Tunable mode coupling in nano-contact spin torque oscillators

Recent experiments on spin torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode-coexistence, mode-hopping, and temperature-driven cross-over between modes. Initial multimode theory has indicated that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nano-contact spin torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space, and demonstrate in the phase portraits, how the manifolds of periodic orbits and fixed points vary with external magnetic field as well as with temperature.Comment: 13 pages, 8 figures; 2 figures (Figs.5 & 6) corrected and redrawn; 2 new figures (Figs.7 & 8) added; Accepted by Physical Review Applie

How sharp are PV measures?

Properties of sharp observables (normalized PV measures) in relation to smearing by a Markov kernel are studied. It is shown that for a sharp observable $P$ defined on a standard Borel space, and an arbitrary observable $M$, the following properties are equivalent: (a) the range of $P$ is contained in the range of $M$; (b) $P$ is a function of $M$; (c) $P$ is a smearing of $M$.Comment: 9 page

Massiivi-tyypin anortosiittien jäännössulien tasapainoinen kiteytyminen: tapaustutkimus 1.64 miljardia vuotta vanhasta Ahvenisto-kompleksista Kaakkois-Suomessa

Fe–Ti–P-rich mafic to intermediate rocks (monzodiorites and oxide–apatite–gabbronorites, OAGNs) are found as small intrusions in most AMCG (anorthosite–magnerite–charnokite–granite) suites. The origin of the monzodioritic rocks is still debated, but in many studies, they are presumed to represent residual liquid compositions after fractionation of anorthositic cumulates. In the 1.64 Ga Ahvenisto complex, SE Finland, monzodioritic rocks occur as minor dike-like lenses closely associated with anorthositic rocks. We report new field, petrographic, and geochemical (XRF, ICP-MS, EMPA) data complemented with crystallization modeling (rhyolite-MELTS, MAGFRAC) for the monzodioritic rocks, apatite–oxide–gabbronorite, and olivine-bearing anorthositic rocks of the Ahvenisto complex. The presented evidence suggest that the monzodioritic rocks closely represent melt compositions while the apatite–oxide–gabbronorite and olivine-bearing anorthositic rocks are cumulates. The monzodioritic rocks seem to form a liquid line of descent (LLD) from primitive olivine monzodiorites to more evolved monzodiorites. Petrological modeling suggests that the interpreted LLD closely corresponds to a residual melt trend left after fractional crystallization (FC) and formation of the cumulate anorthositic rocks and minor apatite–oxide–gabbronorite in shallow magma chambers. Consequent equilibrium crystallization (EC) of separate monzodioritic residual magma batches can produce the observed mineral assemblages and the low Mg numbers measured from olivine (Fo25–45) and pyroxenes (En48–63, Mg#cpx 60–69). The monzodioritic rocks and apatite–oxide–gabbronorites show similar petrological and geochemical characteristics to corresponding rock types in other AMCG suites, and the model described in this study could be applicable to them as well.Peer reviewe

Mesoscopic transport beyond linear response

We present an approach to steady-state mesoscopic transport based on the maximum entropy principle formulation of nonequilibrium statistical mechanics. Our approach is not limited to the linear response regime. We show that this approach yields the quantization observed in the integer quantum Hall effect at large currents, which until now has been unexplained. We also predict new behaviors of non-local resistances at large currents in the presence of dirty contacts.Comment: 14 pages plus one figure (with an insert) (post-script codes appended), RevTeX 3.0, UCF-CM-93-004 (Revised

Termodynaamiset rajat massiivi-tyypin anortosiittien ja niiden kantamagmojen synnylle

Development of computational modeling tools has revolutionized studies of magmatic processes over the last four decades. Their refinement from binary mixing equations to thermodynamically controlled geochemical assimilation models has provided more comprehensive and detailed modeling constraints of an array of magmatic systems. One of the questions that has not yet been vigorously studied using thermodynamic constraints is the origin of massif-type anorthosites. The parental melts to these intrusions are hypothesized to be either mantle-derived high-Al basaltic melts that undergo crustal contamination or monzodioritic melts derived directly from lower crust. On the other hand, many studies suggest that the monzodioritic rocks do not represent parental melts but instead represent crystal remnants of residual liquids left after crystal fractionation of parental melts. Regardless of the source or composition, magmas that produce massif-type anorthosites have been suggested to have undergone polybaric (~1000–100 MPa) fractional crystallization while ascending through the lithosphere. We conducted lower crustal melting, assimilation-fractional crystallization, and isobaric and polybaric fractional crystallization major element modeling using two thermodynamically constrained modeling tools, the Magma Chamber Simulator (MCS) and rhyolite-MELTS, to test the suitability of these tools and to study the petrogenesis of massif-type anorthosites. Comparison of our models with a large suite of whole-rock data suggests that the massif-type anorthosite parental melts were high-Al basalts that were produced when hot mantle-derived partial melts assimilated lower crustal material at Moho levels. These contaminated basaltic parental magmas then experienced polybaric fractional crystallization at different crustal levels (~40 to 5 km) producing residual melts that crystallized as monzodioritic rocks. Model outcomes also support the suggestion that the cumulates produced during polybaric fractional crystallization likely underwent density separation, thus producing the plagioclase-rich anorthositic rocks. The modeled processes are linked to a four-stage model that describes the key petrogenetic processes that generate massif-type anorthosites. The presented framework enables further detailed thermodynamic and geochemical modeling of individual anorthosite intrusions using MCS and involving trace element and isotope constrains.Peer reviewe