concerning computer memory upper-bound. The largest number verified for Collatz conjecture until now in the world is 2(100000) - 1, and this magnitude of extremely large numbers has never been verified. We discovered that this number can return to 1 after 481603 times of 3*x+1 computation, and 863323 times of x/2 computation. At last, we stress that some open problems may be used for the green mining in blockchain-based cryptocurrencies, e.g., BTC. We discuss the applicability of Collatz conjecture for the Proof of Work in Blockchain.

关键词： Collatz Conjecture 3x+1 Problem Computational Algebra algorithmic Number Theory numerical algorithm

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On numerical solving a rigid inclusions problem in 2D elasticity

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2017年第1期68卷 1-18页

作者： Rudoy, Evgeny Lavrentyev Inst Hydrodynam SB RAS Novosibirsk 630090 Russia Novosibirsk State Univ Novosibirsk 630090 Russia

A 2D elastic problem for a body containing a set of bulk and thin rigid inclusions of arbitrary shapes is considered. It is assumed that rigid inclusions are bonded into elastic matrix. To state the equilibrium problem, a variational approach is used. The problem is formulated as a problem of minimization of the energy functional over the set of admissible displacements. Moreover, it is equivalent to a variational equality which holds for test functions belonging to the subspace of functions with the prescribed rigid displacement structure on the inclusions. We propose a novel algorithm of solving the equilibrium problem. The algorithm is based on reducing the original problem to a system of the Dirichlet and Neumann problems. A numerical examination is carried out to demonstrate the efficiency of the proposed technique.

关键词： Bulk rigid inclusion Thin rigid inclusion numerical algorithm Variational approach FEM

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Energy Consumption Optimal Control of the Train Movement

Energy Consumption Optimal Control of the Train Movement

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International Conference on Automation

作者： Myslinski, Andrzej Nahorski, Zbigniew Szulc, Katarzyna Radziszewska, Weronika Syst Res Inst Ul Newelska 6 PL-01447 Warsaw Poland

ISBN: (纸本)9783319771793;9783319771786

The paper is devoted to the solution of the energy minimization problem for a moving train. The train movement is governed by the system of the first order ordinary differential equations where the train speed and the distance along the track are the state variables. The provided locomotive power depends on the control function. The generated traction force is assumed to depend on the velocity of the train and on the control function. Each non-negative value of the control function determines a traction force control while negative values determine a braking force control. The cost functional is defined as the train energy. It is dependent on traction force, speed and control functions. The speed, distance and control functions are assumed bounded. Using the maximum principle and Lagrangian multipliers the system of equations constituting the necessary optimality conditions is formulated. Based on the analysis of the train movement the optimal trajectories in terms of train speed and associated optimal control functions are calculated. A new simplified method is used to calculate the set of the switching times implementing the optimal control function. numerical examples are provided and discussed.

关键词： ODEs train model Semi analytical solutions Energy minimization Maximum principle Optimal switching numerical algorithm

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The Benchmark Problems for the Assessment of numerical algorithms on Fractional-Order Differential Equations

The Benchmark Problems for the Assessment of Numerical Algor...

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第29届中国控制与决策会议

作者： Lu Bai Dingyü Xue School of Information Science and Engineering Northeastern University School of Information Engineenng Shenyang University

There are many numerical algorithms for solving the fractional-order differential equations(FODEs).The numerical algorithms are very different,and it is difficult to compare their *** solve this problem,some different FODEs with the known analytical solution are designed and proposed,they could be used as the benchmark problems for testing the numerical algorithms.A Simulink block diagram scheme is proposed for solving these benchmark problems,and the computing errors and the running times are *** benchmark problems and the solutions are constituted as a framework,and the numerical algorithms for solving the FODEs could be compared in the same *** comparing result could assess which algorithm is better to a concrete FODE.

关键词： Fractional-order differential equation Benchmark problem numerical algorithm Simulink block diagram

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numerical modelling of tides and tsunami waves propagation

MAGAZINE OF CIVIL ENGINEERING

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MAGAZINE OF CIVIL ENGINEERING 2018年第6期82卷 228-242页

作者： Klimovich, V., I Voronkov, O. K. Davidenko, V. M. Ivanov, S. N. JSC BE Vedeneev VNIIG St Petersburg Russia Peter Great St Petersburg Polytech Univ St Petersburg Russia

Modelling of tides and tsunami waves propagation is important problem for the hydraulic engineering practice since it allows to predict characteristics of these phenomena (load, values of run up and flooding zones, propagation times to structures and so on) and to make reasonable choice of design solution for coastal structures. numerical modeling is effective way to simulate tides and tsunami waves propagation. Results of simulations of tides and tsunami waves propagation on the basis of shallow water model are presented and analyzed in the article. It was considered explicit and implicit numerical scheme for solution of shallow water model equations, which were verified on the number of experimental results including experimental data on distribution of dam-break wave propagation on a dry and sloping bottom. It is shown that the numerical data of tides in Persian Gulf are well co-ordinated with the data of tidal tables, both on time and on level of tides in various points. numerical results of tsunami waves propagation in the Krasheninnikov Bay and Kozmino Bay are presented at various angles of tsunami at open boundary of computed area. numerical results of tide currents for Krasheninnikov Bay are presented for various velocities of a wind. Developed programs may be used, particular, for numerical calculations of impact characteristics of tsunami waves on structures in coastal and offshore zones according requirements of Russian normative documents.

关键词： tide tsunami wave long wave numerical algorithm hydraulic structure bay shallow water model

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The Energy-Efficient Operation Problem of a Freight Train Considering Long-Distance Steep Downhill Sections

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ENERGIES 2017年第6期10卷 794-794页

作者： Lin, Xuan Wang, Qingyuan Wang, Pengling Sun, Pengfei Feng, Xiaoyun Southwest Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China Delft Univ Technol Dept Transport & Planning Mekelweg 2 NL-2628 CD Delft Netherlands

With the energy consumption rising in rail transport, the railway sector is showing increasing interest in the energy-efficient operation of freight trains. Freight trains require more complicated driving strategies than ordinary passenger trains do due to their heavy loads, especially in the long-distance steep downhill (LDSD) sections that are very common in freight rail lines in China. This paper studies the energy-efficient operation of a freight train considering LDSD sections. An optimal control model including regenerative and pneumatic braking is developed for the freight train. Then, when a train leaves/enters the LDSD section, we verify the uniqueness of control transitions and discuss the speed profile linkage between LDSD and its adjacent sections, which indicates that the periodic braking should be applied on LDSD sections for optimality. Additionally, given the same running time for the entire journey, our analysis shows that electrical braking-full braking strategy is more energy-efficient than coasting-full braking strategy on LDSD sections. Finally, a numerical algorithm for the optimal driving solution is proposed. The simulation results demonstrate that the driving strategies generated by the proposed algorithm performs better than those from fuzzy predictive control and field operation regarding energy saving.

关键词： freight train energy-efficient operation maximum principle periodic braking numerical algorithm

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