scholarly journals An orthogonal terrain-following coordinate and its preliminary tests using 2-D idealized advection experiments

2014 ◽  
Vol 7 (4) ◽  
pp. 1767-1778 ◽  
Author(s):  
Y. Li ◽  
B. Wang ◽  
D. Wang ◽  
J. Li ◽  
L. Dong
Keyword(s):  
Rotation Angle ◽  
Computational Grids ◽  
Time Step ◽  
Numerical Errors ◽  
Terrain Following ◽  
Steep Terrain ◽  
Definition Of ◽  
Σ Coordinate ◽  
Basis Vectors ◽  
Better Than

Abstract. We have designed an orthogonal curvilinear terrain-following coordinate (the orthogonal σ coordinate, or the OS coordinate) to reduce the advection errors in the classic σ coordinate. First, we rotate the basis vectors of the z coordinate in a specific way in order to obtain the orthogonal, terrain-following basis vectors of the OS coordinate, and then add a rotation parameter b to each rotation angle to create the smoother vertical levels of the OS coordinate with increasing height. Second, we solve the corresponding definition of each OS coordinate through its basis vectors; and then solve the 3-D coordinate surfaces of the OS coordinate numerically, therefore the computational grids created by the OS coordinate are not exactly orthogonal and its orthogonality is dependent on the accuracy of a numerical method. Third, through choosing a proper b, we can significantly smooth the vertical levels of the OS coordinate over a steep terrain, and, more importantly, we can create the orthogonal, terrain-following computational grids in the vertical through the orthogonal basis vectors of the OS coordinate, which can reduce the advection errors better than the corresponding hybrid σ coordinate. However, the convergence of the grid lines in the OS coordinate over orography restricts the time step and increases the numerical errors. We demonstrate the advantages and the drawbacks of the OS coordinate relative to the hybrid σ coordinate using two sets of 2-D linear advection experiments.

scholarly journals An orthogonal curvilinear terrain-following coordinate for atmospheric models

2013 ◽  
Vol 6 (4) ◽  
pp. 5801-5862
Author(s):  
Y. Li ◽  
B. Wang ◽  
D. Wang
Keyword(s):  
Momentum Equation ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Atmospheric Models ◽  
Unified Framework ◽  
Terrain Following ◽  
Steep Terrain ◽  
Definition Of ◽  
Σ Coordinate ◽  
Basis Vectors

Abstract. We have designed an orthogonal curvilinear terrain-following coordinate (the orthogonal σ coordinate, or the OS coordinate) to overcome two well-known problems in the classic σ coordinate, namely, pressure gradient force (PGF) errors and advection errors. First, in the design of basis vectors, we rotate the basis vectors of the z coordinate in a particular way in order to reduce the PGF errors and add a special rotation parameter b to each rotation angel in order to reduce the advection errors. Second, the corresponding definition of each OS coordinate is solved through its basis vectors. Third, the scalar equations of the OS coordinate are solved by expanding the vector equation using the basis vectors. Since the computational form of PGF has only one term in each momentum equation of the OS coordinate, the PGF errors will be significantly reduced, according to Li et al. (2012). When a proper b is chosen, the σ levels over a steep terrain can be significantly smoothed, therefore alleviating the advection errors in the OS coordinate. This is demonstrated by a series of 2-D linear advection experiments under a unified framework.

scholarly journals A Method for Imposing Surface Stress and Heat Flux Conditions in Finite-Difference Models with Steep Terrain

2007 ◽  
Vol 135 (3) ◽  
pp. 906-917 ◽  
Author(s):  
C. C. Epifanio
Keyword(s):  
Finite Difference ◽  
Linear Systems ◽  
Surface Stress ◽  
Test Problems ◽  
Time Step ◽  
Terrain Following ◽  
Thermally Driven ◽  
Stress Boundary Condition ◽  
Steep Terrain ◽  
Stress Boundary

Abstract A numerical implementation of the surface stress boundary condition is presented for finite-difference models in which the terrain slope and curvature cannot necessarily be considered small. The method involves reducing the discretized stress condition in terrain-following coordinates to a pair of coupled linear systems for the two horizontal velocity components at the boundary. The linear systems are then solved iteratively at each model time step to provide the unique boundary values of velocity consistent with the specified values of the stress. Similar methods are used to prescribe the normal flux of heat across the boundary. A related method for imposing stress conditions in two-dimensional vorticity–streamfunction models is also discussed. The effectiveness of the boundary conditions is demonstrated through a series of test problems involving topographic wake flows and thermally driven flows on steep slopes. It is shown that the use of the conventional flat-boundary approximation can lead to substantial errors when the resolved topography is sufficiently steep.

Resolution and measurement in the scanning electron microscope

1987 ◽  
Vol 45 ◽  
pp. 534-537 ◽  
Author(s):  
Michael T. Postek
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Engineering Design ◽  
Resolving Power ◽  
Practical Applications ◽  
Instrument Resolution ◽  
Accurate Definition ◽  
Definition Of ◽  
Scanning Electron ◽  
Better Than

The term ultimate resolution or resolving power is the very best performance that can be obtained from a scanning electron microscope (SEM) given the optimum instrumental conditions and sample. However, as it relates to SEM users, the conventional definitions of this figure are ambiguous. The numbers quoted for the resolution of an instrument are not only theoretically derived, but are also verified through the direct measurement of images on micrographs. However, the samples commonly used for this purpose are specifically optimized for the measurement of instrument resolution and are most often not typical of the sample used in practical applications.SEM RESOLUTION. Some instruments resolve better than others either due to engineering design or other reasons. There is no definitively accurate definition of how to quantify instrument resolution and its measurement in the SEM.

scholarly journals A high-fidelity realization of the Euclid code comparison N-body simulation with Abacus

2019 ◽  
Vol 485 (3) ◽  
pp. 3370-3377 ◽  
Author(s):  
Lehman H Garrison ◽  
Daniel J Eisenstein ◽  
Philip A Pinto
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
High Fidelity ◽  
Step Size ◽  
Time Step ◽  
Code Comparison ◽  
Force Accuracy ◽  
Integration Errors ◽  
Better Than ◽  
Good Agreement

Abstract We present a high-fidelity realization of the cosmological N-body simulation from the Schneider et al. code comparison project. The simulation was performed with our AbacusN-body code, which offers high-force accuracy, high performance, and minimal particle integration errors. The simulation consists of 20483 particles in a $500\ h^{-1}\, \mathrm{Mpc}$ box for a particle mass of $1.2\times 10^9\ h^{-1}\, \mathrm{M}_\odot$ with $10\ h^{-1}\, \mathrm{kpc}$ spline softening. Abacus executed 1052 global time-steps to z = 0 in 107 h on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time-step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with ${\lt }0.3{{\ \rm per\ cent}}$ errors at $k\lt 10\ \mathrm{Mpc}^{-1}\, h$. On large scales, Abacus reproduces linear theory better than 0.01 per cent. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

A numerical approach for structural system identification by observability techniques

2016 ◽  
Author(s):  
Jose Antonio Lozano Galant ◽  
Maria Nogal ◽  
Jun Lei ◽  
Dong Xu ◽  
José Turmo
Keyword(s):  
System Identification ◽  
Numerical Approach ◽  
Mathematical Foundation ◽  
Structural System ◽  
Numerical Errors ◽  
Definition Of ◽  
Structural System Identification ◽  
Symbolic Approach

Observability techniques enable the structural system identification of static structures from a symbolic approach. The main advantage of this method is its deep mathematical foundation that enables the definition of parametric equations for the estimates. Nevertheless, this symbolic approach is not enough for the application of this method on actual structures. To fill this gap, this article presents the introduction into the symbolic structural system identification by observability techniques of a new numerical approach. This application includes the development of an algorithm that reduces the unavoidable numerical errors produced by the lack of precision of computers. The comparison of the observability technique with other existing methods presented in the literature shows that the number of required measurements is significantly lower. Furthermore, contrary to other analysed methods, no information from the undamaged structure is required.

scholarly journals 2D IPO's for Constant Speed Lines, Curves, NURBS

2019 ◽  
Author(s):  
Valere Huypens
Keyword(s):  
Major Axis ◽  
Pulse Method ◽  
Constant Speed ◽  
Sampled Data ◽  
Reference Pulse ◽  
Production Manager ◽  
Definition Of ◽  
The Right ◽  
2D And 3D ◽  
Better Than

<div>Current constant speed IPO's, usually, use Sampled-data IPO's and constant speed lines use the </div><div>wrong initialized software DDA-ipo's, which make these IPO's unusable. The Bresenham- and </div><div>midpoint IPO's are non-constant speed reference pulse IPO's with bounded inaccuracy.</div><div>By adding an ultra-fast 3-lines algorithm "PRM-cs" to the actual midpoint or Bresenham algorithms, </div><div>we convert these midpoint-ipo's to very fast, constant speed, reference pulse IPO's. </div><div>This applies to 2D-lines, 3D-lines, 2D-curves and 2D-NURBS.</div><div>The PRM-cs measures, in real-time, the length of the discrete curve and the PRM-cs is completely new. </div><div>We define the best IPO, the major axis principle and the LSD-priority. </div><div>The major axis principle holds for the actual 3D-line IPO's. These IPO's are, generally, inaccurate, </div><div>but they can be updated to constant speed 3D-line IPO's, when the production manager agrees.</div><div>The Digital Geometric Geometry (DAG) defines the discrete lines globally, but this global </div><div>definition of a discrete 3D-line, gives discrete 3D-lines whose accuracy is much less than the </div><div>accuracy of the best discrete 3D-lines (e.g. 37% worse).</div><div>We describe the three causes of the inaccurate (imperfect) discrete 3D-lines. </div><div>All existing pulse-rate or PRM-ipo's use a wrong initialization, which deteriorates the accuracy. </div><div>We determine the right initialization for the new PRM-cs and the updated PRM-ipo. </div><div>We propose the benchmark-ipo "listSIM-ipo". This constant speed IPO can, also, be used in real-</div><div>time for every 2D- and 3D-curve. </div><div>The 3rd-degree Trident NURB shows that the constant speed reference pulse method is much </div><div>better than the existing sampled-data methods.</div>

scholarly journals Piecewise Legendre spectral-collocation method for Volterra integro-differential equations

2015 ◽  
Vol 18 (1) ◽  
pp. 231-249 ◽  
Author(s):  
Zhendong Gu ◽  
Yanping Chen
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Piecewise Polynomial ◽  
Spectral Collocation ◽  
Numerical Errors ◽  
Piecewise Polynomial Collocation Method ◽  
Theoretical Results ◽  
Polynomial Collocation ◽  
Better Than

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in$h^{m}N^{-m}$-version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

Graded Causation and Normality

2016 ◽  
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Recent Work ◽  
Experimental Philosophy ◽  
Actual Causation ◽  
Definition Of ◽  
Better Than

Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. This chapter shows the definition of causality introduced in Chapter 2 can be extended to defaults, typicality, and normality into account. The resulting framework takes actual causation to be both graded and comparative. Thus, it allows us to say that one cause is better than another. Examples showing the power of the approach are considered.

scholarly journals Prevalence and causes of childhood blindness in Huidong County, South China, primary ascertained by the key informants

2019 ◽  
Vol 4 (1) ◽  
pp. e000240
Author(s):  
Yanping Li ◽  
Jianhua Yan ◽  
Zhonghao Wang ◽  
Wenyong Huang ◽  
Shengsong Huang ◽  
...  
Keyword(s):  
South China ◽  
Cross Sectional Study ◽  
Anatomic Site ◽  
Cross Sectional ◽  
Childhood Blindness ◽  
Key Informants ◽  
The Public ◽  
Definition Of ◽  
Low Prevalence ◽  
Better Than

PurposeThe aim of this study is to ascertain the prevalence and causes of childhood blindness and severe visual impairment (BL/SVI) in Huidong, South China.MethodsThis cross-sectional study was conducted in early 2017 in areas of 139 816 children at the age of 0–15 as the study subjects. We used the trained key informants (KIs) to do preliminary visual test in the communities and refer those children suspected with blindness or unable to count fingers with both eyes at 5 m to hospital for further examination by paediatric ophthalmologist for causes. The WHO’s definition of BL/SVI was used, as blindness is best-corrected visual acuity worse than 0.05 in better eye and SVI is equal to or better than 0.05 but worse than 0.1 in better eye.ResultsThree hundred and fourteen KIs were trained. In total, 42 children with BL/SVI were found, and among them over half (22, 52.4%) were due to posterior segment disorders by anatomic site and 18 (42.9%) children were potentially preventable; these included BL/SVI caused by factors at children’s development in intrauterine and after birth. This established the prevalence of BL/SVI was at 0.31/1000 (95% CI 0.28 to 0.34/1000).ConclusionA low prevalence of childhood blindness was documented in this study. Establishment of surveillance system for disabled children including those with BL/SVI and better health education on eye care to the public according to the surveillance outcomes would help to reduce avoidable children’s BL/SVI further in China.

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