24,691 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
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
A new atmospheric aerosol phase equilibrium model (UHAERO): organic systems
In atmospheric aerosols, water and volatile inorganic and organic species are distributed between the gas and aerosol phases in accordance with thermodynamic equilibrium. Within an atmospheric particle, liquid and solid phases can exist at equilibrium. Models exist for computation of phase equilibria for inorganic/water mixtures typical of atmospheric aerosols; when organic species are present, the phase equilibrium problem is complicated by organic/water interactions as well as the potentially large number of organic species. We present here an extension of the UHAERO inorganic thermodynamic model (Amundson et al., 2006c) to organic/water systems. Phase diagrams for a number of model organic/water systems characteristic of both primary and secondary organic aerosols are computed. Also calculated are inorganic/organic/water phase diagrams that show the effect of organics on inorganic deliquescence behavior. The effect of the choice of activity coefficient model for organics on the computed phase equilibria is explored
Evaluation of structural analysis methods for life prediction
The utility of advanced constitutive models and structural analysis methods are evaluated for predicting the cyclic life of an air-cooled turbine blade for a gas turbine aircraft engine. Structural analysis methods of various levels of sophistication were exercised to obtain the cyclic stress-strain response at the critical airfoil location. Calculated strain ranges and mean stresses from the stress-strain cycles were used to predict crack initiation lives by using the total strain version of the strain range partitioning life prediction method. The major results are given and discussed
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
New interpretation of matter-antimatter asymmetry based on branes and possible observational consequences
Motivated by the AMS project, we assume that after the Big Bang or inflation
epoch, antimatter was repelled onto one brane which is separated from our brane
where all the observational matter resides. It is suggested that CP may be
spontaneously broken, the two branes would correspond to ground states for
matter and antimatter respectively. Generally a complex scalar field which is
responsible for the spontaneous CP violation, exists in the space between the
branes and causes a repulsive force against the gravitation. A possible
potential barrier prevents the mater(antimatter) particles to enter the space
between two branes. However, by the quantum tunnelling, a sizable anti-matter
flux may come to our brane. In this work by considering two possible models,
i.e. the naive flat space-time and Randall-Sundrum models and using the
observational data on the visible matter in our universe as inputs, we derive
the antimatter flux which would be observed by the AMS detector.Comment: 10 pages, 4 figures and 2 tables. Replaced by new versio
Simple de Sitter Solutions
We present a framework for de Sitter model building in type IIA string
theory, illustrated with specific examples. We find metastable dS minima of the
potential for moduli obtained from a compactification on a product of two Nil
three-manifolds (which have negative scalar curvature) combined with
orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete
quantum number is taken large, the curvature, field strengths, inverse volume,
and four dimensional string coupling become parametrically small, and the de
Sitter Hubble scale can be tuned parametrically smaller than the scales of the
moduli, KK, and winding mode masses. A subtle point in the construction is that
although the curvature remains consistently weak, the circle fibers of the
nilmanifolds become very small in this limit (though this is avoided in
illustrative solutions at modest values of the parameters). In the simplest
version of the construction, the heaviest moduli masses are parametrically of
the same order as the lightest KK and winding masses. However, we provide a
method for separating these marginally overlapping scales, and more generally
the underlying supersymmetry of the model protects against large corrections to
the low-energy moduli potential.Comment: 37 pages, harvmac big, 4 figures. v3: small correction
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