* The contents of the program are subject to change without notice.
Wednesday, December 7
DAY1: Wednesday, December 7 10:10 - 11:10
Keynote Speech Let Us Promote Analysis of Electromagnetism Dr. Noboru Kikuchi, Executive Vice President, Member of the Board, TOYOTA Cetnral Research and Development Laboratories, Inc.
Among the tidal wave of innovation that has come to be symbolized by electric cars and wind power generators, a significant transition to high efficiency is being sought after in so-called mature models of electrical instruments such as motors and transformers, as well. In order to respond to this demand, it is effective to draw upon the strengths of analysis technologies like FEA and make achievements in electromagnetic field analysis. From the standpoint of the utilization rate in electromagnetic field analysis design, however, it seems like it has not yet caught up with structural analysis. In the structural analysis field, which has more than a ten year head start on electromagnetic field analysis, is already commercially viable, and has over ten times the number of users, they use a better FEA and have incorporated it "naturally" into product designs. It is also continuing to evolve. Is there really nothing to be learned from this? Is electromagnetic field analysis evolving? There is no doubt that electromagnetic field analysis will become an essential design technology in the future, as well. Or rather, it has to. In order for this to happen, those who are engaged in electromagnetic field analysis must grapple with new challenges without becoming satisfied with the technology and usage methods currently available. In addition, among future analysis technology, multiphysics analysis is a vital issue, and analysis technicians cannot afford to shut themselves up in their own analysis specialties. It is necessary to actively understand the technology and culture of each other's fields. In this presentation I will compare electromagnetic field analysis with structural analysis and talk about what kind of simulation technology is necessary for electromagnetic field analysis to play more of an active role in product designs in the future, and the accompanying challenges in usage techniques. I will also present the direction of CAE as a whole along with the latest research results.
DAY1: Wednesday, December 7 11:10 - 11:40
Global Cases and Coupling Analysis Session Electric Drives for Off-Road Mobile Equipment Mr. Jim Shoemaker, Mgr Vehicle Electrification Technologies, Advanced Product Technology, John Deere
The presentation will discuss the electric drive needs of off road mobile equipment. The duty cycle, continuous power density, operating environment, and required life for off road equipment is quite different from automotive expectations. Virtual Modeling and verification of electric drives is now gaining importance with increasing focus on Analysis led Design. Virtual models can be first used to test variations of electric machine geometry against performance requirements. Because the model is virtual it also allows testing machines to their design limits or even beyond without physical damage, to understand peak capability, and the impact that electric drives can have on efficiency and performance. Virtual design provides the opportunity for the designer to formulate problems in a systematic way and optimize through multiple design iterations.
DAY1: Wednesday, December 7 13:20 - 13:50
Global Cases and Coupling Analysis Session Multiscale Noise and Vibration models for a Switched Reluctance-based drivetrain for EV and HEV Dr. De Langhe Koen, Simulation Division, LMS International
In this paper, an integrated multi-physics approach, coupling JMAG and Virtual.Lab has been developed for the simulation of switched reluctance based drivetrain systems. Two methods are presented - one concerning the NVH modeling of such a motor, while the other focuses on a multiscale thermal model of an electric vehicle. Both methods stem from a detailed functional model of the switched reluctance motor, that is then used as the main base for the thermal and NVH modeling cases. The main objective is to present the design process of both methods and to show how such a method can be used as a vehicle integration tool. Two simulation examples are shown, one for the NVH aspects and the other for the energy management system, to illustrate the capabilities of the methods.
DAY1: Wednesday, December 7 13:50 - 14:20
Global Cases and Coupling Analysis Session Researches on the Behavior of Vibration and Noise of an IPM Motor on HEV Dr. Zeng Jinling, Science Research Department, CHINA FAW GROUP CORPERATION R&D CENTER
Hybrid electric vehicles are becoming more popular, but the higher efficiency and miniaturization requires of the IPM motor result in vibration and noise, which make electric motor as the major vibration and noise source of the hybrid electric vehicle. It is well known that the source of these problems will be difficult to be pinpointed when the motor is mounted in vehicle. Meanwhile, a significant amount of time and money may be cost in manufacturing process of these faulty motors. So, how to quickly identify and reduce the vibration and noise of electric motor has become a necessity. In this paper, a numerical analysis method will be provided to expeditiously predict and understand the behavior of vibration and noise of an IPM motor in the stage of product design.
DAY1: Wednesday, December 7 14:20 - 14:50
Global Cases and Coupling Analysis Session Vibration and Noise Analysis of The Motor for Electric Vehicle Mr. Takayuki Miyakawa, Vehicle Performance Engineering Department, Nissan Motor Co.,LTD
EVs (Electric Vehicles) are a type of zero emission car. The aim is for them to be accepted favorably across a broad market, and in order to make them into attractive cars we seek superior performance in addition to silence. Since EVs, unlike conventional internal-combustion engines, are driven by motors, the Vibration and Noise phenomenon resulting from the motor becomes a problem. A motor's excitation force shifts to the high frequency side compared to an ICE, so it becomes necessary for the motor's vibration and noise analysis to be carried out into higher frequencies. Today we will introduce the motor's vibration and noise analysis using both magnetic field analysis and vibration and noise analysis.
DAY1: Wednesday, December 7 14:50 - 15:20
Global Cases and Coupling Analysis Session Disribution Losses in Claw Pole Machine.-Simulation of eddy Current Dr. Jean-Claude MIPO, Valeo EEM
In order to satisfy new environmental regulations, we have to increase efficiency of alternators. To achieve it, we have to know the distributions of losses. It's not possible to have the distribution of iron losses in rotor and stator, so we need to simulate the iron losses in rotor and stator. We will carry out simulation and test on several range of alternators and different speed. Then we can validate the results of simulation.
DAY1: Wednesday, December 7 16:05 - 16:35
Analysis System Construction Session A Case Example of JMAG-RT Application in an Electrical Automotive MBD Mr. Kei Yonemori, Senior Specialist, Technical Research Center, MAZDA Motor Corporation
In analysis of a motor drive system's performance, the mainstream method narrows things down to a general, ideal condition (a mathematical sine wave drive) that is easy to calculate and argues the pros and cons of a main representative, such as the limit performance of a motor, which is nothing more than a single part of the entire system. In JMAG-Studio alone it is not possible to recreate exactly the operating range and interactions of changes in efficiency when the motor is connected to the surrounding system, so at Mashida, where we were aiming at "a limit design for a dynamic system," we constructed a rapid calculation environment using JMAG-RT that would give us a good overall view of the interactions and trade-off functions of the system interior.
DAY1: Wednesday, December 7 16:35 - 17:05
Analysis System Construction Session JMAG-RT apply to the design quality verification of motor control ECU Mr. Yoshinori Takeuchi, Project Assistant Manager, Corporate ePF Division, DENSO CORPORATION
DENSO is an automotive ECU supplier that has been developing ECUs for controlling traction motors for diversifying H/EVs. The algorithms of ECU must be validated from various aspects whether it fulfills customer's specifications. However, there are many conditions that cannot be tested using a real vehicle. In such cases we use HILS (Hardware-In-the-Loop Simulation). Conventional HILS was not suitable for the validation of algorithms since it lacked motor models that can simulate all of the necessary characteristics in real time. We found JMAG-RT as a possible candidate of model generator, but we had to have motor parameters with sufficient precision. As an ECU supplier, we cannot acquire those data. Instead, we found a method to generate motor models from control parameter maps in the specification of the customer. This idea was implemented by JSOL corporation. Some case studies using JMAG-RT are introduced here applied for the improvement of design quality.
DAY1: Wednesday, December 7 17:05 - 17:35
Analysis System Construction Session Leveraging JMAG-RT and FEA-based Models for High Fidelity Real-Time Test in FPGA Dr. Ben Black, System Engineer, System Engineering, National Instruments
Real-time test in the area of power electronics provides unique challenges that are difficult to address with traditional hardware-in-the-loop (HIL) systems. The high speed discrete switching states of power electronics systems mean that the simulation system needs to run on the order of 1 us to provide useful numerical results, and the benefits during algorithm development are directly related to the fidelity of the model. A good test system allows a control engineer to speed up the design cycle by allowing control testing to start without physical hardware, to test novel control algorithms without endangering hardware and to see potentially un-measureable parameters within the system. To address these issues and to provide a platform for HIL testing of electric motor systems, National Instruments has partnered with JSOL Corporation and developed field programmable gate array (FPGA) models that use JMAG-RT as a means to deploy the high-fidelity of an FEA simulation into the high speed of a FPGA processing node.
DAY1: Wednesday, December 7 17:35 - 18:05
Analysis System Construction Session Optimizing Designs with High Throughput Computing Dr. Brooklin J. Gore, Senior Researcher, Core Computational Technology, MORGRIDGE Institute for Research at the University of Wisconsin-Madison
In this talk, we discuss how JMAG software is being run at the UW-Madison campus in a High Throughput Computing (HTC) environment powered by the open source Condor software. By coupling JMAG with Condor, we were able to improve optimization turnaround by an order of magnitude. We present HTC principles and an introduction to Condor, as well as an overview of the UW Center for High Throughput Computing (CHTC), which serves, among others the Wisconsin Electric Machines and Power Electronics Consortium. For more than two decades the CHTC has been serving the computational needs of a broad range of research and production domains, including scientists and engineers from a wide spectrum of disciplines ranging from semi-conductor test harnesses to turbine blades and electrical machines. We conclude with direction for future joint work.
DAY1: Wednesday, December 7 18:05 - 18:35
Analysis System Construction Session Expanding and Utilizing JMAG-Bus for Developing Motor Systems Mr. Takehiro Miyoshi, Technology Research Division 9, Automobile R&D Center, Honda R&D Co.,Ltd.
CAE analysis is an effective tool for both shortening the development period and improving the quality of motors, but in recent years a considerable amount of skill and man-hours have become necessary for the analysis itself due to the increasing complexity of systems. the current situation is that sufficient time cannot be given to traditional design consideration. We used JMAG-Bus, and by simplifying data input and output and constructing a analysis system that standardized everything up to data management, we were able to shorten the total time for analysis and improve development efficiency. Today I would like to introduce this system and provide case examples of application.
DAY1: Wednesday, December 7 16:05 - 16:35
Induction Heating Session A System of Coordination With Analysis Engineers and the Successes That Follow Mr. Norihide Fujiyama, Senior Manager, Analysis Team Product Deveropment Dept., KOYO THERMO SYSTEMS CO.,LTD
While working on the development of induction heating and struggling with the establishment of CAE technology, I was able to introduce several types of analysis software such as 3D CAD and JMAG. Although the effects of CAE or its results were not understood at the time, I continuously made effort to build upon it's results and promoting CAE to other designers. A dedicated analysis team was established 7 years ago for the purpose of logistics support, and at present we support various areas such as design, development and quality assurance etc.. Since the beginning of CAE introduction, my biggest issue up to this day is how difficult it is to appeal how cost-effective CAE can be. In my lecture, I will introduce some of the early cases when JMAG was first introduced, my analysis techniques that I acquired through trial and error and the drive to promote CAE, and examples of effectively calculating fixed quantities in cost effectiveness.
DAY1: Wednesday, December 7 16:35 - 17:05
Induction Heating Session Development of the self fluxing alloy fusing process with the control system using the simulation Mr. Tomoji Osada, Manager, Reseach&Development Grop, NIPPON THERMONICS.Co.,Ltd.
Self fluxing alloy has the characteristic that objective hardness is provided by performing re-fusion (fusing) after spray. This again molten work is carried out by hands, and stability of the quality and improvement of the work efficiency usually become the problem. Therefore we aim at the quality stability of the self fluxing alloy fusing process and the improvement of the work efficiency by using high frequency induction heating. I utilize induction heating simulation of JMAG as a part of the study. I performed an induction heating experiment for the boiler tubes which a lot of self fluxing alloy was used for this time. I report the result that weighed the differences between experimental value and analysis level at that time.
DAY1: Wednesday, December 7 17:05 - 17:35
Induction Heating Session Effect of magnetic property on the accuracy of induction heating analysis Mr. Hiroshi Yuki, Advanced Technology R&D Center, NTN Corporation
Relative permeability and B-H curve are often used as magnetic property of workpiece on induction heating analysis. Thus, analysis accuracy is compared between relative permeability and B-H curve for identical specimens. As a result, it is revealed that analysis result with B-H curve agrees well with the experiment result. In contrast, there is defference between analysis with relative permeability and experiment result around Curie temperature.
Thursday, December 8
DAY2: Thursday, December 8 09:30 - 10:00
Motor Session Demagnetization Analysis Method using Dy Diffused Magnets and the Most Suitable Dy Diffusion Methods and their Effects for Motor Applications Mr. Mitsutoshi Natsumeda, Kumagaya Works Design Section, Hitachi metals, Ltd.
Dy diffused magnets which could reduce Dy content of Nd-Fe-B sintered magnets are well known as one of the method achieving high performance magnet. We have developed the demagnetization analysis method using Dy diffused magnets which have graded coercive force distribution from surface to inside of magnet. In this paper, it is discussed about the most suitable Dy diffusion methods and magnets using newly developed demagnetization analysis method and also reports their effects for motor applications.
DAY2: Thursday, December 8 10:00 - 10:30
Motor Session A Vibration Analysis Using Numerical Results of Electromagnetic Analysis of the IPM Motor (D-model of IEEJ),Using package softwares, JMAG & CAEFEM Mr. Takushi Fujioka, Manager, Motor Division, FUJITSU GENERAL LIMITED
Countermeasures for motor vibrations are an important theme in motor designs, which are involved with electrical and mechanical designs as well. We used a software package of CAEFEM and JMAG to compute the vibrations in the stator of an IPM motor (IEEJ D-model) and used electromagnetic force calculations at the condition. For this, we input the current waveforms that accounted for PWM inverter carrier harmonics into JMAG, and observed what kinds of vibrations occurred in the carrier components.
DAY2: Thursday, December 8 10:30 - 11:00
Motor Session A Case of Coupled Analysis of JMAG-RT and Circuit Simulator Dr. Hideki Ohguchi, Core Technology Development Gr. Rotating Machinery Technology Development Dept. Product Technology Laboratory Corporate R&D Headquarters, Fuji Electric Co.,Ltd.
The comparison between analytical and experimental results of various motor characteristics is described. The motor is defined as the benchmark model in the investigating R&D Committee of IEEJ. The followings are main motor characteristics.
EMF
Torque
Inductance
Current waveform using coupled analysis of RT-model and circuit simulator
Iron loss
DAY2: Thursday, December 8 11:00 - 11:30
Motor Session Eddy-Current Rotor Position Sensor Mr. Seiji Shimizu, Leader, Business Unit Module&Energy, SUMIDA Electric Co.,Ltd
An Eddy-Current Rotor Position Sensor was developed for traction motors of HEV, EV. It serves - similar to a Resolver - to determine the angular position of the rotor in synchronous motors. It is compact and light weight, even at large rotor size and is proved to be insensitive to magnetic distortion. The arc shaped sensor module offers layout flexibility and allows easy installation and service. There is a good robustness to mechanical tolerance. The unique features of this technology can be very advantageous in applications with corresponding requirements. This article introduces the operating principle, simulation results and layout configurations and shows examples for applications.
DAY2: Thursday, December 8 13:30 - 14:00
Motor Session Variable Characteristics Motors (Matrix motor and CMMF motor) Prof. Kan Akatsu, Associate Professor, Electric Engineering, Shibaura Institute of Technology
Variable Characteristic motors which can change the magnet flux have been focused since these motors can improve the low load efficiency and also can reduce the magnet quantity. This paper introduces 2 new motors, the one has a changeable winding connection; named as Matrix Motor and another one has compounded magnet-motive forces; named as CMMF motor. These motors are realized by integration of motor and power electronics.
DAY2: Thursday, December 8 14:00 - 14:30
Motor Session Voltage Boost Type Drive Circuit without Additional Reactor for Switched Reluctance Motor Dr. Nobukazu Hoshi, Associate Professor, Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science
When switched reluctance motor (SRM) is driven, higher input dc voltage of inverter, which is drive circuit of SRM, is preferred because SRM winding current can rise or fall faster in higher dc voltage. However, in EV application, it is difficult to use high-voltage battery. As a solution, voltage boost converter is inserted between the battery and the inverter. This solution requires additional reactor; thus, the circuit size becomes large. In this presentation, a novel SRM drive circuit with voltage boost function without additional reactor is presented.
DAY2: Thursday, December 8 14:30 - 15:00
Motor Session Development of a Ferrite Permanent Magnet Axial Gap Motor with Segmented Rotor Structure Dr. Masatsugu Takemoto, Associate Professor, Graduate School of Information Science and Technology, Hokkaido University
Permanent magnet synchronous motors using high-performance rare-earth permanent magnets play an important role in hybrid electric vehicle (HEV) propulsion systems. However, rare earth materials employed in the high-performance rare-earth permanent magnets have problems such as price rise and export restriction. Thus, it is essential to develop a rare-earth-free motor for the HEVs. We have proposed a novel ferrite permanent magnet axial gap motor with segmented rotor structure. In order to obtain the fundamental characteristics of this motor, a prototype is fabricated and tested. The experiment results of the prototype are shown in detail. It can be confirmed with the experiment results of the prototype that the proposed motor has the possibility of the development of the rare-earth-free motor enough.
DAY2: Thursday, December 8 09:30 - 10:00
Transformer Session The magnetic simulation using JMAG and Simpleware Dr. Yosuke Iijima, R&D LABORATORY, MATERIALS R&D DEPARTMENT, TAIYO YUDEN CO., LTD.
We carried out a magnetic field simulation for magnetic components using JMAG and Simpleware. The Simpleware can make various types of FEM models from 3D image data. Here, a magnetic simulation has been achieved by importing an FEM model which was made from 3D Computer Tomography (CT) image data. By incorporating that model into JMAG we analyzed the magnetic field. We would like to introduce that analysis case study.
DAY2: Thursday, December 8 10:00 - 10:30
Transformer Session DC Superposition Characteristic Measurement of Reactors and Comparison with the measured values Mr. Kouhei Ueda, Magnetics Development Engineer, Transformer Development Dept., TABUCHI ELECTRIC CO.,LTD.
Among the parameters of Reactors, as to the inductance characteristics, stable Inductance over wide range of DC superposed current range. In oder to achieve this, the design of gap at the core is a very important factor to prevent core saturation. In the initial stage of conventional design routine, the gap length or locations have been determined by the repetitive prototyping of the reactors and this method was obvisouly time consuming and very costly approach for agile engineering. In order to reduce the prototyping and improve the accuracy of design, we at Tabuchi, have been using CAE software such as JMAG and we succeeded in the reduction of prototype numbers by the engineering simulation for optimum gap length and locations. This time, the comparison of CAE result and actual measured results on DC superimposition of reactors has been done. It has been found that simulation did not not reflect the measured value at the early stage of project. The deviation was found due to the minor hysteresis loop on major hysteresis curve. Therefore, actual differential permeability and incremental permeability have been measured and the result was modeled to JMAG modules to get the close simulation result on JMAG analysis.
DAY2: Thursday, December 8 10:30 - 11:00
Transformer Session Core Loss Analysis of the Transformers for Vehicle Power Supplies Mr. Masato Kabetani, Electronics Division Engineering Department, Toyota Industries Corporation
Miniaturization makes the thermal design become an important issue for vehicle electronic power supply development. For efficient thermal design, it is necessary to understand the loss distribution. JMAG is used to analyze transformer and coil. Generally, ferrite material has low electric conductivity and Eddy current loss is neglected. However under the condition of high frequency and high temperature, electric conductivity increase several fold, and become no more negligible. We improve core loss estimation method by dividing Joule loss caused by the Eddy current across the core.
DAY2: Thursday, December 8 13:30 - 14:00
Operation Streamlining Session Magnetic Shield Design Optimization in HDD Writer Mr. Kenkichi Anagawa, Writer design section wafer design team product development group HDD head business division data storage&thin film technology components business group, TDK corporation
As increasing the recording density of the hard disk drive, the data track width is getting narrower. In such a narrow track width, there is the risk that the data in the adjacent tracks might be erased in the write operation. To avoid this erasure, the magnetic shileld should be placed around the main pole to reduce the leakage flux to the adjacent tracks. However, if the magnetic shield absorbs magnetic field too much, the write field might be reduced. Therefore, the optimization of the magnetic shield design is very important. We show the optimization of the magnetic shield design using JMAG. We find the full wrap around shield as the optimized design for the narrow track width writer. Otherwise, we use SolidWorks to simplify writer structure change including shield structure. We carry on using modeFrontier together with JMAG for automatic optimization of writer design.
DAY2: Thursday, December 8 14:00 - 14:30
Operation Streamlining Session Making JMAG analysis handy by CATIA models Ph.D. Hisashi Yajima, Chief, Product development division 3, SMC Corporation
A lot of permanent magnets and electromagnets are used for the actuator and the sensor, etc. now. In SMC Corporation who is the air pressure equipment maker, a permanent magnet and the electromagnet are built into products such as the solenoid valves, cylinders and card motor. Recently, the magnetic field analysis software came to calculate a complex model at short time. Therefore, it has come to be used for the product development. In this paper, it is described to analyze the magnetic field handily by using three dimension model of CAD;CATIA for an analytical model of JMAG.
DAY2: Thursday, December 8 15:50 - 16:20
Designers and In-house Distribution Session Development and design of a loudspeaker using JMAG-Designer Mr. Yoshihide Toyoshima, Senior Engineer, R&D Center, Onkyo Corporation
We use JMAG-Designer mainly for development and design of magnetic circuits for loudspeaker. In this talk, we present an implementation background of JMAG-Designer and how to encourage the efficient use of it as an engineering design tool. In addition, we also introduce the case other than a loudspeaker.
DAY2: Thursday, December 8 16:20 - 16:50
Designers and In-house Distribution Session Development of Bicycle Generator Hub Dynamo Using JMAG Mr. Takeshi Fujiwara, System Engineering Bicycle Components Division, SHIMANO INC.
Our company uses JMAG for design development of bicycle generator to power lights. The generator built into the hub is called Hub dynamo. This structure is a single-phase claw pole generator, when enough power is required from low rotation rate. Bicycle products also must be small and light. Our company introduces Hub dynamo developed by JMAG.
Partner Seminar
DAY1: Wednesday, December 7 12:00 - 12:30
Partner Seminar The State-of-the-Art in Hardware-in-the-Loop Simulation of Motor Drives Mr. Simon Abourida, Opal-RT Technologies, Inc.
Hardware-In-the-Loop simulation (HILS) is an integral part of the design and testing process of electric motor drives and of systems incorporating variable speed drives. And OPAL-RT has been a pioneer in teaming-up with JSOL to provide the most advanced HILS system to motor control and system engineers, to help them conduct an ever increasing number of tests, before field-testing and deploying the final product. In last year's JMAG Users Conference, OPAL-RT presented the current state of Motor HILS based on JMAG-RT and the FPGA platform, and described the hardware and modeling development that was taking place. In this year's JMAG Users Conference, we present the state-of-the-art in Motor HILS, including multiple motors and inverters, all simulated on FPGA, in normal, faulty, and rectification modes, and with motor models based on JMAG-RT software. Key features of the new advanced drive models is its ability to simulate DC filter circuits on the FPGA as well as simulating faults on several location including inverter IGBTs and DC filter components faults as well as faults on motor terminals. Those features demonstrated with a real-life test case, require the implementation of a low-latency floating point electrical circuit solver on a powerful Virtex 6 FPGA chips.
DAY1: Wednesday, December 7 12:40 - 13:10
Partner Seminar Model Based Development and HILS for motor control development Mr. Takashi Miyano, Director, Engineering Department, dSPACE JAPAN K.K.
The Model Based Development (MBD) is increasingly penetrated in the automotive industry as the key development approach for Electrical Control Unit (ECU) in order to get the high quality of software under higher efficiency of development. This MBD method uses the models for controller and plant, and then can share these models in each development phase to increase the development efficiency, thus MBD become more popular in the various fields. This paper explains the MBD method for motor system development and clarifies the additional functions needed for motor developments, especially for HIL implementation.
DAY2: Thursday, December 8 12:45 - 13:15
Partner Seminar The introduction of JMAG-Designer Optimization problem, using modeFRONTIER Direct Interface. Mr. Seiji Nishita, Engineering Supervisor, Integrated Technology Dept. Integrated Simulation Div., CD-adapco JAPAN Co., LTD.
Through connecting with JMAG-Designer, modeFRONTIER has contributed to many JMAG Users, providing Automation, statistical analysis using Design of Experience and Multi-Objective Optimization. At the JMAG User's conference 2010, we have shown modeFRONTIER's JMAG-Designer Direct Interface. This year, we want to show you two examples: (1) Motor shape multi objective optimization (torque: maximize, cogging torque: minimize) (2) Magnetization analysis, making the magnet curve of JMAG analysis correspond to the sin curve.
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Registration
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We wish to thank all of those who applied.
