Using the Asymmetric Gaussian Method to Interpret the Electronic Spectroscopy of the Olivine Family

This paper discusses the mathematical aspects of band fitting and introduces the Asymmetric Gaussian curve and its tangent space for the first time. First, we derive an equation for an Asymmetric Gaussian shape. We then derive a rule for the resolution of two Gaussian shaped bands. We then use the Asymmetrical Gaussian equation to derive a Master Equation to fit two overlapping bands. We identify regions of the fitting space where the Asymmetric Gaussian fit is optimal, sub optimal and not optimal. We then demonstrate the use of the Asymmetric Gaussian curve to fit four overlapping Gaussian bands, and show how this is relevant to the olivine family spectral complex at 1 μm. We develop a modified model of the olivine family spectral complex based on previous work by Runciman and Burns. The limitations of the asymmetric band fitting method and a critical assessment of three commonly used numerical minimization methods are also provided.

Development of computer-controlled atmospheric pressure plasma structuring for 2D/3D pattern on fused silica

Fused silica with structured and continuous patterns is increasingly demanded in advanced imaging and illumination fields because of its excellent properties and functional performance. Atmospheric pressure plasma, based on pure chemical etching under atmospheric pressure, is developed as a promising fabrication technique for fused silica due to its deterministic high material removal rate, controllable removal imprint and no mechanical load. The stable and controllable Gaussian-shape removal function makes computer-controlled plasma tool potential to generate complex structures with high accuracy, efficiency and flexibility. In the paper, computer-controlled atmospheric pressure plasma structuring (APPS) is proposed to fabricate 2D/3D patterns on fused silica optics. The capacitively coupled APPS system with a double-layer plasma torch and its discharge characteristics are firstly developed. By means of multi-physics simulation and process investigation, the stable and controllable Gaussian-shape removal function can be achieved. Two different structuring modes, including discrete and continuous APPS, are explored for 2D/3D patterns. A series of structuring experiments show that different kinds of 2D patterns (including square lens array, hexagon lens array and groove array) as well as complex 3D phase plate patterns have been successfully fabricated, which validates the effectiveness of the proposed APPS of 2D/3D patterns on fused silica optics.

Non-parametric MRI Brain Atlas for the Polish Population

Introduction: The application of magnetic resonance imaging (MRI) to acquire detailed descriptions of the brain morphology in vivo is a driving force in brain mapping research. Most atlases are based on parametric statistics, however, the empirical results indicate that the population brain tissue distributions do not exhibit exactly a Gaussian shape. Our aim was to verify the population voxel-wise distribution of three main tissue classes: gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), and to construct the brain templates for the Polish (Upper Silesian) healthy population with the associated non-parametric tissue probability maps (TPMs) taking into account the sex and age influence.Material and Methods: The voxel-wise distributions of these tissues were analyzed using the Shapiro-Wilk test. The non-parametric atlases were generated from 96 brains of the ethnically homogeneous, neurologically healthy, and radiologically verified group examined in a 3-Tesla MRI system. The standard parametric tissue proportion maps were also calculated for the sake of comparison. The maps were compared using the Wilcoxon signed-rank test and Kolmogorov-Smirnov test. The volumetric results segmented with the parametric and non-parametric templates were also analyzed.Results: The results confirmed that in each brain structure (regardless of the studied sub-population) the data distribution is skewed and apparently not Gaussian. The determined non-parametric and parametric templates were statistically compared, and significant differences were found between the maps obtained using both measures (the maps of GM, WM, and CSF). The impacts of applying the parametric and non-parametric TPMs on the segmentation process were also compared. The GM volumes are significantly greater when using the non-parametric atlas in the segmentation procedure, while the CSF volumes are smaller.Discussion and Conclusion: To determine the population atlases the parametric measures are uncritically and widely used. However, our findings suggest that the mean and parametric measures of such skewed distribution may not be the most appropriate summary statistic to find the best spatial representations of the structures in a standard space. The non-parametric methodology is more relevant and universal than the parametric approach in constructing the MRI brain atlases.

Nonlinear Fokker-Planck Equation for an Overdamped System with Drag Depending on Direction

We investigate a one-dimensional, many-body system consisting of particles interacting via repulsive, short-range forces, and moving in an overdamped regime under the effect of a drag force that depends on direction. That is, particles moving to the right do not experience the same drag as those moving to the left. The dynamics of the system, effectively described by a non-linear, Fokker–Planck equation, exhibits peculiar features related to the way in which the drag force depends on velocity. The evolution equation satisfies an H-theorem involving the Sq nonadditive entropy, and admits particular, exact, time-dependent solutions closely related, but not identical, to the q-Gaussian densities. The departure from the canonical, q-Gaussian shape is related to the fact that in one spatial dimension, in contrast to what occurs in two or more spatial dimensions, the drag’s dependence on direction entails that its dependence on velocity is necessarily (and severely) non-linear. The results reported here provide further evidence of the deep connections between overdamped, many-body systems, non-linear Fokker–Planck equations, and the Sq-thermostatistics.

Development and Validation of a Box and Flux Model to Describe Major, Trace and Potentially Toxic Elements (PTEs) in Scottish Soils

The box and flux model is a mathematical tool used to describe and forecast the major and trace elements perturbations of the Earth biogeochemical cycles. This mathematical tool describes the biogeochemical cycles, using kinetics of first, second and even third order. The theory and history of the box and flux modeling are shortly revised and discussed within the framework of Jim Lovelok’s Gaia theory. The objectives of the investigation were to evaluate the natural versus anthropic load of Potentially Toxic Elements (PTEs) of the Scottish soils, investigate the soil components adsorbing and retaining the PTEs in non-mobile species, evaluate the aging factor of the anthropic PTEs and develop a model which describes the leaching of PTEs in layered soils. In the Scottish land, the soil-to-rock enrichment factorinversely correlates with the boiling point of the PTEs. The same is observed in NW Italy and USA soils, suggesting the common source of the PTEs. The residence time in soils of the measured PTEs linearly correlates with the Soil Organic Matter (SOM). The element property which mostly explains the adsorption capacity for PTEs’ is the ionic potential (IP). The downward migration rates of the PTEs inversely correlate with SOM, and in Scottish soil, they range from 0.5 to 2.0 cm·year−1. Organic Bentoniteis the most important soil phase adsorbing cation bivalent PTEs. The self-remediation time of the polluted soil examined ranged from 50 to 100 years. The aging factor, the adsorption of PTEs’ into non-mobile species, and occlusion into the soil mineral lattice was not effective. The box and flux model developed, tested and validatedhere does not describe the leaching of PTEs following the typical Gaussian shape distribution of the physical diffusion models. Indeed, the mathematical model proposed is sensitive to the inhomogeneity of the layered soils.

Optimizing the Amplifier Bandwidth for Pulse Reception

<p>Detecting and recognizing pulses is a critical task, in fields as widely separated as telecommunications, lidar, and target illumination. In all cases, the signal-to-noise ratio (SNR) is a key parameter that can be used to determine both the potential rate of errors and the probability of correct detection. In this paper the relationship among pulse width, amplifier bandwidth, and SNR is determined through modeling four approximations to pulse shapes and four amplifier lowpass filter configurations. The analysis determined that, given a specific filter and pulse shape, the bandwidth that maximizes SNR is a constant divided by the pulse width. For example, if the pulse has a Gaussian shape and the amplifier incorporates a second-order Chebyshev lowpass filter, this constant is 0.3389. Applying this, if the pulse width is 20 ns the maximum SNR comes for a filter bandwidth of 16.95 MHz, while if the pulse width is 50 µs the SNR is maximized at a 6.778-kHz bandwidth. Passing the signal through a filter also distorts the signal shape; the temporal shift and pulse lengthening are also determined. The calculated values are offered as inputs to a potential trade space that includes SNR, pulse distortion by the filter, and cost.</p>

Optimizing the Amplifier Bandwidth for Pulse Reception

<p>Detecting and recognizing pulses is a critical task, in fields as widely separated as telecommunications, lidar, and target illumination. In all cases, the signal-to-noise ratio (SNR) is a key parameter that can be used to determine both the potential rate of errors and the probability of correct detection. In this paper the relationship among pulse width, amplifier bandwidth, and SNR is determined through modeling four approximations to pulse shapes and four amplifier lowpass filter configurations. The analysis determined that, given a specific filter and pulse shape, the bandwidth that maximizes SNR is a constant divided by the pulse width. For example, if the pulse has a Gaussian shape and the amplifier incorporates a second-order Chebyshev lowpass filter, this constant is 0.3389. Applying this, if the pulse width is 20 ns the maximum SNR comes for a filter bandwidth of 16.95 MHz, while if the pulse width is 50 µs the SNR is maximized at a 6.778-kHz bandwidth. Passing the signal through a filter also distorts the signal shape; the temporal shift and pulse lengthening are also determined. The calculated values are offered as inputs to a potential trade space that includes SNR, pulse distortion by the filter, and cost.</p>

Experimental research methods for CO2 laser cutting of HARDOX400 steel

he laser beam is a source of radiation with concentrated energy. The characteristics of the laser beam (spot energy, focal spot diameter, spot temperature) are aspects theoretically researched in this paper. The intensity of the laser beam transmitted to the surface of the part has a Gaussian shape. A CO2 laser was used in the processing of parts from a HARDOX400 steel sheet with a thickness g = 8mm. The values of the cutting parameters were established by sample tests. An experimental design with 27 observations was analyzed. The width of the cutting slot at the straight profile was measured. Physical quantities derived from the cutting parameters and working parameters used were calculated. Spot energy, cost and interaction time were determined and evaluated using the mathematical model given by GRAPH. The research findings show that the best values of the factors studied converge to average values in minimizing Kerf.

Wind turbine load validation in wakes using wind field reconstruction techniques and nacelle lidar wind retrievals

This study proposes two methodologies for improving the accuracy of wind turbine load assessment under wake conditions by combining nacelle-mounted lidar measurements with wake wind field reconstruction techniques. The first approach consists of incorporating wind measurements of the wake flow field, obtained from nacelle lidars, into random, homogeneous Gaussian turbulence fields generated using the Mann spectral tensor model. The second approach imposes wake deficit time series, which are derived by fitting a bivariate Gaussian shape function to lidar observations of the wake field, on the Mann turbulence fields. The two approaches are numerically evaluated using a virtual lidar simulator, which scans the wake flow fields generated with the dynamic wake meandering (DWM) model, i.e., the target fields. The lidar-reconstructed wake fields are then input into aeroelastic simulations of the DTU 10 MW wind turbine for carrying out the load validation analysis. The power and load time series, predicted with lidar-reconstructed fields, exhibit a high correlation with the corresponding target simulations, thus reducing the statistical uncertainty (realization-to-realization) inherent to engineering wake models such as the DWM model. We quantify a reduction in power and loads' statistical uncertainty by a factor of between 1.2 and 5, depending on the wind turbine component, when using lidar-reconstructed fields compared to the DWM model results. Finally, we show that the number of lidar-scanned points in the inflow and the size of the lidar probe volume are critical aspects for the accuracy of the reconstructed wake fields, power, and load predictions.

Landmark-free, parametric hypothesis tests regarding two-dimensional contour shapes using coherent point drift registration and statistical parametric mapping

This paper proposes a computational framework for automated, landmark-free hypothesis testing of 2D contour shapes (i.e., shape outlines), and implements one realization of that framework. The proposed framework consists of point set registration, point correspondence determination, and parametric full-shape hypothesis testing. The results are calculated quickly (<2 s), yield morphologically rich detail in an easy-to-understand visualization, and are complimented by parametrically (or nonparametrically) calculated probability values. These probability values represent the likelihood that, in the absence of a true shape effect, smooth, random Gaussian shape changes would yield an effect as large as the observed one. This proposed framework nevertheless possesses a number of limitations, including sensitivity to algorithm parameters. As a number of algorithms and algorithm parameters could be substituted at each stage in the proposed data processing chain, sensitivity analysis would be necessary for robust statistical conclusions. In this paper, the proposed technique is applied to nine public datasets using a two-sample design, and an ANCOVA design is then applied to a synthetic dataset to demonstrate how the proposed method generalizes to the family of classical hypothesis tests. Extension to the analysis of 3D shapes is discussed.