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論文

PANDORA Project for the study of photonuclear reactions below $$A=60$$

民井 淳*; Pellegri, L.*; S$"o$derstr$"o$m, P.-A.*; Allard, D.*; Goriely, S.*; 稲倉 恒法*; Khan, E.*; 木戸 英治*; 木村 真明*; Litvinova, E.*; et al.

European Physical Journal A, 59(9), p.208_1 - 208_21, 2023/09

光核反応は原子核構造の観点からも応用の観点からも重要であるにも関わらず、その反応断面積は未だに不定性が大きい。近年、超高エネルギー宇宙線の起源を探るために、鉄よりも軽い原子核の光核反応断面積を正確に知る必要が指摘されている。この状況を打破するため、原子核物理の実験、理論、宇宙物理の共同研究となるPANDORAプロジェクトが始まった。本論文はその計画の概要をまとめたものである。原子核実験ではRCNP、iThembaによる仮想光子実験とELI-NPによる実光子実験などが計画されている。原子核理論では、乱雑位相近似計算、相対論的平均場理論、反対称化分子動力学、大規模殻模型計算などが計画されている。これらで得られた信頼性の高い光核反応データベースと宇宙線伝搬コードを組み合わせ、超高エネルギー宇宙線の起源の解明に挑む。

論文

Discriminative measurement of absorbed dose rates in air from natural and artificial radionuclides in Namie Town, Fukushima Prefecture

小倉 巧也*; 細田 正洋*; 玉熊 佑紀*; 鈴木 崇仁*; 山田 椋平; 根上 颯珠*; 辻口 貴清*; 山口 平*; 城間 吉貴*; 岩岡 和輝*; et al.

International Journal of Environmental Research and Public Health, 18(3), p.978_1 - 978_16, 2021/02

 被引用回数:3 パーセンタイル:70.28(Environmental Sciences)

Ten years have elapsed since the accident at the Fukushima Daiichi Nuclear Power Plant in 2011, and the relative contribution of natural radiation is increasing in Fukushima Prefecture due to the reduced dose of artificial radiation. In order to accurately determine the effective dose of exposure to artificial radiation, it is necessary to evaluate the effective dose of natural as well as artificial components. In this study, we measured the gamma-ray pulse-height distribution over the accessible area of Namie Town, Fukushima Prefecture, and evaluated the annual effective dose of external exposure by distinguishing between natural and artificial radionuclides. The estimated median (range) of absorbed dose rates in air from artificial radionuclides as of April 1, 2020, is 133 (67$$sim$$511) nGy h$$^{-1}$$ in the evacuation order cancellation zone, and 1306 (892$$sim$$2081) nGy h$$^{-1}$$ in the difficult-to-return zone. The median annual effective doses of external exposures from natural and artificial radionuclides were found to be 0.19 and 0.40 mSv in the evacuation order cancellation zone, and 0.25 and 3.9 mSv in the difficult-to-return zone. The latest annual effective dose of external exposure discriminated into natural and artificial radionuclides is expected to be utilized for radiation risk communication.

論文

Development and operation of an electrostatic time-of-flight detector for the Rare RI storage Ring

長江 大輔*; 阿部 康志*; 岡田 俊祐*; 大甕 舜一朗*; 若山 清志*; 細井 駿*; 鈴木 伸司*; 森口 哲朗*; 天野 将道*; 上岡 大起*; et al.

Nuclear Instruments and Methods in Physics Research A, 986, p.164713_1 - 164713_7, 2021/01

 被引用回数:5 パーセンタイル:66.98(Instruments & Instrumentation)

An electrostatic time-of-flight detector named E-MCP has been developed for quick diagnostics of circulating beam and timing measurement in mass spectrometry at the Rare-RI Ring in RIKEN. The E-MCP detector consists of a conversion foil, potential grids, and a microchannel plate. Secondary electrons are released from the surface of the foil when a heavy ion hits it. The electrons are accelerated and deflected by 90$$^{circ}$$ toward the microchannel plate by electrostatic potentials. A thin carbon foil and a thin aluminum-coated mylar foil were used as conversion foils. We obtained time resolutions of 69(1) ps and 43(1) ps (standard deviation) for a $$^{84}$$Kr beam at an energy of 170 MeV/u when using the carbon and the aluminum-coated mylar foils, respectively. A detection efficiency of approximately 90% was obtained for both foils. The E-MCP detector equipped with the carbon foil was installed inside the Rare-RI Ring to confirm particle circulation within a demonstration experiment on mass measurements of nuclei around $$^{78}$$Ge produced by in-flight fission of uranium beam at the RI Beam Factory in RIKEN. Periodic time signals from circulating ions were clearly observed. Revolution times for $$^{78}$$Ge, $$^{77}$$Ga, and $$^{76}$$Zn were obtained. The results confirmed successful circulation of the short-lived nuclei inside the Rare-RI Ring.

論文

$$omega N$$ scattering length from $$omega$$ photoproduction on the proton near the reaction threshold

石川 貴嗣*; 藤村 寿子*; 深澤 宏司*; 橋本 亮*; He, Q.*; 本多 佑記*; 保坂 淳; 岩田 高広*; 甲斐田 俊*; 笠木 治郎太*; et al.

Physical Review C, 101(5), p.052201_1 - 052201_6, 2020/05

Photoproduction of the omega meson on the proton has been experimentally studied near the threshold. The total cross sections are determined at incident energies ranging from 1.09 to 1.15 GeV. The 1/2 and 3/2 spin-averaged scattering length $$a$$$$_{omega p}$$ and effective range $$r$$$$_{omega p}$$ between the CO meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $$a$$$$_{omega p}$$ = (-0.97 $$_{rm -0.16stat-0.00syst}^{rm +0.16stat+0.03syst}$$ + $$i$$(0.07 $$_{rm -0.14stat-0.09syst}^{rm +0.15stat+0.17syst}$$) fm and $$r$$$$_{omega p}$$ = (+2.78 $$_{rm -0.54stat-0.12syst}^{rm +0.67stat+0.11syst}$$) + $$i$$(-0.01 $$_{rm -0.50stat-0.00syst}^{rm +0.46stat+0.06syst}$$) fm, resulting in a repulsive force. The real and imaginary parts for $$a$$$$_{omega p}$$ and $$r$$$$_{omega p}$$ are determined separately for the first time. A small $$P$$-wave contribution does not affect the obtained values.

論文

Cesium concentrations in various environmental media at Namie, Fukushima

Heged$"u$s, M.*; 城間 吉貴*; 岩岡 和輝*; 細田 正洋*; 鈴木 崇仁*; 玉熊 佑紀*; 山田 椋平; 辻口 貴清*; 山口 平*; 小倉 巧也*; et al.

Journal of Radioanalytical and Nuclear Chemistry, 323(1), p.197 - 204, 2020/01

 被引用回数:3 パーセンタイル:32.21(Chemistry, Analytical)

福島県浪江町において、2017年の部分的な避難指示区域の解除後、2つの主要河川の水中及び堆積物中の放射性セシウム濃度を大気中放射性物質濃度とともに測定した。観測された濃度は、ろ過していない河川水中の$$^{137}$$Csで最大384$$pm$$11mBq/L、大気中の$$^{137}$$Csで最大1.28$$pm$$0.09mBq/m$$^{3}$$であり、堆積物中の$$^{137}$$Csでは最大で44900$$pm$$23.4Bq/kgであった。$$^{134}$$Cs/$$^{137}$$Cs比は、これまでの研究報告とよく一致し、浪江町における堆積物中の放射性セシウムの主な起源が1号機である可能性が高いと考えられる。

論文

New precise measurements of muonium hyperfine structure at J-PARC MUSE

Strasser, P.*; 阿部 充志*; 青木 正治*; Choi, S.*; 深尾 祥紀*; 東 芳隆*; 樋口 嵩*; 飯沼 裕美*; 池戸 豊*; 石田 勝彦*; et al.

EPJ Web of Conferences, 198, p.00003_1 - 00003_8, 2019/01

 被引用回数:13 パーセンタイル:99.28

High precision measurements of the ground state hyperfine structure (HFS) of muonium is a stringent tool for testing bound-state quantum electrodynamics (QED) theory, determining fundamental constants of the muon magnetic moment and mass, and searches for new physics. Muonium is the most suitable system to test QED because both theoretical and experimental values can be precisely determined. Previous measurements were performed decades ago at LAMPF with uncertainties mostly dominated by statistical errors. At the J-PARC Muon Science Facility (MUSE), the MuSEUM collaboration is planning complementary measurements of muonium HFS both at zero and high magnetic field. The new high-intensity muon beam that will soon be available at H-Line will provide an opportunity to improve the precision of these measurements by one order of magnitude. An overview of the different aspects of these new muonium HFS measurements, the current status of the preparation for high-field measurements, and the latest results at zero field are presented.

論文

Observation of anisotropic magneto-Peltier effect in nickel

内田 健一*; 大門 俊介*; 井口 亮*; 齊藤 英治

Nature, 558(7708), p.95 - 99, 2018/06

 被引用回数:56 パーセンタイル:91.16(Multidisciplinary Sciences)

The Peltier effect, discovered in 1834, converts a charge current into a heat current in a conductor, and its performance is described by the Peltier coefficient, which is defined as the ratio of the generated heat current to the applied charge current. To exploit the Peltier effect for thermoelectric cooling or heating, junctions of two conductors with different Peltier coefficients have been believed to be indispensable. Here we challenge this conventional wisdom by demonstrating Peltier cooling and heating in a single material without junctions. This is realized through an anisotropic magneto-Peltier effect in which the Peltier coefficient depends on the angle between the directions of a charge current and magnetization in a ferromagnet. By using active thermography techniques, we observe the temperature change induced by this effect in a plain nickel slab. We find that the thermoelectric properties of the ferromagnet can be redesigned simply by changing the configurations of the charge current and magnetization, for instance, by shaping the ferromagnet so that the current must flow around a curve. Our experimental results demonstrate the suitability of nickel for the anisotropic magneto-Peltier effect and the importance of spin-orbit interaction in its mechanism. The anisotropic magneto-Peltier effect observed here is the missing thermoelectric phenomenon in ferromagnetic materials-the Onsager reciprocal of the anisotropic magneto-Seebeck effect previously observed in ferromagnets and its simplicity might prove useful in developing thermal management technologies for electronic and spintronic devices.

論文

New precise measurement of muonium hyperfine structure interval at J-PARC

上野 恭裕*; 青木 正治*; 深尾 祥紀*; 東 芳隆*; 樋口 嵩*; 飯沼 裕美*; 池戸 豊*; 石田 勝彦*; 伊藤 孝; 岩崎 雅彦*; et al.

Hyperfine Interactions, 238(1), p.14_1 - 14_6, 2017/11

 被引用回数:3 パーセンタイル:86.59

MuSEUM is an international collaboration aiming at a new precise measurement of the muonium hyperfine structure at J-PARC (Japan Proton Accelerator Research Complex). Utilizing its intense pulsed muon beam, we expect a ten-fold improvement for both measurements at high magnetic field and zero magnetic field. We have developed a sophisticated monitoring system, including a beam profile monitor to measure the 3D distribution of muonium atoms to suppress the systematic uncertainty.

論文

Spin current generation using a surface acoustic wave generated via spin-rotation coupling

小林 大眞*; 吉川 智英*; 松尾 衛*; 井口 亮*; 前川 禎通; 齊藤 英治; 能崎 幸雄*

Physical Review Letters, 119(7), p.077202_1 - 077202_5, 2017/08

 被引用回数:104 パーセンタイル:97.38(Physics, Multidisciplinary)

We demonstrate the generation of alternating spin current (SC) via spin-rotation coupling (SRC) using a surface acoustic wave (SAW) in a Cu film. Ferromagnetic resonance caused by injecting SAWs was observed in a Ni-Fe film attached to a Cu film, with the resonance further found to be suppressed through the insertion of a SiO$$_{2}$$ film into the interface. The intensity of the resonance depended on the angle between the wave vector of the SAW and the magnetization of the Ni-Fe film. This angular dependence is explicable in terms of the presence of spin transfer torque from a SC generated via SRC.

論文

Thermographic measurements of the spin Peltier effect in metal/yttrium-iron-garnet junction systems

大門 俊介*; 内田 健一*; 井口 亮*; 日置 友智*; 齊藤 英治

Physical Review B, 96(2), p.024424_1 - 024424_12, 2017/07

 被引用回数:34 パーセンタイル:82.44(Materials Science, Multidisciplinary)

The spin Peltier effect (SPE), heat-current generation due to spin-current injection, in various metal (Pt, W, and Au single layers and Pt/Cu bilayer)/ferrimagnetic insulator [yttrium-iron-garnet (YIG)] junction systems has been investigated by means of a lock-in thermography (LIT) method. The SPE is excited by a spin current across the metal/YIG interface, which is generated by applying a charge current to the metallic layer via the spin Hall effect. The LIT method enables the thermal imaging of the SPE free from the Joule-heating contribution. Importantly, we observed spin-current-induced temperature modulation not only in the Pt/YIG and W/YIG systems, but also in the Au/YIG and Pt/Cu/YIG systems, excluding the possible contamination by anomalous Ettingshausen effects due to proximity-induced ferromagnetism near the metal/YIG interface. As demonstrated in our previous study, the SPE signals are confined only in the vicinity of the metal/YIG interface; we buttress this conclusion by reducing a spatial blur due to thermal diffusion in an infrared-emission layer on the sample surface used for the LIT measurements. We also found that the YIG-thickness dependence of the SPE is similar to that of the spin Seebeck effect measured in the same Pt/YIG sample, implying the reciprocal relation between them.

論文

Generation of megahertz-band spin currents using nonlinear spin pumping

渡辺 真悟*; 廣部 大地*; 塩見 雄毅*; 井口 亮*; 大門 俊介*; 亀田 麻衣*; 高橋 三郎*; 齊藤 英治

Scientific Reports (Internet), 7, p.4576_1 - 4576_6, 2017/07

 被引用回数:6 パーセンタイル:29.83(Multidisciplinary Sciences)

Spin pumping enables the generation of d.c. and gigahertz-band (GHz-band) voltages from an applied microwave via magnetization dynamics when combined with inverse spin Hall effects. However, generating such voltages in the in-between frequency region, or the megahertz (MHz) band, has been difficult since ferromagnetic resonance usually occurs in the GHz band. Here we show that in spite of GHz-band microwaves applied, MHz-band voltages can be generated by spin pumping with use of nonlinear magnetization dynamics in Y$$_3$$Fe$$_5$$O$$_{12}$$. The mechanism is ascribed to the MHz-band oscillation of the amplitude of the magnetization precession, which is projected onto a rectified voltage component via spin pumping. The present finding could be useful for frequency down-conversion thanks to the simple and durable structure, continuous-wave operation, and the tunability of an output frequency with low magnetic fields.

論文

Time-resolved study of field-induced suppression of longitudinal spin Seebeck effect

日置 友智*; 井口 亮*; Qiu, Z.*; Hou, D.*; 内田 健一*; 齊藤 英治

Applied Physics Express, 10(7), p.073002_1 - 073002_4, 2017/06

 被引用回数:13 パーセンタイル:56.32(Physics, Applied)

We have investigated the magnetic-field-induced suppression of the longitudinal spin Seebeck effect (LSSE) by using a time-resolved measurement technique at room temperature. The result manifested two distinctive time domains: the short-time domain where the observed voltage is insensitive to the magnetic fields, and the long-time domain where the both response time and the magnitude of the observed voltage decreased simultaneously by the magnetic fields. We estimated the magnon propagation length by fitting the transient LSSE response. The propagation length shows a strong dependence on the applied magnetic field, indicating the importance of long-range and low-frequency magnons in the LSSE.

論文

Concomitant enhancement of the longitudinal spin Seebeck effect and the thermal conductivity in a Pt/YIG/Pt system at low temperatures

井口 亮*; 内田 健一*; 大門 俊介*; 齊藤 英治

Physical Review B, 95(17), p.174401_1 - 174401_7, 2017/05

 被引用回数:46 パーセンタイル:87.78(Materials Science, Multidisciplinary)

We report a simultaneous measurement of a longitudinal spin Seebeck effect (LSSE) and thermal conductivity in a Pt/Y$$_{3}$$Fe$$_{5}$$O$$_{12}$$ (YIG)/Pt system in a temperature range from 10 to 300 K. By directly monitoring the temperature difference in the system, we excluded thermal artifacts in the LSSE measurements. It is found that both the LSSE signal and the thermal conductivity of YIG exhibit sharp peaks at the same temperature, different from previous reports. The maximum LSSE coefficient is found to be $$S_mathrm{LSSE} > 10 mu$$V/K, one-order-of magnitude greater than the previously reported values. The concomitant enhancement of the LSSE and thermal conductivity of YIG suggests the strong correlation between magnon and phonon transport in the LSSE.

論文

Measurement of spin pumping voltage separated from extrinsic microwave effects

井口 亮*; 齊藤 英治

Journal of the Physical Society of Japan, 86(1), p.011003_1 - 011003_13, 2017/01

 被引用回数:58 パーセンタイル:93.72(Physics, Multidisciplinary)

Conversions between spin and charge currents are core technologies in recent spintronics. In this article, we provide methods for estimating inverse spin Hall effects (ISHEs) induced by using microwave-driven spin pumping (SP) as a spin-current generator. ISHE and SP induce an electromotive force at the ferromagnetic or spin-wave resonance, which offers a valuable electric method of studying spin physics in materials. At the resonance, a microwave for exciting the magnetization dynamics induces an additional electromotive force via rf-current rectification and thermoelectric effects. We discuss methods of separating the signals generated from such extrinsic microwave effects by controlling sample structures and configurations. These methods are helpful in performing accurate measurements on ISHE induced by SP, enabling quantitative studies on the conversion between spin and charge currents on various kinds of materials.

論文

One-dimensional spinon spin currents

廣部 大地*; 佐藤 正寛*; 川股 隆行*; 塩見 雄毅*; 内田 健一*; 井口 亮*; 小池 洋二*; 前川 禎通; 齊藤 英治

Nature Physics, 13(1), p.30 - 34, 2017/01

 被引用回数:91 パーセンタイル:96.69(Physics, Multidisciplinary)

Quantum spin fluctuation in a low-dimensional or frustrated magnet breaks magnetic ordering while keeping spin correlation. Such fluctuation has been a central topic in magnetism because of its relevance to high-Tc superconductivity and topological states. However, utilizing such spin states has been quite difficult. In a one-dimensional spin-1/2 chain, a particle-like excitation called a spinon is known to be responsible for spin fluctuation in a paramagnetic state. Spinons behave as a Tomonaga-Luttinger liquid at low energy, and the spin system is often called a quantum spin chain. Here we show that a quantum spin chain generates and carries spin current, which is attributed to spinon spin current. This is demonstrated by observing an anisotropic negative spin Seebeck effect along the spin chains in Sr$$_{2}$$CuO$$_{3}$$. The results show that spin current can flow even in an atomic channel owing to long-range spin fluctuation.

論文

New muonium HFS measurements at J-PARC/MUSE

Strasser, P.*; 青木 正治*; 深尾 祥紀*; 東 芳隆*; 樋口 嵩*; 飯沼 裕美*; 池戸 豊*; 石田 勝彦*; 伊藤 孝; 岩崎 雅彦*; et al.

Hyperfine Interactions, 237(1), p.124_1 - 124_9, 2016/12

 被引用回数:7 パーセンタイル:91.29

At the Muon Science Facility (MUSE) of J-PARC (Japan Proton Accelerator Research Complex), the MuSEUM collaboration is planning new measurements of the ground state hyperfine structure (HFS) of muonium both at zero field and at high magnetic field. The previous measurements were performed both at LAMPF (Los Alamos Meson Physics Facility) with experimental uncertainties mostly dominated by statistical errors. The new high intensity muon beam that will soon be available at MUSE H-Line will provide an opportunity to improve the precision of these measurements by one order of magnitude. An overview of the different aspects of these new muonium HFS measurements, the current status of the preparation, and the results of a first commissioning test experiment at zero field are presented.

論文

Thermal imaging of spin Peltier effect

大門 俊介*; 井口 亮*; 日置 友智*; 齊藤 英治; 内田 健一*

Nature Communications (Internet), 7, p.13754_1 - 13754_7, 2016/12

 被引用回数:97 パーセンタイル:95.46(Multidisciplinary Sciences)

The Peltier effect modulates the temperature of a junction comprising two different conductors in response to charge currents across the junction, which is used in solid-state heat pumps and temperature controllers in electronics. Recently, in spintronics, a spin counterpart of the Peltier effect was observed. The "spin Peltier effect" modulates the temperature of a magnetic junction in response to spin currents. Here we report thermal imaging of the spin Peltier effect; using active thermography technique, we visualize the temperature modulation induced by spin currents injected into a magnetic insulator from an adjacent metal. The thermal images reveal characteristic distribution of spin-current-induced heat sources, resulting in the temperature change confined only in the vicinity of themetal/insulator interface. This finding allows us to estimate the actual magnitude of the temperature modulation induced by the spin Peltier effect, which is more than one order of magnitude greater than previously believed.

論文

Observation of temperature-gradient-induced magnetization

Hou, D.*; Qiu, Z.*; 井口 亮*; 佐藤 浩司*; Vehstedt, E. K.*; 内田 健一*; Bauer, G. E. W.*; 齊藤 英治

Nature Communications (Internet), 7, p.12265_1 - 12265_6, 2016/07

 被引用回数:14 パーセンタイル:64.7(Multidisciplinary Sciences)

Applying magnetic fields has been the method of choice to magnetize non-magnetic materials, but they are difficult to focus. The magneto-electric effect and voltage-induced magnetization generate magnetization by applied electric fields, but only in special compounds or heterostructures. Here we demonstrate that a simple metal such as gold can be magnetized by a temperature gradient or magnetic resonance when in contact with a magnetic insulator by observing an anomalous Hall-like effect, which directly proves the breakdown of time-reversal symmetry. Such Hall measurements give experimental access to the spectral spin Hall conductance of the host metal, which is closely related to other spin caloritronics phenomena such as the spin Nernst effect and serves as a reference for theoretical calculation.

論文

Spin-current-driven thermoelectric generation based on interfacial spin-orbit coupling

Yagmur, A.*; 軽部 修太郎*; 内田 健一*; 近藤 浩太*; 井口 亮*; 吉川 貴史*; 大谷 義近*; 齊藤 英治

Applied Physics Letters, 108(24), p.242409_1 - 242409_4, 2016/06

 被引用回数:6 パーセンタイル:33.55(Physics, Applied)

The longitudinal spin Seebeck effect (SSE) in Bi $$_{2}$$O$$_{3}$$/Cu/yttrium-iron-garnet (YIG) devices has been investigated. When an out-of-plane temperature gradient is applied to the Bi$$_{2}$$O$$_{3}$$/Cu/YIG device, a spin current is generated across the Cu/YIG interface via the SSE and then converted into electric voltage due to the spin$-orbit coupling at the Bi$_{2}$$O$$_{3}$$/Cu interface. The sign of the SSE voltage in the Bi$$_{2}$$O$$_{3}$$/Cu/YIG devices is opposite to that induced by the conventional inverse spin Hall effect in Pt/YIG devices. The SSE voltage in the Bi$$_{2}$$O$$_{3}$$/Cu/YIG devices disappears in the absence of the Bi$$_{2}$$O$$_{3}$$layer and its thermoelectric conversion efficiency is independent of the Cu thickness, indicating the important role of the Bi$$_{2}$$O$$_{3}$$/Cu interface. This result demonstrates that not only the bulk inverse spin Hall effect but also the spin-orbit coupling near the interface can be used for SSE-based thermoelectric generation.

論文

国際核融合エネルギー研究センターの高性能計算機システムHeliosを利用した国内シミュレーション研究プロジェクトの進展

石澤 明宏*; 井戸村 泰宏; 今寺 賢志*; 糟谷 直宏*; 菅野 龍太郎*; 佐竹 真介*; 龍野 智哉*; 仲田 資季*; 沼波 政倫*; 前山 伸也*; et al.

プラズマ・核融合学会誌, 92(3), p.157 - 210, 2016/03

幅広いアプローチ協定に基づいて国際核融合エネルギー研究センター(IFERC)の計算機シミュレーションセンター(CSC)に設置された高性能計算機システムHeliosは、2012年1月に運用を開始し、日欧の磁気核融合シミュレーション研究に供用され、高い利用率の実績を示すとともに、炉心プラズマ物理から炉材料・炉工学にわたる広い分野で多くの研究成果に貢献している。本プロジェクトレビューの目的は、国内の大学や研究機関においてHeliosを利用して進められているシミュレーション研究プロジェクトとその成果を一望するとともに、今後予想される研究の進展を紹介することである。はじめにIFERC-CSCの概要を示した後、各研究プロジェクト毎にその目的、用いられる計算手法、これまでの研究成果、そして今後必要とされる計算を紹介する。

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