A soft magnetic alloy is driven by a slowly increasing applied field
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Electricity, Magnetism & Electromagnetism · Magnetic materials
Many Parts, One Behaviour, Ch Self-organised criticality and avalanches
Problem
A soft magnetic alloy is driven by a slowly increasing applied field. Each sudden jump in magnetisation, a Barkhausen jump, is caused by a domain wall abruptly depinning from a pinning site once the local field exceeds that site's pinning threshold, then re-pinning elsewhere. One recording gives ten Barkhausen pulse sizes, each the change in magnetisation carried by one pulse (the area under its voltage trace), in arbitrary detector units with the smallest resolvable size set to xmin=1: 1,2,3,5,8,13,21,34,55,89.
((a)) Identify, in one sentence each, the slow drive, the threshold and the release for this system, and say what plays the role of the avalanche size s.
((b)) For a density p(x)∝x−α above xmin, the maximum-likelihood estimator is α^=1+n[∑i=1nln(xi/xmin)]−1, with standard error (α^−1)/n. Using the ten pulse sizes above, estimate α and its standard error.
((c)) State whether the estimate is consistent with either of the quoted material-dependent Barkhausen exponents, 1.3 or 1.5, and say what the two-decade rule requires before the fit can be trusted to distinguish between them.