604 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
Improved linear response for stochastically driven systems
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents. However, in the case of stochastically
driven dynamics, one typically resorts to the classical fluctuation-dissipation
formula, which has the drawback of explicitly requiring the probability density
of the statistical state together with its derivative for computation, which
might not be available with sufficient precision in the case of complex
dynamics (usually a Gaussian approximation is used). Here we adapt the
short-time linear response formula for stochastically driven dynamics, and
observe that, for short and moderate response times before numerical
instability develops, it is generally superior to the classical formula with
Gaussian approximation for both the additive and multiplicative stochastic
forcing. Additionally, a suitable blending with classical formula for longer
response times eliminates numerical instability and provides an improved
response prediction even for long response times
Moisture - Gravity Wave Interactions in a Multiscale Environment
Starting from the conservation laws for mass, momentum and energy together with
a three species, bulk microphysic model, a model for the interaction of internal gravity waves and
deep convective hot towers is derived by using multiscale asymptotic techniques.
From the resulting leading order equations, a closed model is obtained by applying weighted
averages to the smallscale hot towers without requiring further closure approximations. The resulting
model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction
of saturated regions on the microscale with two way coupling between the large and small scale.
Moisture reduces the effective stability in the model and defines a potential temperature sourceterm
related to the net effect of latent heat release or consumption by microscale up- and downdrafts.
The dispersion relation and group velocity of the system is analyzed and moisture is found to have
several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases
the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below
which modes turn into evanescent. Further, moisture can cause critical layers.
Numerical examples for steady-state and time-dependent mountain waves are shown and the effects
of moisture on these waves are investigated
Structural, magnetic, dielectric and mechanical properties of (Ba,Sr)MnO ceramics
Ceramic samples, produced by conventional sintering method in ambient air,
6H-SrMnO(6H-SMO), 15R-BaMnO(15R-BMO),
4H-BaSrMnO(4H-BSMO) were studied. In the XRD measurements
for SMO the new anomalies of the lattice parameters at 600-800 K range and the
increasing of thermal expansion coefficients with a clear maximum in a vicinity
at 670 K were detected. The Nel phase transition for BSMO was
observed at =250 K in magnetic measurements and its trace was detected in
dielectric, FTIR, DSC, and DMA experiments. The enthalpy and entropy changes of
the phase transition for BSMO at were determined as 17.5 J/mol and 70
mJ/K mol, respectively. The activation energy values and relaxation times
characteristic for relaxation processes were determined from the Arrhenius law.
Results of ab initio simulations showed that the contribution of the exchange
correlation energy to the total energy is about 30%.Comment: 12 pages, 12 figure
Chemotactic Collapse and Mesenchymal Morphogenesis
We study the effect of chemotactic signaling among mesenchymal cells. We show
that the particular physiology of the mesenchymal cells allows one-dimensional
collapse in contrast to the case of bacteria, and that the mesenchymal
morphogenesis represents thus a more complex type of pattern formation than
those found in bacterial colonies. We finally compare our theoretical
predictions with recent in vitro experiments
A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears
Variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front
speeds provides an efficient tool for statistical speed analysis, as well as a
fast and accurate method for speed computation. A variational principle based
analysis is carried out on the ensemble of KPP speeds through spatially
stationary random shear flows inside infinite channel domains. In the regime of
small root mean square (rms) shear amplitude, the enhancement of the ensemble
averaged KPP front speeds is proved to obey the quadratic law under certain
shear moment conditions. Similarly, in the large rms amplitude regime, the
enhancement follows the linear law. In particular, both laws hold for the
Ornstein-Uhlenbeck process in case of two dimensional channels. An asymptotic
ensemble averaged speed formula is derived in the small rms regime and is
explicit in case of the Ornstein-Uhlenbeck process of the shear. Variational
principle based computation agrees with these analytical findings, and allows
further study on the speed enhancement distributions as well as the dependence
of enhancement on the shear covariance. Direct simulations in the small rms
regime suggest quadratic speed enhancement law for non-KPP nonlinearities.Comment: 28 pages, 14 figures update: fixed typos, refined estimates in
section
Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
The influence of an underlying current on 3-wave interactions of capillary
water waves is studied. The fact that in irrotational flow resonant 3-wave
interactions are not possible can be invalidated by the presence of an
underlying current of constant non-zero vorticity. We show that: 1) wave trains
in flows with constant non-zero vorticity are possible only for two-dimensional
flows; 2) only positive constant vorticities can trigger the appearance of
three-wave resonances; 3) the number of positive constant vorticities which do
trigger a resonance is countable; 4) the magnitude of a positive constant
vorticity triggering a resonance can not be too small.Comment: 6 pages, submitte
On the dynamics of a self-gravitating medium with random and non-random initial conditions
The dynamics of a one-dimensional self-gravitating medium, with initial
density almost uniform is studied. Numerical experiments are performed with
ordered and with Gaussian random initial conditions. The phase space portraits
are shown to be qualitatively similar to shock waves, in particular with
initial conditions of Brownian type. The PDF of the mass distribution is
investigated.Comment: Latex, figures in eps, 23 pages, 11 figures. Revised versio
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