Continuous Data Assimilation with Stochastically Noisy Data

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier-Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which are represented by stochastic noise. Under these assumptions, the data-assimilation algorithm consists of a system of stochastically forced Navier-Stokes equations. The main result of this paper provides explicit conditions on the observation density (resolution) which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solutions which is corresponding to these measurements, in terms of the variance of the noise in the measurements. Specifically, such bounds are given for the the limit supremum, as the time tends to infinity, of the expected value of the $L^2$-norm and of the $H^1$ Sobolev norm of the difference between the approximating solution and the actual solution. Moreover, results on the average time error in mean are stated

The merger boom: an overview

Consolidation and merger of corporations ; Corporations ; Public policy

Are hostile takeovers different?

Consolidation and merger of corporations ; Corporations ; Stockholders

Simulating Brownian suspensions with fluctuating hydrodynamics

Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint need only be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation

The Color Distributions of Globular Clusters in Virgo Elliptical Galaxies

This Letter presents the color distributions of the globular cluster (GC) systems of 12 Virgo elliptical galaxies, measured using data from the Hubble Space Telescope. Bright galaxies with large numbers of detected GC's show two distinct cluster populations with mean V-I colors near 1.01 and 1.26. The GC population of M86 is a clear exception; its color distribution shows a single sharp peak near V-I=1.03. The absence of the red population in this galaxy, and the consistency of the peak colors in the others, may be indications of the origins of the two populations found in most bright elliptical galaxies.Comment: 5 pages, 1 figure, to be published in ApJ Letters Corrections to introductio

X-ray observations of IC348 in light of an updated cluster census

IC348 is an excellent laboratory for studies of low-mass star formation being nearby, compact and rich. A Chandra observation was carried out early in the satellite's lifetime. The extensive new data in optical and infrared wavelengths accumulated in subsequent years have changed the cluster census calling for a re-analysis of the X-ray data.Comment: poster paper to appear in Proc. of the 15th Workshop on Cool Stars, Stellar Systems and the Su