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Orthogonal die random measures, primes, and applications

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arXiv 2020年

作者： Bastian, Caleb Deen Rempala, Grzegorz A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Massive Dynamics PrincetonNJ08542 United States Department of Mathematics Ohio State University ColumbusOH43210 United States Division of Biostatistics Ohio State University ColumbusOH43210 United States

We show that the sequence of thinned uniform random counting measures converges weakly to the Poisson random measure. We call such measures ‘orthogonal dice’ due to their natural connection with certain counting problems and link the sizes of orthogonal dice with the primes by constructing the largest known prime orthogonal die. We give many examples of possible use of the construct of orthogonal dice in various areas of applications including gambling, cosmology, random matrices, approximation theory and circuits. The gambling example reveals for instance that fair six-sided die numbered {1, 2, 3, 4, 5, 6} generate negative covariance in point representations of hands across players, in contrast to seven-sided dice numbered {1, 2, 3, 4, 5, 6, 7} that generate zero covariance and are orthogonal. The cosmology example suggests that a ‘supermassive’ orthogonal die underlies the galaxy point patterns of the Universe. The random matrix application reveals that the variance of the spectral gap of the Gaussian orthogonal ensemble exhibits non-monotone scaling with thinning for the Dirac (empirical) random measure, in contrast to the orthogonal dice where the spectral gap variance is monotone. Finally, the approximation application shows that the discrete Legendre polynomials converge to the Charlier polynomials in Lp for integers p ≥ 1 whereas the electronic circuit/shot noise application identifies electric current as the Ornstein-Uhlenbeck process driven by an orthogonal die random *** Codes 60G57, 60G55, 60F05 Copyright © 2020, The Authors. All rights reserved.

关键词： Poisson distribution

Temperature-Induced Lifshitz Transition and Possible Excitonic Instability in ZrSiSe

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Physical Review Letters 2020年第23期124卷 236601-236601页

作者： F. C. Chen Y. Fei S. J. Li Q. Wang X. Luo J. Yan W. J. Lu P. Tong W. H. Song X. B. Zhu L. Zhang H. B. Zhou F. W. Zheng P. Zhang A. L. Lichtenstein M. I. Katsnelson Y. Yin Ning Hao Y. P. Sun Key Laboratory of Materials Physics Institute of Solid State Physics HFIPS Chinese Academy of Sciences Hefei 230031 China University of Science and Technology of China Hefei 230026 China Department of Physics Zhejiang University Hangzhou 310027 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions High Magnetic Field Laboratory HFIPS Chinese Academy of Sciences Hefei 230031 China College of Mathematics and Physics Beijing University of Chemical Technology Beijing 100029 China School of Physics and Physical Engineering Qufu Normal University Qufu 273165 China Institute for Theoretical Physics University Hamburg Jungiusstrasse 9 D-20355 Hamburg Germany Theoretical Physics and Applied Mathematics Department Ural Federal University Mira Street 19 620002 Ekaterinburg Russia Institute for Molecules and Materials Radboud University Heijendaalseweg 135 NL-6525AJ Nijmegen The Netherlands Collaborative Innovation Center of Microstructures Nanjing University Nanjing 210093 China

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy (spectroscopy) [STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a V-shaped dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures.

关键词： Single crystal materials First-principles calculations Scanning tunneling spectroscopy

CEPC Technical Design Report

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Radiation Detection Technology and Methods 2024年第1期8卷 I0003-I0016,1-1091页

作者： Waleed Abdallah Tiago Carlos Adorno de Freitas Konstantin Afanaciev Shakeel Ahmad Ijaz Ahmed Xiaocong Ai Abid Aleem Wolfgang Altmannshofer Fabio Alves Weiming An Rui An Daniele Paolo Anderle Stefan Antusch Yasuo Arai Andrej Arbuzov Abdesslam Arhrib Mustafa Ashry Sha Bai Yu Bai Yang Bai Vipul Bairathi Csaba Balazs Philip Bambade Yong Ban Tripamo Bandyopadhyay Shou-Shan Bao Desmond P.Barber Ayse Bat Varvara Batozskaya Subash Chandra Behera Alexander Belyaev Michele Bertucci Xiao-Jun Bi Yuanjie Bi Tianjian Bian Fabrizio Bianchi Thomas Biekotter Michela Biglietti Shalva Bilanishvili Deng Binglin Denis Bodrov Anton Bogomyagkov Serge Bondarenko Stewart Boogert Maarten Boonekamp Marcello Borri Angelo Bosotti Vincent Boudry Mohammed Boukidi Igor Boyko Ivanka Bozovic Giuseppe Bozzi Jean-Claude Brient Anastasiia Budzinskaya Masroor Bukhari Vladimir Bytev Giacomo Cacciapaglia Hua Cai Wenyong Cai Wujun Cai Yijian Cai Yizhou Cai Yuchen Cai Haiying Cai Huacheng Cai Lorenzo Calibbi Junsong Cang Guofu Cao Jianshe Cao Antoine Chance Xuejun Chang Yue Chang Zhe Chang Xinyuan Chang Wei Chao Auttakit Chatrabhuti Yimin Che Yuzhi Che Bin Chen Danping Chen Fuqing Chen Fusan Chen Gang Chen Guoming Chen Hua-Xing Chen Huirun Chen Jinhui Chen Ji-Yuan Chen Kai Chen Mali Chen Mingjun Chen Mingshui Chen Ning Chen Shanhong Chen Shanzhen Chen Shao-Long Chen Shaomin Chen Shiqiang Chen Tianlu Chen Wei Chen Xiang Chen Xiaoyu Chen Xin Chen Xun Chen Xurong Chen Ye Chen Ying Chen Yukai Chen Zelin Chen Zilin Chen Gang Chen Boping Chen Chunhui Chen Hok Chuen Cheng Huajie Cheng Shan Cheng Tongguang Cheng Yunlong Chi Pietro Chimenti Wen Han Chiu Guk Cho Ming-Chung Chu Xiaotong Chu Ziliang Chu Guglielmo Coloretti Andreas Crivellin Hanhua Cui Xiaohao Cui Zhaoyuan Cui Brunella D'Anzi Ling-Yun Dai Xinchen Dai Xuwen Dai Antonio De Maria Nicola De Filippis Christophe De La Taille Francesca De Mori Chiara De Sio Elisa Del Core Shuangxue Deng Wei-Tian Deng Zhi Deng Ziyan Deng Bhupal Dev Tang Dewen Biagio Di Micco Ran Ding Siqin Dingl Yadong Ding Haiyi Dong Jianin AGH University of Science and Technology Faculty of Physics and Applied Computer ScienceKrakow Anhui University HefeiAnhui Applied Physics Department Federal Urdu University of ArtsScience and TechnologyIslamabad Banaras Hindu University Institute of ScienceVaranasi Bandirma Onyedi Eylul University Bandirma Beihang University Beijing Beijing Computational Science Research Center Beijing Beijing Conveyi LTD Beijing Beijing Glass Research Institute Co. LtdBeijing Beijing Institute of Technology Beijing Beijing Normal University Beijing Brown University ProvidenceRI Budker Institute of Nuclear Physics Novosibirsk Cadi Ayyad University Laboratory of Fundamental and Applied PhysicsPolydisciplinary FacultyMarrakech Cairo University Giza Center for Theory and Computation National Tsing Hua UniversityHsinchu Central China Normal University WuhanHubei Central South University ChangshaHunan Centro de Fisica Teorica de Particulas Universidade Tecnica de LisboaLisboa Chengdu KaitengSifang Digital Radio&TV Equipment Co. LtdChengduSichuan China academy of engineering physics MianyangSichuan China building materials academy Beijing China Center of Advanced Science and Technology Beijing China Institute of Atomic Energy Beijing China Jiliang University HangzhouZhejiang China Nuclear Instrument CO. LTDBeijing China University of Geosciences Beijing China University of Geosciences WuhanHubei China University of Mining and Technology XuzhouJiangsu China West Normal University NanchongSichuan Chongqing University Department of PhysicsChongqing Chulalongkorn University Bangkok City University of Hong Kong Department of PhysicsHong Kong Cockcroft Institute Daresbury Cornell University IthacaNY CPPM(AMU/IPhU&CNRS/INP) Marseille Dalian Minzu University DalianLiaoning Dalian University of Technology Department of PhysicsDalian Deutsches Elektronen-Synchrotron DESY Hamburg Dzhelepov Laboratory of Nuclear Problems of Joint Institute for Nuclear Research(DLNP JINR) Dubna East China University Of Science And Technol

The Circular Electron Positron Collider(CEPC)is a large scientific project initiated and hosted by China,fostered through extensive collaboration with international *** complex comprises four accelerators:a 30 GeV Linac,a 1.1 GeV Damping Ring,a Booster capable of achieving energies up to 180 GeV,and a Collider operating at varying energy modes(Z,W,H,and tt).The Linac and Damping Ring are situated on the surface,while the subterranean Booster and Collider are housed in a 100 km circumference underground tunnel,strategically accommodating future expansion with provisions for a potential Super Proton Proton Collider(SPPC).The CEPC primarily serves as a Higgs *** its baseline design with synchrotron radiation(SR)power of 30 MW per beam,it can achieve a luminosity of 5×10^(34)cm^(-2)s^(-1)per interaction point(IP),resulting in an integrated luminosity of 13 ab^(-1)for two IPs over a decade,producing 2.6 million Higgs *** the SR power to 50 MW per beam expands the CEPC's capability to generate 4.3 million Higgs bosons,facilitating precise measurements of Higgs coupling at sub-percent levels,exceeding the precision expected from the HL-LHC by an order of *** Technical Design Report(TDR)follows the Preliminary Conceptual Design Report(Pre-CDR,2015)and the Conceptual Design Report(CDR,2018),comprehensively detailing the machine's layout,performance metrics,physical design and analysis,technical systems design,R&D and prototyping efforts,and associated civil engineering ***,it includes a cost estimate and a preliminary construction timeline,establishing a framework for forthcoming engineering design phase and site selection *** is anticipated to begin around 2027-2028,pending government approval,with an estimated duration of 8 *** commencement of experiments and data collection could potentially be initiated in the mid-2030s.

关键词： initiated exceeding precise

Collective neutrino oscillations in three flavors on qubit and qutrit processors

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Physical Review D 2025年第10期111卷 103054-103054页

作者： Luca Spagnoli Noah Goss Alessandro Roggero Ermal Rrapaj Michael J. Cervia Amol V. Patwardhan Ravi K. Naik A. Baha Balantekin Ed Younis David I. Santiago Irfan Siddiqi Sheakha Aldaihan Physics Department University of Trento Via Sommarive 14 I-38123 Trento Italy INFN-TIFPA Trento Institute of Fundamental Physics and Applications Via Sommarive 14 I-38123 Trento Italy Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA INFN-TIFPA Trento Institute of Fundamental Physics and Applications Trento Italy National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA RIKEN iTHEMS Wako Saitama 351-0198 Japan Department of Physics University of Washington Seattle Washington 98195 USA School of Physics and Astronomy University of Minnesota Minneapolis Minnesota 55455 USA Department of Physics New York Institute of Technology New York New York 10023 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA Department of Physics and Astronomy College of Science King Saud University Riyadh 11451 Saudi Arabia

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.

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Boundary Layers of Accretion Discs: Wave-Driven Transport and Disc Evolution

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arXiv 2021年

作者： Coleman, Matthew S.B. Rafikov, Roman R. Philippov, Alexander A. Institute for Advanced Study Einstein Drive PrincetonNJ08540 United States Department of Astrophysical Sciences Princeton University 4 Ivy Lane PrincetonNJ08540 United States Centre for Mathematical Sciences Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Center for Computational Astrophysics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States

Astrophysical objects possessing a material surface (white dwarfs, young stars, etc.) may accrete gas from the disc through the so-called surface boundary layer (BL), in which the angular velocity of the accreting gas experiences a sharp drop. Acoustic waves excited by the supersonic shear in the BL play an important role in mediating the angular momentum and mass transport through that region. Here we examine the characteristics of the angular momentum transport produced by the different types of wave modes emerging in the inner disc, using the results of a large suite of hydrodynamic simulations of the BLs. We provide a comparative analysis of the transport properties of different modes across the range of relevant disc parameters. In particular, we identify the types of modes which are responsible for the mass accretion onto the central object. We find the correlated perturbations of surface density and radial velocity to provide an important contribution to the mass accretion rate. Although the wave-driven transport is intrinsically non-local, we do observe a clear correlation between the angular momentum flux injected into the disc by the waves and the mass accretion rate through the BL. We find the efficiency of angular momentum transport (normalized by thermal pressure) to be a weak function of the flow Mach number. We also quantify the wave-driven evolution of the inner disc, in particular the modification of the angular frequency profile in the disc. Our results pave the way for understanding wave-mediated transport in future three-dimensional, magnetohydrodynamic studies of the BLs. © 2021, CC BY.

关键词： Angular momentum

DeepFlame: A deep learning empowered open-source platform for reacting flow simulations

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arXiv 2022年

作者： Mao, Runze Lin, Minqi Zhang, Yan Zhang, Tianhan John Xu, Zhi-Qin Chen, Zhi X. State Key Laboratory of Turbulence and Complex Systems Aeronautics and Astronautics College of Engineering Peking University Beijing100871 China Ai for Science Institute Beijing100080 China Caep Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mechanics and Aerospace Engineering SUSTech Shenzhen518055 China Institute of Natural Sciences School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China MOE-LSC Qing Yuan Research Institute Shanghai Jiao Tong University Shanghai200240 China

Recent developments in deep learning have brought many inspirations for the scientific computing community and it is perceived as a promising method in accelerating the computationally demanding reacting flow simulations. In this work, we introduce DeepFlame, an open-source C++ platform with the capabilities of utilising machine learning algorithms and pre-trained models to solve for reactive flows. We combine the individual strengths of the computational fluid dynamics library OpenFOAM, machine learning framework Torch, and chemical kinetics program Cantera. The complexity of cross-library function and data interfacing (the core of DeepFlame) is minimised to achieve a simple and clear workflow for code maintenance, extension and upgrading. As a demonstration, we apply our recent work on deep learning for predicting chemical kinetics (Zhang et al. Combust. Flame vol. 245 pp. 112319, 2022) to highlight the potential of machine learning in accelerating reacting flow simulation. A thorough code validation is conducted via a broad range of canonical cases to assess its accuracy and efficiency. The results demonstrate that the convection-diffusion-reaction algorithms implemented in DeepFlame are robust and accurate for both steady-state and transient processes. In addition, a number of methods aiming to further improve the computational efficiency, e.g. dynamic load balancing and adaptive mesh refinement, are explored. Their performances are also evaluated and reported. With the deep learning method implemented in this work, a speed-up of two orders of magnitude is achieved in a simple hydrogen ignition case when performed on a medium-end graphics processing unit (GPU). Further gain in computational efficiency is expected for hydrocarbon and other complex fuels. A similar level of acceleration is obtained on an AI-specific chip - deep computing unit (DCU), highlighting the potential of DeepFlame in leveraging the next-generation computing architecture and hardware. © 202

关键词： Graphics processing unit

Boundary layers of accretion disks: Discovery of vortex-driven modes and other waves

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arXiv 2021年

Disk accretion onto weakly magnetized objects possessing a material surface must proceed via the so-called boundary layer (BL)-a region at the inner edge of the disk, in which the velocity of accreting material abruptly decreases from its Keplerian value. Supersonic shear arising in the BL is known to be conducive to excitation of acoustic waves that propagate into both the accretor and the disk, enabling angular momentum and mass transport across the BL. We carry out a numerical exploration of different wave modes that operate near the BL, focusing on their morphological characteristics in the innermost parts of accretion disk. Using a large suite of simulations covering a broad range of Mach numbers (of the supersonic shear flow in the BL), we provide accurate characterization of the different types of modes, verifying their properties against analytical results, when available. We discover new types of modes, in particular, global spiral density waves launched by vortices forming in the disk near the BL as a result of the Rossby wave instability;this instability is triggered by the vortensity production in that region caused by the nonlinear damping of acoustic waves. Azimuthal wavenumbers of the dominant modes that we observe appear to increase monotonically with the Mach number of the runs, but a particular mix of modes found in a simulation is mildly stochastic. Our results provide a basis for better understanding of the angular momentum and mass transport across the BL as well as the emission variability in accreting objects. © 2021, CC BY.

关键词： Angular momentum

Asymmetric Loop Spectra and Unbroken Phase Protection due to Nonlinearities in PT-Symmetric Periodic Potentials

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Physical Review Letters 2021年第3期127卷 034101-034101页

作者： Yongping Zhang Zhu Chen Biao Wu Thomas Busch Vladimir V. Konotop International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Department of Physics Shanghai University Shanghai 200444 China Institute of Applied Physics and Computational Mathematics Beijing 100094 China International Center for Quantum Materials School of Physics Peking University Beijing 100871 China Wilczek Quantum Center School of Physics and Astronomy Shanghai Jiao Tong University Shanghai 200240 China Collaborative Innovation Center of Quantum Matter Beijing 100871 China Quantum Systems Unit Okinawa Institute of Science and Technology Graduate University Okinawa 904-0495 Japan Centro de Física Teórica e Computacional and Departamento de Física Faculdade de Ciências Universidade de Lisboa Campo Grande 2 Edifício C8 Lisboa 1749-016 Portugal

We demonstrate that the interplay between a nonlinearity and PT symmetry in a periodic potential results in peculiar features of nonlinear periodic solutions. These include thresholdless symmetry breaking and asymmetric (multi-)loop structures of the nonlinear Bloch spectrum, persistence of unbroken PT symmetry even after the gap is closed, nonmonotonic dependence of the PT phase transition on the defocusing nonlinearity, and enhanced stability of the nonlinear states corresponding to the loop structures. The asymmetry and the loop structure of the spectrum are explained within the framework of a two-mode approximation and an effective potential theory and are validated numerically.

关键词： Nonlinear beam dynamics Nonlinear optics Nonlinear waves PT-symmetry

A deep learning-based ODE solver for chemical kinetics

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arXiv 2020年

作者： Zhang, Tianhan Zhang, Yaoyu Weinan, E. Ju, Yiguang Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Qing Yuan Research Institute Shanghai Jiao Tong University Shanghai200240 China Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to solve stiff ordinary differential equation systems. The homogeneous autoignition of DME/air mixture, including 54 species, is adopted as an example to illustrate the validity and accuracy of the algorithm. The training and testing datasets cover a wide range of temperature, pressure, and mixture conditions between 750 – 1200 K, 30 – 50 atm, and equivalence ratio = 0.7 – 1.5. Both the first-stage low-temperature ignition (LTI) and the second-stage high-temperature ignition (HTI) are considered. The methodology highlights the importance of the adaptive data sampling techniques, power transform preprocessing, and binary deep neural network (DNN) design. By using the adaptive random samplings and appropriate power transforms, smooth submanifolds in the state vector phase space are observed, on which two three-layer DNNs can be appropriately trained. The neural networks are end-to-end, which predict temporal gradients of the state vectors directly. The results show that temporal evolutions predicted by DNN agree well with traditional numerical methods in all state vector dimensions, including temperature, pressure, and species concentrations. Besides, the ignition delay time differences are within 1%. At the same time, the CPU time is reduced by more than 20 times and 200 times compared with the HMTS and VODE method, respectively. The current work demonstrates the enormous potential of applying the deep learning algorithm in chemical kinetics and combustion modeling. © 2020, CC BY.

关键词： Numerical methods