Experimental uncertainties associated with particle image velocimetry (PIV) based vorticity algorithms

 We have recently used Particle Image Velocimetry (PIV) to study the dynamics of vortex propagation in reacting and non-reacting flows. In order to do so, it became necessary to assess the uncertainty in PIV-based vorticity data. A computer simulation was developed to investigate how uncertainty propagates throughout the post-processing, numerical data smoothing, and vorticity calculating algorithms commonly used in the analysis of PIV data. Results indicate that the average uncertainty in vorticity per interrogation cell (normalized to the average vorticity, and then surface averaged), for a simple vortex, can be reduced to approximately ±4% with appropriate measures. This value was obtained using PIV autocorrelation software, a local regression technique combined with a Gaussian-smoothing filter. Our best experimental results (these areas with no lost or spurious vectors) are consistent with Stoke’s theorem. Received: 14 August 1996/Accepted: 13 April 1998     

Some calculable contributions to entanglement entropy

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry: its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.     

Test of an optical parametric oscillator (OPO) as a compact and fast tunable stokes source in coherent anti-stokes raman spectroscopy (CARS)

An optical parametric oscillator (OPO), as a novel kind of broadband Stokes source, is employed for coherent anti-Stokes Raman spectroscopy (CARS). Compared to the conventional dye laser configuration OPO-CARS offers practical advantages. The tunable OPO allows a fast and comfortable frequency tuning. The excitation bandwidth of about 35 cm^–1 (FWHM) limits the spectral range of effective and stable single pulse CARS generation but can be used to enhance selected spectral structures.     

Design of experiments on 135 cloned poplar trees to map environmental influence in greenhouse

To find and ascertain phenotypic differences, minimal variation between biological replicates is always desired. Variation between the replicates can originate from genetic transformation but also from environmental effects in the greenhouse. Design of experiments (DoE) has been used in field trials for many years and proven its value but is underused within functional genomics including greenhouse experiments. We propose a strategy to estimate the effect of environmental factors with the ultimate goal of minimizing variation between biological replicates, based on DoE. DoE can be analyzed in many ways. We present a graphical solution together with solutions based on classical statistics as well as the newly developed OPLS methodology.In this study, we used DoE to evaluate the influence of plant specific factors (plant size, shoot type, plant quality, and amount of fertilizer) and rotation of plant positions on height and section area of 135 cloned wild type poplar trees grown in the greenhouse. Statistical analysis revealed that plant position was the main contributor to variability among biological replicates and applying a plant rotation scheme could reduce this variation.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.