First-order-reversal-curve analysis of Pr-Fe-B-based exchange spring magnets

Ribbons of nominal composition (Pr(9.5)Fe(84.5)B(6))(0.96)Cr(0.01)(TiC)(0.03) were produced by arc-melting and melt-spinning the alloys on a Cu wheel. X-ray diffraction (XRD) reveals two main phases, one based upon alpha-Fe and the other upon Pr(2)Fe(14)B. The ribbons show exchange spring behavior with H (c) = 12.5 kOe and (BH)(max) = 13.6 MGOe when these two phases are well coupled. Transmission electron microscopy revealed the coupled behavior is observed when the microstructure consists predominantly of alpha-Fe grains (diameter similar to 100 nm.) surrounded by hard material containing Pr(2)Fe(14)B. The microstructure is discussed in terms of a calculation by Skomski and Coey. A first-order-reversal-curve (FORC) analysis was performed for both a well-coupled sample and a poorly coupled sample. The FORC diagrams show two strong peaks for both the poorly coupled sample and for the well-coupled material. In both cases, the localization of the FORC probability suggests magnetizing interactions between particles. Switching field distributions were calculated and are consistent with the sample microstructure.

Hopf Bifurcations in a Watt Governor with a Spring

This paper pursues the study carried out in [ 10], focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor system. Here are studied Hopf bifurcations of codimensions two, three and four and the pertinent Lyapunov stability coefficients and bifurcation diagrams. This allows to determine the number, types and positions of bifurcating small amplitude periodic orbits. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.