20,383 research outputs found
Nonlinear stability and ergodicity of ensemble based Kalman filters
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are
data assimilation methods used to combine high dimensional, nonlinear dynamical
models with observed data. Despite their widespread usage in climate science
and oil reservoir simulation, very little is known about the long-time behavior
of these methods and why they are effective when applied with modest ensemble
sizes in large dimensional turbulent dynamical systems. By following the basic
principles of energy dissipation and controllability of filters, this paper
establishes a simple, systematic and rigorous framework for the nonlinear
analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the
dynamical properties of boundedness and geometric ergodicity. The time uniform
boundedness guarantees that the filter estimate will not diverge to machine
infinity in finite time, which is a potential threat for EnKF and ESQF known as
the catastrophic filter divergence. Geometric ergodicity ensures in addition
that the filter has a unique invariant measure and that initialization errors
will dissipate exponentially in time. We establish these results by introducing
a natural notion of observable energy dissipation. The time uniform bound is
achieved through a simple Lyapunov function argument, this result applies to
systems with complete observations and strong kinetic energy dissipation, but
also to concrete examples with incomplete observations. With the Lyapunov
function argument established, the geometric ergodicity is obtained by
verifying the controllability of the filter processes; in particular, such
analysis for ESQF relies on a careful multivariate perturbation analysis of the
covariance eigen-structure.Comment: 38 page
Pair Production of MSSM Higgs Bosons in the Non-decoupling Region at the LHC
We consider the Higgs boson signals from pair production at the LHC within
the framework of the MSSM in the non-decoupling (low-m_A) region. In light of
the recent observation of a SM-like Higgs boson, we argue that the exploration
for Higgs pair production at the LHC is a crucial next step to probe the MSSM
Higgs sector. We emphasize that the production of H^\pm A^0 and H^{+}H^{-}
depends only on the electroweak gauge couplings while all the leading Higgs
production channels via gluon fusion, vector-boson fusion, and Higgsstrahlung
depend on additional free Higgs sector parameters. In the non-decoupling
region, the five MSSM Higgs bosons are all relatively light and pair production
signals may be accessible. We find that at the 8 TeV LHC, a 5\sigma signal for
H^\pm A^0, H^\pm h^0 -> \tau^{\pm}\nu b\bar b and H^{+}H^{-} -> \tau^{+}\nu
\tau^{-}\nu are achievable with an integrated luminosity of 7 (11) fb^{-1} and
24 (48) fb^{-1}, respectively for m_A=95 (130) GeV. At the 14 TeV LHC, a
5\sigma signal for these two channels would require as little as 4 (7) fb^{-1}
and 10 (19) fb^{-1}, respectively.Comment: 20 pages, 8 figures and 3 tables. Version to appear in PR
Heterotic Vortex Strings
We determine the low-energy N=(0,2) worldsheet dynamics of vortex strings in
a large class of non-Abelian N=1 supersymmetric gauge theories.Comment: 44 pages, 3 figures. v2: typos corrected, reference adde
Enhanced heat transport by turbulent two-phase Rayleigh-B\'enard convection
We report measurements of turbulent heat-transport in samples of ethane
(CH) heated from below while the applied temperature difference straddled the liquid-vapor co-existance curve . When the sample
top temperature decreased below , droplet condensation occurred
and the latent heat of vaporization provided an additional heat-transport
mechanism.The effective conductivity increased linearly with
decreasing , and reached a maximum value that was an
order of magnitude larger than the single-phase . As
approached the critical pressure, increased dramatically even
though vanished. We attribute this phenomenon to an enhanced
droplet-nucleation rate as the critical point is approached.Comment: 4 gages, 6 figure
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