Automatic calibration of powder diffraction experiments using two-dimensional detectors

2007 ◽  
Vol 22 (1) ◽  
pp. 3-19 ◽  
Author(s):  
P. Rajiv ◽  
B. Hinrichsen ◽  
R. Dinnebier ◽  
M. Jansen ◽  
M. Joswig
Keyword(s):  
Powder Diffraction ◽  
Computational Cost ◽  
Nonlinear Least Squares ◽  
Calibration Method ◽  
High Signal ◽  
Automatic Calibration ◽  
Experimental Calibration ◽  
One Dimensional ◽  
Least Squares Fit ◽  
Image Artefacts

Calibration of powder diffraction experiments using area detectors is essential to extract high quality one-dimensional powder diffraction pattern. Precise calibration necessitates a sensible characterization of the Debye-Scherrer rings formed on the detector plane. An algorithm, designed and developed to automate this process, is described in this paper. All the parameters required for an experimental calibration are extracted using robust pattern recognition techniques. Several image preprocessing methods are employed, reducing the computational cost but retaining high signal quality. A modified version of a one-dimensional Hough transformation is used to determine the final parameters of the ellipses. After extraction, the parameters are optimized using nonlinear least squares fit. The presented algorithm is insensitive to image artefacts and was successfully applied to a large number of calibration images. The performance of the algorithm is demonstrated by the comparison of results obtained from the presented automatic calibration method and an existing manual method.

Crystal structure of the anticancer drug carmustine determined by X-ray powder diffraction

2021 ◽  
pp. 1-3
Author(s):  
Carina Schlesinger ◽  
Edith Alig ◽  
Martin U. Schmidt
Keyword(s):  
Crystal Structure ◽  
Anticancer Drug ◽  
Powder Diffraction ◽  
Room Temperature ◽  
Powder Diffraction Data ◽  
Orthorhombic Space Group ◽  
Commercial Sample ◽  
One Dimensional ◽  
X Ray ◽  
Hydrogen Bond Pattern

The structure of the anticancer drug carmustine (1,3-bis(2-chloroethyl)-1-nitrosourea, C5H9Cl2N3O2) was successfully determined from laboratory X-ray powder diffraction data recorded at 278 K and at 153 K. Carmustine crystallizes in the orthorhombic space group P212121 with Z = 4. The lattice parameters are a = 19.6935(2) Å, b = 9.8338(14) Å, c = 4.63542(6) Å, V = 897.71(2) ų at 153 K, and a = 19.8522(2) Å, b = 9.8843(15) Å, c = 4.69793(6) Å, V = 921.85(2) ų at 278 K. The Rietveld fits are very good, with low R-values and smooth difference curves of calculated and experimental powder data. The molecules form a one-dimensional hydrogen bond pattern. At room temperature, the investigated commercial sample of carmustine was amorphous.

An experimental calibration method for digital Abbe refractometer

2013 ◽  
Author(s):  
Hao Liu ◽  
Ke-cheng Yang ◽  
Wenping Guo ◽  
Jie Dai ◽  
Junwei Ye ◽  
...  
Keyword(s):  
Calibration Method ◽  
Experimental Calibration ◽  
Abbe Refractometer

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

scholarly journals Fractal fits to Riemann zeros

2007 ◽  
Vol 85 (4) ◽  
pp. 345-357 ◽  
Author(s):  
P B Slater
Keyword(s):  
Potential Model ◽  
Sine Series ◽  
Dominant Term ◽  
One Dimensional ◽  
Smooth Potential ◽  
Smooth Part ◽  
Least Squares Fit ◽  
The One ◽  
Higher Order Corrections ◽  
03.65 Sq

Wu and Sprung (Phys. Rev. E, 48, 2595 (1993)) reproduced the first 500 nontrivial Riemann zeros, using a one-dimensional local potential model. They concluded — as did van Zyl and Hutchinson (Phys. Rev. E, 67, 066211 (2003)) — that the potential possesses a fractal structure of dimension d = 3/2. We model the nonsmooth fluctuating part of the potential by the alternating-sign sine series fractal of Berry and Lewis A(x,γ). Setting d = 3/2, we estimate the frequency parameter (γ), plus an overall scaling parameter (σ) that we introduce. We search for that pair of parameters (γ,σ) that minimizes the least-squares fit Sn(γ,σ) of the lowest n eigenvalues — obtained by solving the one-dimensional stationary (nonfractal) Schrodinger equation with the trial potential (smooth plus nonsmooth parts) — to the lowest n Riemann zeros for n = 25. For the additional cases, we study, n = 50 and 75, we simply set σ = 1. The fits obtained are compared to those found by using just the smooth part of the Wu–Sprung potential without any fractal supplementation. Some limited improvement — 5.7261 versus 6.392 07 (n = 25), 11.2672 versus 11.7002 (n = 50), and 16.3119 versus 16.6809 (n = 75) — is found in our (nonoptimized, computationally bound) search procedures. The improvements are relatively strong in the vicinities of γ = 3 and (its square) 9. Further, we extend the Wu-Sprung semiclassical framework to include higher order corrections from the Riemann–von Mangoldt formula (beyond the leading, dominant term) into the smooth potential. PACS Nos.: 02.10.De, 03.65.Sq, 05.45.Df, 05.45.Mt

scholarly journals Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

2016 ◽  
Vol 54 (1) ◽  
pp. 17-33
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Computational Cost ◽  
Nonlinear Least Squares ◽  
Least Square ◽  
Error Tolerance ◽  
Local Analysis ◽  
Large Radius ◽  
Special Cases ◽  
Local Convergence Analysis ◽  
Least Square Problems

Abstract We present a local convergence analysis of inexact Gauss-Newton-like method (IGNLM) for solving nonlinear least-squares problems in a Euclidean space setting. The convergence analysis is based on our new idea of restricted convergence domains. Using this idea, we obtain a more precise information on the location of the iterates than in earlier studies leading to smaller majorizing functions. This way, our approach has the following advantages and under the same computational cost as in earlier studies: A large radius of convergence and more precise estimates on the distances involved to obtain a desired error tolerance. That is, we have a larger choice of initial points and fewer iterations are also needed to achieve the error tolerance. Special cases and numerical examples are also presented to show these advantages.

scholarly journals Wind Turbine Noise Reduction from Seismological Data

2021 ◽  
Author(s):  
Janis Heuel ◽  
Wolfgang Friederich
Keyword(s):  
Signal To Noise Ratio ◽  
Low Cost ◽  
Computational Cost ◽  
Noise Signal ◽  
Noise Model ◽  
Threshold Function ◽  
High Signal ◽  
Time Data ◽  
Negative Effects ◽  
Before And After

<p>Over the last years, installations of wind turbines (WTs) increased worldwide. Owing to<br>negative effects on humans, WTs are often installed in areas with low population density.<br>Because of low anthropogenic noise, these areas are also well suited for sites of<br>seismological stations. As a consequence, WTs are often installed in the same areas as<br>seismological stations. By comparing the noise in recorded data before and after<br>installation of WTs, seismologists noticed a substantial worsening of station quality leading<br>to conflicts between the operators of WTs and earthquake services.</p><p>In this study, we compare different techniques to reduce or eliminate the disturbing signal<br>from WTs at seismological stations. For this purpose, we selected a seismological station<br>that shows a significant correlation between the power spectral density and the hourly<br>windspeed measurements. Usually, spectral filtering is used to suppress noise in seismic<br>data processing. However, this approach is not effective when noise and signal have<br>overlapping frequency bands which is the case for WT noise. As a first method, we applied<br>the continuous wavelet transform (CWT) on our data to obtain a time-scale representation.<br>From this representation, we estimated a noise threshold function (Langston & Mousavi,<br>2019) either from noise before the theoretical P-arrival (pre-noise) or using a noise signal<br>from the past with similar ground velocity conditions at the surrounding WTs. Therefore, we<br>installed low cost seismometers at the surrounding WTs to find similar signals at each WT.<br>From these similar signals, we obtain a noise model at the seismological station, which is<br>used to estimate the threshold function. As a second method, we used a denoising<br>autoencoder (DAE) that learns mapping functions to distinguish between noise and signal<br>(Zhu et al., 2019).</p><p>In our tests, the threshold function performs well when the event is visible in the raw or<br>spectral filtered data, but it fails when WT noise dominates and the event is hidden. In<br>these cases, the DAE removes the WT noise from the data. However, the DAE must be<br>trained with typical noise samples and high signal-to-noise ratio events to distinguish<br>between signal and interfering noise. Using the threshold function and pre-noise can be<br>applied immediately on real-time data and has a low computational cost. Using a noise<br>model from our prerecorded database at the seismological station does not improve the<br>result and it is more time consuming to find similar ground velocity conditions at the<br>surrounding WTs.</p>

Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models

2014 ◽  
Author(s):  
Erasmo Carrera ◽  
Enrico Zappino
Keyword(s):  
Mechanical Design ◽  
Computational Cost ◽  
Advanced Materials ◽  
Complex Structures ◽  
Displacement Fields ◽  
One Dimensional ◽  
Classical Models ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Dimensional Models

One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.

scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot ◽  
A. S. Tijsseling ◽  
M. C. M. Rutten ◽  
F. N. van de Vosse
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
One Dimensional ◽  
Arterial Blood

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

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