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Baba R, Fujimaki K, Uemura C, Matsuo Y, Nakahara A, Muramatsu A. Assisting and eliminating memory effects of paste by adding polysaccharides. Phys Rev E 2023; 108:054602. [PMID: 38115423 DOI: 10.1103/physreve.108.054602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 10/12/2023] [Indexed: 12/21/2023]
Abstract
A densely packed colloidal suspension, called a paste, is known to remember the direction of its motion because of its plasticity. Because the memory in the paste determines the preferential direction for crack propagation, the desiccation crack pattern morphology depends on memory of its motions (memory effect of paste). Two types of memory effects are memory of vibration and memory of flow. When a paste is dried, it usually shows an "isotropic and random cellular" desiccation crack pattern. However, when a paste is vibrated before drying and it remembers the direction of its vibrational motion, primary desiccation cracks propagate in a direction perpendicular to its vibrational motion before drying (memory of vibration). Once it flows and remembers the direction of its flow motion, primary desiccation cracks propagate in the direction parallel to its flow motion (memory of flow). Anisotropic network formation via interparticle attraction among colloidal particles in a suspension is the dominant factor affecting a paste's memory of its motion. Calcium carbonate (CaCO_{3}) paste remembers the direction of its vibrational motion, but not its own flow direction because Coulombic repulsion among charged CaCO_{3} colloidal particles prevents the formation of a network structure in a flow. For this study, we strove to assist and eliminate CaCO_{3} paste memory effects by adding polysaccharides. First, to characterize memory in paste, we propose a method of image analysis to quantify the strength and the direction of the anisotropy of desiccation crack patterns using Shannon's information entropy. Next, we conduct experiments to add polysaccharide to CaCO_{3} paste, revealing that the addition of a small amount of polysaccharide to CaCO_{3} paste assists the paste in remembering its own flow motion. Findings also indicate that the addition of a large amount of polysaccharide prevents the formation of both memories of its flow and vibrational motion and eliminates the memory effects of paste. We then perform "flocculation and sedimentation" experiments to investigate the interaction among CaCO_{3} colloidal particles in a solution. Results show that, in an aqueous solution with low polysaccharide concentration, CaCO_{3} colloidal particles flocculate each other and quickly form a sediment in a short time, whereas, in an aqueous solution with high polysaccharide concentration, a longer time is necessary for flocculation and sedimentation. Because the addition of small amounts of polysaccharides to CaCO_{3} paste induces polymer bridging between colloidal particles as interparticle attraction, it helps to produce a macroscopic network structure which retains memory of its flow motion and thereby assists the formation of memory of flow, whereas the addition of large amounts of polysaccharides induces interparticle repulsion, which prevents the formation of memory effects of all types.
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Affiliation(s)
- Ryu Baba
- Department of Aerospace Engineering, College of Science and Technology, Nihon University, Funabashi 274-8501, Japan
| | - Kazuhiro Fujimaki
- Department of Aerospace Engineering, College of Science and Technology, Nihon University, Funabashi 274-8501, Japan
| | - Chihiro Uemura
- Department of Space and Astronautical Science, School of Physical Science, SOKENDAI (The Graduate University for Advanced Studies), Sagamihara 252-5210, Japan, and DigitalBlast, Inc., Tokyo 101-0051, Japan
| | - Yousuke Matsuo
- Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi 274-8501, Japan
| | - Akio Nakahara
- Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi 274-8501, Japan
| | - Akinori Muramatsu
- Department of Aerospace Engineering, College of Science and Technology, Nihon University, Funabashi 274-8501, Chiba, Japan
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2
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Clemmer JT, Robbins MO. Universal behavior in fragmenting brittle, isotropic solids across material properties. Phys Rev E 2023; 108:034902. [PMID: 37849166 DOI: 10.1103/physreve.108.034902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 08/24/2023] [Indexed: 10/19/2023]
Abstract
A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a nontrivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean-square grain mass across rates and system sizes. Consistent scaling persists across all material properties studied, although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses and depends on elastic properties of the solid.
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Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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3
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Liang J, Yang D, Xiao Y, Chen S, Dadap JI, Rottler J, Ye Z. Shear Strain-Induced Two-Dimensional Slip Avalanches in Rhombohedral MoS 2. NANO LETTERS 2023; 23:7228-7235. [PMID: 37358360 DOI: 10.1021/acs.nanolett.3c01487] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/27/2023]
Abstract
Slip avalanches are ubiquitous phenomena occurring in three-dimensional materials under shear strain, and their study contributes immensely to our understanding of plastic deformation, fragmentation, and earthquakes. So far, little is known about the role of shear strain in two-dimensional (2D) materials. Here we show some evidence of 2D slip avalanches in exfoliated rhombohedral MoS2, triggered by shear strain near the threshold level. Utilizing interfacial polarization in 3R-MoS2, we directly probe the stacking order in multilayer flakes and discover a wide variety of polarization domains with sizes following a power-law distribution. These findings suggest that slip avalanches can occur during the exfoliation of 2D materials, and the stacking orders can be changed via shear strain. Our observation has far-reaching implications for the development of new materials and technologies, where precise control over the atomic structure of these materials is essential for optimizing their properties as well as for our understanding of fundamental physical phenomena.
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Affiliation(s)
- Jing Liang
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Dongyang Yang
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Yunhuan Xiao
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Sean Chen
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Jerry I Dadap
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Joerg Rottler
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Ziliang Ye
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
- Quantum Matter Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
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4
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Microstructure of a heavily irradiated metal exposed to a spectrum of atomic recoils. Sci Rep 2023; 13:1684. [PMID: 36717656 PMCID: PMC9886950 DOI: 10.1038/s41598-022-27087-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 12/26/2022] [Indexed: 02/01/2023] Open
Abstract
At temperatures below the onset of vacancy migration, metals exposed to energetic ions develop dynamically fluctuating steady-state microstructures. Statistical properties of these microstructures in the asymptotic high exposure limit are not universal and vary depending on the energy and mass of the incident ions. We develop a model for the microstructure of an ion-irradiated metal under athermal conditions, where internal stress fluctuations dominate the kinetics of structural evolution. The balance between defect production and recombination depends sensitively not only on the total exposure to irradiation, defined by the fluence, but also on the energy of the incident particles. The model predicts the defect content in the high dose limit as an integral of the spectrum of primary knock-on atom energies, with the finding that low energy ions produce a significantly higher amount of damage than high energy ions at comparable levels of exposure to radiation.
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5
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Clemmer JT, Robbins MO. Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates. PHYSICAL REVIEW LETTERS 2022; 129:078002. [PMID: 36018706 DOI: 10.1103/physrevlett.129.078002] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Revised: 05/29/2022] [Accepted: 07/21/2022] [Indexed: 06/15/2023]
Abstract
Using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.
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Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Meng J, Huang Y, Leung DM, Li L, Adebiyi AA, Ryder CL, Mahowald NM, Kok JF. Improved Parameterization for the Size Distribution of Emitted Dust Aerosols Reduces Model Underestimation of Super Coarse Dust. GEOPHYSICAL RESEARCH LETTERS 2022; 49:e2021GL097287. [PMID: 35866061 PMCID: PMC9286626 DOI: 10.1029/2021gl097287] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Revised: 03/28/2022] [Accepted: 04/05/2022] [Indexed: 06/15/2023]
Abstract
Aircraft measurement campaigns have revealed that super coarse dust (diameter >10 μm) surprisingly accounts for approximately a quarter of aerosols by mass in the atmosphere. However, most global aerosol models either underestimate or do not include super coarse dust abundance. To address this problem, we use brittle fragmentation theory to develop a parameterization for the emitted dust size distribution that includes emission of super coarse dust. We implement this parameterization in the Community Earth System Model (CESM) and find that it brings the model in good agreement with aircraft measurements of super coarse dust close to dust source regions. However, the CESM still underestimates super coarse dust in dust outflow regions. Thus, we conclude that the model underestimation of super coarse atmospheric dust is in part due to the underestimation of super coarse dust emission and likely in part due to errors in deposition processes.
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Affiliation(s)
- Jun Meng
- Department of Atmospheric and Oceanic SciencesUniversity of CaliforniaLos AngelesCAUSA
| | - Yue Huang
- Department of Atmospheric and Oceanic SciencesUniversity of CaliforniaLos AngelesCAUSA
- Now at Earth InstituteColumbia UniversityNew YorkNYUSA
- Now at NASA Goddard Institute for Space StudiesNew YorkNYUSA
| | - Danny M. Leung
- Department of Atmospheric and Oceanic SciencesUniversity of CaliforniaLos AngelesCAUSA
| | - Longlei Li
- Department of Earth and Atmospheric SciencesCornell UniversityIthacaNYUSA
| | - Adeyemi A. Adebiyi
- Department of Atmospheric and Oceanic SciencesUniversity of CaliforniaLos AngelesCAUSA
- Now at Department of Life & Environmental SciencesUniversity of CaliforniaMercedCAUSA
| | | | | | - Jasper F. Kok
- Department of Atmospheric and Oceanic SciencesUniversity of CaliforniaLos AngelesCAUSA
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7
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Mazzarisi O, de Azevedo-Lopes A, Arenzon JJ, Corberi F. Maximal Diversity and Zipf's Law. PHYSICAL REVIEW LETTERS 2021; 127:128301. [PMID: 34597111 DOI: 10.1103/physrevlett.127.128301] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Revised: 06/18/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps's law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets.
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Affiliation(s)
- Onofrio Mazzarisi
- Max Planck Institute for Mathematics in the Sciences, Inselstrae 22, 04103 Leipzig, Germany
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Amanda de Azevedo-Lopes
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
| | - Jeferson J Arenzon
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
- Instituto Nacional de Ciência e Tecnologia-Sistemas Complexos, 22290-180 Rio de Janeiro RJ, Brazil
| | - Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
- INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
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8
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Kooij S, van Dalen G, Molinari JF, Bonn D. Explosive fragmentation of Prince Rupert's drops leads to well-defined fragment sizes. Nat Commun 2021; 12:2521. [PMID: 33947855 PMCID: PMC8097073 DOI: 10.1038/s41467-021-22595-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 03/16/2021] [Indexed: 11/25/2022] Open
Abstract
Anyone who has ever broken a dish or a glass knows that the resulting fragments range from roughly the size of the object all the way down to indiscernibly small pieces: typical fragment size distributions of broken brittle materials follow a power law, and therefore lack a characteristic length scale. The origin of this power-law behavior is still unclear, especially why it is such an universal feature. Here we study the explosive fragmentation of glass Prince Rupert’s drops, and uncover a fundamentally different breakup mechanism. The Prince Rupert’s drops explode due to their large internal stresses resulting in an exponential fragment size distribution with a well-defined fragment size. We demonstrate that generically two distinct breakup processes exist, random and hierarchical, that allows us to fully explain why fragment size distributions are power-law in most cases but exponential in others. We show experimentally that one can even break the same material in different ways to obtain either random or hierarchical breakup, giving exponential and power-law distributed fragment sizes respectively. That a random breakup process leads to well-defined fragment sizes is surprising and is potentially useful to control fragmentation of brittle solids. Fragmentation of breaking glass as a brittle solid is a problem of equal practical and theoretical importance. Kooij et al. demonstrate that the fragment size distribution can surprisingly be both, either power-law or exponential, depending on how a particular specimen is broken.
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Affiliation(s)
- Stefan Kooij
- Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, The Netherlands.
| | - Gerard van Dalen
- Unilever Research and Development Vlaardingen, Olivier van Noortlaan, Vlaardingen, The Netherlands
| | - Jean-François Molinari
- Department of Materials Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Daniel Bonn
- Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, The Netherlands
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9
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Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems. MATHEMATICS 2021. [DOI: 10.3390/math9060635] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.
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10
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Fox-Rabinovich G, Gershman IS, Yamamoto K, Dosbaeva J, Veldhuis S. Effect of the Adaptive Response on the Wear Behavior of PVD and CVD Coated Cutting Tools during Machining with Built Up Edge Formation. NANOMATERIALS 2020; 10:nano10122489. [PMID: 33322353 PMCID: PMC7764160 DOI: 10.3390/nano10122489] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 12/07/2020] [Accepted: 12/08/2020] [Indexed: 11/16/2022]
Abstract
The relationship between the wear process and the adaptive response of the coated cutting tool to external stimuli is demonstrated in this review paper. The goal of the featured case studies is to achieve control over the behavior of the tool/workpiece tribo-system, using an example of severe tribological conditions present under machining with intensive built-up edge (BUE) formation. The built-ups developed during the machining process are dynamic structures with a dual role. On one hand they exhibit protective functions but, on the other hand, the process of built-up edge formation is similar to an avalanche. Periodical growth and breakage of BUE eventually leads to tooltip failure and catastrophe of the entire tribo-system. The process of BUE formation is governed by the stick-slip phenomenon occurring at the chip/tool interface which is associated with the self-organized critical process (SOC). This process could be potentially brought under control through the engineered adaptive response of the tribo-system, with the goal of reducing the scale and frequency of the occurring avalanches (built-ups). A number of multiscale frictional processes could be used to achieve this task. Such processes are associated with the strongly non-equilibrium process of self-organization during friction (nano-scale tribo-films formation) as well as physical-chemical and mechanical processes that develop on a microscopic scale inside the coating layer and the carbide substrate. Various strategies for achieving control over wear behavior are presented in this paper using specific machining case studies of several hard-to-cut materials such as stainless steels, titanium alloy (TiAl6V4), compacted graphitic iron (CGI), each of which typically undergoes strong built-up edge formation. Various categories of hard coatings deposited by different physical vapor deposition (PVD) and chemical vapor deposition (CVD) methods are applied on cutting tools and the results of their tribological and wear performance studies are presented. Future research trends are outlined as well.
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Affiliation(s)
- German Fox-Rabinovich
- Department of Mechanical Engineering, McMaster Manufacturing Research Institute (MMRI), McMaster University, Hamilton, ON L8S 4L8 Canada; (J.D.); (S.V.)
- Correspondence:
| | - Iosif S. Gershman
- Joint Stock Company Railway Research Institute, Moscow State Technological University “Stankin” (MSTU “STANKIN”), 127994 Moscow, Russia;
| | - Kenji Yamamoto
- Applied Physics Research Laboratory, Kobe Steel Ltd., 1-5-5 Takatsuda-dai, Nishi-ku, Kobe, Hyogo 651-2271, Japan;
| | - Julia Dosbaeva
- Department of Mechanical Engineering, McMaster Manufacturing Research Institute (MMRI), McMaster University, Hamilton, ON L8S 4L8 Canada; (J.D.); (S.V.)
| | - Stephen Veldhuis
- Department of Mechanical Engineering, McMaster Manufacturing Research Institute (MMRI), McMaster University, Hamilton, ON L8S 4L8 Canada; (J.D.); (S.V.)
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11
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Abstract
Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra-shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.
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12
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Nakahara A, Hiraoka T, Hayashi R, Matsuo Y, Kitsunezaki S. Mechanism of memory effect of paste which dominates desiccation crack patterns. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:rsta.2017.0395. [PMID: 30478207 PMCID: PMC6282403 DOI: 10.1098/rsta.2017.0395] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/08/2018] [Indexed: 06/09/2023]
Abstract
When a densely packed colloidal suspension, called a paste, behaves as plastic fluid, it can remember the direction of its motion it has experienced, such as vibrational motion and flow. These memories kept in paste can be visualized as the morphology of crack patterns that appear when the paste is dried. For example, when a paste remembers the direction of vibrational motion, all primary desiccation cracks propagate in the direction perpendicular to the direction of the vibrational motion that the paste has experienced. On the other hand, when a paste remembers the direction of flow motion, all primary cracks propagate along the flow direction. To find out the mechanism of memory effect of vibration, we perform experiments to rewrite memory in paste by applying additional vibration to the paste along a different direction before the paste is dried. By investigating the process of rewriting memory in paste, we find the competitive phenomena between quasi-linear effect and nonlinear effect, which were studied in each theoretical model based on residual tension theories. That is, at the initial stage of the memory-imprinting process of the vibrational motion, the mechanism predicted by the quasi-linear analysis based on residual tension theory holds, but, as the paste is vibrated repeatedly, the mechanism shown by the nonlinear analysis gradually come to play a dominant role in the memory effect.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.
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Affiliation(s)
- Akio Nakahara
- College of Science and Technology, Nihon University, 7-24-1 Narashino-dai, Funabashi 274-8501, Japan
| | - Tomoki Hiraoka
- College of Science and Technology, Nihon University, 7-24-1 Narashino-dai, Funabashi 274-8501, Japan
| | - Rokuya Hayashi
- College of Science and Technology, Nihon University, 7-24-1 Narashino-dai, Funabashi 274-8501, Japan
| | - Yousuke Matsuo
- College of Science and Technology, Nihon University, 7-24-1 Narashino-dai, Funabashi 274-8501, Japan
| | - So Kitsunezaki
- Research Group of Physics, Division of Natural Sciences, Faculty of Nara Women's University, Nara 630-8506, Japan
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13
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Saha J, Kumar J, Heinrich S. On the approximate solutions of fragmentation equations. Proc Math Phys Eng Sci 2018. [DOI: 10.1098/rspa.2017.0541] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A numerical model based on the finite volume scheme is proposed to approximate the binary breakage problems. Initially, it is considered that the particle fragments are characterized by a single property, i.e. particle’s volume. We then investigate the extension of the proposed model for solving breakage problems considering two properties of particles. The efficiency to estimate the different moments with good accuracy and simple extension for multi-variable problems are the key features of the proposed method. Moreover, the mathematical convergence analysis is performed for one-dimensional problems. All mathematical findings and numerical results are validated over several test problems. For numerical validation, we propose the extension of Bourgade & Filbet (2008
Math. Comput.
77
, 851–882. (
doi:10.1090/S0025-5718-07-02054-6
)) model for solving two-dimensional pure breakage problems. In this aspect, numerical treatment of the two-dimensional binary breakage models using finite volume methods can be treated to be the first instance in the literature.
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Affiliation(s)
- Jitraj Saha
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Jitendra Kumar
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Stefan Heinrich
- Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Hamburg 21073, Germany
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14
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Elçi EM, Weigel M, Fytas NG. Fragmentation of fractal random structures. PHYSICAL REVIEW LETTERS 2015; 114:115701. [PMID: 25839290 DOI: 10.1103/physrevlett.114.115701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2014] [Indexed: 06/04/2023]
Abstract
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.
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Affiliation(s)
- Eren Metin Elçi
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, England
| | - Martin Weigel
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, England
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
| | - Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, England
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15
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Domokos G, Kun F, Sipos AÁ, Szabó T. Universality of fragment shapes. Sci Rep 2015; 5:9147. [PMID: 25772300 PMCID: PMC4360630 DOI: 10.1038/srep09147] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2014] [Accepted: 02/12/2015] [Indexed: 11/17/2022] Open
Abstract
The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment shapes still remained a fundamental challenge. We performed a thorough experimental study of the problem fragmenting various types of materials by slowly proceeding weathering and by rapid breakup due to explosion and hammering. We demonstrate that the shape of fragments obeys an astonishing universality having the same generic evolution with the fragment size irrespective of materials details and loading conditions. There exists a cutoff size below which fragments have an isotropic shape, however, as the size increases an exponential convergence is obtained to a unique elongated form. We show that a discrete stochastic model of fragmentation reproduces both the size and shape of fragments tuning only a single parameter which strengthens the general validity of the scaling laws. The dependence of the probability of the crack plan orientation on the linear extension of fragments proved to be essential for the shape selection mechanism.
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Affiliation(s)
- Gábor Domokos
- Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Műegyetem rkp. 3., K242, 1111 Budapest, Hungary
| | - Ferenc Kun
- Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, P.O.Box: 5, Hungary
| | - András Árpád Sipos
- Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Műegyetem rkp. 3., K242, 1111 Budapest, Hungary
| | - Tímea Szabó
- Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Műegyetem rkp. 3., K242, 1111 Budapest, Hungary
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16
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Pál G, Varga I, Kun F. Emergence of energy dependence in the fragmentation of heterogeneous materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062811. [PMID: 25615152 DOI: 10.1103/physreve.90.062811] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2014] [Indexed: 06/04/2023]
Abstract
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of universality depending mainly on the dimensionality and on the brittle-ductile mechanical response of the system. Recently, experiments and computer simulations have reported an energy dependence of the exponent increasing with the imparted energy. These novel findings question the phase transition picture of fragmentation phenomena, and have also practical importance for industrial applications. Based on large scale computer simulations here we uncover a robust mechanism which leads to the emergence of energy dependence in fragmentation processes resolving controversial issues on the problem: studying the impact induced breakup of platelike objects with varying thickness in three dimensions we show that energy dependence occurs when a lower dimensional fragmenting object is embedded into a higher dimensional space. The reason is an underlying transition between two distinct fragmentation mechanisms controlled by the impact velocity at low plate thicknesses, while it is hindered for three-dimensional bulk systems. The mass distributions of the subsets of fragments dominated by the two cracking mechanisms proved to have an astonishing robustness at all plate thicknesses, which implies that the nonuniversality of the complete mass distribution is the consequence of blending the contributions of universal partial processes.
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Affiliation(s)
- Gergő Pál
- Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary
| | - Imre Varga
- Department of Informatics Systems and Networks, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
| | - Ferenc Kun
- Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary
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17
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Miller PW, Ouellette NT. Impact fragmentation of model flocks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042806. [PMID: 24827292 DOI: 10.1103/physreve.89.042806] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2013] [Indexed: 06/03/2023]
Abstract
Predicting the bulk material properties of active matter is challenging since these materials are far from equilibrium and standard statistical-mechanics approaches may fail. We report a computational study of the surface properties of a well known active matter system: aggregations of self-propelled particles that are coupled via an orientational interaction and that resemble bird flocks. By simulating the impact of these models flocks on an impermeable surface, we find that they fragment into subflocks with power-law mass distributions, similar to shattering brittle solids but not to splashing liquid drops. Thus, we find that despite the interparticle interactions, these model flocks do not possess an emergent surface tension.
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Affiliation(s)
- Pearson W Miller
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Nicholas T Ouellette
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
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18
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Li J, Huang Q, Ren X. Dynamic Initiation and Propagation of Multiple Cracks in Brittle Materials. MATERIALS 2013; 6:3241-3253. [PMID: 28811433 PMCID: PMC5521245 DOI: 10.3390/ma6083241] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2013] [Revised: 07/10/2013] [Accepted: 07/24/2013] [Indexed: 11/28/2022]
Abstract
Brittle materials such as rock and ceramic usually exhibit apparent increases of strength and toughness when subjected to dynamic loading. The reasons for this phenomenon are not yet well understood, although a number of hypotheses have been proposed. Based on dynamic fracture mechanics, the present work offers an alternate insight into the dynamic behaviors of brittle materials. Firstly, a single crack subjected to stress wave excitations is investigated to obtain the dynamic crack-tip stress field and the dynamic stress intensity factor. Second, based on the analysis of dynamic stress intensity factor, the fracture initiation sizes and crack size distribution under different loading rates are obtained, and the power law with the exponent of −2/3 is derived to describe the fracture initiation size. Third, with the help of the energy balance concept, the dynamic increase of material strength is directly derived based on the proposed multiple crack evolving criterion. Finally, the model prediction is compared with the dynamic impact experiments, and the model results agree well with the experimentally measured dynamic increasing factor (DIF).
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Affiliation(s)
- Jie Li
- Department of Building Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China.
| | - Qiaoping Huang
- Department of Building Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China.
- Tongji Architectural Design (Group) Co., Ltd., 1239 Siping Road, Shanghai 200092, China.
| | - Xiaodan Ren
- Department of Building Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China.
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19
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Schröder M, Rahbari SHE, Nagler J. Crackling noise in fractional percolation. Nat Commun 2013; 4:2222. [DOI: 10.1038/ncomms3222] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2012] [Accepted: 07/01/2013] [Indexed: 11/09/2022] Open
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20
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Massip F, Arndt PF. Neutral evolution of duplicated DNA: an evolutionary stick-breaking process causes scale-invariant behavior. PHYSICAL REVIEW LETTERS 2013; 110:148101. [PMID: 25167038 DOI: 10.1103/physrevlett.110.148101] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/03/2023]
Abstract
Recently, an enrichment of identical matching sequences has been found in many eukaryotic genomes. Their length distribution exhibits a power law tail raising the question of what evolutionary mechanism or functional constraints would be able to shape this distribution. Here we introduce a simple and evolutionarily neutral model, which involves only point mutations and segmental duplications, and produces the same statistical features as observed for genomic data. Further, we extend a mathematical model for random stick breaking to analytically show that the exponent of the power law tail is -3 and universal as it does not depend on the microscopic details of the model.
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Affiliation(s)
- Florian Massip
- Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
| | - Peter F Arndt
- Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
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21
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Nakayama H, Matsuo Y, Takeshi O, Nakahara A. Position control of desiccation cracks by memory effect and Faraday waves. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:1. [PMID: 23306446 DOI: 10.1140/epje/i2013-13001-8] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Revised: 11/30/2012] [Accepted: 12/04/2012] [Indexed: 05/15/2023]
Abstract
Pattern formation of desiccation cracks on a layer of a calcium carbonate paste is studied experimentally. This paste is known to exhibit a memory effect, which means that a short-time application of horizontal vibration to the fresh paste predetermines the direction of the cracks that are formed after the paste is dried. While the position of the cracks (as opposed to their direction) is still stochastic in the case of horizontal vibration, the present work reports that their positioning is also controllable, at least to some extent, by applying vertical vibration to the paste and imprinting the pattern of Faraday waves, thus breaking the translational symmetry of the system. The experiments show that the cracks tend to appear in the node zones of the Faraday waves: in the case of stripe-patterned Faraday waves, the cracks are formed twice more frequently in the node zones than in the anti-node zones, presumably due to the localized horizontal motion. As a result of this preference of the cracks to the node zones, the memory of the square lattice pattern of Faraday waves makes the cracks run in the oblique direction differing by 45 degrees from the intuitive lattice direction of the Faraday waves.
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Affiliation(s)
- Hiroshi Nakayama
- Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi, 274-8501, Chiba, Japan
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22
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Saveliev VL, Gorokhovski MA. Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061112. [PMID: 23367898 DOI: 10.1103/physreve.86.061112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2012] [Indexed: 06/01/2023]
Abstract
Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.
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Affiliation(s)
- V L Saveliev
- Institute of Ionosphere, National Center of Space Research and Technology, 050020 Almaty, Kazakhstan
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23
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Kok JF, Parteli EJR, Michaels TI, Karam DB. The physics of wind-blown sand and dust. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:106901. [PMID: 22982806 DOI: 10.1088/0034-4885/75/10/106901] [Citation(s) in RCA: 158] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.
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Affiliation(s)
- Jasper F Kok
- Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA.
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24
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Bosbach J, Weiss S, Ahlers G. Plume fragmentation by bulk interactions in turbulent Rayleigh-Bénard convection. PHYSICAL REVIEW LETTERS 2012; 108:054501. [PMID: 22400934 DOI: 10.1103/physrevlett.108.054501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2011] [Indexed: 05/31/2023]
Abstract
Using compressed gases with Prandtl numbers near 0.7, we obtained flow visualizations of turbulent Rayleigh-Bénard convection in a cylindrical sample with an aspect ratio Γ≡D/L≅10 (D is the diameter and L the height) by the shadowgraph method. Focusing on the plumes under the top plate, we found that their length had a log-normal distribution, suggesting a fragmentation process. Fragmentation events could be visually identified in the images and involved plume interactions with bulk fluctuations or upwelling domain walls. We found the mean spacing between plumes to vary with the Rayleigh number in proportion to the volume-averaged Kolmogorov length of the turbulent bulk fluctuations, providing further evidence for plume-bulk interactions.
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Affiliation(s)
- Johannes Bosbach
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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25
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Yamamoto K, Yamazaki Y. Power-law behavior in a cascade process with stopping events: a solvable model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011145. [PMID: 22400550 DOI: 10.1103/physreve.85.011145] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2011] [Revised: 12/12/2011] [Indexed: 05/31/2023]
Abstract
The present paper proposes a stochastic model to be solved analytically, and a power-law-like distribution is derived. This model is formulated based on a cascade fracture with the additional effect that each fragment at each stage of a cascade ceases fracture with a certain probability. When the probability is constant, the exponent of the power-law cumulative distribution lies between -1 and 0, depending not only on the probability but the distribution of fracture points. Whereas, when the probability depends on the size of a fragment, the exponent is less than -1, irrespective of the distribution of fracture points. The applicability of our model is also discussed.
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Affiliation(s)
- Ken Yamamoto
- Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo, Japan
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26
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Nakahara A, Shinohara Y, Matsuo Y. Control of crack pattern using memory effect of paste. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/319/1/012014] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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27
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dos Santos FPM, Barbosa VC, Donangelo R, Souza SR. Experimental analysis of lateral impact on planar brittle material: spatial properties of cracks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:026115. [PMID: 21929072 DOI: 10.1103/physreve.84.026115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2011] [Indexed: 05/31/2023]
Abstract
The breakup of alkaline glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a phenomenological model suggests that bifurcations along the cracks' paths are more likely to take place closer to the impact region than far away from it, i.e., the bifurcation probability seems to lower as the perpendicular distance from the impacted lateral increases. It is also found that many observables are not sensitive to the plate material used in this work, as long as the fragment multiplicities corresponding to the fragmentation of the plates are similar. This gives support to the universal properties of the fragmentation process reported in previous experiments. However, even under the just mentioned circumstances, some spatial observables are capable of distinguishing the material of which the plates are made, which therefore suggests that this universality should be carefully investigated.
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Affiliation(s)
- F P M dos Santos
- Instituto de Física, Universidade Federal do Rio de Janeiro Cidade Universitária, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil.
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28
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A scaling theory for the size distribution of emitted dust aerosols suggests climate models underestimate the size of the global dust cycle. Proc Natl Acad Sci U S A 2010; 108:1016-21. [PMID: 21189304 DOI: 10.1073/pnas.1014798108] [Citation(s) in RCA: 341] [Impact Index Per Article: 24.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Mineral dust aerosols impact Earth's radiation budget through interactions with clouds, ecosystems, and radiation, which constitutes a substantial uncertainty in understanding past and predicting future climate changes. One of the causes of this large uncertainty is that the size distribution of emitted dust aerosols is poorly understood. The present study shows that regional and global circulation models (GCMs) overestimate the emitted fraction of clay aerosols (< 2 μm diameter) by a factor of ∼2-8 relative to measurements. This discrepancy is resolved by deriving a simple theoretical expression of the emitted dust size distribution that is in excellent agreement with measurements. This expression is based on the physics of the scale-invariant fragmentation of brittle materials, which is shown to be applicable to dust emission. Because clay aerosols produce a strong radiative cooling, the overestimation of the clay fraction causes GCMs to also overestimate the radiative cooling of a given quantity of emitted dust. On local and regional scales, this affects the magnitude and possibly the sign of the dust radiative forcing, with implications for numerical weather forecasting and regional climate predictions in dusty regions. On a global scale, the dust cycle in most GCMs is tuned to match radiative measurements, such that the overestimation of the radiative cooling of a given quantity of emitted dust has likely caused GCMs to underestimate the global dust emission rate. This implies that the deposition flux of dust and its fertilizing effects on ecosystems may be substantially larger than thought.
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29
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Levy S, Molinari JF, Vicari I, Davison AC. Dynamic fragmentation of a ring: predictable fragment mass distributions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:066105. [PMID: 21230703 DOI: 10.1103/physreve.82.066105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2010] [Indexed: 05/30/2023]
Abstract
We employ a finite element framework, coupled to cohesive elements, to model material decohesion of a uniformly expanding ring. Our study focuses on the average fragment mass, the distribution of fragment masses, and the heaviest fragments. The computed fragment mass distributions are best captured by generalized gamma distributions, regardless of the model parameters. However, the distribution of the heaviest fragments depends on toughness, specimen size, and loading rate.
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Affiliation(s)
- S Levy
- LSMS-IIC-ENAC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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30
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dos Santos FPM, Barbosa VC, Donangelo R, Souza SR. Experimental analysis of lateral impact on planar brittle material. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046108. [PMID: 20481787 DOI: 10.1103/physreve.81.046108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2009] [Revised: 03/25/2010] [Indexed: 05/29/2023]
Abstract
The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments' geometrical properties constitutes a more stringent test of the theoretical models' assumptions than the size distribution.
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Affiliation(s)
- F P M dos Santos
- Instituto de Física, Universidade Federal do Rio de Janeiro, Cidade Universitária, CP 68528, Rio de Janeiro, RJ 21941-972, Brazil.
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31
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Timár G, Blömer J, Kun F, Herrmann HJ. New universality class for the fragmentation of plastic materials. PHYSICAL REVIEW LETTERS 2010; 104:095502. [PMID: 20366993 DOI: 10.1103/physrevlett.104.095502] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2009] [Indexed: 05/24/2023]
Abstract
We present an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene particles of spherical shape against a hard wall. Experiments reveal a power law mass distribution of fragments with an exponent close to 1.2, which is significantly different from the known exponents of three-dimensional bulk materials. A 3D discrete element model is introduced which reproduces both the large permanent deformation of the polymer during impact and the novel value of the mass distribution exponent. We demonstrate that the dominance of shear in the crack formation and the plastic response of the material are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena.
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Affiliation(s)
- G Timár
- Department of Theoretical Physics, University of Debrecen, P. O. Box:5, H-4010 Debrecen, Hungary
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32
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Aström JA. Difference between fracture of thin brittle sheets and two-dimensional fracture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:046113. [PMID: 19905396 DOI: 10.1103/physreve.80.046113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2009] [Revised: 08/04/2009] [Indexed: 05/28/2023]
Abstract
Recently there has been some suggestions that fragmentation of thin brittle sheets is qualitatively different from pure two-dimensional fragmentation. The obvious reason for such a discrepancy is the possibility of the sheet to deform out of plane. There is a generic crack-branching mechanism that creates power-law fragment size distribution in the small fragment range for two-dimensional (2D) and three-dimensional bulk fragmentation with the power exponent (2D-1)/D. For thin sheets, the power exponent seems to be close to 1.2 which differs from the D=2 exponent 1.5. In order to make a distinct separation between sheet and 2D fragmentation, high-resolution fragment size distributions are required for fragmentation models with minimal differencies other than dimensionality. Here a very efficient numerical model which can be switched from 2D fragmentation to out-of-plane sheet fragmentation with minimal changes is used to produce high-resolution fragment size distribution for the two cases. The model results cast some doubt on the existence of separate universality classes for sheet and 2D fragmentation.
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Affiliation(s)
- J A Aström
- CSC-IT Center for Science, Esbo, Finland.
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33
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Cruz Hidalgo R, Pagonabarraga I. Driven fragmentation of granular gases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061305. [PMID: 18643255 DOI: 10.1103/physreve.77.061305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2008] [Indexed: 05/26/2023]
Abstract
The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f(c) approximately exp(-cn) , with n approximately 1.2 , regarding less the fragmentation mechanisms.
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Affiliation(s)
- Raúl Cruz Hidalgo
- AMADE, Departament de Física, Departament de Enginyeria Mecànica i de la Construcció Industrial, Universitat de Girona, Avenida Montilivi s/n, Girona, Spain
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34
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Carmona HA, Wittel FK, Kun F, Herrmann HJ. Fragmentation processes in impact of spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051302. [PMID: 18643061 DOI: 10.1103/physreve.77.051302] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2007] [Indexed: 05/26/2023]
Abstract
We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.
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Affiliation(s)
- H A Carmona
- Centro de Ciências e Tecnologia, Universidade Estadual do Ceará, 60740-903 Fortaleza, Ceará, Brazil
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35
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36
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Xu L, Barcos L, Nagel SR. Splashing of liquids: Interplay of surface roughness with surrounding gas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:066311. [PMID: 18233921 DOI: 10.1103/physreve.76.066311] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2007] [Revised: 10/26/2007] [Indexed: 05/25/2023]
Abstract
We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these control parameters: Prompt splashing is due to surface roughness and corona splashing is due to instabilities produced by the surrounding gas. The size distribution of ejected droplets reveals the length scales of the underlying droplet-creation process in both cases.
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Affiliation(s)
- Lei Xu
- The James Franck Institute and Department of Physics, The University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, USA
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37
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Boudaoud A, Bico J, Roman B. Elastocapillary coalescence: aggregation and fragmentation with a maximal size. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:060102. [PMID: 18233803 DOI: 10.1103/physreve.76.060102] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2007] [Indexed: 05/25/2023]
Abstract
Aggregation processes generally lead to broad distributions of sizes involving exponential tails. Here, experiments on the capillary-driven coalescence of regularly spaced flexible structures yields a self-similar distribution of sizes with no tail. At a given step, the physical process imposes a maximal size for the aggregates, which appears as the relevant scale for the distribution. A simple toy model involving the aggregation of nearest neighbors exhibits the same statistics. A mean-field theory accounting for a maximal size is in agreement with both experiments and numerics. This approach is extended to iterative fragmentation processes where the largest object is broken at each step.
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Affiliation(s)
- Arezki Boudaoud
- Laboratoire de Physique Statistique, UMR 8550 du CNRS/ENS/Paris 6/Paris 7, 24 rue Lhomond, Paris Cedex 5, France
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Kekäläinen P, Aström JA, Timonen J. Solution for the fragment-size distribution in a crack-branching model of fragmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:026112. [PMID: 17930109 DOI: 10.1103/physreve.76.026112] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2007] [Indexed: 05/25/2023]
Abstract
It is well established that rapidly propagating cracks in brittle material are unstable such that they generate side branches. It is also known that cracks are attracted by free surfaces, which means that they attract each other. This information is used here to formulate a generic model of fragmentation in which the small-size part of the fragment-size distribution results from merged crack branches in the damage zones along the paths of the propagating cracks. This model is solved under rather general assumptions for the fragment-size distribution. The model leads to a generic distribution S(-gamma) exp(-S/S(0)) for fragment sizes S, where gamma = 2d-1/d with d the Euclidean dimension, and S(0) is a material dependent parameter.
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Affiliation(s)
- P Kekäläinen
- Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
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39
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Moukarzel CF, Fernández-Sabido SF, Ruiz-Suárez JC. Phase transition in liquid drop fragmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061127. [PMID: 17677240 DOI: 10.1103/physreve.75.061127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2007] [Indexed: 05/16/2023]
Abstract
A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl . Upon varying the gas pressure, a critical value is found where the size distribution becomes a pure power law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in nuclear multifragmentation studies. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2 . The sizes of the largest and average fragments, on the other hand, do not go to zero abruptly but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian.
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Affiliation(s)
- Cristian F Moukarzel
- CINVESTAV del IPN Unidad Mérida, Departamento de Física Aplicada, 97310 Mérida, Yucatán, Mexico.
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Katsuragi H, Ihara S, Honjo H. Explosive fragmentation of a thin ceramic tube using pulsed power. PHYSICAL REVIEW LETTERS 2005; 95:095503. [PMID: 16197225 DOI: 10.1103/physrevlett.95.095503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2005] [Indexed: 05/04/2023]
Abstract
This study experimentally examined the explosive fragmentation of thin ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin copper wire, and high voltage was applied to the wire using a pulsed power generator. This melted the wire and the resulting vapor put pressure on the ceramic tube, causing it to fragment. We examined the statistical properties of the fragment mass distribution. The cumulative fragment mass distribution obeyed the double exponential or power law with exponential decay. Both distributions agreed well with the experimental data. Finally, we obtained universal scaling for fragmentation, which is applicable to both impact and explosive fragmentation.
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Affiliation(s)
- Hiroaki Katsuragi
- Department of Applied Science for Electronics and Materials, Kyushu University, Fukuoka 816-8580, Japan.
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41
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Audoly B, Neukirch S. Fragmentation of rods by cascading cracks: why spaghetti does not break in half. PHYSICAL REVIEW LETTERS 2005; 95:095505. [PMID: 16197227 DOI: 10.1103/physrevlett.95.095505] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2004] [Indexed: 05/04/2023]
Abstract
When thin brittle rods such as dry spaghetti pasta are bent beyond their limit curvature, they often break into more than two pieces, typically three or four. With the aim of understanding these multiple breakings, we study the dynamics of a bent rod that is suddenly released at one end. We find that the sudden relaxation of the curvature at this end leads to a burst of flexural waves, whose dynamics are described by a self-similar solution with no adjustable parameters. These flexural waves locally increase the curvature in the rod, and we argue that this counterintuitive mechanism is responsible for the fragmentation of brittle rods under bending. A simple experiment supporting the claim is presented.
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Affiliation(s)
- Basile Audoly
- Laboratoire de Modélisation en Mécanique, CNRS/Université Paris VI, 4 place Jussieu, Paris, France
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42
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Linna RP, Aström JA, Timonen J. Dimensional effects in dynamic fragmentation of brittle materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:015601. [PMID: 16090029 DOI: 10.1103/physreve.72.015601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2005] [Indexed: 05/03/2023]
Abstract
It has been shown previously that dynamic fragmentation of brittle D -dimensional objects in a D -dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent 2-1/D . We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of approximately 1.17 .
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Affiliation(s)
- R P Linna
- Department of Physics, University of Jyväskylä, P. O. Box 35, FIN-40351 Jyväskylä, Finland
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Araripe LE, Andrade JS, Costa Filho RN. Memory effects on the statistics of fragmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036119. [PMID: 15903505 DOI: 10.1103/physreve.71.036119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2004] [Indexed: 05/02/2023]
Abstract
We investigate through extensive molecular dynamics simulations the fragmentation process of two-dimensional Lennard-Jones systems. After thermalization, the fragmentation is initiated by a sudden increment to the radial component of the particles' velocities. We study the effect of temperature of the thermalized system as well as the influence of the impact energy of the "explosion" event on the statistics of mass fragments. Our results indicate that the cumulative distribution of fragments follows the scaling ansatz F(m) proportional to m(1-alpha)exp-(m/m(0))(gamma), where m is the mass, m(0) and gamma are cutoff parameters, and alpha is a scaling exponent that is dependent on the temperature. More precisely, we show clear evidence that there is a characteristic scaling exponent alpha for each macroscopic phase of the thermalized system, i.e., that the nonuniversal behavior of the fragmentation process is dictated by the state of the system before it breaks down.
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Affiliation(s)
- L E Araripe
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
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Wittel FK, Kun F, Herrmann HJ, Kröplin BH. Breakup of shells under explosion and impact. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016108. [PMID: 15697659 DOI: 10.1103/physreve.71.016108] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2004] [Revised: 10/22/2004] [Indexed: 05/24/2023]
Abstract
A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on eggshells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class, different from that of two- and three-dimensional bulk systems.
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Affiliation(s)
- F K Wittel
- Institute for Statics and Dynamics of Aerospace Structures, University of Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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Katsuragi H, Sugino D, Honjo H. Crossover of weighted mean fragment mass scaling in two-dimensional brittle fragmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:065103. [PMID: 15697423 DOI: 10.1103/physreve.70.065103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2004] [Indexed: 05/24/2023]
Abstract
We performed vertical and horizontal sandwich two-dimensional brittle fragmentation experiments. The weighted mean fragment mass was scaled using the multiplicity mu. The scaling exponent crossed over at log(10) mu(c) approximately equal to -1.4 . In the small mu (<< mu(c) ) regime, the binomial multiplicative (BM) model was suitable and the fragment mass distribution obeyed log-normal form. However, in the large mu (>> mu(c) ) regime, in which a clear power-law cumulative fragment mass distribution was observed, it was impossible to describe the scaling exponent using the BM model. We also found that the scaling exponent of the cumulative fragment mass distribution depended on the manner of impact (loading conditions): it was 0.5 in the vertical sandwich experiment and approximately 1.0 in the horizontal sandwich experiment.
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Affiliation(s)
- Hiroaki Katsuragi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan.
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Lejeune A, Perdang J. Thermodynamics from three-dimensional many-body fragmentation simulations on a cellular automaton model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046201. [PMID: 15600489 DOI: 10.1103/physreve.70.046201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2004] [Indexed: 05/24/2023]
Abstract
The thermal equilibrium of many-body systems subject to finite range interactions is investigated numerically, by means of a multipurpose 3D cellular automaton dynamic model developed by the authors. The numerical experiments, carried out at fixed number of bodies, volume and energy, demonstrate the formation of an equilibrium among 3D aggregates of bodies. The distribution of the aggregates against size obeys a power law of (negative) exponent tau approximately 2.2 (against 1.3 in 2D). Our experiments, indicating that the exponent is insensitive to the precise parameter values and the precise parametrization of the interactions, are consistent with the idea of the existence of a universality class corresponding to the thermal equilibrium. The numerical value for the exponent tau is in agreement with the theoretical thermal equilibrium analyses based on various other approaches, numerical and semianalytical, indicating that the cellular automaton approach provides an adequate methodology to investigate thermal equilibria. In this paper, as an illustration of this method, we refer to the problem of formation of clusters of nucleons in heavy ion collisions of nuclei leading on to fragmentation. The theoretical tau value, however, corresponding to the thermal equilibrium among the aggregation clusters, is 15 percent lower than the empirical value ( approximately 2.6 ) , as measured in laboratory nuclear fragmentation experiments induced by collision. There is then only a very approximate correspondence between the experimental and the thermal equilibrium value. On the basis of the results of this paper and of a previous paper of this series, we conjecture that the approximate agreement is due to a partial establishment of a thermodynamic equilibrium during the collision of the nuclei. The thermal equilibrium gives the main contribution to the observed tau value; the deviation from this possibly universal value is largely the consequence of the lack of full thermal equilibrium in actual laboratory experiments. This conjecture is extended to interpret the observed ubiquity of power laws of exponents exceeding 2.2, which refer to the distribution of various types of matter in 3D space.
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Affiliation(s)
- A Lejeune
- Université de Liège, Institut de Physique, B5 Sart-Tilman, B-4000 Liège 1, Belgium.
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Aström JA, Linna RP, Timonen J, Møller PF, Oddershede L. Exponential and power-law mass distributions in brittle fragmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:026104. [PMID: 15447542 DOI: 10.1103/physreve.70.026104] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2004] [Indexed: 05/24/2023]
Abstract
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s(-(2D-1)/D) f(1) (- (2/lambda)(D) s)+ f(2) (- s(-1 )(0 ) (lambda+ s(1/D) )(D) ), where D is the Euclidean dimension of the space, lambda is the penetration depth, and f(1) and f(2) can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s(0) was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s(0) close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1, L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
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Affiliation(s)
- J A Aström
- Center for Scientific Computing, P. O. Box 405, FIN-02101 Esbo, Finland
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48
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Wittel F, Kun F, Herrmann HJ, Kröplin BH. Fragmentation of shells. PHYSICAL REVIEW LETTERS 2004; 93:035504. [PMID: 15323834 DOI: 10.1103/physrevlett.93.035504] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2004] [Indexed: 05/24/2023]
Abstract
We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.
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Affiliation(s)
- F Wittel
- Institute of Statics and Dynamics of Aerospace Structures, University of Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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49
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Aström JA, Ouchterlony F, Linna RP, Timonen J. Universal dynamic fragmentation in D dimensions. PHYSICAL REVIEW LETTERS 2004; 92:245506. [PMID: 15245098 DOI: 10.1103/physrevlett.92.245506] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2003] [Indexed: 05/24/2023]
Abstract
A generic model is introduced for brittle fragmentation in D dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for D=2. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for D=3. In the experiments the nonzero grain size of rock causes deviation from the ideal model distribution in the small-size limit. The size of the cutoff seems to diverge at the minimum energy sufficient for fragmentation to occur, but the scaling exponent is not universal.
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Affiliation(s)
- J A Aström
- Centre for Scientific Computing, P.O. Box 405, FIN-02101 Esbo, Finland
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50
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Katsuragi H, Sugino D, Honjo H. Scaling of impact fragmentation near the critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:046105. [PMID: 14683000 DOI: 10.1103/physreve.68.046105] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2003] [Indexed: 05/24/2023]
Abstract
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low-impact-energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control-parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power law. The exponent of this power law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher-order moments of the fragment mass distributions, and obtained multiscaling exponents that agreed with those of the simple biased cascade model.
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Affiliation(s)
- Hiroaki Katsuragi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan.
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