5,339 research outputs found
Noise-Induced Stabilization of Planar Flows I
We show that the complex-valued ODE
\begin{equation*}
\dot z_t = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0,
\end{equation*} which necessarily has trajectories along which the dynamics
blows up in finite time, can be stabilized by the addition of an arbitrarily
small elliptic, additive Brownian stochastic term. We also show that the
stochastic perturbation has a unique invariant measure which is heavy-tailed
yet is uniformly, exponentially attracting. The methods turn on the
construction of Lyapunov functions. The techniques used in the construction are
general and can likely be used in other settings where a Lyapunov function is
needed. This is a two-part paper. This paper, Part I, focuses on general
Lyapunov methods as applied to a special, simplified version of the problem.
Part II of this paper extends the main results to the general setting.Comment: Part one of a two part pape
Boundary between the thermal and statistical polarization regimes in a nuclear spin ensemble
As the number of spins in an ensemble is reduced, the statistical uctuations
in its polarization eventually exceed the mean thermal polarization. This
transition has now been surpassed in a number of recent nuclear magnetic
resonance experiments, which achieve nanometer-scale detection volumes. Here,
we measure nanometer- scale ensembles of nuclear spins in a KPF6 sample using
magnetic resonance force microscopy. In particular, we investigate the
transition between regimes dominated by thermal and statistical nuclear
polarization. The ratio between the two types of polarization provides a
measure of the number of spins in the detected ensemble
Cosmogenic nuclides in cometary materials: Implications for rate of mass loss and exposure history
As planned, the Rosetta mission will return to earth with a 10-kg core and a 1-kg surface sample from a comet. The selection of a comet with low current activity will maximize the chance of obtaining material altered as little as possible. Current temperature and level of activity, however, may not reliably indicate previous values. Fortunately, from measurements of the cosmogenic nuclide contents of cometary material, one may estimate a rate of mass loss in the past and perhaps learn something about the exposure history of the comet. Perhaps the simplest way to estimate the rate of mass loss is to compare the total inventories of several long-lived cosmogenic radionuclides with the values expected on the basis of model calculations. Although model calculations have become steadily more reliable, application to bodies with the composition of comets will require some extension beyond the normal range of use. In particular, the influence of light elements on the secondary particle cascade will need study, in part through laboratory irradiations of volatile-rich materials. In the analysis of cometary data, it would be valuable to test calculations against measurements of short-lived isotopes
Localized excited charge carriers generate ultrafast inhomogeneous strain in the multiferroic BiFeO
We apply ultrafast X-ray diffraction with femtosecond temporal resolution to
monitor the lattice dynamics in a thin film of multiferroic BiFeO after
above-bandgap photoexcitation. The sound-velocity limited evolution of the
observed lattice strains indicates a quasi-instantaneous photoinduced stress
which decays on a nanosecond time scale. This stress exhibits an inhomogeneous
spatial profile evidenced by the broadening of the Bragg peak. These new data
require substantial modification of existing models of photogenerated stresses
in BiFeO: the relevant excited charge carriers must remain localized to be
consistent with the data
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