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Kalimuddin S, Chatterjee S, Bera A, Afzal H, Bera S, Roy DS, Das S, Debnath T, Bansal B, Mondal M. Exceptionally Slow, Long-Range, and Non-Gaussian Critical Fluctuations Dominate the Charge Density Wave Transition. PHYSICAL REVIEW LETTERS 2024; 132:266504. [PMID: 38996319 DOI: 10.1103/physrevlett.132.266504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 05/02/2024] [Accepted: 05/23/2024] [Indexed: 07/14/2024]
Abstract
(TaSe_{4})_{2}I is a well-studied quasi-one-dimensional compound long-known to have a charge-density wave (CDW) transition around 263 K. We argue that the critical fluctuations of the pinned CDW order parameter near the transition can be inferred from the resistance noise on account of their coupling to the dissipative normal carriers. Remarkably, the critical fluctuations of the CDW order parameter are slow enough to survive the thermodynamic limit and dominate the low-frequency resistance noise. The noise variance and relaxation time show rapid growth (critical opalescence and critical slowing down) within a temperature window of ϵ≈±0.1, where ϵ is the reduced temperature. This is very wide but consistent with the Ginzburg criterion. We further show that this resistance noise can be quantitatively used to extract the associated critical exponents. Below |ϵ|≲0.02, we observe a crossover from mean-field to a fluctuation-dominated regime with the critical exponents taking anomalously low values. The distribution of fluctuations in the critical transition region is skewed and strongly non-Gaussian. This non-Gaussianity is interpreted as the breakdown of the validity of the central limit theorem as the diverging coherence volume becomes comparable to the macroscopic sample size. The large magnitude critical fluctuations observed over an extended temperature range, as well as the crossover from the mean-field to the fluctuation-dominated regime highlight the role of the quasi-one-dimensional character in controlling the phase transition.
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Mozo Luis EE, Oliveira FA, de Assis TA. Accessibility of the surface fractal dimension during film growth. Phys Rev E 2023; 107:034802. [PMID: 37073068 DOI: 10.1103/physreve.107.034802] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 03/06/2023] [Indexed: 04/20/2023]
Abstract
Fractal properties on self-affine surfaces of films growing under nonequilibrium conditions are important in understanding the corresponding universality class. However, measurement of the surface fractal dimension has been intensively investigated and is still very problematic. In this work, we report the behavior of the effective fractal dimension in the context of film growth involving lattice models believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. Our results, which are presented for growth in a d-dimensional substrate (d=1,2) and use the three-point sinuosity (TPS) method, show universal scaling of the measure M, which is defined in terms of discretization of the Laplacian operator applied to the height of the film surface, M=t^{δ}g[Θ], where t is the time, g[Θ] is a scale function, δ=2β, Θ≡τt^{-1/z}, β, and z are the KPZ growth and dynamical exponents, respectively, and τ is a spatial scale length used to compute M. Importantly, we show that the effective fractal dimensions are consistent with the expected KPZ dimensions for d=1,2, if Θ≲0.3, which include a thin film regime for the extraction of the fractal dimension. This establishes the scale limits in which the TPS method can be used to accurately extract effective fractal dimensions that are consistent with those expected for the corresponding universality class. As a consequence, for the steady state, which is inaccessible to experimentalists studying film growth, the TPS method provided effective fractal dimension consistent with the KPZ ones for almost all possible τ, i.e., 1≲τ<L/2, where L is the lateral size of the substrate on which the deposit is grown. In the growth of thin films, the true fractal dimension can be observed in a narrow range of τ, the upper limit of which is of the same order of magnitude as the correlation length of the surface, indicating the limits of self-affinity of a surface in an experimentally accessible regime. This upper limit was comparatively lower for the Higuchi method or the height-difference correlation function. Scaling corrections for the measure M and the height-difference correlation function are studied analytically and compared for the Edwards-Wilkinson class at d=1, yielding similar accuracy for both methods. Importantly, we extend our discussion to a model representing diffusion-dominated growth of films and find that the TPS method achieves the corresponding fractal dimension only at steady state and in a narrow range of the scale length, compared to that found for the KPZ class.
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Affiliation(s)
- Edwin E Mozo Luis
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil
| | - Fernando A Oliveira
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil
- Instituto de Física, Universidade de Brasília, 70910-900, Brasília, DF, Brazil
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340, Niterói, RJ, Brazil
| | - Thiago A de Assis
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340, Niterói, RJ, Brazil
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Ashley BK, Hassan U. Digital filtering dissemination for optimizing impedance cytometry signal quality and counting accuracy. Biomed Microdevices 2022; 24:36. [PMID: 36305954 PMCID: PMC9635870 DOI: 10.1007/s10544-022-00636-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/04/2022] [Indexed: 11/29/2022]
Abstract
Improving biosensor performance which utilize impedance cytometry is a highly interested research topic for many clinical and diagnostic settings. During development, a sensor's design and external factors are rigorously optimized, but improvements in signal quality and interpretation are usually still necessary to produce a sensitive and accurate product. A common solution involves digital signal processing after sample analysis, but these methods frequently fall short in providing meaningful signal outcome changes. This shortcoming may arise from a lack of investigative research into selecting and using signal processing functions, as many choices in current sensors are based on either theoretical results or estimated hypotheses. While a ubiquitous condition set is improbable across diverse impedance cytometry designs, there lies a need for a streamlined and rapid analytical method for discovering those conditions for unique sensors. Herein, we present a comprehensive dissemination of digital filtering parameters applied on experimental impedance cytometry data for determining the limits of signal processing on signal quality improvements. Various filter orders, cutoff frequencies, and filter types are applied after data collection for highest achievable noise reduction. After designing and fabricating a microfluidic impedance cytometer, 9 µm polystyrene particles were measured under flow and signal quality improved by 6.09 dB when implementing digital filtering. This approached was then translated to isolated human neutrophils, where similarly, signal quality improved by 7.50 dB compared to its unfiltered original data. By sweeping all filtering conditions and devising a system to evaluate filtering performance both by signal quality and object counting accuracy, this may serve as a framework for future systems to determine their appropriately optimized filtering configuration.
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Affiliation(s)
- Brandon K Ashley
- Department of Biomedical Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ, 08854, USA
| | - Umer Hassan
- Department of Electrical Engineering, Department of Biomedical Engineering, and Global Health Institute Rutgers, the State University of New Jersey, Piscataway, NJ, 08854, USA.
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4
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Zarfaty L, Barkai E, Kessler DA. Discrete Sampling of Extreme Events Modifies Their Statistics. PHYSICAL REVIEW LETTERS 2022; 129:094101. [PMID: 36083641 DOI: 10.1103/physrevlett.129.094101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Revised: 04/25/2022] [Accepted: 07/27/2022] [Indexed: 06/15/2023]
Abstract
Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated stochastic process change its EV distribution? We explore this question for correlated random variables modeled via Langevin dynamics for a particle in a potential field. For potentials growing at infinity faster than linearly and for long measurement times, we find that the EV distribution of the discretely sampled process diverges from that of the full continuous dataset and converges to that of independent and identically distributed random variables drawn from the process's equilibrium measure. However, for processes with sublinear potentials, the long-time limit is the EV statistics of the continuously sampled data. We treat processes whose equilibrium measures belong to the three EV attractors: Gumbel, Fréchet, and Weibull. Our Letter shows that the EV statistics can be extremely sensitive to the sampling rate of the data.
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Affiliation(s)
- Lior Zarfaty
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - David A Kessler
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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Abstract
Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.
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6
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Bramwell ST. Analytic form of a two-dimensional critical distribution. Phys Rev E 2022; 105:034142. [PMID: 35428110 DOI: 10.1103/physreve.105.034142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 03/04/2022] [Indexed: 06/14/2023]
Abstract
This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin-wave model, or width fluctuations of a two-dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values.
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Affiliation(s)
- Steven T Bramwell
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
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7
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Ashley BK, Hassan U. Time-domain signal averaging to improve microparticles detection and enumeration accuracy in a microfluidic impedance cytometer. Biotechnol Bioeng 2021; 118:4428-4440. [PMID: 34370302 PMCID: PMC8589102 DOI: 10.1002/bit.27910] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 07/30/2021] [Accepted: 08/01/2021] [Indexed: 01/12/2023]
Abstract
Microfluidic impedance cytometry is a powerful system to measure micro and nano-sized particles and is routinely used in point-of-care disease diagnostics and other biomedical applications. However, small objects near a sensor's detection limit are plagued with relatively significant background noise and are difficult to identify for every case. While many data processing techniques can be utilized to reduce noise and improve signal quality, frequently they are still inadequate to push sensor detection limits. Here, we report the first demonstration of a novel signal averaging algorithm effective in noise reduction of microfluidic impedance cytometry data, improving enumeration accuracy, and reducing detection limits. Our device uses a 22 µm tall × 100 µm wide (with 30 µm wide focused aperture) microchannel and gold coplanar microelectrodes that generate an electric field, recording bipolar pulses from polystyrene microparticles flowing through the channel. In addition to outlining a modified moving signal averaging technique theoretically and with a model data set, we also performed a compendium of characterization experiments including variations in flow rate, input voltage, and particle size. Multivariate metrics from each experiment are compared including signal amplitude, pulse width, background noise, and signal-to-noise ratio (SNR). Incorporating our technique resulted in improved SNR and counting accuracy across all experiments conducted, and the limit of detection improved from 5 to 1 µm particles without modifying microchannel dimensions. Succeeding this, we envision implementing our modified moving average technique to develop next-generation microfluidic impedance cytometry devices with an expanded dynamic range and improved enumeration accuracy. This can be exceedingly useful for many biomedical applications, such as infectious disease diagnostics where devices may enumerate larger-scale immune cells alongside sub-micron bacterium in the same sample.
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Affiliation(s)
- Brandon K. Ashley
- Department of Biomedical Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ, 08854, USA
| | - Umer Hassan
- Department of Biomedical Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ, 08854, USA
- Department of Electrical and Computer Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ, 08854, USA
- Global Health Institute, Rutgers, the State University of New Jersey, New Brunswick, NJ, 08901, USA
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8
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De Bruyne B, Majumdar SN, Schehr G. Generating discrete-time constrained random walks and Lévy flights. Phys Rev E 2021; 104:024117. [PMID: 34525540 DOI: 10.1103/physreve.104.024117] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 07/27/2021] [Indexed: 11/07/2022]
Abstract
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly accounts for the bridge constraint. It is illustrated on various jump distributions and is shown to be very efficient in practice. In addition, we show how to generalize the method to other types of constrained random walks such as generalized bridges, excursions, and meanders.
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Affiliation(s)
- Benjamin De Bruyne
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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9
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Luis EEM, Carrasco ISS, de Assis TA, Reis FDAA. Statistics of adatom diffusion in a model of thin film growth. Phys Rev E 2020; 102:012805. [PMID: 32794924 DOI: 10.1103/physreve.102.012805] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 06/30/2020] [Indexed: 11/07/2022]
Abstract
We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number N are determined in films with average thicknesses close to 50 and 100 monolayers for a broad range of values of the diffusion-to-deposition ratio R and of the probability ε that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with Rε≲1, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as 〈N〉∼R^{0.38±0.01}, and the distribution of that number decays approximately as exp[-(N/〈N〉)^{0.80±0.07}]. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between 〈N〉 and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, 〈N〉 crosses over to another regime when Rε^{3.0±0.3}∼1, which indicates high mobility of all adatoms at terrace borders. The distributions P(N) change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and 〈N〉∼Rε^{1.85±0.15}, which is explained by an analogy with submonolayer growth. Thus, the statistics of adatom hops on growing film surfaces is related to universal and nonuniversal features of the growth model and with properties of trapping models if the hopping time is limited by the landscape and not by the deposition of other layers.
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Affiliation(s)
- Edwin E Mozo Luis
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia, Brazil
| | - Ismael S S Carrasco
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói, Rio de Janeiro, Brazil
| | - Thiago A de Assis
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia, Brazil
| | - Fábio D A Aarão Reis
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói, Rio de Janeiro, Brazil
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10
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Palma G, Niedermayer F, Rácz Z, Riveros A, Zambrano D. Finite-size corrections to scaling of the magnetization distribution in the two-dimensional XY model at zero temperature. Phys Rev E 2016; 94:022145. [PMID: 27627284 DOI: 10.1103/physreve.94.022145] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Indexed: 11/07/2022]
Abstract
The zero-temperature, classical XY model on an L×L square lattice is studied by exploring the distribution Φ_{L}(y) of its centered and normalized magnetization y in the large-L limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of Φ_{L}(y), and the limit distribution Φ_{L→∞}(y)=Φ_{0}(y) is obtained with high precision. The two leading finite-size corrections Φ_{L}(y)-Φ_{0}(y)≈a_{1}(L)Φ_{1}(y)+a_{2}(L)Φ_{2}(y) are also extracted both from numerics and from analytic calculations. We find that the amplitude a_{1}(L) scales as ln(L/L_{0})/L^{2} and the shape correction function Φ_{1}(y) can be expressed through the low-order derivatives of the limit distribution, Φ_{1}(y)=[yΦ_{0}(y)+Φ_{0}^{'}(y)]^{'}. Thus, Φ_{1}(y) carries the same universal features as the limit distribution and can be used for consistency checks of universality claims based on finite-size systems. The second finite-size correction has an amplitude a_{2}(L)∝1/L^{2} and one finds that a_{2}Φ_{2}(y)≪a_{1}Φ_{1}(y) already for small system size (L>10). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the XY model at low temperatures, including T=0.
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Affiliation(s)
- G Palma
- Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile
| | - F Niedermayer
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Switzerland
| | - Z Rácz
- MTA-ELTE Theoretical Physics Research Group, Budapest, Hungary
| | - A Riveros
- Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile
| | - D Zambrano
- Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaíso, Chile
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11
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Wu JH, Jia Q. A universal mechanism of extreme events and critical phenomena. Sci Rep 2016; 6:21612. [PMID: 26880219 PMCID: PMC4754907 DOI: 10.1038/srep21612] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Accepted: 01/27/2016] [Indexed: 11/09/2022] Open
Abstract
The occurrence of extreme events and critical phenomena is of importance because they can have inquisitive scientific impact and profound socio-economic consequences. Here we show a universal mechanism describing extreme events along with critical phenomena and derive a general expression of the probability distribution without concerning the physical details of individual events or critical properties. The general probability distribution unifies most important distributions in the field and demonstrates improved performance. The shape and symmetry of the general distribution is determined by the parameters of the fluctuations. Our work sheds judicious insights into the dynamical processes of complex systems with practical significance and provides a general approach of studying extreme and critical episodes in a combined and multidisciplinary scheme.
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Affiliation(s)
- J. H. Wu
- Peter Grünberg Research Center, Nanjing University of Posts and Telecommunications of China, Nanjing 210003, China
- Pioneer Research Center for Biomedical Nanocrystals, Korea University, Seoul 136-713, South Korea
| | - Q. Jia
- Department of Management, Hohai University, Nanjing 211100, China
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12
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Nicodemi M. Extreme Value Statistics. ENCYCLOPEDIA OF COMPLEXITY AND SYSTEMS SCIENCE 2015:1-10. [DOI: 10.1007/978-3-642-27737-5_197-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2013] [Accepted: 11/12/2015] [Indexed: 09/02/2023]
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13
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Rorai C, Mininni PD, Pouquet A. Turbulence comes in bursts in stably stratified flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:043002. [PMID: 24827327 DOI: 10.1103/physreve.89.043002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2013] [Indexed: 06/03/2023]
Abstract
There is a clear distinction between simple laminar and complex turbulent fluids; however, in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity that disappear slowly in time. This phenomenon is ill understood and poorly modeled and yet it is central to our understanding of weather and climate dynamics. We present here data from direct numerical simulations of stratified turbulence on grids of 20483 points that display the somewhat paradoxical result of measurably stronger events for more stable flows, not only in the temperature and vertical velocity derivatives as commonplace in turbulence, but also in the amplitude of the fields themselves, contrary to what happens for homogenous isotropic turbulent flows. A flow visualization suggests that the extreme values take place in Kelvin-Helmoltz overturning events and fronts that develop in the field variables. These results are confirmed by the analysis of a simple model that we present. The model takes into consideration only the vertical velocity and temperature fluctuations and their vertical derivatives. It indicates that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid nonlinear amplification of energy stored in waves and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations in a range of parameters corresponding to the well-known saturation regime of stratified turbulence.
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Affiliation(s)
- C Rorai
- Nordita, Roslagstullsbacken 23, 106 91 Stockholm, Sweden and ICTP, Strada Costiera 11, 34151 Trieste, Italy
| | - P D Mininni
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, C1053ABJ Buenos Aires, Argentina and IFIBA, CONICET, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - A Pouquet
- Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
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14
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Fyodorov YV, Keating JP. Freezing transitions and extreme values: random matrix theory, ζ (1/2 + it) and disordered landscapes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2014; 372:20120503. [PMID: 24344336 PMCID: PMC3866466 DOI: 10.1098/rsta.2012.0503] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials pN(θ) of large N×N random unitary (circular unitary ensemble) matrices UN; i.e. the extreme value statistics of pN(θ) when N → ∞. In addition, we argue that it leads to multi-fractal-like behaviour in the total length μN(x) of the intervals in which |pN(θ)|>N(x), x>0, in the same limit. We speculate that our results extend to the large values taken by the Riemann zeta function ζ(s) over stretches of the critical line s = 1/2 + it of given constant length and present the results of numerical computations of the large values of ζ(1/2 + it). Our main purpose is to draw attention to the unexpected connections between these different extreme value problems.
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Affiliation(s)
- Yan V. Fyodorov
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
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15
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Arlego M, Grynberg MD. Scaling and width distributions of parity-conserving interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052408. [PMID: 24329280 DOI: 10.1103/physreve.88.052408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2013] [Indexed: 06/03/2023]
Abstract
We present an alternative finite-size approach to a set of parity-conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and Dhar in related systems [Phys. Rev. Lett. 73, 2135 (1994)], we circumvent the subdiffusive dynamics and examine close-to-equilibrium aspects of these interfaces by assembling states of much smaller, numerically accessible scales. As a result, roughening exponents, height correlations, and width distributions exhibiting universal scaling functions are evaluated for interfaces virtually grown out of dimers and trimers on large-scale substrates. Dynamic exponents are also studied by finite-size scaling of the spectrum gaps of evolution operators.
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Affiliation(s)
- M Arlego
- Departamento de Física, Universidad Nacional de La Plata, 1900 La Plata, Argentina
| | - M D Grynberg
- Departamento de Física, Universidad Nacional de La Plata, 1900 La Plata, Argentina
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16
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Alfinito E, Reggiani L. Evidence of Gumbel distributions of conductance fluctuations in bacteriorhodopsin thin films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:375103. [PMID: 23963350 DOI: 10.1088/0953-8984/25/37/375103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
By considering a set of experiments carried out on bacteriorhodopsin in vitro by Casuso et al (2007 Phys. Rev. E 76 041919), we extract the conductance as function of the applied voltage. The microscopic interpretation of experiments shows that charge transfer is ruled by a direct tunneling (DT) mechanism at low bias and by a Fowler–Nordheim (FN) tunneling mechanism at high bias. A nucleation region at the cross-over between the DT and FN regimes can be identified. A theoretical analysis of conductance fluctuations is performed by calculating the corresponding variance and the probability density functions (PDFs): these constitute a powerful indicator in order to understand the internal dynamics of the system. Conductance fluctuations are non-Gaussian and follow well the standard generalized Gumbel distributions G(a). In particular, at low bias, the PDFs are bimodal and can be resolved in at least a couple of G(a) functions with different values of the shape parameter a. The nucleation region is characterized by a single Gumbel distribution, G(1). At increasing bias, the G(1) distribution turns in a bimodal distribution. We discuss possible correlations between the voltage dependence of the G(a) and the microscopic mechanisms that determine the electrical response of the system.
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Oliveira TJ, Alves SG, Ferreira SC. Kardar-Parisi-Zhang universality class in (2+1) dimensions: universal geometry-dependent distributions and finite-time corrections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:040102. [PMID: 23679356 DOI: 10.1103/physreve.87.040102] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2013] [Indexed: 06/02/2023]
Abstract
The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t(-β), where β is the growth exponent. Our results support a generalization of the ansatz h=v(∞)t+(Γt)(β)χ+η+ζt(-β) to higher dimensions, where v(∞), Γ, ζ, and η are nonuniversal quantities whereas β and χ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ class in two-dimensional systems.
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Affiliation(s)
- T J Oliveira
- Departamento de Física, Universidade Federal de Viçosa, 36570-000 Viçosa, Minas Gerais, Brazil
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Dwivedi SK, Jalan S. Extreme-value statistics of networks with inhibitory and excitatory couplings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042714. [PMID: 23679456 DOI: 10.1103/physreve.87.042714] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2012] [Revised: 03/14/2013] [Indexed: 06/02/2023]
Abstract
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network, which accounts for the stability of an underlying system, decreases linearly as a function of inhibitory connection probability up to a particular threshold value, after which it exhibits rich behaviors with the distribution manifesting generalized extreme value statistics. Fluctuations in the largest eigenvalue remain somewhat robust against an increase in system size but reflect a strong dependence on the number of connections, indicating that systems having more interactions among its constituents are likely to be more unstable.
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Affiliation(s)
- Sanjiv Kumar Dwivedi
- Complex Systems Lab, Indian Institute of Technology Indore, M-Block, IET-DAVV Campus Khandwa Road, Indore 452017, India
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LeBlanc M, Angheluta L, Dahmen K, Goldenfeld N. Universal fluctuations and extreme statistics of avalanches near the depinning transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022126. [PMID: 23496478 DOI: 10.1103/physreve.87.022126] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2012] [Indexed: 06/01/2023]
Abstract
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities v(m) during avalanches described by the mean-field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.
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Affiliation(s)
- Michael LeBlanc
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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Majumdar S, Sood AK. Statistical properties of entropy-consuming fluctuations in jammed states of laponite suspensions: Fluctuation relations and generalized Gumbel distribution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041404. [PMID: 22680472 DOI: 10.1103/physreve.85.041404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2011] [Revised: 12/04/2011] [Indexed: 06/01/2023]
Abstract
We report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the generalized Gumbel (GG) distribution like many other equilibrium and nonequilibrium systems with high degree of correlations but do not obey the Gallavotti-Cohen steady-state fluctuation relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution.
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Affiliation(s)
- Sayantan Majumdar
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Rambeau J, Bustingorry S, Kolton AB, Schehr G. Maximum relative height of elastic interfaces in random media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041131. [PMID: 22181111 DOI: 10.1103/physreve.84.041131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2011] [Indexed: 05/31/2023]
Abstract
The distribution of the maximal relative height (MRH) of self-affine one-dimensional elastic interfaces in a random potential is studied. We analyze the ground-state configuration at zero driving force, and the critical configuration exactly at the depinning threshold, both for the random-manifold and random-periodic universality classes. These configurations are sampled by exact numerical methods, and their MRH distributions are compared with those with the same roughness exponent and boundary conditions, but produced by independent Fourier modes with normally distributed amplitudes. Using Pickands' theorem we derive an exact analytical description for the right tail of the latter. After properly rescaling the MRH distributions we find that corrections from the Gaussian independent modes approximation are, in general, small, as previously found for the average width distribution of depinning configurations. In the large size limit all corrections are finite except for the ground state in the random-periodic class whose MRH distribution becomes, for periodic boundary conditions, indistinguishable from the Airy distribution. We find that the MRH distributions are, in general, sensitive to changes of boundary conditions.
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Affiliation(s)
- Joachim Rambeau
- Laboratoire de Physique Théorique d'Orsay, Université Paris Sud 11 and CNRS, Orsay, France.
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Majumdar S, Sood AK. Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:015302. [PMID: 21867248 DOI: 10.1103/physreve.84.015302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 06/17/2011] [Indexed: 05/31/2023]
Abstract
We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power p(t), at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.
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Affiliation(s)
- Sayantan Majumdar
- Department of Physics, Indian Institute of Science, Bangalore, India
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Blender R, Zhu X, Fraedrich K. Observations and modelling of 1/<i>f</i>-noise in weather and climate. ADVANCES IN SCIENCE AND RESEARCH 2011. [DOI: 10.5194/asr-6-137-2011] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract. Data with power spectra close to S(f)~1/f is denoted as 1/f or flicker noise. High resolution measurements during TOGA/COARE for temperature, humidity, and wind speed (1\\,min resolution) reveal 1/f spectra while precipitation shows no power-law scaling during the same period. However, a binary time series indicating the precipitation events (1 for precipitation, 0 for no precipitation) shows a clear 1/f spectrum in line with the remaining boundary layer data. For extreme events in time series with 1/f spectra the return time distribution is well approximated by a Weibull-distribution for short and long return times. The daily discharge of the Yangtze river shows high volatility which is linked to the intra-annual 1/f spectrum. The discharge fluctuations detected in different time windows are represented by a single function (a so-called data collapse) similar to the universal behavior found for turbulence and various physical systems at criticality. The collapse is well described by the Gumbel distribution.
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Palatella L, Pennetta C. Distribution of first-return times in correlated stationary signals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041102. [PMID: 21599110 DOI: 10.1103/physreve.83.041102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2011] [Indexed: 05/30/2023]
Abstract
We present an analytical expression for the first return time (FRT) probability density function of a stationary correlated signal. Precisely, we start by considering a stationary discrete-time Ornstein-Uhlenbeck (OU) process with exponential decaying correlation function. The first return time distribution for this process is derived by adopting a well-known formalism typically used in the study of the FRT statistics for nonstationary diffusive processes. Then, by a subordination approach, we treat the case of a stationary process with power-law tail correlation function and diverging correlation time. We numerically test our findings, obtaining in both cases a good agreement with the analytical results. We notice that neither in the standard OU nor in the subordinated case a simple form of waiting time statistics, like stretched-exponential or similar, can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior.
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Affiliation(s)
- Luigi Palatella
- CNISM UdR of Lecce and Dipartimento di Fisica, Università del Salento, Via Arnesano, I-73100 Lecce, Italy
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Györgyi G, Moloney NR, Ozogány K, Rácz Z, Droz M. Renormalization-group theory for finite-size scaling in extreme statistics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041135. [PMID: 20481705 DOI: 10.1103/physreve.81.041135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2010] [Indexed: 05/29/2023]
Abstract
We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.
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Affiliation(s)
- G Györgyi
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland.
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O’Malley L, Korniss G, Caraco T. Ecological Invasion, Roughened Fronts, and a Competitor’s Extreme Advance: Integrating Stochastic Spatial-Growth Models. Bull Math Biol 2009; 71:1160-88. [PMID: 19219509 DOI: 10.1007/s11538-009-9398-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2008] [Accepted: 01/15/2009] [Indexed: 10/21/2022]
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Nicodemi M. Extreme Value Statistics. ENCYCLOPEDIA OF COMPLEXITY AND SYSTEMS SCIENCE 2009:3317-3323. [DOI: 10.1007/978-0-387-30440-3_197] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Oliveira TJ, Aarão Reis FDA. Maximal- and minimal-height distributions of fluctuating interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:041605. [PMID: 18517633 DOI: 10.1103/physreve.77.041605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2007] [Indexed: 05/26/2023]
Abstract
Maximal- and minimal-height distributions (MAHD, MIHD) of two-dimensional interfaces grown with the nonlinear equations of Kardar-Parisi-Zhang (KPZ, second order) and of Villain-Lai-Das Sarma (VLDS, fourth order) are shown to be different. Two universal curves may be MAHD or MIHD of each class depending on the sign of the relevant nonlinear term, which is confirmed by results of several lattice models in the KPZ and VLDS classes. The difference between MAHD and MIDH is connected with the asymmetry of the local height distribution. A simple, exactly solvable deposition-erosion model is introduced to illustrate this feature. The average extremal heights scale with the same exponent of the average roughness. In contrast to other correlated systems, generalized Gumbel distributions do not fit those MAHD and MIHD, nor those of Edwards-Wilkinson growth.
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Affiliation(s)
- T J Oliveira
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil
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30
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Zygadło R. Power-law distribution as a result of asynchronous random switching between Malthus and Verhulst kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021130. [PMID: 18352010 DOI: 10.1103/physreve.77.021130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2007] [Indexed: 05/26/2023]
Abstract
It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power-law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Lévy noise at the macroscopic level.
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Affiliation(s)
- Ryszard Zygadło
- Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, Kraków, Poland
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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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Balankin AS. Dynamic scaling approach to study time series fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:056120. [PMID: 18233731 DOI: 10.1103/physreve.76.056120] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2006] [Revised: 07/26/2007] [Indexed: 05/25/2023]
Abstract
We propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits us to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.
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Affiliation(s)
- Alexander S Balankin
- Grupo Mecánica Fractal, Instituto Politécnico Nacional, México D.F., México 07738
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Burkhardt TW, Györgyi G, Moloney NR, Rácz Z. Extreme statistics for time series: distribution of the maximum relative to the initial value. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041119. [PMID: 17994948 DOI: 10.1103/physreve.76.041119] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2007] [Indexed: 05/25/2023]
Abstract
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/falpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRHI). The exact MRHI distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha , the distribution is determined from simulations. We find that the MRHI distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRHI distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some nonperiodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRHI distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.
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Affiliation(s)
- T W Burkhardt
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
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Guclu H, Korniss G, Toroczkai Z. Extreme fluctuations in noisy task-completion landscapes on scale-free networks. CHAOS (WOODBURY, N.Y.) 2007; 17:026104. [PMID: 17614691 DOI: 10.1063/1.2735446] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.
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Affiliation(s)
- H Guclu
- Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, MS-B258, Los Alamos, New Mexico 87545, USA
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Bena I, Majumdar SN. Universal extremal statistics in a freely expanding Jepsen gas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051103. [PMID: 17677018 DOI: 10.1103/physreve.75.051103] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2007] [Indexed: 05/16/2023]
Abstract
We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of (N+1) hard-point particles. The particles undergo binary elastic collisions, but move ballistically in between collisions. The gas is initially uniformly distributed in a box [-L,0] with the "leader" (or the rightmost particle) at X=0 , and a random positive velocity, independently drawn from a distribution phi(V) , is assigned to each particle. The gas expands freely at subsequent times. We compute analytically the distribution of the leader's velocity at time t , and also the mean and the variance of the number of collisions that are undergone by the leader up to time t . We show that in the thermodynamic limit and at fixed time t>>1 (the so-called "growing regime"), when interactions are strongly manifest, the velocity distribution exhibits universal scaling behavior of only three possible varieties, depending on the tail of phi(V) . The associated scaling functions are entirely different from the usual extreme-value distributions of uncorrelated random variables. In this growing regime the mean and the variance of the number of collisions of the leader up to time t increase logarithmically with t , with universal prefactors that are computed exactly. The implications of our results in the context of biological evolution modeling are pointed out.
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Affiliation(s)
- Ioana Bena
- Département de Physique Théorique, Université de Genève, Genève 4, Switzerland.
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Györgyi G, Moloney NR, Ozogány K, Rácz Z. Maximal height statistics for 1/f(alpha) signals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021123. [PMID: 17358329 DOI: 10.1103/physreve.75.021123] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Indexed: 05/14/2023]
Abstract
Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one-dimensional interfaces) displaying a 1/f(alpha) power spectrum. For 0<or=alpha<1 (regime of decaying correlations), we observe that the mathematically established limiting distribution (Fisher-Tippett-Gumbel distribution) is approached extremely slowly as the sample size increases. The convergence is rapid for alpha>1 (regime of strong correlations) and a highly accurate picture gallery of distribution functions can be constructed numerically. Analytical results can be obtained in the limit alpha-->infinity and, for large alpha, by perturbation expansion. Furthermore, using path integral techniques we derive a trace formula for the distribution function, valid for alpha=2n even integer. From the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary alpha>1 is found to be in agreement with simulations. Comparison of the extreme and roughness statistics of the interfaces reveals similarities in both the small and large argument asymptotes of the distribution functions.
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Affiliation(s)
- G Györgyi
- Institute for Theoretical Physics - HAS Research Groups, Eötvös University, Pázmány sétány 1/a, 1117 Budapest, Hungary.
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Fedorenko AA, Le Doussal P, Wiese KJ. Universal distribution of threshold forces at the depinning transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041110. [PMID: 17155025 DOI: 10.1103/physreve.74.041110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2006] [Indexed: 05/12/2023]
Abstract
We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group technique, we compute the distribution of pinning forces in the quasistatic limit. This distribution is universal up to two parameters, the average critical force and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.
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Affiliation(s)
- Andrei A Fedorenko
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
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Nukala PKVV, Zapperi S, Simunović S. Crack surface roughness in three-dimensional random fuse networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:026105. [PMID: 17025501 DOI: 10.1103/physreve.74.026105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2005] [Indexed: 05/12/2023]
Abstract
Using large system sizes with extensive statistical sampling, we analyze the scaling properties of crack roughness and damage profiles in the three-dimensional random fuse model. The analysis of damage profiles indicates that damage accumulates in a diffusive manner up to the peak load, and localization sets in abruptly at the peak load, starting from a uniform damage landscape. The global crack width scales as W approximately L(0.5) and is consistent with the scaling of localization length xi approximately L(0.5) used in the data collapse of damage profiles in the postpeak regime. This consistency between the global crack roughness exponent and the postpeak damage profile localization length supports the idea that the postpeak damage profile is predominantly due to the localization produced by the catastrophic failure, which at the same time results in the formation of the final crack. Finally, the crack width distributions can be collapsed for different system sizes and follow a log-normal distribution.
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Affiliation(s)
- Phani Kumar V V Nukala
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6164, USA
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Guclu H, Korniss G, Novotny MA, Toroczkai Z, Rácz Z. Synchronization landscapes in small-world-connected computer networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066115. [PMID: 16906922 DOI: 10.1103/physreve.73.066115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2005] [Indexed: 05/11/2023]
Abstract
Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by "simulating the simulations," based on the exact algorithmic rules, supported by coarse-grained arguments.
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Affiliation(s)
- H Guclu
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180-3590, USA
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40
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Bertin E, Clusel M. Generalized extreme value statistics and sum of correlated variables. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/24/001] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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41
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Palma G. Temperature dependence of universal fluctuations in the two-dimensional harmonic XY model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:046130. [PMID: 16711901 DOI: 10.1103/physreve.73.046130] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2005] [Indexed: 05/09/2023]
Abstract
We compute exact analytical expressions for the skewness and kurtosis in the two-dimensional harmonic XY model. These quantities correspond to the third and fourth normalized moments of the probability density function (PDF) of the magnetization of the model. From their behavior, we conclude that they depend explicitly on the system temperature even in the thermodynamic limit, and hence the PDF itself must depend on it. Our results correct the hypothesis called universal fluctuations, they confirm and extend previous results which showed a T dependence of the PDF, including perturbative expansions within the XY model up to first order in temperature.
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Affiliation(s)
- G Palma
- Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile.
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Eichner JF, Kantelhardt JW, Bunde A, Havlin S. Extreme value statistics in records with long-term persistence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:016130. [PMID: 16486239 DOI: 10.1103/physreve.73.016130] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2005] [Indexed: 05/06/2023]
Abstract
Many natural records exhibit long-term correlations characterized by a power-law decay of the autocorrelation function, C(s) approximately s-gamma, with time lag s and correlation exponent 0<gamma<1. We study how the presence of such correlations affects the statistics of the extreme events, i.e., the maximum values of the signal within time segments of the fixed duration R. We find numerically that (i) the integrated distribution function of the maxima converges to a Gumbel distribution for large R similar to uncorrelated signals, (ii) the deviations for finite R depend on the initial distribution of the records and on their correlation properties, (iii) the maxima series exhibit long-term correlations similar to those of the original data, and most notably (iv) the maxima distribution as well as the mean maxima significantly depend on the history, in particular on the previous maximum. The last item implies that conditional mean maxima and conditional maxima distributions (with the value of the previous maximum as condition) should be considered for an improved extreme event prediction. We provide indications that this dependence of the mean maxima on the previous maximum occurs also in observational long-term correlated records.
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Affiliation(s)
- Jan F Eichner
- Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany
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Balankin AS, Susarrey O, Paredes RG, Morales L, Samayoa D, López JA. Intrinsically anomalous roughness of admissible crack traces in concrete. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:065101. [PMID: 16485995 DOI: 10.1103/physreve.72.065101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2005] [Indexed: 05/06/2023]
Abstract
We study the roughness of postmortem cracks in concrete plates of different size. We find that the set of admissible crack paths exhibits an intrinsically anomalous roughness; nevertheless, any individual crack trace in concrete is essentially self-affine. We also find that both the local and the global amplitudes of crack traces are distributed according to a log-logistic distribution characterized by the same scaling exponent, whereas the mean-square width distribution is best fitted by the Pearson distribution, while the log-normal distribution also provides quite good adjustments and cannot be clearly rejected.
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Affiliation(s)
- Alexander S Balankin
- Sección de Posgrado e Investigación, ESIME, Instituto Politécnico Nacional, México and Grupo "Mecánica Fractal," México 07738
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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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45
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Bertin E. Global fluctuations and Gumbel statistics. PHYSICAL REVIEW LETTERS 2005; 95:170601. [PMID: 16383810 DOI: 10.1103/physrevlett.95.170601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2005] [Indexed: 05/05/2023]
Abstract
We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.
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Affiliation(s)
- Eric Bertin
- Department of Theoretical Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
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Lee DS. Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces. PHYSICAL REVIEW LETTERS 2005; 95:150601. [PMID: 16241710 DOI: 10.1103/physrevlett.95.150601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2005] [Indexed: 05/05/2023]
Abstract
We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal [EQUATION: SEE TEXT]and the asymptotic behavior of the whole distribution for [EQUATION: SEE TEXT] for m finite with N2 and K the interface size and tension, respectively. The standardized form of P(m) does not depend on N or K, but shows a good agreement with Gumbel's first asymptote distribution with a particular noninteger parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.
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Affiliation(s)
- Deok-Sun Lee
- Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
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Aarão Reis FDA. Numerical study of roughness distributions in nonlinear models of interface growth. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:032601. [PMID: 16241498 DOI: 10.1103/physreve.72.032601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2004] [Indexed: 05/05/2023]
Abstract
We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi, and Zhang (KPZ) and in the Villain, Lai, and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm the expected scaling of the distribution and show a stretched exponential tail approximately as exp(-x0.8), with a significant asymmetry near the maximum. Conserved restricted solid-on-solid models belonging to the VLDS class were simulated in d=1 and d=2. The tail in d=1 has the form exp(-x2) and, in d=2, has a simple exponential decay, but is quantitatively different from the distribution of the linear fourth-order (Mullins-Herring) theory. It is not possible to fit any of the above distributions to those of 1/f(alpha) noise interfaces, in contrast with recently studied models with depinning transitions.
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Affiliation(s)
- F D A Aarão Reis
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói Rio de Janeiro, Brazil
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Banks ST, Bramwell ST. Temperature-dependent fluctuations in the two-dimensionalXYmodel. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/0305-4470/38/25/001] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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49
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Zapperi S, Nukala PKVV, Simunović S. Crack roughness and avalanche precursors in the random fuse model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026106. [PMID: 15783377 DOI: 10.1103/physreve.71.026106] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2004] [Revised: 11/22/2004] [Indexed: 05/24/2023]
Abstract
We analyze the scaling of the crack roughness and of avalanche precursors in the two-dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents (zeta, zeta(loc) ) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as s(0) approximately L(D) , with a universal fractal dimension D , the distribution exponent tau differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value tau=5/2 .
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Affiliation(s)
- Stefano Zapperi
- INFM UdR Roma 1 and SMC, Dipartimento di Fisica, Università La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy
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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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