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Rao A, Sanjay S, Dey V, Ahmadi M, Yadav P, Venugopalrao A, Bhat N, Kooi B, Raghavan S, Nukala P. Realizing avalanche criticality in neuromorphic networks on a 2D hBN platform. MATERIALS HORIZONS 2023; 10:5235-5245. [PMID: 37740285 DOI: 10.1039/d3mh01000g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
Networks and systems which exhibit brain-like behavior can analyze information from intrinsically noisy and unstructured data with very low power consumption. Such characteristics arise due to the critical nature and complex interconnectivity of the brain and its neuronal network. We demonstrate a system comprising of multilayer hexagonal boron nitride (hBN) films contacted with silver (Ag), which can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between the high resistance state (HRS) and the low resistance state (LRS). In the HRS, Ag clusters (nodes) intercalate in the van der Waals gaps of hBN forming a network of tunnel junctions, whereas the LRS contains a network of Ag filaments. The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. These networks can be tuned from one to another with voltage as a control parameter. For the first time, two different neural networks are realized in a single CMOS compatible, 2D material platform.
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Affiliation(s)
- Ankit Rao
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Sooraj Sanjay
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Vivek Dey
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Majid Ahmadi
- Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
| | - Pramod Yadav
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Anirudh Venugopalrao
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Navakanta Bhat
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Bart Kooi
- Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
- CogniGron Center, University of Groningen, Groningen, 9747 AG, The Netherlands
| | - Srinivasan Raghavan
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
| | - Pavan Nukala
- Centre for Nano Science and Engineering, Indian Institute of Science, Bengaluru 560012, India.
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2
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Wiese KJ. Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:086502. [PMID: 35943081 DOI: 10.1088/1361-6633/ac4648] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 12/23/2021] [Indexed: 06/15/2023]
Abstract
Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.
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Affiliation(s)
- Kay Jörg Wiese
- Laboratoire de physique, Département de physique de l'ENS, École normale supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France
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3
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Hong X, Desmond KW, Chen D, Weeks ER. Clogging and avalanches in quasi-two-dimensional emulsion hopper flow. Phys Rev E 2022; 105:014603. [PMID: 35193244 DOI: 10.1103/physreve.105.014603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 12/22/2021] [Indexed: 11/07/2022]
Abstract
We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.
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Affiliation(s)
- Xia Hong
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Kenneth W Desmond
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Dandan Chen
- State Key Laboratory of Radiation Medicine and Protection, School of Radiation Medicine and Protection, Soochow University, Suzhou 215123, China.,School of Radiation Medicine and Protection, Medical College of Soochow University, Suzhou 215123, China
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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4
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Schulman LS. Apparent Power Laws Can Occur without Criticality. ENTROPY 2021; 23:e23111486. [PMID: 34828184 PMCID: PMC8624822 DOI: 10.3390/e23111486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 11/09/2021] [Indexed: 11/16/2022]
Abstract
Power laws often lead to the conclusion that self-organized criticality is at work. This is not the case, and power laws can also occur away from criticality or can occur for other reasons.
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5
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Ter Burg C, Wiese KJ. Mean-field theories for depinning and their experimental signatures. Phys Rev E 2021; 103:052114. [PMID: 34134250 DOI: 10.1103/physreve.103.052114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 04/17/2021] [Indexed: 06/12/2023]
Abstract
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position u of its center of mass and the statistics of the forces F(u). There are two proposals how to model the latter: as a random walk (ABBM model), or as uncorrelated forces at integer u (discretized particle model, DPM). While for many experiments the ABBM model (in the literature misleadingly equated with mean-field theory) makes quantitatively correct predictions for the distributions of velocities, or avalanche size and duration, the microscopic disorder force-force correlations cannot grow linearly, and thus unboundedly as a random walk, with distance. Even the effective (renormalized) disorder forces which do so at small distances are bounded at large distances. To describe both regimes, we model forces as an Ornstein-Uhlenbeck process. The latter has the statistics of a random walk at small scales, and is uncorrelated at large scales. By connecting to results in both limits, we solve the model largely analytically, allowing us to describe in all regimes the distributions of velocity, avalanche size, and duration. To establish experimental signatures of this transition, we study the response function, and the correlation function of position u, velocity u[over ̇], and forces F under slow driving with velocity v>0. While at v=0 force or position correlations have a cusp at the origin and then decay at least exponentially fast to zero, this cusp is rounded at a finite driving velocity. We give a detailed analytic analysis for this rounding by velocity, which allows us, given experimental data, to extract the timescale of the response function, and to reconstruct the force-force correlator at v=0. The latter is the central object of the field theory, and as such contains detailed information about the universality class in question. We test our predictions by careful numerical simulations extending over up to ten orders in magnitude.
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Affiliation(s)
- Cathelijne Ter Burg
- Laboratoire de Physique de l'Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France
| | - Kay Jörg Wiese
- Laboratoire de Physique de l'Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France
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6
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Tückmantel P, Gaponenko I, Caballero N, Agar JC, Martin LW, Giamarchi T, Paruch P. Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in Pb(Zr_{0.2}Ti_{0.8})O_{3} Thin Films. PHYSICAL REVIEW LETTERS 2021; 126:117601. [PMID: 33798378 DOI: 10.1103/physrevlett.126.117601] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Revised: 10/28/2020] [Accepted: 01/26/2021] [Indexed: 06/12/2023]
Abstract
Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98-2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered-the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.
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Affiliation(s)
- Philippe Tückmantel
- Department of Quantum Matter Physics, University of Geneva, CH-1211, Geneva, Switzerland
| | - Iaroslav Gaponenko
- Department of Quantum Matter Physics, University of Geneva, CH-1211, Geneva, Switzerland
| | - Nirvana Caballero
- Department of Quantum Matter Physics, University of Geneva, CH-1211, Geneva, Switzerland
| | - Joshua C Agar
- Department of Material Science and Engineering, University of California, Berkeley, California 94720, USA
| | - Lane W Martin
- Department of Material Science and Engineering, University of California, Berkeley, California 94720, USA
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, University of Geneva, CH-1211, Geneva, Switzerland
| | - Patrycja Paruch
- Department of Quantum Matter Physics, University of Geneva, CH-1211, Geneva, Switzerland
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7
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Cheng C, Zadeh AA, Kondic L. Correlating the force network evolution and dynamics in slider experiments. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124902007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.
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8
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Non-Gaussian tail in the force distribution: a hallmark of correlated disorder in the host media of elastic objects. Sci Rep 2020; 10:19452. [PMID: 33173105 PMCID: PMC7655960 DOI: 10.1038/s41598-020-76529-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Accepted: 10/09/2020] [Indexed: 11/11/2022] Open
Abstract
Inferring the nature of disorder in the media where elastic objects are nucleated is of crucial importance for many applications but remains a challenging basic-science problem. Here we propose a method to discern whether weak-point or strong-correlated disorder dominates based on characterizing the distribution of the interaction forces between objects mapped in large fields-of-view. We illustrate our proposal with the case-study system of vortex structures nucleated in type-II superconductors with different pinning landscapes. Interaction force distributions are computed from individual vortex positions imaged in thousands-vortices fields-of-view in a two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated in point-disordered media present Gaussian distributions of the interaction force components. In contrast, if the media have dilute and randomly-distributed correlated disorder, these distributions present non-Gaussian algebraically-decaying tails for large force magnitudes. We propose that detecting this deviation from the Gaussian behavior is a fingerprint of strong disorder, in our case originated from a dilute distribution of correlated pinning centers.
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9
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Najafi MN, Cheraghalizadeh J, Luković M, Herrmann HJ. Geometry-induced nonequilibrium phase transition in sandpiles. Phys Rev E 2020; 101:032116. [PMID: 32289889 DOI: 10.1103/physreve.101.032116] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 01/29/2020] [Indexed: 11/07/2022]
Abstract
We study the sandpile model on three-dimensional spanning Ising clusters with the temperature T treated as the control parameter. By analyzing the three-dimensional avalanches and their two-dimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOC_{T=∞}), along with a tricritical point (at T_{c}, the critical temperature of the host) between them. The transition between these two criticalities is induced by the transition in the support. The SOC_{T=∞} universality class is characterized by the exponent of the avalanche size distribution τ^{T=∞}=1.27±0.03, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets Durin and Zapperi [Phys. Rev. Lett. 84, 4705 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.4705]. The tricritical point is characterized by its own critical exponents. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP), and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of ε≡T-T_{c}/T_{c}, defining further critical exponents. Importantly, the finite-size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents β=0.19±0.02 and ν=0.75±0.05. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against T with the numerical value D_{f}=1.25±0.01.
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Affiliation(s)
- M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - J Cheraghalizadeh
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - M Luković
- Computational Physics, IfB, ETH Zurich, Stefano-Franscini-Platz 3, CH-8093 Zurich, Switzerland.,Cellulose and Wood Materials, Empa Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland
| | - H J Herrmann
- ESPCI, CNRS UMR 7636 - Laboratoire PMMH, F-75005 Paris, France
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10
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Clemmer JT, Robbins MO. Anisotropic avalanches and critical depinning of three-dimensional magnetic domain walls. Phys Rev E 2019; 100:042121. [PMID: 31770980 DOI: 10.1103/physreve.100.042121] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 11/07/2022]
Abstract
Simulations with more than 10^{12} spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field H. The interface advances in a series of avalanches whose size diverges at a critical external field H_{c}. Finite-size scaling is applied to determine critical exponents and test scaling relations. Growth is intrinsically anisotropic with the height of an avalanche normal to the interface ℓ_{⊥} scaling as the width along the interface ℓ_{∥} to a power χ=0.85±0.01. The total interface roughness is consistent with self-affine scaling with a roughness exponent ζ≈χ that is much larger than values found previously for the RFIM and related models that explicitly break orientational symmetry by requiring the interface to be single-valued. Because the RFIM maintains orientational symmetry, the interface develops overhangs that may surround unfavorable regions to create uninvaded bubbles. Overhangs complicate measures of the roughness exponent but decrease in importance with increasing system size.
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Affiliation(s)
- Joel T Clemmer
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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11
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Barés J, Bonamy D, Rosso A. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks. Phys Rev E 2019; 100:023001. [PMID: 31574622 DOI: 10.1103/physreve.100.023001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 11/07/2022]
Abstract
Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Daniel Bonamy
- SPEC/SPHYNX, DSM/IRAMIS CEA Saclay, Bat. 772, F-91191 Gif-sur-Yvette, France
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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12
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Abed Zadeh A, Barés J, Socolar JES, Behringer RP. Seismicity in sheared granular matter. Phys Rev E 2019; 99:052902. [PMID: 31212553 DOI: 10.1103/physreve.99.052902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 06/09/2023]
Abstract
We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.
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Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Joshua E S Socolar
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Robert P Behringer
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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13
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Singh A, Lee JCT, Avila KE, Chen Y, Montoya SA, Fullerton EE, Fischer P, Dahmen KA, Kevan SD, Sanyal MK, Roy S. Scaling of domain cascades in stripe and skyrmion phases. Nat Commun 2019; 10:1988. [PMID: 31040276 PMCID: PMC6491444 DOI: 10.1038/s41467-019-09934-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Accepted: 04/09/2019] [Indexed: 11/30/2022] Open
Abstract
The origin of deterministic macroscopic properties often lies in microscopic stochastic motion. Magnetic fluctuations that manifest as domain avalanches and chaotic magnetization jumps exemplify such stochastic motion and have been studied in great detail. Here we report Fourier space studies of avalanches in a system exhibiting competing magnetic stripe and skyrmion phase using a soft X-ray speckle metrology technique. We demonstrate the existence of phase boundaries and underlying critical points in the stripe and skyrmion phases. We found that distinct scaling and universality classes are associated with these domain topologies. The magnitude and frequency of abrupt magnetic domain jumps observed in the stripe phase are dramatically reduced in the skyrmion phase. Our results provide an incisive way to probe and understand phase stability in systems exhibiting complex spin topologies. Switching of magnetic materials often occurs through discrete random avalanches. Singh et al. observe sharply reduced avalanches in the topologically protected skyrmion phase of a Fe/Gd heterostructure and obtain different critical behaviour in the stripe and skyrmion phases, suggesting distinct universality classes.
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Affiliation(s)
- A Singh
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata, West Bengal, 700064, India
| | - J C T Lee
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.,Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - K E Avila
- Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA
| | - Y Chen
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - S A Montoya
- Center for Memory and Recording Research, University of California San Diego, La Jolla, CA, 92093, USA
| | - E E Fullerton
- Center for Memory and Recording Research, University of California San Diego, La Jolla, CA, 92093, USA
| | - P Fischer
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.,Department of Physics, University of California, Santa Cruz, CA, 95064, USA
| | - K A Dahmen
- Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA
| | - S D Kevan
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - M K Sanyal
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata, West Bengal, 700064, India
| | - S Roy
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.
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14
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Abed Zadeh A, Barés J, Behringer RP. Crackling to periodic dynamics in granular media. Phys Rev E 2019; 99:040901. [PMID: 31108659 DOI: 10.1103/physreve.99.040901] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2018] [Indexed: 06/09/2023]
Abstract
We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.
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Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Robert P Behringer
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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15
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Abstract
Many systems crackle, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials. Despite the diversity in essence, the noise emitted in these dynamical systems consists of avalanche-like events with broad range of sizes and durations, characterized by power-law avalanche distributions and typical average avalanche shape that are fingerprints describing the universality class of the underlying avalanche dynamics. Here we focus on the crackling noise in ferromagnets and scrutinize the traditional statistics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films having different thicknesses. We show how scaling exponents and average shape of the avalanches evolve with the structural character of the materials and film thickness. We find quantitative agreement between experiment and theoretical predictions of models for the magnetic domain wall dynamics, and then elucidate the universality classes of Barkhausen avalanches in ferromagnetic films. Thereby, we observe for the first time the dimensional crossover in the domain wall dynamics and the outcomes of the interplay between system dimensionality and range of interactions governing the domain wall dynamics on Barkhausen avalanches.
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16
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Spasojević D, Mijatović S, Navas-Portella V, Vives E. Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model. Phys Rev E 2018; 97:012109. [PMID: 29448319 DOI: 10.1103/physreve.97.012109] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Indexed: 11/07/2022]
Abstract
We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L×L×l which explain the size-driven critical crossover from two dimensions (l=const, L→∞) to three dimensions (l∝L→∞). A model of effective critical disorder R_{c}^{eff}(l,L) with a unique fitting parameter and no free parameters in the R_{c}^{eff}(l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia
| | | | - Víctor Navas-Portella
- Centre de Recerca Matematica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain; Barcelona Graduate School of Mathematics (BGSMath), Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain; and Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, E-08007 Barcelona, Spain
| | - Eduard Vives
- Departament de Matèria Condensada, Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Catalonia, Spain
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17
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Dutta S, Siddiqui SA, Currivan-Incorvia JA, Ross CA, Baldo MA. The Spatial Resolution Limit for an Individual Domain Wall in Magnetic Nanowires. NANO LETTERS 2017; 17:5869-5874. [PMID: 28813156 DOI: 10.1021/acs.nanolett.7b03199] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Magnetic nanowires are the foundation of several promising nonvolatile computing devices, most notably magnetic racetrack memory and domain wall logic. Here, we determine the analog information capacity in these technologies, analyzing a magnetic nanowire containing a single domain wall. Although wires can be deliberately patterned with notches to define discrete positions for domain walls, the line edge roughness of the wire can also trap domain walls at dimensions below the resolution of the fabrication process, determining the fundamental resolution limit for the placement of a domain wall. Using a fractal model for the edge roughness, we show theoretically and experimentally that the analog information capacity for wires is limited by the self-affine statistics of the wire edge roughness, a relevant result for domain wall devices scaled to regimes where edge roughness dominates the energy landscape in which the walls move.
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18
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Durin G, Bohn F, Corrêa MA, Sommer RL, Le Doussal P, Wiese KJ. Quantitative Scaling of Magnetic Avalanches. PHYSICAL REVIEW LETTERS 2016; 117:087201. [PMID: 27588876 DOI: 10.1103/physrevlett.117.087201] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2016] [Indexed: 06/06/2023]
Abstract
We provide the first quantitative comparison between Barkhausen noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean field. We study different classes of soft magnetic materials, including polycrystals and amorphous samples-which are characterized by long-range and short-range elasticity, respectively-both for thick and thin samples, i.e., with and without eddy currents. The temporal avalanche shape at fixed size as well as observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents.
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Affiliation(s)
- G Durin
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy
- ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy
| | - F Bohn
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-900 Natal, RN, Brazil
| | - M A Corrêa
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-900 Natal, RN, Brazil
| | - R L Sommer
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil
| | - P Le Doussal
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
| | - K J Wiese
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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19
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Kurbah L, Thongjaomayum D, Shukla P. Nonequilibrium random-field Ising model on a diluted triangular lattice. Phys Rev E 2015; 91:012131. [PMID: 25679594 DOI: 10.1103/physreve.91.012131] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2013] [Indexed: 11/07/2022]
Abstract
We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number z(eff) in the range 3≤z(eff)≤6. We find that the model supports critical behavior in the range 4<z(eff)≤6, but the critical exponents are independent of z(eff). The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.
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Affiliation(s)
- Lobisor Kurbah
- Physics Department, North Eastern Hill University, Shillong-793 022, India
| | | | - Prabodh Shukla
- Physics Department, North Eastern Hill University, Shillong-793 022, India
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20
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Bohn F, Corrêa MA, Carara M, Papanikolaou S, Durin G, Sommer RL. Statistical properties of Barkhausen noise in amorphous ferromagnetic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032821. [PMID: 25314495 DOI: 10.1103/physreve.90.032821] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 06/04/2023]
Abstract
We investigate the statistical properties of the Barkhausen noise in amorphous ferromagnetic films with thicknesses in the range between 100 and 1000 nm. From Barkhausen noise time series measured with the traditional inductive technique, we perform a wide statistical analysis and establish the scaling exponents τ,α,1/σνz, and ϑ. We also focus on the average shape of the avalanches, which gives further indications on the domain-wall dynamics. Based on experimental results, we group the amorphous films in a single universality class, characterized by scaling exponents τ=1.28±0.02,α=1.52±0.3, and 1/σνz=ϑ=1.83±0.03, values compatible with that obtained for several bulk amorphous magnetic materials. Besides, we verify that the avalanche shape depends on the universality class. By considering the theoretical models for the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium found in literature, we interpret the results and identify an experimental evidence that these amorphous films, within this thickness range, present a typical three-dimensional magnetic behavior with predominant short-range elastic interactions governing the domain-wall dynamics. Moreover, we provide experimental support for the validity of a general scaling form for the average avalanche shape for non-mean-field systems.
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Affiliation(s)
- F Bohn
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
| | - M A Corrêa
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
| | - M Carara
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, RS, Brazil
| | - S Papanikolaou
- Department of Mechanical Engineering and Materials Science and Department of Physics, Yale University, New Haven, Connecticut 06520-8286, USA
| | - G Durin
- INRIM, Strada delle Cacce 91, 10135 Torino, Italy and ISI Foundation, Viale S. Severo 65, 10133 Torino, Italy
| | - R L Sommer
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil
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21
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Le Doussal P, Wiese KJ. Avalanche dynamics of elastic interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022106. [PMID: 24032774 DOI: 10.1103/physreve.88.022106] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2013] [Indexed: 06/02/2023]
Abstract
Slowly driven elastic interfaces, such as domain walls in dirty magnets, contact lines wetting a nonhomogeneous substrate, or cracks in brittle disordered material proceed via intermittent motion, called avalanches. Here we develop a field-theoretic treatment to calculate, from first principles, the space-time statistics of instantaneous velocities within an avalanche. For elastic interfaces at (or above) their (internal) upper critical dimension d≥d(uc) (d(uc)=2,4 respectively for long-ranged and short-ranged elasticity) we show that the field theory for the center of mass reduces to the motion of a point particle in a random-force landscape, which is itself a random walk [Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model]. Furthermore, the full spatial dependence of the velocity correlations is described by the Brownian-force model (BFM) where each point of the interface sees an independent Brownian-force landscape. Both ABBM and BFM can be solved exactly in any dimension d (for monotonous driving) by summing tree graphs, equivalent to solving a (nonlinear) instanton equation. We focus on the limit of slow uniform driving. This tree approximation is the mean-field theory (MFT) for realistic interfaces in short-ranged disorder, up to the renormalization of two parameters at d=d(uc). We calculate a number of observables of direct experimental interest: Both for the center of mass, and for a given Fourier mode q, we obtain various correlations and probability distribution functions (PDF's) of the velocity inside an avalanche, as well as the avalanche shape and its fluctuations (second shape). Within MFT we find that velocity correlations at nonzero q are asymmetric under time reversal. Next we calculate, beyond MFT, i.e., including loop corrections, the one-time PDF of the center-of-mass velocity u[over ·] for dimension d<d(uc). The singularity at small velocity P(u[over ·])~1/u[over ·](a) is substantially reduced from a=1 (MFT) to a=1-2/9(4-d)+... (short-ranged elasticity) and a=1-4/9(2-d)+... (long-ranged elasticity). We show how the dynamical theory recovers the avalanche-size distribution, and how the instanton relates to the response to an infinitesimal step in the force.
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Affiliation(s)
- Pierre Le Doussal
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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22
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Le Doussal P, Petković A, Wiese KJ. Distribution of velocities and acceleration for a particle in Brownian correlated disorder: inertial case. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061116. [PMID: 23005060 DOI: 10.1103/physreve.85.061116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2012] [Indexed: 06/01/2023]
Abstract
We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It is the extension of the mean-field Alessandro-Beatrice- Bertotti-Montorsi (ABBM) model in presence of an inertial mass m. While the ABBM model can be solved exactly, its extension to inertia exhibits complicated history dependence due to oscillations and backward motion. The characteristic scales for avalanche motion are studied from numerics and qualitative arguments. To make analytical progress, we consider two variants which coincide with the original model whenever the particle moves only forward. Using a combination of analytical and numerical methods together with simulations, we characterize the distributions of instantaneous acceleration and velocity, and compare them in these three models. We show that for large driving velocity, all three models share the same large-deviation function for positive velocities, which is obtained analytically for small and large m, as well as for m=6/25. The effect of small additional thermal and quantum fluctuations can be treated within an approximate method.
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Affiliation(s)
- Pierre Le Doussal
- Laboratoire de Physique Théorique-CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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23
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Le Doussal P, Wiese KJ. First-principles derivation of static avalanche-size distributions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061102. [PMID: 23005046 DOI: 10.1103/physreve.85.061102] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2011] [Indexed: 06/01/2023]
Abstract
We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an efficient and systematic method to compute the statistics of avalanche sizes and manifold displacements. The tree-level calculation, i.e., mean-field limit, is obtained by solving a saddle-point equation. Graphically, it can be interpreted as the sum of all tree graphs. The 1-loop corrections are computed using results from the functional renormalization group. At the upper critical dimension the shock statistics is described by the Brownian force model (BFM), the static version of the so-called Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model in the nonequilibrium context of depinning. This model can itself be treated exactly in any dimension and its shock statistics is that of a Lévy process. Contact is made with classical results in probability theory on the Burgers equation with Brownian initial conditions. In particular we obtain a functional extension of an evolution equation introduced by Carraro and Duchon, which recursively constructs the tree diagrams in the field theory.
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Affiliation(s)
- Pierre Le Doussal
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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24
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Jo HH, Ha M. Universality classes and crossover behaviors in non-Abelian directed sandpiles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041101. [PMID: 21230232 DOI: 10.1103/physreve.82.041101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2010] [Indexed: 05/30/2023]
Abstract
We study universality classes and crossover behaviors in non-Abelian directed sandpile models in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the algebraic decay of the grain density along the propagation direction of an avalanche. Crossover scaling behaviors are observed in the grain density due to the interplay between the toppling randomness and the parity of the threshold value. In the presence of such crossovers, we show that the broadness of the grain distribution plays a crucial role in resolving the ambiguity of the universality class. Finally, we claim that the metastable pattern analysis is important as much as the conventional analysis of avalanche dynamics.
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Affiliation(s)
- Hang-Hyun Jo
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
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25
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Zhou NJ, Zheng B. Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031139. [PMID: 21230057 DOI: 10.1103/physreve.82.031139] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2010] [Revised: 09/05/2010] [Indexed: 05/30/2023]
Abstract
With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field (DRFIM). We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this should be an important mechanism leading the DRFIM model to a different universality class from the Edwards-Wilkinson equation with quenched disorder.
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Affiliation(s)
- N J Zhou
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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26
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Le Doussal P, Wiese KJ. Size distributions of shocks and static avalanches from the functional renormalization group. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051106. [PMID: 19518415 DOI: 10.1103/physreve.79.051106] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2009] [Indexed: 05/27/2023]
Abstract
Interfaces pinned by quenched disorder are often used to model jerky self-organized critical motion. We study static avalanches, or shocks, defined here as jumps between distinct global minima upon changing an external field. We show how the full statistics of these jumps is encoded in the functional-renormalization-group fixed-point functions. This allows us to obtain the size distribution P(S) of static avalanches in an expansion in the internal dimension d of the interface. Near and above d=4 this yields the mean-field distribution P(S) approximately S;{-3/2}e;{-S4S_{m}} , where S_{m} is a large-scale cutoff, in some cases calculable. Resumming all one-loop contributions, we find P(S) approximately S;{-tau}exp(C(SS_{m});{1/2}-B/4(S/S_{m});{delta}) , where B , C , delta , and tau are obtained to first order in =4-d . Our result is consistent to O() with the relation tau=tau_{zeta}:=2-2/d+zeta , where zeta is the static roughness exponent, often conjectured to hold at depinning. Our calculation applies to all static universality classes, including random-bond, random-field, and random-periodic disorders. Extended to long-range elastic systems, it yields a different size distribution for the case of contact-line elasticity, with an exponent compatible with tau=2-1/d+zeta to O(=2-d) . We discuss consequences for avalanches at depinning and for sandpile models, relations to Burgers turbulence and the possibility that the relation tau=tau_{zeta} be violated to higher loop order. Finally, we show that the avalanche-size distribution on a hyperplane of codimension one is in mean field (valid close to and above d=4 ) given by P(S) approximately K_{13}(S)S , where K is the Bessel- K function, thus tau_{hyperplane}=4/3 .
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Affiliation(s)
- Pierre Le Doussal
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, CNRS, 24 rue Lhomond, 75231 Paris Cedex, France
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27
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Le Doussal P, Wiese KJ. Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051105. [PMID: 19518414 DOI: 10.1103/physreve.79.051105] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2008] [Indexed: 05/27/2023]
Abstract
We review how the renormalized force correlator Delta(micro) , the function computed in the functional renormalization-group (RG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a one-dimensional random-force landscape. The limit of small velocity allows one to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Fréchet. For each class we obtain analytically the universal function Delta(micro) , the corrections to the critical force, and the joint probability distribution of avalanche sizes s and waiting times w . We find P(s)=P(w) for all three cases. All results are checked numerically. For a Brownian force landscape, known as the Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model, avalanche distributions and Delta(micro) can be computed for any velocity. For two-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor Delta_{ij}(micro[over ]) , and to extract the anisotropic scaling exponents zeta_{x}>zeta_{y} . We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered, e.g., in some models of global warming. We give the joint distribution of the time s between two successive records and their difference in value w .
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Affiliation(s)
- Pierre Le Doussal
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
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28
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Chandni U, Ghosh A, Vijaya HS, Mohan S. Criticality of tuning in athermal phase transitions. PHYSICAL REVIEW LETTERS 2009; 102:025701. [PMID: 19257290 DOI: 10.1103/physrevlett.102.025701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2008] [Indexed: 05/27/2023]
Abstract
We experimentally address the importance of tuning in athermal phase transitions, which are triggered only by a slowly varying external field acting as tuning parameter. Using higher order statistics of fluctuations, evidence consistent with the existence a singular critical instability is detected, in spite of an apparent universal self-similar kinetics over a broad range of driving force. The results as well as the experimental technique are likely to be of significance to many slowly driven nonequilibrium systems from geophysics to material science which display avalanche dynamics.
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Affiliation(s)
- U Chandni
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India.
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29
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Pérez-Reche FJ, Truskinovsky L, Zanzotto G. Driving-induced crossover: from classical criticality to self-organized criticality. PHYSICAL REVIEW LETTERS 2008; 101:230601. [PMID: 19113534 DOI: 10.1103/physrevlett.101.230601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2008] [Revised: 11/04/2008] [Indexed: 05/27/2023]
Abstract
We propose a spin model with quenched disorder which exhibits in slow driving two drastically different types of critical nonequilibrium steady states. One of them corresponds to classical criticality requiring fine-tuning of the disorder. The other is a self-organized criticality which is insensitive to disorder. The crossover between the two types of criticality is determined by the mode of driving. As one moves from "soft" to "hard" driving the universality class of the critical point changes from a classical order-disorder to a quenched Edwards-Wilkinson universality class. The model is viewed as prototypical for a broad class of physical phenomena ranging from magnetism to earthquakes.
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Xia J, Gould H, Klein W, Rundle JB. Near-mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable-range stress transfer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031132. [PMID: 18517354 DOI: 10.1103/physreve.77.031132] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2007] [Revised: 02/20/2008] [Indexed: 05/26/2023]
Abstract
Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.
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Affiliation(s)
- Junchao Xia
- Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
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31
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de Queiroz SLA. Wavelet transforms in a critical interface model for Barkhausen noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021131. [PMID: 18352011 DOI: 10.1103/physreve.77.021131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Revised: 08/08/2007] [Indexed: 05/26/2023]
Abstract
We discuss the application of wavelet transforms to a critical interface model which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of the surface tension), the effective interface roughness exponent zeta is approximately 1.20 , close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as 1/f(1.5) for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
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32
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Tiampo KF, Rundle JB, Klein W, Holliday J, Sá Martins JS, Ferguson CD. Ergodicity in natural earthquake fault networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:066107. [PMID: 17677325 DOI: 10.1103/physreve.75.066107] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2006] [Revised: 04/08/2007] [Indexed: 05/16/2023]
Abstract
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F. Tiampo, J. B. Rundle, W. Klein, J. S. Sá Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal evolution.
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Affiliation(s)
- K F Tiampo
- Department of Earth Sciences, University of Western Ontario, London, Ontario, N6A 5B7 Canada.
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33
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de Queiroz SLA. Roughness of time series in a critical interface model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:066104. [PMID: 16486007 DOI: 10.1103/physreve.72.066104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2005] [Revised: 08/01/2005] [Indexed: 05/06/2023]
Abstract
We study roughness probability distribution functions (PDFs) of the time signal for a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. Starting with time "windows" of data collection much larger than the system's internal "loading time" (related to demagnetization effects), we show that the initial Gaussian shape of the PDF evolves into a double-peaked structure as window width decreases. We advance a plausible physical explanation for such a structure, which is broadly compatible with the observed numerical data. Connections to experiment are suggested.
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro RJ, Brazil.
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Deutsch JM, Mai T. Mechanism for nonequilibrium symmetry breaking and pattern formation in magnetic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016115. [PMID: 16090044 DOI: 10.1103/physreve.72.016115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2005] [Indexed: 05/03/2023]
Abstract
Magnetic thin films exhibit a strong variation in properties depending on their degree of disorder. Recent coherent x-ray speckle experiments on magnetic films have measured the loss of correlation between configurations at opposite fields and at the same field, upon repeated field cycling. We perform finite temperature numerical simulations on these systems that provide a comprehensive explanation for the experimental results. The simulations demonstrate, in accordance with experiments, that the memory of configurations increases with film disorder. We find that nontrivial microscopic differences exist between the zero field spin configuration obtained by starting from a large positive field and the zero field configuration starting at a large negative field. This seemingly paradoxical behavior is due to the nature of the vector spin dynamics and is also seen in the experiments. For low disorder, there is an instability which causes the spontaneous growth of linelike domains at a critical field, also in accord with experiments. It is this unstable growth, which is highly sensitive to thermal noise, that is responsible for the small correlation between patterns under repeated cycling. The domain patterns, hysteresis loops, and memory properties of our simulated systems match remarkably well with the real experimental systems.
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Affiliation(s)
- J M Deutsch
- Department of Physics, University of California, Santa Cruz, California 95064, USA
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Parteli EJR, Gomes MAF, Brito VP. Nontrivial temporal scaling in a Galilean stick-slip dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036137. [PMID: 15903523 DOI: 10.1103/physreve.71.036137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2004] [Revised: 12/14/2004] [Indexed: 05/02/2023]
Abstract
We examine the stick-slip fluctuating response of a rough massive nonrotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The experiments presented here, which are reminiscent of Galileo's works with rolling objects on inclines, have brought in the last years important insights into the friction between surfaces in relative motion and are of relevance for earthquakes, differing from classical block-spring models by the mechanism of energy input in the system. Robust nontrivial temporal scaling laws appearing in the dynamics of this system are reported, and it is shown that the time-support where dissipation occurs approaches a statistical fractal set with a fixed value of dimension. The distribution of periods of inactivity in the intermittent motion of the cylinder is also studied and found to be closely related to the lacunarity of a random version of the classic triadic Cantor set on the line.
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Affiliation(s)
- E J R Parteli
- Institut für Computerphysik, ICP, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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Queiroz SLAD. Search for universal roughness distributions in a critical interface model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016134. [PMID: 15697685 DOI: 10.1103/physreve.71.016134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2004] [Revised: 10/08/2004] [Indexed: 05/24/2023]
Abstract
We study the probability distributions of interface roughness, sampled among successive equilibrium configurations of a single-interface model used for the description of Barkhausen noise in disordered magnets, in space dimensionalities d = 2 and 3. The influence of a self-regulating (demagnetization) mechanism is investigated, and evidence is given to show that it is irrelevant, which implies that the model belongs to the Edwards-Wilkinson universality class. We attempt to fit our data to the class of roughness distributions associated to 1/falpha noise. Periodic, free, "window," and mixed boundary conditions are examined, with rather distinct results as regards quality of fits to 1/falpha distributions.
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro RJ, Brazil.
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Deutsch JM, Dhar A, Narayan O. Return to return point memory. PHYSICAL REVIEW LETTERS 2004; 92:227203. [PMID: 15245257 DOI: 10.1103/physrevlett.92.227203] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2003] [Indexed: 05/24/2023]
Abstract
We describe a new class of systems exhibiting return point memory (RPM), different from those discussed before in the context of ferromagnets. We show numerically that one-dimensional random Ising antiferromagnets have exact RPM when evolving from a large field, but not when started at finite field, unlike the ferromagnetic case. This implies that the standard approach to understanding ferromagnetic RPM will fail for this case. We also demonstrate RPM with a set of variables that keeps track of spin flips at each site. Conventional RPM for the spins is a projection of this result, suggesting that spin flip variables might be a more fundamental representation of the dynamics. We also present a mapping that embeds the antiferromagnetic chain in a two-dimensional ferromagnet, and prove RPM for spin-exchange dynamics in the interior of the chain with this mapping.
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Affiliation(s)
- J M Deutsch
- Department of Physics, University of California, Santa Cruz, California 95064, USA
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Schwarz A, Liebmann M, Kaiser U, Wiesendanger R, Noh TW, Kim DW. Visualization of the Barkhausen effect by magnetic force microscopy. PHYSICAL REVIEW LETTERS 2004; 92:077206. [PMID: 14995882 DOI: 10.1103/physrevlett.92.077206] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2003] [Indexed: 05/24/2023]
Abstract
By visualization of the Barkhausen effect using magnetic force microscopy we are able to provide detailed information about the physical principles that govern the magnetization reversal of a granular ferromagnetic thin film with perpendicular anisotropy. Individual Barkhausen volumes are localized and distinguished as either newly nucleated or grown by domain wall propagation. The Gaussian size distribution of nucleated Barkhausen volumes indicates an uncorrelated random process, while grown Barkhausen volumes exhibit an inverse power law distribution, which points towards a critical behavior during domain wall motion.
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Affiliation(s)
- Alexander Schwarz
- Institute of Applied Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany.
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de Queiroz SLA. Dimensional crossover and universal roughness distributions in Barkhausen noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:026126. [PMID: 14995539 DOI: 10.1103/physreve.69.026126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2003] [Indexed: 05/24/2023]
Abstract
We investigate the dimensional crossover of scaling properties of avalanches (domain-wall jumps) in a single-interface model, used for the description of Barkhausen noise in disordered magnets. By varying the transverse aspect ratio A=L(y)/L(x) of simulated samples, the system dimensionality changes from two to three. We find that perturbing away from d=2 is a relevant field. The exponent tau characterizing the power-law scaling of avalanche distributions varies between 1.06(1) for d=2 and 1.275(15) for d=3, according to a crossover function f(x), x identical with (L-1x)(phi)/A, with phi=0.95(3). We discuss the possible relevance of our results to the interpretation of thin-film measurements of Barkhausen noise. We also study the probability distributions of interface roughness, sampled among successive equilibrium configurations in the Barkhausen noise regime. Attempts to fit our data to the class of universality distributions associated to 1/f(alpha) noise give alpha approximately 1-1.1 for d=2 and 3 (provided that suitable boundary conditions are used in the latter case).
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, Rio de Janeiro, Brazil.
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Tiampo KF, Rundle JB, Klein W, Martins JSS, Ferguson CD. Ergodic dynamics in a natural threshold system. PHYSICAL REVIEW LETTERS 2003; 91:238501. [PMID: 14683219 DOI: 10.1103/physrevlett.91.238501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2003] [Indexed: 05/24/2023]
Abstract
Numerical simulations suggest that certain driven, dissipative mean-field threshold systems, including earthquake models, can be characterized by statistical properties often associated with ergodic dynamics, in the same sense as stochastic Brownian motion. We applied a fluctuation metric proposed by Thirumalai and Mountain [Phys. Rev. E 47, 479 (1993)]] for statistically stationary systems and find that the natural earthquake fault system in California demonstrates similar ergodic dynamics.
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Affiliation(s)
- K F Tiampo
- CIRES, University of Colorado, Boulder, Colorado 80309, USA
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Kim DH, Choe SB, Shin SC. Direct observation of Barkhausen avalanche in Co thin films. PHYSICAL REVIEW LETTERS 2003; 90:087203. [PMID: 12633456 DOI: 10.1103/physrevlett.90.087203] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2002] [Indexed: 05/24/2023]
Abstract
We report direct full-field magneto-optical observations of Barkhausen avalanches in Co polycrystalline thin films at criticality. We provide experimental evidence for the validity of a phenomenological model of the Barkhausen avalanche originally proposed by Cizeau, Zapperi, Durin, and Stanley [Phys. Rev. Lett. 79, 4669 (1997)]], where the model describes a 180 degrees -type flexible domain wall deformed by a localized defect with consideration of long-range dipolar interaction. The Barkhausen jump areas show a power-law scaling distribution with critical exponent tau approximately 1.33 for all the samples having different thickness from 5 to 50 nm, which is in accord with the two-dimensional prediction of the model.
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Affiliation(s)
- Dong-Hyun Kim
- Department of Physics and Center for Nanospinics of Spintronic Materials, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
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Mehta AP, Mills AC, Dahmen KA, Sethna JP. Universal pulse shape scaling function and exponents: critical test for avalanche models applied to Barkhausen noise. PHYSICAL REVIEW E 2002; 65:046139. [PMID: 12005958 DOI: 10.1103/physreve.65.046139] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2001] [Indexed: 11/07/2022]
Abstract
In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the nonequilibrium zero-temperature Random Field Ising Model, we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents tau and 1/sigma nu z in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling functions as well as between different experiments.
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Affiliation(s)
- Amit P Mehta
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Rundle JB, Tiampo KF, Klein W, Sa Martins JS. Self-organization in leaky threshold systems: the influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting. Proc Natl Acad Sci U S A 2002; 99 Suppl 1:2514-21. [PMID: 11875204 PMCID: PMC128570 DOI: 10.1073/pnas.012581899] [Citation(s) in RCA: 122] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization in earthquake threshold systems at two distinct scales: (i) The "microscopic" laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive the results obtained from sliding friction experiments, and (ii) the "macroscopic" earthquake fault-system scale, in which the physics of strongly correlated earthquake fault systems can be understood by using time-dependent state vectors defined in a Hilbert space of eigenstates, similar in many respects to the mathematics of quantum mechanics. In all of these systems, long-range interactions induce the existence of locally ergodic dynamics. The existence of dissipative effects leads to the appearance of a "leaky threshold" dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of background fluctuations. At the macroscopic earthquake fault-system scale, these ideas show considerable promise as a means of forecasting future earthquake activity.
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Affiliation(s)
- J B Rundle
- Colorado Center for Chaos and Complexity and Cooperative Institute for Research in Environmental Sciences (CIRES) and Department of Physics, 216 UCB, University of Colorado, Boulder, CO 80309-0216, USA.
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de Queiroz SL, Bahiana M. Finite driving rates in interface models of Barkhausen noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066127. [PMID: 11736256 DOI: 10.1103/physreve.64.066127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2001] [Indexed: 05/23/2023]
Abstract
We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model was used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with nontrivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay approximately omega(-t), with t<2 for finite driving rates, revealing the influence of the internal structure of avalanches.
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Affiliation(s)
- S L de Queiroz
- de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil
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Abstract
Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behaviour over a huge range of sizes, their behaviour is likely to be independent of microscopic and macroscopic details, and progress can be made by the use of simple models. The fact that these models and real systems can share the same behaviour on many scales is called universality. We illustrate these ideas by using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses, and we highlight some continuing challenges in this still-evolving field.
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Affiliation(s)
- J P Sethna
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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46
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Puppin E. Statistical properties of barkhausen noise in thin Fe films. PHYSICAL REVIEW LETTERS 2000; 84:5415-5418. [PMID: 10990957 DOI: 10.1103/physrevlett.84.5415] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/1999] [Indexed: 05/23/2023]
Abstract
The statistical properties of Barkhausen noise in an epitaxial Fe film grown on MgO have been characterized with magneto-optical Kerr effect measurements. The data reveal that magnetization reversal takes place via sudden jumps between a discrete number of randomly distributed magnetic configurations. The smallest jumps occur on a scale length of 10 &mgr;m and their amplitude distribution can be fitted with a power law: P(DeltaM) = DeltaM-alpha with alpha = 1.1 and DeltaM spanning over several decades.
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Affiliation(s)
- E Puppin
- Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica, Politecnico di Milano, P.za L. da Vinci 32-20133 Milano, Italy
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Durin G, Zapperi S. Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets. PHYSICAL REVIEW LETTERS 2000; 84:4705-4708. [PMID: 10990776 DOI: 10.1103/physrevlett.84.4705] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/1999] [Indexed: 05/23/2023]
Abstract
We investigate the scaling properties of the Barkhausen effect by recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents tau = 1.50+/-0.05 or tau = 1.27+/-0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments.
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Affiliation(s)
- G Durin
- Istituto Elettrotecnico Nazionale Galileo Ferraris and INFM, Corso M. d'Azeglio 42, I-10125 Torino, Italy
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Schaffer E, Wong PZ. Contact line dynamics near the pinning threshold: a capillary rise and fall experiment. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5257-77. [PMID: 11031574 DOI: 10.1103/physreve.61.5257] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/1999] [Indexed: 04/15/2023]
Abstract
We used video microscopy to study the pinning dynamics of air/water contact lines in vertical glass capillaries. Stick-slip behavior and avalanches are observed in tubes with rough interior walls and strong pinning forces. In tubes with smooth interior walls, we find that receding contact lines in falling water columns show no evidence of pinning, but advancing contact lines in rising water columns exhibit algebraic slow down. The measured value of the critical exponent beta varies from run to run, but it is always larger than unity. Furthermore, we find that the rise dynamics varies with the waiting time preceding the experiments. These observations led us to conclude that the wetting film on the surface and other microscopic changes in the slipping region near the contact line affect the macroscopic dynamics. We discuss the differences between the real system and the existing theories that might explain the results. We also present a brief review of other studies of contact line dynamics and a numerical study of a one-dimensional model.
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Affiliation(s)
- E Schaffer
- Department of Physics and Astronomy, University of Massachusetts, Amherst 01003, USA
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Tadic B, Nowak U. Barkhausen avalanches in anisotropic ferromagnets with 180 degrees domain walls. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:4610-4613. [PMID: 11088264 DOI: 10.1103/physreve.61.4610] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/1999] [Indexed: 05/23/2023]
Abstract
We show that Barkhausen noise in two-dimensional disordered ferromagnets with extended domain walls is characterized by the avalanche size exponent tau(s)=1.54 at low disorder. With increasing disorder the characteristic domain size is reduced relative to the system size due to nucleation of new domains and a dynamic phase transition occurs to the scaling behavior with tau(s)=1.30. The exponents decrease at finite driving rate. The results agree with recently observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied anisotropic stress is varied.
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Affiliation(s)
- B Tadic
- Jozef Stefan Institute, P.O. Box 3000, 1001 Ljubljana, Slovenia
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Vazquez A, Sotolongo-Costa O. Dynamics of a domain wall in soft-magnetic materials: barkhausen effect and relation with sandpile models. PHYSICAL REVIEW LETTERS 2000; 84:1316-1319. [PMID: 11017507 DOI: 10.1103/physrevlett.84.1316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/1999] [Indexed: 05/23/2023]
Abstract
The CZDE model [P. Cizeau, S Zapperi, G. Durin, and H. E. Stanley, Phys. Rev. Lett. 79, 4669 (1997)] for the dynamics of a domain wall in soft-magnetic materials is investigated. The equation of motion for the domain wall is reduced to a dimensionless form where the control parameters are clearly identified. In this way we show that in soft-magnetic materials with low anisotropies the noise can be approximated by a columnar disorder, and perturbation theory gives a good estimate of the avalanche exponents. Moreover, the resulting exponents are found to be identical to those obtained for directed Abelian sandpile models. The analogies and differences with these models and the question of self-organized criticality in the Barkhausen effect are discussed.
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Affiliation(s)
- A Vazquez
- Department of Theoretical Physics, Faculty of Physics, Havana University, Havana 10400, Cuba
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