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Vlasko-Vlasov VK, Divan R, Rosenmann D, Welp U, Glatz A, Kwok WK. Multiquanta flux jumps in superconducting fractal. Sci Rep 2023; 13:12601. [PMID: 37537249 PMCID: PMC10400563 DOI: 10.1038/s41598-023-39733-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 07/30/2023] [Indexed: 08/05/2023] Open
Abstract
We study the magnetic field response of millimeter scale fractal Sierpinski gaskets (SG) assembled of superconducting equilateral triangular patches. Directly imaged quantitative induction maps reveal hierarchical periodic filling of enclosed void areas with multiquanta magnetic flux, which jumps inside the voids in repeating bundles of individual flux quanta Φ0. The number Ns of entering flux quanta in different triangular voids of the SG is proportional to the linear size s of the void, while the field periodicity of flux jumps varies as 1/s. We explain this behavior by modeling the triangular voids in the SG with effective superconducting rings and by calculating their response following the London analysis of persistent currents, Js, induced by the applied field Ha and by the entering flux. With changing Ha, Js reaches a critical value in the vertex joints that connect the triangular superconducting patches and allows the giant flux jumps into the SG voids through phase slips or multiple Abrikosov vortex transfer across the vertices. The unique flux behavior in superconducting SG patterns, may be used to design tunable low-loss resonators with multi-line high-frequency spectrum for microwave technologies.
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Affiliation(s)
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Daniel Rosenmann
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Ulrich Welp
- Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Andreas Glatz
- Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA
- Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA
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The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform. Symmetry (Basel) 2021. [DOI: 10.3390/sym13101922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.
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On the κ-Deformed Cyclic Functions and the Generalized Fourier Series in the Framework of the κ-Algebra. ENTROPY 2015. [DOI: 10.3390/e17052812] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Padilla L, Mártin HO, Iguain JL. Anisotropic anomalous diffusion modulated by log-periodic oscillations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011106. [PMID: 23005367 DOI: 10.1103/physreve.86.011106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2012] [Indexed: 06/01/2023]
Abstract
We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites where the diffusion of a single random walk presents an anomalous anisotropic behavior modulated by log-periodic oscillations. The anisotropy is revealed by two different random-walk exponents ν(x) and ν(y) in the x and y directions, respectively. The values of these exponents as well as the periods of the oscillations are obtained analytically and confirmed by Monte Carlo simulations.
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Affiliation(s)
- L Padilla
- Instituto de Investigaciones Físicas de Mar del Plata and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, AR-7600 Mar del Plata, Argentina.
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Padilla L, Mártin HO, Iguain JL. Anomalous diffusion with log-periodic modulation in a selected time interval. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:020105. [PMID: 21405803 DOI: 10.1103/physreve.83.020105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2010] [Indexed: 05/30/2023]
Abstract
On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic-periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the modulating oscillations are washed out but subdiffusion remains as in the perfect self-similar case. Also, if disorder distribution is appropriately chosen the oscillations are localized in a selected time interval. Both the overall random walk exponent and the period of the oscillations are analytically obtained and confirmed by Monte Carlo simulations.
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Affiliation(s)
- L Padilla
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR) and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina.
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Padilla L, Mártin HO, Iguain JL. Log-periodic oscillations for diffusion on self-similar finitely ramified structures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011124. [PMID: 20866582 DOI: 10.1103/physreve.82.011124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2010] [Indexed: 05/29/2023]
Abstract
Under certain circumstances, the time behavior of a random walk is modulated by logarithmic-periodic oscillations. Using heuristic arguments, we give a simple explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order. On these media, the time dependence of the mean-square displacement shows log-periodic modulations around a leading power law, which can be understood on the basis of a hierarchical set of diffusion constants. Both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples, one is fractal and the other is nonfractal, and confirmed by Monte Carlo simulations. The last example shows that the anomalous diffusion can arise from substrates without holes of all sizes.
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Affiliation(s)
- L Padilla
- Departamento de Física FCEyN, Instituto de Investigaciones Físicas de Mar del Plata, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina
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Shen TY, Tai K, McCammon JA. Statistical analysis of the fractal gating motions of the enzyme acetylcholinesterase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:041902. [PMID: 11308872 DOI: 10.1103/physreve.63.041902] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2000] [Indexed: 05/23/2023]
Abstract
The enzyme acetylcholinesterase has an active site that is accessible only by a "gorge" or main channel from the surface, and perhaps by secondary channels such as the "back door." Molecular-dynamics simulations show that these channels are too narrow most of the time to admit substrate or other small molecules. Binding of substrates is therefore "gated" by structural fluctuations of the enzyme. Here, we analyze the fluctuations of these possible channels, as observed in the 10.8-ns trajectory of the simulation. The probability density function of the gorge proper radius (defined in the text) was calculated. A double-peak feature of the function was discovered and therefore two states with a threshold were identified. The relaxation (transition probability) functions of these two states were also calculated. The results revealed a power-law decay trend and an oscillation around it, which show properties of fractal dynamics with a "complex exponent." The cross correlation of potential energy versus proper radius was also investigated. We discuss possible physical models behind the fractal protein dynamics; the dynamic hierarchical model for glassy systems is evaluated in detail.
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Affiliation(s)
- T Y Shen
- Department of Physics, University of California San Diego, La Jolla, CA 92093-0365, USA
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Saleur H, Sammis CG, Sornette D. Discrete scale invariance, complex fractal dimensions, and log-periodic fluctuations in seismicity. ACTA ACUST UNITED AC 1996. [DOI: 10.1029/96jb00876] [Citation(s) in RCA: 144] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Kutnjak-Urbanc B, Zapperi S, Milosevic S, Stanley HE. Sandpile model on the Sierpinski gasket fractal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:272-277. [PMID: 9965069 DOI: 10.1103/physreve.54.272] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Horane EM, Castro JI, Buscaglia GC, López A. Transition between different quantum states in a mesoscopic system: The superconducting ring. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:9296-9300. [PMID: 9982431 DOI: 10.1103/physrevb.53.9296] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Castro JI, López A. Variational approach to superconductive networks. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7495-7503. [PMID: 9979696 DOI: 10.1103/physrevb.52.7495] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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12
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Kaufman M, Berger T, Gujrati PD, Bowman D. Polymerization on the diamond hierarchical lattice: The Migdal-Kadanoff renormalization-group scheme. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:4371-4378. [PMID: 9903630 DOI: 10.1103/physreva.41.4371] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jeffery M, Green C, Tyagi S, Gilmore R. Reproducible magnetic features of high-Tc superconductors in weak fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:9054-9060. [PMID: 9947631 DOI: 10.1103/physrevb.39.9054] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Niu Q, Nori F. Theory of superconducting wire networks and Josephson-junction arrays in magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:2134-2150. [PMID: 9948447 DOI: 10.1103/physrevb.39.2134] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Fourcade B, Tremblay A. Anomalies in the multifractal analysis of self-similar resistor networks. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:2352-2358. [PMID: 9899128 DOI: 10.1103/physreva.36.2352] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gordon JM, Goldman AM. Magnetoresistance measurements on fractal wire networks. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:4909-4914. [PMID: 9940669 DOI: 10.1103/physrevb.35.4909] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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