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Spasojević D, Marinković M, Jovković D, Janićević S, Laurson L, Djordjević A. Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations. Phys Rev E 2024; 109:024110. [PMID: 38491707 DOI: 10.1103/physreve.109.024110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 01/29/2024] [Indexed: 03/18/2024]
Abstract
In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Miloš Marinković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P. O. Box 162, 11000 Belgrade, Republic of Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Republic of Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P. O. Box 692, FI-33014 Tampere, Finland
| | - Antonije Djordjević
- School of Electrical Engineering, University of Belgrade, 11000 Belgrade, Republic of Serbia and Serbian Academy of Sciences and Arts, 11000 Belgrade, Republic of Serbia
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Neslušan M, Pitoňák M, Minárik P, Kollár P, Životský O. Influence of domain walls thickness, density and alignment on Barkhausen noise emission in low alloyed steels. Sci Rep 2023; 13:5687. [PMID: 37029152 PMCID: PMC10082025 DOI: 10.1038/s41598-023-32792-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 04/02/2023] [Indexed: 04/09/2023] Open
Abstract
This study deals with the characterization of low alloyed steels of different yield strengths (varying in the range of 235-1100 MPa) via Barkhausen noise emission. The study investigates the potential of this technique to distinguish among the low alloyed steels and all significant aspects contributing to Barkhausen noise, such as the residual stress state, microstructure expressed in terms of dislocation density, grain size, prevailing phase, as well as associated aspects of the domain wall substructure (domain wall thickness, energy, their spacing and density in the matrix). Barkhausen noise in the rolling as well as transversal direction grows along with the yield strength (up to 500 MPa) and the corresponding grain refinement of ferrite. As soon as the martensite transformation occurs in a high strength matrix, this evolution saturates, and remarkable magnetic anisotropy is developed when Barkhausen noise in the transversal direction grows at the expense of the rolling direction. The contribution of residual stresses as well as the domain wall thickness is only minor, and the evolution of Barkhausen noise is driven by the density of the domain walls and their realignment.
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Affiliation(s)
- M Neslušan
- University of Žilina, Univerzitná 1, 010 26, Žilina, Slovakia.
| | - M Pitoňák
- University of Žilina, Univerzitná 1, 010 26, Žilina, Slovakia
| | - P Minárik
- University of Žilina, Univerzitná 1, 010 26, Žilina, Slovakia
- Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16, Praha 2, Czech Republic
| | - P Kollár
- Institute of Physics, Faculty of Science, P. J. Šafárik University in Košice, Park Angelium 9, 040 01, Kosice, Slovakia
| | - O Životský
- Faculty of Electrical Engineering and Computer Science, VŠB - Technical University of Ostrava, 17. Listopadu 2172/15, 708 00, Ostrava-Poruba, Czech Republic
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Spasojević D, Graovac S, Janićević S. Interplay of disorder and type of driving in disordered ferromagnetic systems. Phys Rev E 2022; 106:044107. [PMID: 36397527 DOI: 10.1103/physreve.106.044107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 09/19/2022] [Indexed: 06/16/2023]
Abstract
We investigate the effects of adiabatic, quasistatic, and finite-rate types of driving on the evolution of disordered three-dimensional ferromagnetic systems, studied within the frame of the nonequilibrium athermal random field Ising model. The effects were examined in all three domains of disorder (low, high, and transitional) for all types of driving, and in a wide range of driving rates for quasistatic and finite-rate driving, providing an extensive overview and comparison of the joint effects that the disorder, type of driving, and rate regime have on the system's behavior.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Stefan Graovac
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
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Scott JJR, Casals B, Luo KF, Haq A, Mariotti D, Salje EKH, Arredondo M. Avalanche criticality in LaAlO[Formula: see text] and the effect of aspect ratio. Sci Rep 2022; 12:14818. [PMID: 36050337 PMCID: PMC9437108 DOI: 10.1038/s41598-022-18390-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 08/10/2022] [Indexed: 11/25/2022] Open
Abstract
Ferroic domain dynamics, as a function of external stimuli, can be collectively described as scale-invariant avalanches characterised by a critical exponent that are sensitive to the complexity of the domain microstructure. The understanding and manipulation of these avalanches lies at the heart of developing novel applications such as neuromorphic computing. Here we combine in situ heating optical observations and mean-field analysis to investigate the collective domain behaviour in pure-ferroelastic lanthanum aluminate (LaAlO[Formula: see text]) as a function of aspect ratio, the ratio of sample length to width, where the movement of the domains is predominantly driven by thermal stresses via thermal expansion/contraction during heat cycling. Our observations demonstrate that the aspect ratio induces (1) distinctive domain microstructures at room temperature, (2) a deviation of dynamical behaviour at high temperatures and (3) critical exponent mixing in the higher aspect ratio samples that accompanies this behaviour. While the critical exponents of each aspect ratio fall within mean-field predicted values, we highlight the effect that the aspect ratio has in inducing exponent mixing. Hence, furthering our understanding towards tuning and controlling avalanches which is crucial for fundamental and applied research.
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Affiliation(s)
- John J. R. Scott
- School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN Northern Ireland, UK
| | - Blai Casals
- Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ England, UK
| | - King-Fa Luo
- School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN Northern Ireland, UK
| | - Atta Haq
- School of Engineering, Ulster University, Jordanstown, BT37 0QB Northern Ireland, UK
| | - Davide Mariotti
- School of Engineering, Ulster University, Jordanstown, BT37 0QB Northern Ireland, UK
| | - Ekhard K. H. Salje
- Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ England, UK
| | - Miryam Arredondo
- School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN Northern Ireland, UK
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Yao Y, Zhan X, Sendeku MG, Yu P, Dajan FT, Zhu C, Li N, Wang J, Wang F, Wang Z, He J. Recent progress on emergent two-dimensional magnets and heterostructures. NANOTECHNOLOGY 2021; 32:472001. [PMID: 34315143 DOI: 10.1088/1361-6528/ac17fd] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
Intrinsic two-dimensional (2D) magnetic materials own strong long-range magnetism while their characteristics of the ultrathin thickness and smooth surface provide an ideal platform for manipulating the magnetic properties at 2D limit. This makes them to be potential candidates in various spintronic applications compared to their corresponding bulk counterparts. The discovery of magnetic ordering in 2D CrI3and Gr2Ge2Te6nanostructures stimulated tremendous research interest in both experimental and theoretical studies on various intrinsic magnets at 2D limit. This review gives a comprehensive overview of the recent progress on the emergent 2D magnets and heterostructures. Firstly, several kinds of typical 2D magnetic materials discovered in the last few years and their fabrication methods are summarized in detail. Secondly, the current strategies for manipulating magnetic properties in 2D materials are further discussed. Then, the recent advances on the construction of representative van der Waals magnetic heterostructures and their respective performance are provided. With the hope of motivating the researchers in this area, we finally offered the challenges and outlook on 2D magnetism.
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Affiliation(s)
- Yuyu Yao
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
- Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Sino-Danish Center for Education, Beijing 100049, People's Republic of China
| | - Xueying Zhan
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Marshet Getaye Sendeku
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Peng Yu
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Fekadu Tsegaye Dajan
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Chuanchao Zhu
- Institute for Quantum Information & State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, People's Republic of China
| | - Ningning Li
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
- Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Sino-Danish Center for Education, Beijing 100049, People's Republic of China
| | - Junjun Wang
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Feng Wang
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
| | - Zhenxing Wang
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Jun He
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, People's Republic of China
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Graovac S, Mijatović S, Spasojević D. Mechanism of subcritical avalanche propagation in three-dimensional disordered systems. Phys Rev E 2021; 103:062123. [PMID: 34271753 DOI: 10.1103/physreve.103.062123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
We present a numerical study on necessary conditions for the appearance of infinite avalanche below the critical point in disordered systems that evolve throughout metastable states. The representative of those systems is the nonequilibrium athermal random-field Ising model. We investigate the impact on propagation of infinite avalanche of both the interface of flipped spins at the avalanche's starting point and the number of independent islands of flipped spins in the system at the moment when the avalanche starts. To deduce what effects are originated due to finite system's size, and to distinguish them from the real necessary conditions for the appearance of the infinite avalanche, we examined lattices of different sizes as well as other key parameters for the avalanche propagation.
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Affiliation(s)
- Stefan Graovac
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
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Jovković D, Janićević S, Mijatović S, Laurson L, Spasojević D. Effects of external noise on threshold-induced correlations in ferromagnetic systems. Phys Rev E 2021; 103:062114. [PMID: 34271613 DOI: 10.1103/physreve.103.062114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 05/17/2021] [Indexed: 11/07/2022]
Abstract
In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.
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Affiliation(s)
- Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O. Box 162, 11000 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
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Mijatović S, Jovković D, Spasojević D. Nonequilibrium athermal random-field Ising model on hexagonal lattices. Phys Rev E 2021; 103:032147. [PMID: 33862757 DOI: 10.1103/physreve.103.032147] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 03/08/2021] [Indexed: 11/07/2022]
Abstract
We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O.B. 162, 11000 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
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Mijatović S, Branković M, Graovac S, Spasojević D. Avalanche properties in striplike ferromagnetic systems. Phys Rev E 2020; 102:022124. [PMID: 32942372 DOI: 10.1103/physreve.102.022124] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2020] [Accepted: 07/24/2020] [Indexed: 11/07/2022]
Abstract
We present numerical findings on the behavior of the athermal nonequilibrium random-field Ising model of spins at the thin striplike L_{1}×L_{2}×L_{3} cubic lattices with L_{1}<L_{2}<L_{3}. Changing of system sizes highly influences the evolution and shape of avalanches. The smallest avalanches [classified as three-dimension- (3D) like] are unaffected by the system boundaries, the larger are sandwiched between the top and bottom system faces so are 2D-like, while the largest are extended over the system lateral cross section and propagate along the length L_{3} like in 1D systems. Such a structure of avalanches causes double power-law distributions of their size, duration, and energy with larger effective critical exponent corresponding to 3D-like and smaller to 2D-like avalanches. The distributions scale with thickness L_{1} and are collapsible following the proposed scaling predictions which, together with the distributions' shape, might be important for analysis of the Barkhausen noise experimental data for striplike samples. Finally, the impact of system size on external field that triggers the largest avalanche for a given disorder is presented and discussed.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Milica Branković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Stefan Graovac
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
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Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques. ENTROPY 2020; 22:e22030336. [PMID: 33286110 PMCID: PMC7516807 DOI: 10.3390/e22030336] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Revised: 03/03/2020] [Accepted: 03/11/2020] [Indexed: 01/10/2023]
Abstract
Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n - 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.
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Flannigan C, Tan CD, Scott JF. Electrical studies of Barkhausen switching noise in ferroelectric lead zirconate titanate (PZT) and BaTiO 3: critical exponents and temperature-dependence. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:055403. [PMID: 31610531 DOI: 10.1088/1361-648x/ab4d87] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Previous studies of Barkhausen noise in PZT have been limited to the energy spectrum (slew rate response voltages versus time), showing agreement with avalanche models; in barium titanate other exponents have been measured acoustically, but only at ambient temperatures. In the present study we report the Omori exponent (0.95 [Formula: see text] 0.03) for aftershocks in PZT and extend the barium titanate studies to a wider range of temperature.
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Affiliation(s)
- C Flannigan
- Schools of Physics and of Chemistry, University of St Andrews, St Andrews KY16 9SS, United Kingdom
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Mijatović S, Jovković D, Janićević S, Spasojević D. Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems. Phys Rev E 2019; 100:032113. [PMID: 31639960 DOI: 10.1103/physreve.100.032113] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Indexed: 11/07/2022]
Abstract
In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.
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Affiliation(s)
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, POB 162, 11000 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, POB 60, 34000 Kragujevac, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 44, 11001 Belgrade, Serbia
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Aguilar-Molina AM, Angulo-Brown F, Muñoz-Diosdado A. Multifractal Spectrum Curvature of RR Tachograms of Healthy People and Patients with Congestive Heart Failure, a New Tool to Assess Health Conditions. ENTROPY (BASEL, SWITZERLAND) 2019; 21:e21060581. [PMID: 33267295 PMCID: PMC7515070 DOI: 10.3390/e21060581] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Revised: 06/06/2019] [Accepted: 06/07/2019] [Indexed: 05/28/2023]
Abstract
We calculate the multifractal spectra of heartbeat RR-interval time series (tachograms) of healthy subjects and patients with congestive heart failure (CHF). From these time series, we obtained new subseries of 6 h durations when healthy persons and patients were asleep and awake respectively. For each time series and subseries, we worked out the multifractal spectra with the Chhabra and Jensen method and found that their graphs have different shapes for CHF patients and healthy persons. We suggest to measure two parameters: the curvature around the maximum and the symmetry for all these multifractal spectra graphs, because these parameters were different for healthy and CHF subjects. Multifractal spectra of healthy subjects tend to be right skewed especially when the subjects are asleep and the curvature around the maximum is small compared with the curvature around the maximum of the CHF multifractal spectra; that is, the spectra of patients tend to be more pointed around the maximum. In CHF patients, we also have encountered differences in the curvature of the multifractal spectra depending on their respective New York Heart Association (NYHA) index.
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Affiliation(s)
- Ana María Aguilar-Molina
- Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. No.9 U.P. Zacatenco, Mexico City 07738, Mexico
| | - Fernando Angulo-Brown
- Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. No.9 U.P. Zacatenco, Mexico City 07738, Mexico
| | - Alejandro Muñoz-Diosdado
- Unidad Profesional Interdisciplinaria de Biotecnología, Instituto Politécnico Nacional, Av. Acueducto s/n, Barrio la Laguna, Ticomán, Mexico City 07340, Mexico
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