Controlling balance in an ensemble Kalman filter

We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore, our filter with the weak constraint on imbalance produces good rms error statistics which outperform those of ensemble Kalman filters without balance constraints for the fast fields

On finite-size Lyapunov exponents in multiscale systems

We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches between them. The surprising result is that due to the presence of regimes the error growth rate can be a non-monotonic function of initial error amplitude. In particular, troughs in the large scales of FSLE spectra is shown to be a signature of slow regimes, whereas fast regimes are shown to cause large peaks in the spectra where error growth rates far exceed those estimated from the maximal Lyapunov exponent. We present analytical results explaining these signatures and corroborate them with numerical simulations. We show further that these peaks disappear in stochastic parametrizations of the fast chaotic processes, and the associated FSLE spectra reveal that large scale predictability properties of the full deterministic model are well approximated whereas small scale features are not properly resolved.Comment: Accepted for publication in Chao

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow

On the Validity of the 0-1 Test for Chaos

In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics

Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Lane-formation vs. cluster-formation in two dimensional square-shoulder systems: A genetic algorithm approach

Introducing genetic algorithms as a reliable and efficient tool to find ordered equilibrium structures, we predict minimum energy configurations of the square shoulder system for different values of corona width $\lambda$. Varying systematically the pressure for different values of $\lambda$ we obtain complete sequences of minimum energy configurations which provide a deeper understanding of the system's strategies to arrange particles in an energetically optimized fashion, leading to the competing self-assembly scenarios of cluster-formation vs. lane-formation.Comment: 5 pages, 6 figure

X-ray Spectroscopy of Candidate Ultracompact X-ray Binaries

We present high-resolution spectroscopy of the neutron star/low-mass X-ray binaries (LMXBs) 4U 1850-087 and 4U 0513-40 as part of our continuing study of known and candidate ultracompact binaries. The LMXB 4U 1850-087 is one of four systems in which we had previously inferred an unusual Ne/O ratio in the absorption along the line of sight, most likely from material local to the binaries. However, our recent Chandra X-ray Observatory LETGS spectrum of 4U 1850-087 finds a Ne/O ratio by number of 0.22+/-0.05, smaller than previously measured and consistent with the expected interstellar value. We propose that variations in the Ne/O ratio due to source variability, as previously observed in these sources, can explain the difference between the low- and high-resolution spectral results for 4U 1850-087. Our XMM-Newton RGS observation of 4U 0513-40 also shows no unusual abundance ratios in the absorption along the line of sight. We also present spectral results from a third candidate ultracompact binary, 4U 1822-000, whose spectrum is well fit by an absorbed power-law + blackbody model with absorption consistent with the expected interstellar value. Finally, we present the non-detection of a fourth candidate ultracompact binary, 4U 1905+000, with an upper limit on the source luminosity of < 1 x 10^{32} erg s^{-1}. Using archival data, we show that the source has entered an extended quiescent state.Comment: 8 pages, 3 figures, accepted for publication to the Astrophysical Journa