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

Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communication

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl

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]

A Bound on Mixing Efficiency for the Advection-Diffusion Equation

An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. For a given stirring velocity field, the mixing efficiency is measured in terms of an equivalent diffusivity, which is the molecular diffusivity that would be required to achieve the same level of fluctuations in the scalar concentration in the absence of stirring, for the same source distribution. The bound on the equivalent diffusivity depends only on the functional "shape" of both the source and the advecting field. Direct numerical simulations performed for a simple advecting flow to test the bounds are reported.Comment: 10 pages, 2 figures, JFM format (included

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.Comment: 7 pages, 2 figures, to appear in Euro. Phys. Let

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

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.