Turbulent spectrum of the Earth's ozone field

The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $E_c(k)$. In terms of wavenumber $E_c(k)$ is shown to be $O(k^{-2/3})$ in the inverse cascade regime, $O(k^{-2})$ in the enstrophy cascade regime with the spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $Re\approx 10^{10}$.Comment: RevTeX file, 4 pages, 4 postscript figures available upon request from Richard Everson <[email protected]

A POD reduced order model for resolving angular direction in neutron/photon transport problems

publisher: Elsevier articletitle: A POD reduced order model for resolving angular direction in neutron/photon transport problems journaltitle: Journal of Computational Physics articlelink: http://dx.doi.org/10.1016/j.jcp.2015.04.043 content_type: article copyright: Copyright © 2015 Elsevier Inc. All rights reserved.publisher: Elsevier articletitle: A POD reduced order model for resolving angular direction in neutron/photon transport problems journaltitle: Journal of Computational Physics articlelink: http://dx.doi.org/10.1016/j.jcp.2015.04.043 content_type: article copyright: Copyright © 2015 Elsevier Inc. All rights reserved.publisher: Elsevier articletitle: A POD reduced order model for resolving angular direction in neutron/photon transport problems journaltitle: Journal of Computational Physics articlelink: http://dx.doi.org/10.1016/j.jcp.2015.04.043 content_type: article copyright: Copyright © 2015 Elsevier Inc. All rights reserved

Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods

Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen--Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University, London, U

On POD analysis of PIV measurements applied to mixing in a stirred vessel with a shear thinning fluid

P.O.D. technique is applied to 2D P.I.V. data in the field of hydrodynamics in a mixing tank with a Rushton turbine and a shear thinning fluid. Classical eigen-value spectrum is presented and phase portrait of P.O.D. coefficients are plotted and analyzed in terms of trailing vortices. A spectrum of dissipation rate of kinetic energy is introduced and discussed. Length scales associated to each P.O.D. modes are proposed

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method

Perturbation Theory Without Diagrams: The Polaron Case

Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines two new coefficients are obtained corresponding to a four- and five-loop calculation. Several analytical and numerical procedures have been implemented which were crucial for obtaining reliable results.Comment: 32 pages, 7 figures, 4 tables, Latex, v2: misprints corrected, small changes in text following referee comments and PR style conventions, matches published versio

A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries

A model order reduction&nbsp;technique is combined with an embedded boundary finite element&nbsp;method&nbsp;with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM), recently proposed in Main and Scovazzi, J Comput Phys [17]. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method&nbsp;always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM&nbsp;allows for a smooth transition of the reduced modes across the immersed&nbsp;domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples

Fully developed turbulence and the multifractal conjecture

We review the Parisi-Frisch MultiFractal formalism for Navier--Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.Comment: Special Issue dedicated to E. Brezin and G. Paris

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure