Paul H. Bryant

Thin‐film magnetic patterns in an external field

The behavior of ideally soft ferromagnetic films in the presence of a weak coplanar magnetic field is explored by the method of characteristics. Solutions are found which have no internal field or in some cases have field‐free zones. Results are specifically given for circular and elliptic disks, the infinite strip, and the semi‐infinite plane. The disk solutions have internal domain walls.

Magnetization and domain structure of cylinders and spheres in subsaturating fields

We explore the magnetization patterns and domain walls which may occur in ferromagnetic cylinders and spheres in a certain range of sizes, placed in a uniform external magnetic field below saturation. The solutions found are field‐free inside the sample. The analysis is explicitly carried out for circular and elliptic cylinders and spheres, and may be extended to general ellipsoids.

Spin-wave turbulence

Abstract A high resolution study is made of spin-wave dynamics above the Suhl threshold in a sphere of yttrium iron garnet driven by microwave ferromagnetic resonance. In different regions of parameter space observed behavior includes: excitation of a single spatial spin-wave mode at threshold; when two modes are excited, low frequency collective oscillations with a period doubling route to chaos; nonperiodic relaxation oscillations when three modes are excited, quasiperiodic route to chaos; abrupt hysteretic onset of wide-band chaos. These results are accounted for in a unified way by numerical iteration of a model: coupled quantum oscillators representing the photons of the cavity and the magnons, including four-magnon scattering processes.

The nonlinear effects of noise on parametric amplification: an analysis of noise rise in Josephson junctions and other systems

We take a new look at an old problem; namely, the observed ‘‘noise rise’’ in superconducting Josephson junction parametric amplifiers. By exploiting recent insights from dynamical systems theory, we show how the interplay or random noise and (nonchaotic) deterministic dynamics can result in a noise rise like that observed in experiments. Our analysis leads to a universal first‐order equation which applies to all similar systems in the high‐gain regime. We propose several predictions which can be tested experimentally, including that a similar noise rise should occur in modulated semiconductor injection lasers. We also analyze a previously unknown mode of operation—a ‘‘six‐photon’’ mode associated with a symmetry breaking bifurcation—and discuss its potential advantages over the previously studied three‐ and four‐photon modes.

Modeling the behavior of the magnetic force microscope

Results of some numerical simulations are presented that model the behavior of the magnetic force microscope under various probe/sample configurations. Analysis is carried out under the assumption of uniform magnetization of an axially symmetric probe of various types including: sphere, cylinder, conical tip, and rounded magnetically coated conical tip. In these cases the analysis can be made by studying the effective magnetic surface charge on the probe. We also consider the case of a spherical probe with magnetization that can rotate in response to the local field. The sample configurations studied are also of the axially symmetric type, which can be used to model the fields generated by arrays of cylindrical samples, e.g., alumite.

Micromagnetics below saturation

In the limit of negligible exchange and anisotropy (except uniaxial), certain shapes of magnetic samples in certain subsaturating field configurations can be analyzed analytically to obtain magnetization and domain wall patterns. Here we consider two cases: (1) generalized cylindrical objects of arbitrary cross section (with several specific examples given) and (2) a general ellipsoid. We also discuss a ‘‘tipping instability’’ which might occur in an ellipsoid with uniaxial anisotropy, resulting in a sudden transition from a ‘‘curling’’ state to a ‘‘transverse vortex’’ state.

Is the Blazhko Effect the Beating of a Near-resonant Double-mode Pulsation?

In this paper it is shown that the Blazhko effect may result from a near-resonant type of multi-mode pulsation, where two (or sometimes more) periodic oscillations with slightly different frequencies gradually slip in phase, producing a beat frequency type of modulation. Typically one of these oscillations is strongly non-sinusoidal. Two oscillations are sufficient for the standard Blazhko effect; additional oscillations are needed to explain multi-frequency modulation. Previous work on this hypothesis by Arthur N. Cox and others is extended in this paper by developing a simple (non-hydro) model that can accurately reproduce several important features found in Kepler data for RR Lyr, including the pulsation waveform, the upper and lower Blazhko envelope functions and the motion, disappearance and reappearance of the bump feature. The non-sinusoidal oscillation is probably generated by the fundamental mode and the other oscillations are probably generated by nonradial modes. This model provides an explanation for the strong asymmetry observed in the side peak spectra of most RR Lyrae stars. The motion and disappearance of the bump feature are shown to be an illusion, just an artifact of combining the oscillations. V445 Lyr is presented as an example with dual modulation. The mysterious double-maxima waveform observed for this star is explained, providing additional strong evidence that this beating-modes hypothesis is correct. Problems with other recent explanations of the Blazhko effect are discussed in some detail.

A HYBRID MODE MODEL OF THE BLAZHKO EFFECT, SHOWN TO ACCURATELY FIT KEPLER DATA FOR RR Lyr

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.

Nonlinear dynamics of spin waves (invited)

For a yttrium‐iron‐garnet sphere at room temperature, an experimental study is made of the first‐order Suhl spin‐wave instability using perpendicular pumping at 9.2 GHz with the dc field parallel to the [111] crystal axis. The dynamical behavior of the magnetization is observed with high resolution by varying two control parameters, dc field (580<H0<2100 G) and microwave pump power (1<Pin <200 mW). Within this parameter space quite varied behavior is found: (i) onset of the Suhl instability by excitation of a single spin‐wave mode with very narrow linewidth (<0.5 G); (ii) when two or more modes are excited, interactions lead to collective oscillations (‘‘auto‐oscillations’’) with a systematic dependence of frequency (104–106 Hz) on pump power, these oscillations displaying period‐doubling to chaos; (iii) quasiperiodicity, locking, and chaos occur when three or more modes are excited; (iv) abrupt transition to wide band power spectra (i.e., turbulence), with hysteresis; (v) irregular relaxation oscillation...

Extensional singularity dimensions for strange attractors

A new set of dimension-like invariants is obtained, which characterize aspects of the attractor not usually examined. This study also demonstrates a new method for determining Lyapunov exponents and introduces “tailored attractors” for which the Lyapunov exponents and fractal dimension may be precisely set.