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

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

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