Memoirs Faculty of Engineering

ISSN 0078－6659 OF ENG THE FACULTY MEMOIRS OF MEMOIRS OF THE FACULTY OF ENGINEERING This Memoirs is annually issued. Selected original works of the members of the OSAKA CITY UNIVERSITY Faculty of Engineering are compiled herein. Abstracts of paper presented elsewhere INEERING OSAKA during the current year are also compiled in the latter part of the volume. All communications with respect to Memoirs should be addressed to: Dean of the Graduate School of Engineering Osaka City University CITY 3-3-138, Sugimoto, Sumiyoshi-ku Osaka 558-8585, Japan UNIVERSITY VOL. 57 Editors DECEMBER 2016 Yoshinori KANJO Souichi SAEKI Masafumi MURAJI Eiji SHIKOH Noritsugu KOMETANI Tetsu TOKUONO VOL. 57. 2016 PUBLISHED BY THE GRADUATE SCHOOL OF ENGINEERING OSAKA CITY UNIVERSITY 1611-0546 大阪市立大学工学部工学部英文紀要VOL.57（2016） 1-4 見本スミ This Memoirs is annually issued. Selected original works of the members of the Faculty of Engineering are compiled herein. Abstracts of paper presented elsewhere during the current year are also compiled in the latter part of the volume. All communications with respect to Memoirs should be addressed to: Dean of the Graduate School of Engineering Osaka City University 3-3-138, Sugimoto, Sumiyoshi-ku Osaka 558-8585, Japan Editors Yoshinori KANJO Souichi SAEKI Masafumi MURAJI Eiji SHIKOH Noritsugu KOMETANI Tetsu TOKUONO 1611-0546 大阪市立大学工学部工学部英文紀要VOL.57（2016） 2-3 スミ MEMOIRS OF THE FACULTY OF ENGINEERING OSAKA CITY UNIVERSITY VOL. 57 DECEMBER 2016 CONTENTS Regular Articles ·························································································· 1 Mechanical and Physical Engineering Mechanical Engineering Error Control of Single-Point Energy from First-principles Band Calculations Ippei KISHIDA ··················································································· 1 Urban Engineering Urban Design and Engineering Questionnaire Survey of Riverfront Residents After Nature-oriented Water Amenity Development Project of a Minor River in a Built-up Area Yasumasa FUKUSHIMA and Takashi UCHIDA ·············································· 11 Numerical Study on Effect of Edge distance on the Mechanical Behavior after Major Slip of High Strength Frictional Bolted Joints Hitoshi MORIYAMA and Takashi YAMAGUCHI ·········································· 27 Abstracts of Papers Published in Other Journals ············································ 35 Mechanical and Physical Engineering Mechanical Engineering ······································································· 37 Physical Electronics and Informatics Applied Physics and Electronics ······························································ 54 Electrical and Information Engineering ····················································· 66 Applied Chemistry and Bioengineering Applied Chemistry and Bioengineering ······················································ 69 Urban Engineering Architecture and Building Engineering ······················································ 88 Urban Design and Engineering ······························································· 90 ISSN 0078－6659 MEMOIRS OF THE FACULTY OF ENGINEERING OSAKA CITY UNIVERSITY ―――――――― VOL. 57 ―――――――― DECEMBER 2016 PUBLISHED BY THE GRADUATE SCHOOL OF ENGINEERING OSAKA CITY UNIVERSITY Error Control of Single-Point Energy from First-principles Band Calculations Ippei KISHIDA* ( Received October 7, 2016) Synopsis Quantitative analysis of errors in computational science was established. Total energies of fcc and hcp Mg crystals were performed by single-point calculations of first-principles band calculations. Errors in the total energies originated from k-sampling, n, and from cutoff energy of plane wave for core potentials, Ecutoff , were examined. The highest condition calculated value was found to be more suitable for the best estimate, which was alternatively used to the true value, than an arithmetic average and a weighted average. Error components -3 originated from n and Ecutoff fit well to an and aexp(bEcutoff ), respectively. A whole error was obtained by the propagation of errors in statistics. The value of the total energy including the error was expressed in conventional notation using standard deviation like Etotal = -1.1516 ±0.0004 [eV]. This technique is able to point out the main error component and the efficient condition to obtain a higher precision. This also made it possible to construct the algorithm that automatically optimizes an accuracy. keywords: error analysis; error component; best estimate; standard deviation; first-principles band calculations; 1. Introduction There has been increasing necessity of investigating much materials because of the progress of materials science. First-principles calculation, which is only based on the quantum theory, is a powerful technique to analyze physical and chemical properties of materials. A lot of achievements has been already reported in thermal stability,1-4) electric potential,5-8) ionic conduction,9-13) and so on. Although first-principles band calculation can obtain electronic states and total energies with high precision, it is a numerical computation and is not free from errors. In experimental science, error analysis is well systematized and the contained error in measured values are widely performed by an average and a standard deviation of multiple measurements. Since each trial of experimental measurements generally show different values, the error can be analyzed statistically. In computational science, the same program with the same conditions basically reproduces the same results.14) The accuracy of a computer is the reason why the same technique as experiments cannot be used. And the accuracy is also a reason why the importance of correctly estimating an error in the calculation tends to be disregarded. However, an error control is important not only for experiments but also for computations. It is necessary to estimate the errors of results such as significant figures required for discussion. An error can be roughly divided into a system error and a random error.15) The system error is mainly originated from the measurement process. It is desired to devise the experimental process in order to shrink the system error, rather than to analyze it with a statistical method. The system error in the first-principles band calculation includes approximations for N-body problem, design of core potentials, and so on. Most of them have been reduced by a lot of theoretical scientists and code developers. There are great achievements, e.g., projector augmented wave(PAW) potentials for core potentials,16,17) generalized gradient approximation (GGA)18) with +U potential19-21) for a exchange correlation term, and special point method22) and tetrahedron method23) with Blöchl correlation24) for k-point sampling of space integration. In addition, the effect of the system error is cancellable by computing the difference between the calculated values with the same conditions. In many cases, therefore, the system error is less likely to become a big problem as a standpoint of an end-user. The errors originated from k-mesh and cutoff energy of plane wave for core potentials, Ecutoff , must be examined in the responsibility of an end-user of calculations on actual materials. It is appropriate to consider that these errors are the independent and random error. There were few strict arguments on the accuracy that depends on these conditions. The significant figures may be decided experientially and semi-quantitatively by overestimating errors to approach on the safe side. The present study establishes the method for quantitative estimation of the error included in a calculated value. We discuss on the total energy, which includes errors originated from k-mesh and plane-wave cutoff energy. Although geometry optimizations were often performed in actual calculations, the present study dealt only with single-point calculations. This is because a simple system was required to establish a theory of error analysis in the first-principles band calculations. The geometry * Research Associate, Department of Mechanical Engineering －1－ optimization is more complicated to handle than single-point calculation; e.g., evaluation of force on ions and stress on cell,25) truncating condition of ionic loop, an assumption of a fitting function of errors originated from smearing,26) and multiple output values to be discussed including lattice constant and ionic coordinates. Nevertheless, it is possible to apply the present technique to geometry optimization. This paper provides a general framework of an error analysis in the computational science. Precise error analysis was conducted by statistical procedure on calculation parameters that affects the accuracy of a calculated value. Establishing a systematized theory of error analysis, computational researchers will be able to use proper conditions for more minute discussion and to perform larger-scale calculations with suitable load. Moreover, this technique enables automatic determination of conditions, which can become one step for fully automated materials calculation. Now, databases of material properties from first-principles are being accumulated, e.g.,Materials Project,27) MatNavi28) and AFLOW.29) The present work can aid to add the information of accuracy of the calculated values to the databases. 2. Methodology A. Computational conditions and evaluated values The present study focused on a total energy of a cell, Etotal , as a calculated value among much information obtained

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