Hysteresis, Avalanches, and Noise: Numerical Methods

In studying the avalanches and noise in a model of hysteresis loops we have developed two relatively straightforward algorithms which have allowed us to study large systems efficiently. Our model is the random-field Ising model at zero temperature, with deterministic albeit random dynamics. The first algorithm, implemented using sorted lists, scales in computer time as O(N log N), and asymptotically uses N (sizeof(double)+ sizeof(int)) bits of memory. The second algorithm, which never generates the random fields, scales in time as O(N \log N) and asymptotically needs storage of only one bit per spin, about 96 times less memory than the first algorithm. We present results for system sizes of up to a billion spins, which can be run on a workstation with 128MB of RAM in a few hours. We also show that important physical questions were resolved only with the largest of these simulations

Universal Pulse Shape Scaling Function and Exponents: A Critical Test for Avalanche Models applied to Barkhausen Noise

In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the non-equilibrium zero temperature Random Field Ising Model (RFIM), we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents $\tau$ and $1/\sigma\nu z$ in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling functions as well as between different experiments.Comment: 19 pages (in preprint format), 5 figures, 1 tabl

Hysteresis and Avalanches in the Random Anisotropy Ising Model

The behaviour of the Random Anisotropy Ising model at T=0 under local relaxation dynamics is studied. The model includes a dominant ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occuring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump to a rather smooth loop exhibiting only tiny avalanches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.Comment: 40 pages, 21 figures, Accepted for publication in Phys. Rev.

Comparison of endocardial electromechanical mapping with radionuclide perfusion imaging to assess myocardial viability and severity of myocardial ischemia in angina pectoris

The assessment of left ventricular electromechanical activity using a novel, nonfluoroscopic 3-dimensional mapping system demonstrates considerable differences in electrical and mechanical activities within regions of myocardial infarction or ischemia. We sought to determine whether these changes correlate with indexes of myocardial perfusion, viability, or ischemia. A 12-segment comparative analysis was performed in 61 patients (45 men, 61 ± 12 years old) with class III to IV angina, having reversible and/or fixed myocardial perfusion defects on single-photon emission computed tomographic perfusion imaging. A dual-isotope protocol was used, consisting of rest and 4-hour redistribution thallium images followed by adenosine technetium-99m sestamibi imaging. Average rest endocardial unipolar voltage (UpV) and local shortening (LS) mapping values were compared with visually derived perfusion scores. There was gradual and proportional reduction in regional UpV and LS in relation to thallium-201 uptake score at rest (p = 0.0001 and p = 0.0002, respectively) and redistribution studies (p = 0.0001 and p = 0.003, respectively). UpV ≥7.4 mV and LS ≥5.0% had a sensitivity of 78% and 65%, respectively, with a specificity of 68% and 67% for detecting viable myocardium. UpV values of 12.3 and 5.4 mV had 90% specificity and sensitivity, respectively, to predict viable tissue. UpV, but not LS, values differentiated between normal segments and those with adenosine-induced severe perfusion defects (11.8 ± 5.3 vs 8.8 ± 4.1 mV, p = 0.005). Catheter-based left ventricular assessment of electromechanical activity correlates with the degree of single-photon emission computed tomographic perfusion abnormality and can identify myocardial viability with a greater accuracy than myocardial ischemia