Micromagnetic simulations of the magnetization precession induced by a spin polarized current in a point contact geometry

This paper is devoted to numerical simulations of the magnetization dynamics driven by a spin-polarized current in extended ferromagnetic multilayers when a point-contact setup is used. We present (i) detailed analysis of methodological problems arising by such simulations and (ii) physical results obtained on a system similar to that studied in Rippard et al., Phys. Rev. Lett., v. 92, 027201 (2004). We demonstrate that the usage of a standard Slonczewski formalism for the phenomenological treatment of a spin-induced torque leads to a qualitative disagreement between simulation results and experimental observations and discuss possible reasons for this discrepancy.Comment: Invited paper on MMM2005 (San Jose); accepted for publication in J. Applied Physic

Variational bound on energy dissipation in turbulent shear flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits structure, namely a pronounced minimum at intermediate Reynolds numbers, and recovers the Busse bound in the asymptotic regime. The most notable feature is a bifurcation of the minimizing wavenumbers, giving rise to simple scaling of the optimized variational parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz file from [email protected]

Magnetization precession due to a spin polarized current in a thin nanoelement: numerical simulation study

In this paper a detailed numerical study (in frames of the Slonczewski formalism) of magnetization oscillations driven by a spin-polarized current through a thin elliptical nanoelement is presented. We show that a sophisticated micromagnetic model, where a polycrystalline structure of a nanoelement is taken into account, can explain qualitatively all most important features of the magnetization oscillation spectra recently observed experimentally (S.I. Kiselev et al., Nature, vol. 425, p. 380 (2003), namely: existence of several equidistant spectral bands, sharp onset and abrupt disappearance of magnetization oscillations with increasing current, absence of the out-of-plane regime predicted by a macrospin model and the relation between frequencies of so called small-angle and quasichaotic oscillations. However, a quantitative agreement with experimental results (especially concerning the frequency of quasichaotic oscillations) could not be achieved in the region of reasonable parameter values, indicating that further model refinement is necessary for a complete understanding of the spin-driven magnetization precession even in this relatively simple experimental situation.Comment: Submitted to Phys. Rev. B; In this revised version figure positions on the page have been changed to ensure correct placements of the figure caption

On the universality of a class of annihilation-coagulation models

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are established. For the one-dimensional case, it is shown how correlations in the initial state can lead to non-universal amplitudes for time-dependent particles density.Comment: 18 pages with no figures. Latex file using REVTE

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Coherent State path-integral simulation of many particle systems

The coherent state path integral formulation of certain many particle systems allows for their non perturbative study by the techniques of lattice field theory. In this paper we exploit this strategy by simulating the explicit example of the diffusion controlled reaction $A+A\to 0$. Our results are consistent with some renormalization group-based predictions thus clarifying the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference correcte

Coulomb Drag between One-Dimensional Wigner Crystal Rings

We consider the Coulomb drag between two metal rings in which the long range Coulomb interaction leads to the formation of a Wigner crystal. The first ring is threaded by an Ahranov Bohm flux creating a persistent current J_0. The second ring is brought in close proximity to the second and due to the Coulomb interaction between the two rings a drag current J_D is produced in the second. We investigate this system at zero temperature for perfect rings as well as the effects of impurities. We show that the Wigner crystal state can in principle lead to a higher ratio of drag current to drive current J_D/J_0 than in weakly interacting electron systems.Comment: 12 pages, 10 figure

Fluctuations and stability in front propagation

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce-budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.Comment: 5 pages, 5 figure

Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.Comment: 5 pages, 5 figures, to appear in Phys. Rev.

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation