Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs-Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with $O(N)$ computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications

Fishing Gear Statistics of Virginia 1929-1977

The commercial fishery of Virginia uses over 30 gear types to capture the species in this report. We have selected 19 gears for illustration and description, and 10 species for detailed analysis. The species selected for analysis were chosen from the list of 18 presented in Hoagman and Rathbone (1980) which provided landings and value information Statewide and for the James, York, and Rappahannock Rivers 1955- 77. The gear statistics provided here cover 1929-77, but the rivers are not treated separately \ The river data has been incorporated into the statistics reported a Virginia Totals and Averages. The National Marine Fisheries Service (NMF S) provided the basic information of catch, value, and gear breakdowns by species in their U.S. Fishery Digest annual reports. The statistics for gear number are tabulations of licenses granted the fishermen, 2 but the catch by gear are estimates by NMFS based on the sampling program that gathers all landings information through ground survey and telephone contacts . The program is considered accurate within 5% of the actual catch. No adjustment has been made to the dollar values to convert them to standard or uninflated dollars over the 1929-77 period. The tables report the value received by the fishermen upon sale to the fish dealer

Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"

Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"Comment: 2 pages, 1 figur

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

Stochastic method for in-situ damage analysis

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic excitations with correlated noise as it appears in real-world situations. In particular an experimental set-up of undamaged and damaged beam structures was exposed to a noisy excitation under turbulent wind conditions. The method of reconstructing stochastic equations from measured data has been extended to realistic noisy excitations like those given here. In our analysis the deterministic part is separated from the stochastic dynamics of the system and we show that the slope of the deterministic part, which is linked to mechanical features of the material, changes sensitively with increasing damage. The results are more significant than corresponding changes in eigenfrequencies, as commonly used for structural health monitoring.Comment: This paper is accepted by European Physical Journal B on November 2. 2012. 5 pages, 5 figures, 1 tabl

On different cascade-speeds for longitudinal and transverse velocity increments

We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker- Planck equation from which a generalization of the Karman equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the difference in the scaling properties of these two structure functions.Comment: 4 pages, 5 figures, now with corrected postscrip