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Johannes Kepler published his Astronomia nova in 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he appl...
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Johannes Kepler published his Astronomia nova in 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of this novel methods, and called for a new Apollonius to offer a formal mathematical deduction. He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis.
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An advection correction procedure is used to mitigate temporal interpolation errors in trajectory analyses constructed from gridded (in space and time) velocity data. The procedure is based on a technique introduced by Gal-Chen to...
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An advection correction procedure is used to mitigate temporal interpolation errors in trajectory analyses constructed from gridded (in space and time) velocity data. The procedure is based on a technique introduced by Gal-Chen to reduce radar data analysis errors arising for the nonsimultaneity of the data collection. Experiments are conducted using data from a high-resolution Cloud Model 1 (CM1) numerical model simulation of a supercell storm initialized within an environment representative of the 24 May 2011 El Reno, Oklahoma, tornadic supercell storm. Trajectory analyses using advection correction are compared to traditional trajectory analyses using linear time interpolation. Backward trajectories are integrated over a 5-min period for a range of data input time intervals and for velocity-pattern-translation estimates obtained from different analysis subdomain sizes (box widths) and first-guess options. The use of advection correction reduces trajectory end-point position errors for a large majority of the trajectories in the analysis domain, with substantial improvements for trajectories launched in the vicinity of the model storm's gust front and in bands within the rear-flank downdraft. However, the pattern-translation components retrieved by this procedure may be nonunique if the data input time intervals are too large.
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An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high-degree (>720) solid spherical harmonics at many scattered points in the space above the surface ...
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An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high-degree (>720) solid spherical harmonics at many scattered points in the space above the surface of the Earth. The algorithm is based on representation of the geomagnetic field elements in solid ellipsoidal harmonics and application of tensor product needlets. Open source FORTRAN and MATLAB realizations of this algorithm that rely on data from the Enhanced Magnetic Models 2015, 2017 (EMM2015, EMM2017) have been developed and extensively tested. The capabilities of the software are demonstrated on the example of the north, east and down components of the geomagnetic field as well as the derived horizontal intensity, total intensity, inclination and declination. For the range from -417 m under the Earth reference ellipsoid up to 1000 km above it the FORTRAN and MATLAB versions of the software run 465 and 189 times faster than the respective FORTRAN and MATLAB versions of the software using the standard spherical harmonic series method, while the accuracy is less than 1 nT and the memory (RAM) usage is 9 GB.
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Scientific design of a railway track formation requires an understanding of the subgrade behavior and the factors affecting it. These include the effective resilient stiffness during train passage, which is likely to depend on the...
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Scientific design of a railway track formation requires an understanding of the subgrade behavior and the factors affecting it. These include the effective resilient stiffness during train passage, which is likely to depend on the stress history and the stress state of the ground, and the stress path followed during loading. This study investigates the last of these, by means of a two-dimensional dynamic finite-element analysis. The effects of train speed, acceleration/braking, geometric variation in rail head level, and a single unsupported sleeper are considered. Results indicate that dynamic effects start to become apparent when the train speed is greater than 10% of the Rayleigh wave speed, v_c, of the subgrade. At a train speed of 0.5v_c, the shear stresses will be underestimated by 30% in a static analysis, and at train speeds greater than v_c the stresses due to dynamic effects increase dramatically. Train acceleration/braking may increase shear stresses and horizontal displacements in the soil, and hence the requirement for track maintenance at locations where trains routinely brake or accelerate. For heavy haul freight trains, long wavelength variations in rail head level may lead to significantly increased stresses at passing frequencies (defined as the train speed divided by the wavelength of the variation in level) greater than 15, and short wavelength variations at passing frequencies of 60-70. Stress increases adjacent to an unsupported sleeper occur in the ballast and subballast layers, but rapidly become insignificant with increasing depth.
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Magnetization of a bulk high T/sub c/ superconductor (HTSC) is evaluated with the numerical simulation codes. The field-cooled magnetization of the HTSC is analyzed by using the critical state model. The pulse magnetization proces...
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Magnetization of a bulk high T/sub c/ superconductor (HTSC) is evaluated with the numerical simulation codes. The field-cooled magnetization of the HTSC is analyzed by using the critical state model. The pulse magnetization process is also analyzed by using the flux creep-flow model. The numerical solutions are discussed to clarify the time dependent effects in the reported experimental results on the pulse magnetization.
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The magnetic shielding efficiency of a cylindrical shield is studied starting from the experimentally determined hysteresis loops of the nonlinear shielding material. The magnetic transfer relation model is used in the frequency d...
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The magnetic shielding efficiency of a cylindrical shield is studied starting from the experimentally determined hysteresis loops of the nonlinear shielding material. The magnetic transfer relation model is used in the frequency domain. This analytical model can be evaluated very fast, but works only for linear material. Therefore, the nonlinear shield is divided into a number of linear sublayers with constant complex permeability, which is modelled by an analytical complex function, fitted from the experimental hysteresis loops. The shielding factors are calculated by the analytical model as a function of the imposed field amplitude. They are validated by a finite element model and compared with measured shielding factors of cylindrical tubes. The correspondence is good for the three considered shields: a shield in aluminium (shielding by induced currents), a shield in Fe-Si steel (mainly shielding by flux shunting) and a multilayered shield in aluminium and Fe-Si steel.
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In principle, this could be a four-word essay because the short answer is, "no, of course not!" Indeed, my asking the question entails a slight personal risk: I certainly don't want to alienate my friends who are numerical analyst...
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In principle, this could be a four-word essay because the short answer is, "no, of course not!" Indeed, my asking the question entails a slight personal risk: I certainly don't want to alienate my friends who are numerical analysts. I've worked happily, if not exactly in, then certainly someplace near the field of numerical analysis for many years. I've even taught it (not a guarantee against being boring, I know) and coauthored a book on one of the field's many active subareas.
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Purpose The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence. Design/meth...
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Purpose The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence. Design/methodology/approach The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case. Findings The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique. Originality/value The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.
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Background and Objective: So far, no scientific papers have reported on the termite population of subterranean termite Coptotermes curvignathus especially when they attack the wooden components in the building. This information is...
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Background and Objective: So far, no scientific papers have reported on the termite population of subterranean termite Coptotermes curvignathus especially when they attack the wooden components in the building. This information is crucial for termite control such as system development, specifically capable of non-destructively detecting and predicting a termite population. A study was conducted to determine the termite population on the various volumes of pine boards. Materials and Methods: In this study, the exhaustive trapping technique was applied to the termite colonies. Thirty boards, infested with termites, were collected, after which the volumes were measured and dismantled carefully to determine termite population. A statistical analysis of linear regression is used to analyze the relationship between board volume (x) and termite population (y). Results: This survey showed that the board infested by C. curvignathus was dominated by termite workers (75.21±6.5101%) compared to termite soldiers (24.79±6.5101%). Based on the numerical analysis, the linear regression model (y = 40.09368+0.55031x) provides an overview of the number of termites present for a feeding test and provides an analysis of the extent to which the design of detection system will be able to predict a termite population. Conclusion: This research showed that the larger the board volume, the larger the termite population, since the larger board has an abundance of food sources containing large amounts of cellulose. This cellulose attracts termites to live inside it and also stops the process of further foraging.
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Several methods of a posteriori error estimation and adaptive refinement controlling in finite element analysis of 3-D steady-state eddy current field are described in this paper. An improved Z-Z method and a more efficient method...
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Several methods of a posteriori error estimation and adaptive refinement controlling in finite element analysis of 3-D steady-state eddy current field are described in this paper. An improved Z-Z method and a more efficient method of CIL are presented. The numerical models of TEAM Workshop Problem 7 and 21A are used to verify the validity of the presented method.
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