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Critical slowing down and hyperuniformity on approach to jamming

Physical Review E 2016年第1期94卷 012902-012902页

作者： Steven Atkinson Ge Zhang Adam B. Hopkins Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called “pressure-leak” test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N≈103 bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of “critical slowing down” as the packing's collective rearrangements in configuration space become locally confined by high-dimensional “bottlenecks” from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for d

关键词： Granular materials Packing & jamming problems

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Static structural signatures of nearly jammed disordered and ordered hard-sphere packings: Direct correlation function

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Physical Review E 2016年第3期94卷 032902-032902页

作者： Steven Atkinson Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed “hyperuniformity”) has paved the way for the analysis of jamming as an “inverted critical point” in which the direct correlation function c(r), rather than the total correlation function h(r), diverges. We expand on the notion that c(r) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the nth derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c(r) with regards to singularities it inherits from h(r). These relations provide a concrete means of identifying features that must be expressed in c(r) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c(r)∝−1/r as r→0 that accompanies the formation of the delta function at c(D) that indicates the formation of contacts in all cases, and show that this scaling behavior is,

关键词： Jamming

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Multimuons in cosmic-ray events as seen in ALICE at the LHC

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Journal of Cosmology and Astroparticle Physics 2025年第4期2025卷 009-009页

作者： Acharya, S. Agarwal, A. Aglieri Rinella, G. Aglietta, L. Agnello, M. Agrawal, N. Ahammed, Z. Ahmad, S. Ahn, S.U. Ahuja, I. Akindinov, A. Akishina, V. Al-Turany, M. Aleksandrov, D. Alessandro, B. Alfanda, H.M. Alfaro Molina, R. Ali, B. Alici, A. Alizadehvandchali, N. Alkin, A. Alme, J. Alocco, G. Alt, T. Altamura, A.R. Altsybeev, I. Alvarado, J.R. Alvarez, C.O.R. Anaam, M.N. Andrei, C. Andreou, N. Andronic, A. Andronov, E. Anguelov, V. Antinori, F. Antonioli, P. Apadula, N. Aphecetche, L. Appelshäuser, H. Arata, C. Arcelli, S. Arnaldi, R. Arneiro, J.G.M.C.A. Arsene, I.C. Arslandok, M. Augustinus, A. Averbeck, R. Averyanov, D. Azmi, M.D. Baba, H. Badalà, A. Bae, J. Bae, Y. Baek, Y.W. Bai, X. Bailhache, R. Bailung, Y. Bala, R. Balbino, A. Baldisseri, A. Balis, B. Banoo, Z. Barbasova, V. Barile, F. Barioglio, L. Barlou, M. Barman, B. Barnaföldi, G.G. Barnby, L.S. Barreau, E. Barret, V. Barreto, L. Bartels, C. Barth, K. Bartsch, E. Bastid, N. Basu, S. Batigne, G. Battistini, D. Batyunya, B. Bauri, D. Bazo Alba, J.L. Bearden, I.G. Beattie, C. Becht, P. Behera, D. Belikov, I. Bell Hechavarria, A.D.C. Bellini, F. Bellwied, R. Belokurova, S. Beltran, L.G.E. Beltran, Y.A.V. Bencedi, G. Bensaoula, A. Beole, S. Berdnikov, Y. Berdnikova, A. Bergmann, L. Besoiu, M.G. Betev, L. Bhaduri, P.P. Bhasin, A. Bhattacharjee, B. Bianchi, L. Bielčík, J. Bielčíková, J. Bigot, A.P. Bilandzic, A. Biro, G. Biswas, S. Bize, N. Blair, J.T. Blau, D. Blidaru, M.B. Bluhme, N. Blume, C. Bock, F. Bodova, T. Bok, J. Boldizsár, L. Bombara, M. Bond, P.M. Bonomi, G. Borel, H. Borissov, A. Borquez Carcamo, A.G. Botta, E. Bouziani, Y.E.M. Bratrud, L. Braun-Munzinger, P. Bregant, M. Broz, M. Bruno, G.E. Buchakchiev, V.D. Buckland, M.D. Budnikov, D. Buesching, H. Bufalino, S. Buhler, P. Burmasov, N. Buthelezi, Z. Bylinkin, A. Bysiak, S.A. Cabanillas Noris, J.C. Cabrera, M.F.T. Caines, H. Caliva, A. Calvo Villar, E. Camacho, J.M.M. Camerini, P. Canedo, F.D.M. Cantway, S.L. Carabas, M. Carballo, A.A. Carnesecchi, F. Caron, R. Carvalho, L.A.D. Castillo Castel A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation Yerevan Armenia AGH University of Krakow Cracow Poland Bogolyubov Institute for Theoretical Physics National Academy of Sciences of Ukraine Kiev Ukraine Bose Institute Department of Physics Centre for Astroparticle Physics and Space Science (CAPSS) Kolkata India California Polytechnic State University San Luis Obispo CA United States Central China Normal University Wuhan China Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN) Havana Cuba Centro de Investigación y de Estudios Avanzados (CINVESTAV) Mérida Mexico City Mexico Chicago State University Chicago IL United States China Institute of Atomic Energy Beijing China China University of Geosciences Wuhan China Chungbuk National University Cheongju South Korea Comenius University Bratislava Faculty of Mathematics Physics and Informatics Bratislava Slovakia Creighton University Omaha NE United States Department of Physics Aligarh Muslim University Aligarh India Department of Physics Pusan National University Pusan South Korea Department of Physics Sejong University Seoul South Korea Department of Physics University of California Berkeley CA United States Department of Physics University of Oslo Oslo Norway Department of Physics and Technology University of Bergen Bergen Norway Dipartimento di Fisica Università di Pavia Pavia Italy Dipartimento di Fisica dell’Università Sezione INFN Cagliari Italy Dipartimento di Fisica dell’Università Sezione INFN Trieste Italy Dipartimento di Fisica dell’Università Sezione INFN Turin Italy Dipartimento di Fisica e Astronomia dell’Università Sezione INFN Bologna Italy Dipartimento di Fisica e Astronomia dell’Università Sezione INFN Catania Italy Dipartimento di Fisica e Astronomia dell’Università Sezione INFN Padova Italy Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università Gruppo Collegato INFN Salerno Italy Dipartimento DISAT del Politecnico Sezione

ALICE is a large experiment at the CERN Large Hadron Collider. Located 52 meters underground, its detectors are suitable to measure muons produced by cosmic-ray interactions in the atmosphere. In this paper, the studies of the cosmic muons registered by ALICE during Run 2 (2015–2018) are described. The analysis is limited to multimuon events defined as events with more than four detected muons (N_µ > 4) and in the zenith angle range 0^◦ < θ < 50^◦. The results are compared with Monte Carlo simulations using three of the main hadronic interaction models describing the air shower development in the atmosphere: QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d. The interval of the primary cosmic-ray energy involved in the measured muon multiplicity distribution is about 4×10¹⁵ < E_prim < 6×10¹⁶ eV. In this interval none of the three models is able to describe precisely the trend of the composition of cosmic rays as the energy increases. However, QGSJET-II-04 is found to be the only model capable of reproducing reasonably well the muon multiplicity distribution, assuming a heavy composition of the primary cosmic rays over the whole energy range, while SIBYLL 2.3d and EPOS-LHC underpredict the number of muons in a large interval of multiplicity by more than 20% and 30%, respectively. The rate of high muon multiplicity events (N_µ > 100) obtained with QGSJET-II-04 and SIBYLL 2.3d is compatible with the data, while EPOS-LHC produces a significantly lower rate (55% of the measured rate). For both QGSJET-II-04 and SIBYLL 2.3d, the rate is close to the data when the composition is assumed to be dominated by heavy elements, an outcome compatible with the average energy E_prim ∼ 10¹⁷ eV of these events. This result places significant constraints on more exotic production mechanisms. © 2025 The Author(s).

关键词： cosmic ray experiments cosmic rays detectors

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A multi-scale Gaussian beam parametrix for the wave equation: The Dirichlet boundary value problem.

arXiv

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arXiv 2017年

作者： Berra, Michele de Hoop, Maarten V. Romero, José Luis corso Duca degli Abruzzi 24 Torino10129 Italy Department of Computational and Applied Mathematics Rice University 6100 Main MS-134 HoustonTX77005 United States Acoustics Research Institute Austrian Academy of Sciences Wohllebengasse 12-14 Vienna1040 Austria

We present a construction of a multi-scale Gaussian beam parametrix for the Dirichlet boundary value problem associated with the wave equation, and study its convergence rate to the true solution in the highly oscillatory regime. The construction elaborates on the wave-atom parametrix of Bao, Qian, Ying, and Zhang and extends to a multi-scale setting the technique of Gaussian beam propagation from a boundary of Katchalov, Kurylev and Lassas.35L05, 35L20, 35S05, 42C15.35L05, 35L20, 35S05, 42C15 Copyright © 2017, The Authors. All rights reserved.

关键词： Gaussian beams

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Basic results on Crisp boolean petri nets 1

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1st International Conference on Modern Mathematical Methods and High Performance Computing in Science and Technology, M3HPCST 2015

作者： Singh, Gajendra Pratap Kansal, Sangita School of Computational and Integrative Sciences Jawaharlal Nehru University New Mehrauli Road New Delhi110067 India Department of Applied Mathematics Delhi Technological University New Delhi110042 India

ISBN: (数字)9789811014543

ISBN: (纸本)9789811014536

The concept of Petri net as a discrete event-driven dynamical system was invented by Carl Adam Petri in his doctoral thesis ‘Communication with Automata’ in 1962. Petri nets are one of the best defined approach to modeling of discrete and concurrent systems. The dynamics of Petri nets represent the long-term behavior of the modeled system. Petri nets combine mathematical concepts with a pictorial representation of the dynamical behavior of the modeled systems. A Petri net is a bipartite directed graph consisting of two type of nodes, namely, place nodes and transition nodes. Directed arcs connect places to transitions and transitions to places to represent flow relation. In this paper, we present some basic results on 1-safe Petri net that generates every binary n-vector exactly once as marking vectors in its reachability tree, known as crisp Boolean Petri net. These results can be used for characterizing crisp Boolean Petri nets. © Springer Science+Business Media Singapore 2016.

关键词： Petri nets

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Probability current in zero-spin relativistic quantum mechanics

arXiv

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arXiv 2017年

作者： Fülöp, Tamás Matolcsi, Tamás Department of Energy Engineering Budapest University of Technology and Economics 3 Műegyetem rkp. Budapest1111 Hungary Department of Applied Analysis and Computational Mathematics Eötvös Loránd University 1/C Pázmány P. Stny. Budapest1117 Hungary

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein-Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.1. Copyright © 2017, The Authors. All rights reserved.

关键词： Equations of motion

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Allele-defined genome of the autopolyploid sugarcane Saccharum spontaneum L (vol 50, pg 1565, 2018)

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NATURE GENETICS 2018年第12期50卷 1754-1754页

作者： Zhang, Jisen Zhang, Xingtan Tang, Haibao Zhang, Qing Hua, Xiuting Ma, Xiaokai Zhu, Fan Jones, Tyler Zhu, Xinguang Bowers, John Wai, Ching Man Zheng, Chunfang Shi, Yan Chen, Shuai Xu, Xiuming Yue, Jingjing Nelson, David R. Huang, Lixian Li, Zhen Xu, Huimin Zhou, Dong Wang, Yongjun Hu, Weichang Lin, Jishan Deng, Youjin Pandey, Neha Mancini, Melina Zerpa, Dessiree Nguyen, Julie K. Wang, Liming Yu, Liang Xin, Yinghui Ge, Liangfa Arro, Jie Han, Jennifer O. Chakrabarty, Setu Pushko, Marija Zhang, Wenping Ma, Yanhong Ma, Panpan Lv, Mingju Chen, Faming Zheng, Guangyong Xu, Jingsheng Yang, Zhenhui Deng, Fang Chen, Xuequn Liao, Zhenyang Zhang, Xunxiao Lin, Zhicong Lin, Hai Yan, Hansong Kuang, Zheng Zhong, Weimin Liang, Pingping Wang, Guofeng Yuan, Yuan Shi, Jiaxian Hou, Jinxiang Lin, Jingxian Jin, Jingjing Cao, Peijian Shen, Qiaochu Jiang, Qing Zhou, Ping Ma, Yaying Zhang, Xiaodan Xu, Rongrong Liu, Juan Zhou, Yongmei Jia, Haifeng Ma, Qing Qi, Rui Zhang, Zhiliang Fang, Jingping Fang, Hongkun Song, Jinjin Wang, Mengjuan Dong, Guangrui Wang, Gang Chen, Zheng Ma, Teng Liu, Hong Dhungana, Singha R. Huss, Sarah E. Yang, Xiping Sharma, Anupma Trujillo, Jhon H. Martinez, Maria C. Hudson, Matthew Riascos, John J. Schuler, Mary Chen, Li-Qing Braun, David M. Li, Lei Yu, Qingyi Wang, Jianping Wang, Kai Schatz, Michael C. Heckerman, David Van Sluys, Marie-Anne Souza, Glaucia Mendes Moore, Paul H. Sankoff, David VanBuren, Robert Paterson, Andrew H. Nagai, Chifumi Ming, Ray Fujian Agriculture and Forestry University and University of Illinois at Urbana-Champaign School of Integrative Biology Joint Center for Genomics and Biotechnology National Sugarcane Engineering Technology Research Center Fujian Provincial Key Laboratory of Haixia Applied Plant Systems Biology Key Laboratory of Genetics Breeding and Multiple Utilization of Corps Ministry of Education Fujian Agriculture and Forestry University Fuzhou China Department of Plant Biology University of Illinois at Urbana-Champaign Urbana IL USA Hawaii Agriculture Research Center Kunia HI USA Institute for Plant Physiology and Ecology Chinese Academy of Sciences Shanghai China Department of Plant Biology University of Georgia Athens GA USA Department of Horticulture Michigan State University East Lansing MI USA Department of Mathematics and Statistics University of Ottawa Ottawa Ontario Canada Department of Microbiology Immunology and Biochemistry University of Tennessee HSC Memphis TN USA Chinese Academy of Sciences-Max-Planck-Gesellschaft Partner Institute for Computational Biology Chinese Academy of Sciences Shanghai China China Tobacco Gene Research Center Zhengzhou Tobacco Research Institute of CNTC Zhengzhou China Division of Biological Sciences University of Missouri Columbia MO USA Department of Agronomy University of Florida Gainesville FL USA Texas A&M AgriLife Research Texas A&M University System Dallas TX USA Centro de Investigación de la Caña de Azúcar de Colombia (Cenicaña) Cali Colombia Department of Crop Sciences University of Illinois at Urbana-Champaign Urbana IL USA Departments of Computer Science and Biology Johns Hopkins University Baltimore MD USA Microsoft Research Redmond WA USA Departamento de Botânica Instituto de Biociências Universidade de São Paulo São Paulo Brazil Departamento de Bioquímica Instituto de Química Universidade de São Paulo São Paulo Brazil

Modern sugarcanes are polyploid interspecific hybrids, combining high sugar content from Saccharum officinarum with hardiness, disease resistance and ratooning of Saccharum spontaneum. Sequencing of a haploid S. spontaneum, AP85-441, facilitated the assembly of 32 pseudo-chromosomes comprising 8 homologous groups of 4 members each, bearing 35,525 genes with alleles defined. The reduction of basic chromosome number from 10 to 8 in S. spontaneum was caused by fissions of 2 ancestral chromosomes followed by translocations to 4 chromosomes. Surprisingly, 80% of nucleotide binding site-encoding genes associated with disease resistance are located in 4 rearranged chromosomes and 51% of those in rearranged regions. Resequencing of 64 S. spontaneum genomes identified balancing selection in rearranged regions, maintaining their diversity. Introgressed S. spontaneum chromosomes in modern sugarcanes are randomly distributed in AP85-441 genome, indicating random recombination among homologs in different S. spontaneum accessions. The allele-defined Saccharum genome offers new knowledge and resources to accelerate sugarcane improvement.

关键词： Genomics Plant genetics

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Ground-state phase diagram of an anisotropic spin-12 model on the triangular lattice

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Physical Review B 2017年第16期95卷 165110-165110页

作者： Qiang Luo Shijie Hu Bin Xi Jize Zhao Xiaoqun Wang Department of Physics Renmin University of China Beijing 100872 China Department of Physics and Research Center Optimas Technical University Kaiserslautern 67663 Kaiserslautern Germany College of Physics Science and Technology Yangzhou University Yangzhou 225002 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics and Astronomy Shanghai Jiao Tong University Shanghai 200240 China Collaborative Innovation Center for Advanced Microstructures Nanjing 210093 China

Motivated by a recent experiment on the rare-earth material YbMgGaO4 [Y. Li et al., Phys. Rev. Lett. 115, 167203 (2015)], which found that the ground state of YbMgGaO4 is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-1/2 model that was proposed to describe YbMgGaO4. Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a 120∘ phase and two distinct stripe phases. The transitions from the two stripe phases to the 120∘ phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material YbMgGaO4. These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in YbMgGaO4.

关键词： Frustrated magnetism Quantum criticality Spin liquid Spin-orbit coupling

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Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans

arXiv

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arXiv 2017年

作者： Wentz, J.M. Mendenhall, A. Bortza, D.M. Department of Applied Mathematics University of Colorado BoulderCO80309-0526 United States Interdisciplinary Quantitative Biology Graduate Program University of Colorado BoulderCO80309-0596 United States Department of Pathology University of Washington SeattleWA98109-1024 United States

Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein 16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypothesized mechanism that could lead to this patterned response and develop a mathematical model of this system to test our hypothesis. We propose that the patterned expression of heat shock protein is caused by a diffusion-driven instability within the pseudocoelom, or fluid-filled cavity, that borders the intestinal cells in C. elegans. This instability is due to the interactions between two classes of insulin like peptides that serve antagonistic roles. We examine output from the developed model and compare it to experimental data on heat shock protein expression. Furthermore, we use the model to gain insight on possible biological parameters in the system. The model presented is capable of producing patterns similar to what is observed experimentally and provides a first step in mathematically modeling aging-related mechanisms in C. elegans. Keywords: Caenorhabditis elegans, Insulin-like Signaling, HSP-16.2, Reaction-Diffusion, Aging Copyright © 2017, The Authors. All rights reserved.

关键词： Insulin

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Polynomials and the exponent of matrix multiplication

arXiv

引用

arXiv 2017年

作者： Chiantini, Luca Hauenstein, Jonathan D. Ikenmeyer, Christian Landsberg, J.M. Ottaviani, Giorgio Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche Università di Siena Italy Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Max Planck Institute for Informatics Saarland Informatics Campus Germany Department of Mathematics Texas A&M University College Station TX United States Dipartimento di Matematica e Informatica "Ulisse Dini" Università di Firenze Italy

We define tensors, corresponding to cubic polynomials, which have the same exponent ω as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor sMhni defined on an n×n matrix A by sMhni(A) = trace(A3). The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent ω.68Q17, 14N05, 14Q20, 15A69 Copyright © 2017, The Authors. All rights reserved.

关键词： Tensors

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