Experimental verification of rotating detonation engine with film cooling

分类： 动力与电气工程 >> 工程热物理学 提交时间： 2024-03-26

Jingtian Yu Songbai Yao Jingzhe Li Jianghong Li Rujia Wang Bin Wang Wenwu Zhang

摘要： We conduct an experimental investigation on the integration of film cooling for thermal protection in a 72-mm cylindrical rotating detonation engine (RDE). The cooling scheme employs the injection of cooling air through a series of cat-ear-shaped film cooling holes densely distributed along the outer wall of the cylindrical combustor. Our findings reveal successful initiation of the RDE and sustained propagation of the rotating detonation wave (RDW) when film cooling is activated.

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A possible new amphicyonid from the Miocene of the Linxia Basin

分类： 生物学 >> 生物进化论 提交时间： 2024-03-20

JIANGZUO Qi-Gao GAO Yuan Alberto VALENCIANO LU Dan WANG Shi-qi

摘要： Here we report a new form of amphicyonid from an uncertain locality in the LinxiaBasin. The derived dental traits imply an affinity to Magericyon, previously known from Europe and possibly southern Asia. The specimen suggests a higher diversity of amphicyonids in eastern Asia than previously thought, and more discovery with stratigraphic information will be needed to elucidate the evolution of Amphicyonidae in eastern Asia.

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Taxonomic revision of Sinoeugnathus kueichowensis from the Middle Triassic of Guizhou and Yunnan, China

分类： 生物学 >> 生物进化论 提交时间： 2024-03-15

FENG Dong-Hao XU Guang-Hui MA Xin-Ying REN Yi

摘要： The previously alleged ‘eugnathid amiiform’ Sinoeugnathus kueichowensis is asmall-sized halecomorph from the Middle Triassic (Ladinian) marine deposits of Guizhou andYunnan, China. A morphological redescription and taxonomic revision of this taxon are providedbased on a detailed examination of 15 new specimens. Among them, IVPP V24315 (standardlength = 64 mm) is appointed as the neotype, given that the holotype is missing. Studies of thesespecimens revealed some morphological details previously undescribed or misidentified forthis taxon, including a hatchet-shaped antorbital, two broad suborbitals, a sensory canal in themaxilla, and three pairs of extrascapulars. For the first time, Sinoeugnathus was incorporatedinto an analysis of halecomorph phylogeny, and the results recover it as the sister taxon of theAnisian Subortichthys from Luoping, Yunnan, and both are grouped with two Ladinian generaAllolepidotus and Eoeugnathus from the Monte San Giorgio area into a monophyletic group(namely Subortichthyidae fam. nov. herein) at the base of Ionoscopiformes. This taxonomicreassessment of Subortichthys provides new insights into the phylogeny and paleogeographicevolution of Ionoscopiformes.

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A restudy of Rhinocerotini fossils from the Miocene Jiulongkou Fauna of China

分类： 生物学 >> 生物进化论 提交时间： 2024-03-15

LI Shi-Jie DENG Tao

摘要： All the extant rhino species belong to Rhinocerotini and either have one horn (a nasal horn) or two horns (a nasal horn and frontal horn). So far, the earliest Rhinocerotini to have been identified in China is the “Dicerorhinus” cixianensis, which was based on a juvenile skull with an associated mandible from the Middle Miocene locality of Jiulongkou in Cixian County, HebeiProvince of northern China. Our analyses suggest that there are similarities between this specimenand the modern genus, Dicerorhinus, but it differs in several cranial traits and therefore cannotbe assigned to the modern genus. Instead, it is closer to the Middle Miocene Lartetotheriumfrom Europe, especially the specimen from La Retama in Spain and should be assigned to thatgenus, indicating the presence of intracontinental dispersal at this time. The Jiulongkou faunais the only Middle Miocene fauna with Rhinocerotini in China, and, together with the faunalcomposition, this implies a more humid and closed environment, in contrast to those found inwestern China. We suggest that the position of the posterior border of the nasal notch is a goodindication of the specimen’s evolutionary level in Rhinocerotini. The anterior position of the nasalnotch as seen in modern Dicerorhinus, together with its certain similarities to L. cixianensis aswell as its differences with more specialized species of the Dihoplus-Pliorhinus-Stephanorhinus-Coelodonta lineage, supports the conclusion that Dicerorhinus experienced little change during anearly 10 Myr evolutionary history, possibly due to the low selection pressure seen in the tropical/subtropical forests in southeastern Asia.

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Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

分类： 物理学 >> 核物理学 提交时间： 2024-03-10

Chuang Shen Yin-Shun Zhu Fu-San Chen

摘要： Currently, three types of superconducting magnets are used in particle accelerators: cos2uptheta, CCT, and serpentine. However, all three coil configurations have complex spatial geometries, which make magnet manufacturing and strain-sensitive superconductor applications difficult. Compared with the three existing quadrupole coils, the racetrack quadrupole coil has a simple shape and manufacturing process, but there have been few theoretical studies. In this paper, the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented. The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density. Then, a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10-4. Finally, considering the practical engineering needs of the accelerator interaction region, electromagnetic design examples of racetrack quadrupole magnets with high gradients, large apertures, and small apertures are described, and the application prospects of racetrack quadrupole coils are analyzed.

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Morphometric analysis of the cervical vertebral series in extant birds with implications for Mesozoic avialan feeding ecology

分类： 生物学 >> 人类学 提交时间： 2024-03-06

Liu Bi-Ying Thomas A. STIDHAM Wang Xiao-Ping Li Zhi-Heng Zhou Zhong-He

摘要： The inference of Mesozoic avialan bird diets previously relied on traditional methods such as morphological comparisons among taxa and direct evidence such as identifiable stomach contents. However, the application of these approaches has been limited because of uncommon preservation of relevant fossil evidence. We searched for additional informative characteristics to help develop new methods to assess the diet of fossil birds. In particular, the morphology of the avialan neck is highly modularized and plays roles in multiple functions including food acquisition. The structure of and variation among the cervical vertebrae likely reflects the demands of feeding ecology in fossil and extant birds because the avialan neck evolved to, at least in part, replace the forelimbs by assisting with activities such as cranioinertial feeding and other ecological functions. Here, we utilize morphometric and statistical analyses to establish an initial quantitative relationship between cervical morphology and dietary modes in both extant and extinct birds. This morphometric framework derived from the cervical morphology of living birds is used as a basis to estimate the diet categories of five taxa of Mesozoic birds. The results indicate that there is a quantitative correlation between cervical morphology differentiation and their interrelated feeding modes. The enantiornithine taxa examined exhibit cervical morphologies similar to extant insectivorous or carnivorous birds. The ornithurine species show cervical morphologies that are more aligned with generalist or herbivorous birds, and exhibit preliminary morphological features tied to aquatic adaptions. These findings are consistent in part with other direct fossil evidence, as well as hypotheses developed from other skeletal comparisons. Therefore, the cervical vertebral series, as a skeletal system closely linked to food acquisition, can serve as one of the valuable metrics to provide information for inferring the diet of long extinct Mesozoic birds.

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Beam Flux Measurement Using Photon Activation Analysis Method at SLEGS

分类： 物理学 >> 核物理学 提交时间： 2024-02-16

Yang Yuxuan Wang Hongwei Zhao Weijuan Zhang Yue Li Zhicai Hao Zirui Chen Kaijie Wang Zhenwei Sun Qiankun Fan Gongtao Xu Hanghua Liu Longxiang

摘要： The Shanghai Laser Electron Gamma Source(SLEGS) has delivered a quasi-monochromatic, continuously energy-tunable gamma-ray beam. Based on the photon activation analysis(PAA) method, SLEGS has built and developed a photon activation analysis platform, including online activation and offline low-background HPGe detector measurement systems, as an alternative to direct measurement methods and a cross-tests at low throughput. Due to the short half-lives spanning from minutes to days and characteristics such as ease of fabrication, cost-effectiveness, and stability, gold (197Au) and zinc (64Zn) emerge as favorable activation targets in the gamma-ray beam flux monitor. Notably, their utility shows a multitude of advantages in monitoring the gamma-ray beam flux typically 105 photons/s with the energy of 13.16 to 19.08 MeV under the condition of the 3 mm coarse collimator. Especially in high-flux $\gamma$-ray beam experiments can be well applied.

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Gas Microchannel Plate–Pixel Detector for X-ray Polarimetry

分类： 核科学技术 >> 核科学与技术 提交时间： 2024-01-06

Huan-Bo Feng Hong-Bang Liu Dong Wang Zi-Li Li Shu-Lin Liu Qian Liu Hang-Zhou Li Bin-Long Wang Yan-Jun Xie Zong-Wang Fan Hui Wang Ran Chen Di-Fan Yi, Rui-Ting Ma Fei Xie Bo Peng Xiang-Ming Sun Jin Li En-Wei Liang

摘要： POLAR-2 is a gamma-ray burst (GRB) polarimeter that is designed to study the polarization in GRB radiation emissions, aiming to improve our knowledge of related mechanisms. POLAR-2 is expected to utilize an on#2;board polarimeter that is sensitive to soft X-rays (210 keV), called low-energy polarization detector (LPD). We have developed a new soft X-ray polarization detector prototype based on gas microchannel plates (GMCPs) and pixel chips (Topmetal). The GMCPs have bulk resistance, which prevents charging-up effects and ensures gain stability during operation. The detector is composed of low-outgassing materials and is gas-sealed using a laser welding technique, ensuring long-term stability. A modulation factor of 41.28% 0.64% is obtained for a 4.5 keV polarized X-ray beam. A residual modulation of 1.96% 0.58% at 5.9 keV is observed for the entire sensitive area.

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Conceptual Design of a 714-MHz RFQ for Compact Proton Injectors and Development of a New Tuning Algorithm on its Aluminium Prototype

分类： 物理学 >> 核物理学 提交时间： 2023-12-28

Yixing Lu Wencheng Fang Yusen Guo Zhentang Zhao

摘要： Radio frequency quadrupoles (RFQs), which are crucial components of proton injectors, significantly affect the performance of proton accelerator facilities. An RFQ with a high frequency of 714 MHz dedicated to compact proton injectors for medical applications is designed in this study. The RFQ is designed to accelerate proton beams from 50 keV to 4 MeV within a short length of 2 m and can be matched closely with the downstream drift tube linac to capture more particles through a preliminary optimization. To develop an advanced RFQ, challenging techniques, including fabrication and tuning method, must be evaluated and verified using a prototype. An aluminium prototype is derived from the conceptual design of the RFQ and then redesigned to confirm the radio frequency performance, fabrication procedure, and feasibility of the tuning algorithm. Eventually, a new tuning algorithm based on the response matrix and least-squares method is developed, which yields favorable results based on the prototype, i.e., the errors of the dipole and quadrupole components reduced to a low level after several tuning iterations. Benefiting from the conceptual design and techniques obtained from the prototype, the formal mechanical design of the 2-m RFQ is ready for the next manufacturing step.

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Study on the corrosion behavior of 316H stainless steel in molten NaCl-KCl-MgCl2 salts with and without purification

分类： 物理学 >> 核物理学 提交时间： 2023-11-16

Hua Ai Xinmei Yang Huajian Liu Bingchuan Chen Ling Han Hua Sun Yanjun Chen Yuan Qian Jian-Qiang Wang

摘要： The corrosion behavior of 316H stainless steel (SS) in the impure and purified NaCl-KCl-MgCl2 salt was investigated at 700 C . Results indicate that the main deleterious impurity induced corrosion in the impure salt was the absorbed moisture, present in the form of MgCl26H2O. 316H SS occurred severe intergranular corrosion with a corrosion depth of 130 m for 1000 h in the impure NaCl-KCl-MgCl2 salt. In contrast, the purification treatment of molten chloride salt by the dissolved Mg metal can remove the absorbed moisture, and the corresponding reactions were also discussed. As a result, the corrosiveness of NaCl-KCl-MgCl2 salt is reduced significantly. 316H SS occurred slight uniform corrosion with a depth of less than 5 m for 3000 h in the purified NaCl-KCl-MgCl2 salt.

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BL02U1: The Relocated Macromolecular Crystallography Beamline at the Shanghai Synchrotron Radiation Facility

分类： 物理学 >> 核物理学 提交时间： 2023-11-15

Ke Liu Huan Zhou Qin Xu Huating Kong Kunhao Zhang Weiwei Wang Minjun Li Zhijun Wang Qiangyan Pan Xingya Wang Feng Yu Qisheng Wang

摘要： Macromolecular crystallography beamline BL17U1 at the Shanghai Synchrotron Radiation Facility hasbeenrelocated, upgraded, and given a newID (BL02U1). It now deliversX-rays intheenergyrangeof616 keV, withafocusedbeamof11.6m 4.8 m andphotonfluxgreater than 10^12phs/s. Thehighcredibilityandstabilityofthebeamandgoodtimingsynchronizationof the equipmentsignificantly improvetheexperimentalefficiency. SinceJune2021, whenitofficially openedtousers, over4200 hofbeamtimehavebeenprovidedto over200 researchgroupstocollectdataatthebeamline. Its goodperformanceandstableoperationhave led to the resolution of several structuresbasedondatacollectedatthebeamline.

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Measurement of the Br(n,gamma) cross sections up to stellar s-process temperatures at the CSNS Back-n

分类： 物理学 >> 核物理学 分类： 物理学 >> 地球物理学、天文学和天体物理学 提交时间： 2023-09-12

Yang, Gaole An, Zhendong Jiang, Wei Li,Xiankai Qiu, Weiwei Liao, Zhengfa Zhuang, Ziyue Zhang, Xiaoping Chen,Shengli Xiao, Erxi Fang,Xiao Li,XinXiang Hu, Xinrong Jiang, Bing Wang, Jincheng Ren, Jie Luo, Wen Zhu, ZhiChao Lan, Haoyang Cao, Zongwei

摘要： The neutron capture cross sections (${n, upgamma}$) of Bromine was performed with the time-of-flight (TOF) technique at the Back-n facility of the China Spallation Neutron Source (CSNS). Prompt $ upgamma$-rays originating from neutron-induced capture events were detected by four C${}_6$D${}_6$ detectors. The pulse height weighting technique (PHWT) and the double-bunch unfolding method based on the Bayesian theory were used in the data analysis. To obtain reliable measurement results, background deductions, normalization, and corrections were carefully considered. The multilevel R-matrix Bayesian code SAMMY was used to extract the resonance parameters in the resolved resonance region (RRR). The average cross sections in unresolved resonance region the was obtained from 10 to 400 keV. The experimental results were compared with the data of several evaluated libraries and previous experiments in the resolved and unresolved resonance region. The TALYS code was used to describe the average cross sections in the unresolved resonance region. Astrophysical Maxwell average cross sections (MACSs) of ${}^{79,81}$Br from $ kT $ = 5 to 100 keV was calculated over a sufficiently wide range of neutron energies. At a thermal energy of $kT=30$ keV, the MACS value for ${}^{79}$Br 638$ pm$64 mb is in good agreement with the KADoNiS recommended value. By contrast, the value of 293$ pm$29 mb for ${}^{81}$Br is substantially higher than those of the evaluated database and the KADoNiS recommended value.

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Pulse-shaping method for real-time neutron/gamma discrimination at low sampling rates

分类： 物理学 >> 核物理学 提交时间： 2023-09-11

Jiaxin, Li Huiliang, Hou Yuefeng, Huang Maosong, Cheng Zhimin, Dai

摘要： The NaI:Tl scintillator is an innovative material for dual-gamma-ray and neutron detection with a low 6Li concentration. To achieve real-time n/ discrimination, a zero-crossing time comparison algorithm based on trapezoidal pulse shaping was developed. The algorithm can operate efficiently at low sampling rates and was implemented on a single-probe portable digital n/ discriminator based on a feld-programmable gate array (FPGA). The discriminator and NaI:Tl,6Li detector were tested in a neutron-gamma mixed field produced by an 241Am-Be neutron source to evaluate the performance of the algorithm. The Figure of Merits (FoM) was measured as 2.88 at a sampling rate of 50 MHz, indicating that the discriminator with its embedded algorithm has a promising n/ discrimination capability. Efficient discrimination at sampling rates of 40 and 25 MHz demonstrates that the capability of this method is not limited by low sampling rates.

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Discrimination of pp solar neutrinos and 14C double pile-up events in a large-scale LS detector

分类： 核科学技术 >> 核科学与技术 提交时间： 2023-08-27

Chen, Guoming Zhang, Xin Yu, Zeyuan Zhang, Siyuan Xu, Yu Wu, Wenjie Wang, Yaoguang Huang, Yongbo

摘要： As a unique probe, precision measurement of textit{pp} solar neutrinos is important for studying the Sun's energy mechanism, monitoring thermodynamic equilibrium, and studying neutrino oscillation in the vacuum-dominated region. For a large-scale liquid scintillator detector, one bottleneck for textit{pp} solar neutrino detection comes from pile-up events of intrinsic $^{14}$C decays. This paper presents a few approaches to discriminate textit{pp} solar neutrinos and $^{14}$C pile-up events by considering the difference in their time and spatial distributions. In this work, a Geant4-based Monte Carlo simulation is constructed. Then multivariate analysis and deep learning technology were adopted respectively to investigate the capability of $^{14}$C pile-up reduction. As a result, the BDTG model and VGG network showed good performance in discriminating textit{pp} solar neutrinos and $^{14}$C double pile-up events. hl{At the $^{14}$C concentration assumption $5 times10^{-18} g/g$,} their signal significance can achieve 10.3 and 15.6 using only one day of statistics. In this case, the signal efficiency is 51.1 % for discrimination using the BDTG model when rejecting 99.18 % $^{14}$C double pile-up events, and the signal efficiency is 42.7 % for the case using the VGG network when rejecting 99.81 % $^{14}$C double pile-up events.

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Development of Short Prototype of Dual Aperture Quadrupole Magnet for CEPC Ring

分类： 物理学 >> 核物理学 提交时间： 2023-06-16

Yang, Mei Chen, Fusn

摘要： Abstract Main quadrupole magnets are critical for the Circular Electron and Positron Collider (CEPC), and are specifically designed as dual aperture quadrupole (DAQ) magnets. However, the field crosstalk between the two apertures presents challenges. As the CEPC will work at four beam energies of Z, W, Higgs and ttbar mode, the DAQ magnets will operate at four field gradients spanning from 3.18 to 12.63 T/m. The first short quadrupole magnet prototype with the bore diameter of 76 mm and magnetic length of 1.0 m revealed the problems of large magnetic field harmonics and a magnetic center shift within the beam energy range. Accordingly, a compensation method was proposed in this work to solve the field crosstalk effect. By adjusting the gap height at the middle of the two apertures, the field harmonics and magnetic center shift are significantly reduced. After optimization, the short prototype was modified using a new scheme. The field simulations are validated from the magnetic measurement results. Further, the multipole field meets the requirements at the four beam energies. The detailed magnetic field optimization, field harmonics adjustment, and measurement results are presented herein.

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Combination of a reaction cell and an ultra-high vacuum system for the in situ preparation and characterization of a model catalyst

分类： 核科学技术 >> 辐射物理与技术 提交时间： 2023-06-01

Yijing Zang Shucheng Shi Yong Han Hui Zhang Weijia Wang Peng Liu Mao Ye Zhi Liu

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Commissioning and Operation of the Cryostat for 3W1 SC Wiggler

分类： 物理学 >> 核物理学 提交时间： 2023-05-31

Xu,Miaofu Zhang,Xiangzhen Ye,Rui Wang,Jincan Bian,Xiaojuan Gao,Yao Li,Minxian Chen,Fusan Yang,Xiaochen Ge,Rui

摘要： A 3W1 superconducting wiggler (SCW) with the pole gap of 68 mm was successfully tested and installed in a BEPC II storage ring in November, 2019. The goal of zero liquid helium consumption was achieved, and the cryogenic system exhibited a 12% residual cooling capacity (approximately 0.69 W @4.2K). The 3W1-SCW was set to operate at 2.49 T and has been operating for more than seven months. Three instances of magnet quenching occurred during the normal operation. The evaporated helium gas can be recycled to the helium gas recycling system when the pressure in the helium tank is higher than the parameter value（the setpoint of the presssur value is 1.2 bara）. The cryogenic system can be recovered within 4 h if sufficient liquid helium is available to inject into the cryostat.

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GOAT: a simulation code for high intensity beams

分类： 物理学 >> 核物理学 提交时间： 2023-05-31

Lei Wang Jiancheng Yang Mingxuan Chang Fu Ma

摘要： A simulation code, GOAT, is developed to simulate single-bunch intensity-dependent effects and their interplay in the proton ring (pRing) of the Electron-Ion Collider in China (EicC) project. GOAT is a scalable and portable macroparticle tracking code written in Python and coded by object-oriented programming technology. It allows for transverse and longitudinal tracking, including impedance, space charge effect, electron cloud effect, and beam-beam interaction. In this paper, physical models and numerical approaches for the four types of high-intensity effects, together with the benchmark results obtained through other simulation codes or theories, are presented and discussed. In addition, a numerical application of the cross-talk simulation between the beam-beam interaction and transverse impedance is shown, and a dipole instability is observed below the respective instability threshold. Different mitigation measures implemented in the code are used to suppress the instability. The flexibility, completeness, and advancement demonstrate that GOAT is a powerful tool for beam dynamics studies in the EicC project or other high-intensity accelerators.

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Assessment of the induced radioactivity in the treatment room of the heavy‑ion medical machine in Wuwei using PHITS

分类： 核科学技术 >> 辐射物理与技术 提交时间： 2023-05-31

Luo, Ying Hunag, Shengcong Zhang, Hui Mao, Haijun Li, Qiang Dai, Zhongying

摘要： Carbon-ion radiotherapy (CIRT) offers unique physical and biological advantages over photon radiotherapy. However, somematerials and devices in the CIRT treatment room become radioactive under bombardment by therapeutic carbon-ion beamsdue to nuclear reactions, thereby leading to possible radiation hazards to medical staff and additional and unwanted dosesto patients. This study assessed the level of induced radioactivity in the treatment room of the Heavy-Ion Medical Machine(HIMM) in Wuwei. Monte Carlo simulations using PHITS were performed for a conservative case under the conditions ofmaximum beam energy and intensity provided by the HIMM facility. The geometry and configuration of Treatment Room2 of the HIMM facility in Wuwei were adopted. We evaluated the activation of air, the phantom, and the components ofthe beamline, such as the primary collimator (PC), ridge filter (RF), and multileaf collimator (MLC). For air activation,we calculated the medical staff immersion external exposure and inhalation internal exposure caused by the correspondingradionuclides. For phantom activation, we estimated the additional dose to the patients family members owing to secondaryphotons after treatment. In addition, the exemption or non-exemption of the component material activation was assessed.The results showed that external radiation caused by air activation was the main source of the annual effective dose atapproximately 0.5mSv/y. The induced radioactivity exposure to family members of a patient after CIRT was approximately40Sv, sufficiently lower than the public dose limit of 1mSv/a. The induced radioactivity of the PC, RF, and MLC was allabove the exempt levels after the devices were retired, whereas the induced radioactivity of the RS and compensator couldreach the exempt levels after one patient session. Our study indicated that medical staff engaged in CIRT should stay awayfrom the high-dose-rate area of induced radioactivity along the beam direction, shorten the residence time in the treatmentroom as much as possible, and store the activated components in isolation after the equipment is out of use. Thus, this studyprovides guidance for accurately assessing the level of induced radioactivity in the treatment room for CIRT.

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On Two Factors Affecting the Efficiency of MILP Models in Automated Cryptanalyses

分类： 数学 >> 应用数学 提交时间： 2023-02-15

Xu, Shengyuan Feng, Xiutao Wang, Yongxing

摘要： In recent years, mixed integer linear programming (MILP, in short) gradually becomes a popular tool of automated cryptanalyses in symmetric ciphers, which can be used to search differential characteristics and linear approximations with high probability/correlation. A key problem in the MILP method is how to build a proper model that can be solved efficiently in the MILP solvers like Gurobi or Cplex. It is known that a MILP problem is NP-hard, and the numbers of variables and inequalities are two important measures of its scale and time complexity. Whilst the solution space and the variables in many MILP models built for symmetric cryptanalyses are fixed without introducing dummy variables, the cardinality, i.e., the number of inequalities, is a main factor that might affect the runtime of MILP models. We notice that the norm of a MILP model, i.e., the maximal absolute value of all coefficients in its inequalities, is also an important factor affecting its runtime. In this work we will illustrate the effects of two parameters cardinality and norm of inequalities on the runtime of Gurobi by a large number of cryptanalysis experiments. Here we choose the popular MILP solver Gurobi and view it a black box, construct a large number of MILP models with different cardinalities or norms by means of differential analyses and impossible differential analyses for some classic block ciphers with SPN structure, and observe their runtimes in Gurobi. As a result, our experiments show that although minimizing the number of inequalities and the norm of coefficients might not always minimize the runtime, it is still a better choice in most situations.

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